Education 4.0 and Dr. David Kellermann

Dr. David Kellermann from the University of New South Wales spoke to the Utah Valley University (UVU) community at a recent UVU Digital Transformation Seminar. His topic was Education 4.0 and the integrated tools he uses to enhance his students’ engagement and learning. His presentation can be seen here, by members of the UVU community, and on YouTube. This post will briefly discuss past and current educational practices, introduce Education 4.0 and highlight a few key takeaways from Dr. Kellermann’s lecture.

Education: Past and Present

Education 1.0 was developed centuries ago and was refined up through the 20th century. Education 2.0 began when educators and students started using digital technology to enhance their educational experience. Education 3.0 is best characterized by the availability of learning content through mechanisms other than traditional higher education. Today, many have access to the Internet, YouTube, Microsoft Learn, LinkedIn Learning, Pluralsight, and other rich content providers. Learning resources are available to students when and where they want them and at little or no cost.

However, higher education institutions are still creating much of their own content and providing it on their terms. Course offerings, schedules, student information, and institutional content are often consumed by and exposed through monolithic and dated tools such as student information systems (SISs), learning management systems (LMSs), etc. Often the organizations delivering these tools harvest a vast amount of institutional and student information to improve their offerings and develop new technologies to market. To make matters worse, the more intellectual investment we make in such tools, the more difficult it is to move to something better.

Many of our students want to move beyond this traditional educational model. They are demanding Education 4.0 functionality such as collaborative real-time editing, video calls/communication, chat interaction, mobile functionality, cloud storage, and the ubiquitous use of AI and natural language processing. In his lecture, Dr. Kellermann noted that even his Education 3.0 online work consisted of a collection of PDF lecture notes and an associated list of video captured lectures. He realized that the content on YouTube and other sites was superior in many ways. This inspired him to make online learning better and even superior to on-campus learning.

Education 4.0

Education 4.0 parallels the 4th industrial revolution (Industry 4.0), where data, artificial intelligence (AI), machine learning, robots, the Internet of things (IoT), and automation dominate. Future jobs will require higher levels of proficiency in these and other technical fields. In a general sense, Education 4.0 must provide the training for a future Industry 4.0 workforce.

Education 4.0 is transforming our academic approach, including the design, delivery, and assessment of teaching and learning. We have to transform content creation and acquisition, delivery mechanisms, learning spaces, assessment approaches, student mentoring, advising services, and learning tools. Education 4.0 students must use and be immersed in the tools that Industry 4.0 demands: data analysis, artificial intelligence, machine learning, automation, robotics, Internet of things, etc.


There are many interesting aspects of Dr. Kellermann’s setup and work. I’ll point out a few here, but you may well find others that you find more compelling in his lecture. His work is clearly in the realm of Education 4.0 so hang on, keep your arms and legs within the ride at all times, and enjoy a glimpse of the future.

Microsoft Teams

At the center of Dr. Kellermann’s toolset is Microsoft Teams. However, he uses a variety of Microsoft tools to add functionality to his class offerings. If you are unfamiliar with Teams, you can learn more about it from the UVU Digital Transformation Learning Gallery. Just think of your class as a team and Teams being the tool that allows you to share files with them, chat with them, initiate video meetings, interact with applications in real-time, assess student accomplishment, give them feedback, and share applications with them. It’s the hub that every topic below depends on.

Dr. Kellermann creates a team for each class, including all students in the class, his assistants, and himself. Teams have channels, and he creates a channel for each week of his class. Each channel contains learning objects, assessment tools, assignments, etc., related to a particular topic. Within each channel, there are tabs that are essentially applications. There may be a chat tab, a gradebook tab, an assignment tab, etc. Each channel may have the same tabs or a different set of tabs depending on the need.

Technology Setup

Dr. Kellermann’s technology setup is novel and intriguing. I may miss a few details, but essentially he has two camera views and a screen view to stream to his students. He can switch between these three views with a simple handheld remote. The primary camera view is of him lecturing beside a Microsoft Surface Hub. From here, he can use Teams to display a class notebook created using OneNote, present Powerpoint presentations, review documents, etc. The Surface Hub allows multi-touch functionality and on-screen marking with digital ink.

The second camera view is from a camera on top of the Surface Hub. This view is useful when working on a problem on the Surface Hub, as we might do on a whiteboard. This enables him to work “at the board” while still facing the remote students.

The screen view of the Surface Hub allows fine detail to be viewed by a remote audience. The surface hub displays branding for the institution and a picture in picture feature allowing Dr. Kellermann to be seen even during screen sharing. It also includes a chat area where students and Dr. Kellermann can communicate and, more importantly, where students can communicate freely and answer one another’s questions.

Dr. Kellermann also has a separate screen where he can easily view chats and acquire questions to be answered. Finally, he has included reasonable lighting, a good sound system, and a color adapting light source to backlight the screen. You’ll fully appreciate the setup after viewing him in action.

Class Recordings

Class recordings can be very useful for students. Using Teams, a class recording is as simple as pushing a virtual button. The entire meeting, including the chats, are recorded and stored in Microsoft Streams. Once in Streams, recordings are transcribed, and the resulting texts are available for reading, searching, etc. It is simple to search the transcription for topics of interest, click on that portion of the transcription, and the associated video starts playing at that point. Recorded videos can be manipulated using Microsoft’s Power Automate to create a video gallery that can be included within Teams as a tab within the associated class.

Legacy Courseware

We all know it is a tremendous amount of work to move developed courseware from one learning management system to another. Dr. Kellermann points out that he no longer uses an LMS at all, but moving courseware to a completely different type of tool all at once isn’t easy either. Not to fear, an LMS can be easily added to Teams as a tab within a course. What’s better is that since the students are within a class in Teams, they have already authenticated. When they go to the LMS tab, they don’t need to authenticate again, and they are taken directly to the class associated with their class in Teams. This ability allows for a metered transition from a class using an LMS to one no longer dependent on it. This enables faculty and staff to collaboratively determine a smooth and well-supported migration.

Bots and Artificial Intelligence

Dr. Kellermann has invested significant time and resources into developing a question bot, called QBot, based on Microsoft’s Bot Framework. He has made QBot publicly available on GitHub. When a student inserts a question in the chat window and references @Q, the QBot looks up the class and section the student is in, determines the teacher’s assistants associated with the class, and sends them a cell phone notification indicating they have a question to respond to.

Also, QBot uses natural language processing and AI to parse the question and determines if it “knows,” with a high probability, the answer to the question. If QBot is confident, it responds immediately with an answer. Remember where we discussed the transcriptions from recorded class lectures? QBot also has access to those transcriptions, and if it believes that the question is addressed in a lecture, it points the student to that very moment of class instruction. If QBot isn’t confident that it “knows” the answer, it remains silent. However, it recognizes when the teacher’s assistant responds and uses that answer to enhance its collection of question and answer pairs; better luck next time. It should be noted that AI is not used to replace people but connect them and enhance their interactions.

Data, Data, and More Data

With the class in Teams, there is a vast amount of resulting data that can be used to enhance education. This data is private to the institution and not accessible by the tool provider, in this case, Microsoft. For example, attendance, quiz outcomes, homework scores, and test results for each student for each topic are easily extracted. Another Microsoft tool, Power BI, can create dashboards for visualizing and acting on this data. Additionally, AI can be employed to look at previous semester data with associated final exam and class scores to predict where each student needs help. This data can be used to construct a personalized study guide to maximize student learning and help them succeed.


We are currently at the end of an era, Education 3.0, but our students are running ahead of us and expecting us to join them in the era of Education 4.0. To join our students, we must transform the institution; we must change our technology architectures, culture, tools, processes, and practices. Dr. David Kellermann has worked hard to develop a set of tools and practices that work well for him. I am confident that each institution, each faculty, and our great students will find a slightly different set of tools and practices that are right for them. I’m excited about Education 4.0 at Utah Valley University and can’t wait to see the student success it yields!

Digital Transformation Strategy


A strategy should inform an institution where business process improvements will have the largest impact on realizing its mission. Both for-profit and non-profit institutions should pursue projects and initiatives that help them reach their strategic goals. A strategy should help guide what projects and initiatives are pursued.

In a for-profit institution, the main strategy is to increase profits. Projects should be pursued if they have the potential to increase revenue, decrease expense, or both. In such a setting, it is reasonably straightforward to compute a financial return on investment (ROI) for digital transformation projects and initiatives and use it to prioritize them.

In a non-profit institution of higher education, our main strategy is to help students succeed. Projects and initiatives should be pursued to help the institution reach its strategic goals. Computing a financial ROI in this setting is not straightforward and perhaps not beneficial; therefore, we need an alternative mechanism for prioritizing which projects and initiatives to pursue. The ideal metric is a measure of a project’s ability to decrease the gap between where an institution is concerning its strategic goals and where it will be after the project is complete, i.e., its strategic value. Those projects with the most potential to decrease the strategic gap have the highest strategic value and should be pursued.

This post will describe the creation of the strategy map for the UVU Division of Digital Transformation. I’ll also describe three ontologies we’ve created:

  • An impact ontology that illustrates the impact divisional business processes should have on our strategic objectives.
  • A performance ontology that describes the impact our business processes are currently having on our strategic objectives.
  • A project ontology that illustrates each project’s strategic value or its ability to close strategic gaps.

The impact and performance ontologies are used to determine the strategic gap between possible impact and current performance. The project ontology determines which projects have high strategic value in closing the identified strategic gaps. Finally, a list of projects and initiatives, prioritized using their strategic value, is presented.

Utah Valley University

In early 2019, Utah Valley University (UVU) organized a Digital Transformation Task Force, which issued its final report in April 2019. In their report, the task force defined digital transformation like this:

“Digital transformation is the process of applying technology to fundamentally change how organizations operate and provide value to those served. Digital transformation requires an integrated enterprise approach to workflow, process, data management, technology, and culture.”

The use of digital technology and an accompanying change in culture will allow the university to reduce complexity, function efficiently, and provide delightful products, processes, and services to our students, faculty, and staff. While digital transformation strategies and tactics must be aligned with the institutional mission and strategic initiatives, they must also be easily understood and implemented by those participating in the transformation of digital technology, culture, and institutional practice.

Institutional Mission and Strategy

Digital transformation efforts must be aligned with institutional goals and strategy. UVU has an exceptional strategy document entitled Vision 2030. Vision 2030 includes the UVU Mission Statement that reads, “Utah Valley University is an integrated university and community college that educates every student for success in work and life through excellence in engaged teaching, services, and scholarship.” Vision 2030 outlines three strategies, with accompanying priority initiatives, employed to accomplish its mission:

  1. Enhance student success and accelerate completion of meaningful credentials
    • Implement the UVU Completion Plan 2.0 (2019-2023)
    • Assess and remove barriers at every stage of the student life cycle
    • Support completion through comprehensively designed curriculum and services
    • Enhance educational quality through the recruitment and retention of excellent and engaging faculty and staff
  2. Improve accessibility, flexibility, and affordability for all current and future UVU students
    • Build out a coordinated multi-campus plan
    • Expand flexible educational and online offerings
    • Strengthen outreach to and support for underrepresented students
    • Maintain commitment to affordability and accessibility
  3. Strengthen partnerships for community, workforce, and economic development
    • Create seamless processes and practices for student transition from K-12 to UVU
    • Improve industry partnerships to meet workforce and community needs
    • Strengthen engaged learning and community engagement opportunities for students, faculty, and staff

Strategy Map

A strategy map is a diagram that shows an organization’s strategy on a single page. A strategy map has three significant uses:

  1. It helps every employee understand their organization’s overall strategy and where they fit in.
  2. It helps keep everyone literally on the same page.
  3. It helps employees see how their work helps the institution meet its strategic objectives.

At the top and center of a strategy map, we place the organization’s mission or vision statement. Stacked down the map’s left side are four perspectives: financial, customers or stakeholders, internal processes, and enablers. A for-profit enterprise would typically place the perspectives from top to bottom in the order previously described. In a non-profit organization like UVU, we place the financial perspective at the bottom. Making money is not our aim, but financial objectives support everything else we do.

Within each perspective, we place a small number of strategic objectives. Arrows indicate how one or more strategic objectives help accomplish others. Finally, we add a weight to each strategic objective indicating the amount of effort and resource we want to commit to them currently. While most aspects of the strategy map remain as is for a considerable length of time, the weights assigned to each objective should be regularly reviewed and potentially adjusted to meet changing needs.

We created a strategy map for Digital Transformation at UVU with Brett Knowles and others at Hirebook. Brett and his colleagues patiently helped us craft our strategy, asked probing questions that refined our language, and acquainted us with powerful ontologies and techniques to connect our project work with our strategic objectives.

Figure 1: Strategy map for the UVU Division of Digital Transformation, including strategic objectives and associated weights.

At the top and center of the strategy map, illustrated in Figure 1, is an abbreviated form of the UVU Mission Statement. You can see the four perspectives down the figure’s left side: stakeholders, internal processes, enablers, and financial. We’ve added brief definitions of each perspective to help us remember who or what is included in each. Within each perspective, we have added strategic objectives.

Within the financial perspective, we have a single strategic objective, Plan, Budget, and Assess, which represents the UVU planning and budgeting process known as PBA. We used a shared governance approach, with much discussion and compromise, to determine the weight associated with each strategic objective. In this case, we determined that we’ll spend 10% of our effort and resources on this objective. This strategic objective supports all other objectives in the strategy map. Arrows have been omitted for clarity.

The enablers perspective contains three strategic objectives: Be Responsive, Invest in Staff Development, and Manifest UVU Values. Accomplishing these strategic objectives is essential to enable the organization to accomplish the strategic objectives above them. We must invest in staff development to ensure they continue to be productive professionals who can deliver high-quality results. The staff must also be responsive, i.e., react quickly and positively to institutional concerns and needs. Finally, they must manifest UVU values of exceptional care, exceptional accountability, and exceptional results. This perspective will receive 35% of our effort and resources.

The perspective dealing with internal processes contains four strategic objectives: Practice Exceptional Product Portfolio Management, Provide Transformative Solutions, Strengthen Our Partnerships, and Deliver Delightful Experiences. Our division doesn’t currently have a strong practice in product portfolio management. We must develop this process to enable the delivery of the other three strategic objectives in this perspective. A strong product portfolio management process will strengthen our relationships with internal partners and enable our organization to provide transformative solutions. Together these three strategic objectives will enable our division to deliver delightful experiences to our stakeholders. This perspective will currently receive 50% of our attention and resources.

The stakeholders perspective includes three strategic objectives: Achieve Student Success, Include All Learners, and Engage Our Partners. While we organize our division, strengthen our internal processes, and develop our staff, we will only expend 5% of our effort and resources on these strategic objectives. However, these objectives are shared by all divisions at UVU. We expect that pursuing the strategic objectives in the internal processes and enablers perspectives will increase other divisions’ ability to focus on these important strategic objectives.

Impact Ontology

An impact ontology describes the impact that business processes ideally have on strategic objectives. The UVU Division of Digital Transformation has nine major business processes:

  1. Financial
  2. Product Portfolio Management
  3. Operations
  4. Service Management
  5. Human Resources
  6. Research and Development
  7. Data Delivery
  8. Risk and Security Management
  9. Digital Transformation Strategic Planning

Note that these nine business processes are not necessarily organizational units.

Figure 2: Impact ontology for the UVU Division of Digital Transformation, including major business processes, strategic objectives, and indicators of the potential impact business processes ideally have on associated strategic objectives.

The impact ontology illustrated in Figure 2 shows the impact that business objectives have on achieving strategic objectives. Our nine business processes are included across the top. The strategic objectives and associated weights from the strategy map are included down the figure’s left side. We have a value from zero to five at the intersection of each business process and strategic objective. Like the strategic objective weights, these values were obtained through a shared governance exercise and much discussion. Zeros indicate that the associated business objective has no impact on reaching the associated strategic objective. In contrast, fives indicate that the associated business process strongly influences reaching the associated strategic objective. The grey levels are added to aid in identifying impactful business processes. For the UVU Division of Digital Transformation, the Operations business process impacts our strategic objective of Delivering Delightful Experiences but does not impact our objective of Invest in Staff Development.

We can glean other interesting information from an impact ontology. For example, intersections containing fours or fives identify business processes that greatly impact the associated strategic objectives. We should monitor these processes using key performance indicators (KPIs) and improve them. Additionally, a business process owner can use the column associated with their business process to determine where to deploy their best people and the most resource for the greatest impact. Finally, looking across a row tells us which business processes should be represented in activities intended to enhance the institution’s ability to achieve the associated strategic objective.

Performance Ontology

The performance ontology illustrated in Figure 3 shows a relationship between business processes and strategic objectives.

Figure 3: Performance ontology for the UVU Division of Digital Transformation, including major business processes, strategic objectives, impact measures, and indicators of how the current performance of business processes are impacting associated strategic objectives.

In this case, the relationship we’re mapping is how well our organization performs each business process to pursue associated strategic objectives. Like the previously discussed impact ontology, the performance ontology includes our nine business processes across the top. The strategic objectives and associated weights are included down the figure’s left side. For convenience, we have included the impact ontology values from Figure 2. We have added a score from one to five, indicating how our organization performs each business process to pursue associated strategic objectives. These scores were obtained through self-evaluation and much discussion. In the future, these scores should be obtained through the measurement and evaluation of key performance indicators (KPIs). The color-coding indicates the magnitude of the strategic gap. The strategic gap is calculated by taking the difference between the impact a business process should have on a strategic objective and the actual performance we’re achieving and then multiplying by the strategic objective’s weight.

The color-coding of the performance ontology directs attention to important areas where there is a strategic gap. For example, the Data Delivery business process and Deliver Delightful Experiences strategic objective. In this case, the difference between the potential impact of the business process, determined to be a four, and our current performance, determined to be a two, multiplied by a strategic objective weighting of 17 creates a significant strategic gap of 34, is color-coded red, and demands our attention. The Operations business process has a potential impact of four on Manifest UVU Values while our performance receives a value of two. The impact and performance values are identical to those of the previous example. Still, a lower strategic objective weighting of 7 results in a strategic gap of 14, is color-coded yellow, and deserves less attention. Similarly, the Data Delivery business process’s desired impact on Achieve Student Success is a four while our performance yields a two. A strategic gap exists, but because the importance of that strategic objective is low, the strategic gap of 4 doesn’t warrant our attention and is color-coded green.

Strategic Gap

As previously described, the difference between impact and performance, weighted by the importance of a strategic objective, results in a strategic gap measure.

Figure 4: Strategic Objective Gap graph where the total bar height indicates the desired level of impact, the blue bars represent the current performance level, and the yellow bars the magnitude of the existing strategic gap.

The yellow portion of each bar illustrated in Figure 4 represents the total strategic gap for the associated strategic objective. The yellow portion’s height is the difference between the desired impact, total bar height, and our current performance, height of the blue portion. In the figure, the strategic objectives are ordered from greatest to the least strategic gap. The largest strategic gap in Figure 4 is for the Deliver Delightful Experiences strategic objective.

Each bar’s height is the total impact we desire to exert on each of the strategic objectives. This is computed for each strategic objective by multiplying the strategic objective’s weight and the sum of the business process impacts for the given strategic objective. This result is multiplied by five to enhance visualization.

The blue portion of each bar represents our current performance towards each of the strategic objectives. This is computed for each strategic objective by multiplying the strategic objective’s weight and the sum of the business process performance values for the given strategic objective. This result is also multiplied by five to enhance visualization.

Project Ontology

The previous section illustrated a process for determining which strategic objectives have significant strategic gaps and need attention. We want to pursue the projects and initiatives with the highest strategic value or the greatest promise of decreasing strategic gaps. Figure 5 shows the project ontology, where we can discover which projects have that promise.

Figure 5: Project ontology showing the impact various projects have on closing the strategic gap for each strategic objective, their strategic value.

The project ontology includes the strategic objectives on the figure’s left side and across the top a list of potential projects and their costs. The costs are in $100,000 increments and include cash and the value of required labor.

The values within the ontology range from zero (blank) to five, where zero indicates the associated project has no ability to close the strategic gap of the associated strategic objective. These projects have no strategic value concerning the associated strategic objective. Five indicates that the associated project has high strategic value and will significantly decrease the strategic gap of the associated strategic objective. For example, a project to create a mobile application will result in a product that significantly closes the gap for several strategic objectives, including Achieve Student Success, Include All Learners, Deliver Delightful Experiences, Provide Transformative Solutions, Strengthen Our Partnerships, Be Responsive, and Manifest UVU Values. This project has a high strategic value.

Figure 6: Strategic Objective Gap Closing graph illustrates the ability of a suite of proposed projects in closing the strategic gap for various strategic objectives.

In Figure 6, the yellow bars represent the strategic gap for each strategic objective, as described in the previous section. The red dots indicate the sum of the projects’ strategic values that impact the associated strategic objective. The successful completion of the proposed projects, which have significant strategic value, would nearly eliminate the strategic gap associated with several objectives: Deliver Delightful Experiences, Be Responsive, Strengthen Our Partnerships, Achieve Student Success, Include All Learners, and Engage Our Partners. In contrast, the other strategic objectives receive insufficient project work of sufficient strategic value to eliminate their strategic gaps.

If resources are fully allocated, the results illustrated in this figure may be used to adjust what projects and initiatives are pursued to distribute the strategic value more uniformly. Alternatively, if more resources are available to pursue additional projects, the graph indicates where strategic value is needed, which may be used to select appropriate projects.

Project Priority and Value

As shown in the previous section, a suite of projects may significantly decrease strategic gaps. However, the ability to close a strategic gap may also be attributed to individual projects. We should pursue projects and initiatives that have significant strategic value, i.e., significantly decrease strategic gaps.

Figure 7: Initiative Impact illustrates the strategic gap closing value of each of the proposed projects and initiatives. The dark blue bars illustrate project value in terms of strategic value per dollar spent.

Figure 7 illustrates the strategic value or gap-closing ability of each project and initiative. The initiative with the highest strategic value is creating a business intelligence unit and associated governance and processes. Projects to create a new web site, intranet portal, and mobile application are also strategically valuable.

The dark blue bars in Figure 7 indicate the impact value of each project. This is simply a project’s strategic value divided by the project’s cost. The MS Telephony project may not be strategically impactful, but it saves the institution money and has nearly zero cost.

As a division, we will seek approval and funding to pursue the strategically most impactful projects, those with high value, and those that save the institution money that may be applied to other high impact projects.


As pointed out earlier, a strategy should inform where improvements in business processes should be made and what projects and initiatives should be pursued. In this post, I described a process to determine the gap between an organization’s desired performance level and its current performance concerning strategic objectives. Also, a method to determine the strategic value of projects and initiatives was described. Combining these two activities enables us to evaluate proposed projects and initiatives in terms of which will best help us meet our strategic objectives. In environments where ROI is difficult to determine, this is a powerful tool to help us realize our mission.

My Career Change

Monday, March 16, 2020, I ended a 31-year career at Brigham Young University (BYU) and started in a new role at Utah Valley University (UVU). I accepted the newly created position of Vice President of Digital Transformation and CIO. I was hopeful that I could stay above the tactical problems associated with IT systems and focus on the institution’s digital transformation. While that was a worthy goal, COVID-19 put a damper on most strategic thinking and a significant focus on getting 4,000 courses online and ensuring that the Office of IT-supported that effort.

While the initial intent was to get to know my new team, help them understand my expectations and plans, and hire an admin and an associate vice president, COVID-19 put an end to all of that. My initial introduction to the team was a virtual team meeting, and our message was to stay safe, stay alive, and work from home if you can.

This week wasn’t the perfect traditional first week, but it was ideal for me to join the team at UVU. I think I have already contributed, and I hope to contribute much more as we move forward. I am encouraged by how quickly the cabinet, led by President Astrid S. Tuminez, adapts to new challenges and moves to new communication mechanisms and processes. She’s a great leader, and her team is anxious to serve UVU students. We hope the students are safe and ready to learn remotely.

Astrophotography: Images of Andromeda and Orion’s Nebula


Since acquiring my first telescope nearly 40 years ago, I have dreamed of capturing images of the Andromeda Galaxy (M31) and Orion’s Nebula (M42). Well, finally the day, or rather nights, came for collecting the light from these distant beauties.

This post describes the location where the presented images were collected and the settings used to collect them. In addition, two observations are included.

Dark Skies

My home suffers from skies polluted with city lights, lights from a nearby high school, and of course lights from neighbors. So my search for dark skies began. Living in Utah, dark skies are within an hour or two drive, but finding a night or two free from other activities, clouds, and a bright moon is not easy.

On November 9, 2018, my wife and I took our RV and telescope to the Wedge Overlook Campground in Utah. The outing and location are described on our Trailer Travels blog. This location is quite dark, our weekend was free, and there was no moon. The only challenge was the temperature which dipped well into the 20s. However, for astrophotography, this wasn’t much of a challenge. I simply framed the objects, started the exposure sequences, and went into the RV and watched movies in a warm environment; it was great.

The Images

The equipment used to collect the presented images is described in my First Attempt post. For the Andromeda Galaxy (M31) images, I collected 100 sub-exposures. Each sub was exposed for 30 seconds for a total exposure time of 50 minutes. Keep in mind that these images are shot at f/2 using the CPC 1100 and the Hyperstar system. This would be equivalent to 100 sub-exposures with exposure durations of 4 minutes each on an f/5.6 system, about 6.7 hours of total exposure time.

I’d love to try many more exposures and many more exposures at shorter exposure times and compare results. However, on this outing, I tried collecting light from many objects rather than focusing on a few. I won’t repeat that mistake. Each sub-exposure was collected with a camera gain of 93 (unity gain) and an offset of 12.

In addition to the sub-exposures described above, flats, darks, and bias frames were collected and processed as described in my previous post. The resulting image of the Andromeda Galaxy (M31) was processed in Adobe Camera Raw and finished with Adobe Photoshop.

For the Orion Nebula (M42) images, I collected 10 sub-exposures of 30 seconds each and 100 sub-exposures of 5 seconds each. This is a total exposure time of 13.3 minutes. Again, keep in mind that these images are shot at f/2 and are equivalent to 10 sub-exposures of 240 seconds each plus 100 sub-exposures of 40 seconds each, for a total of 1.8 hours.

As before, flats, darks, and bias frames were collected and processed as described in my First Attempt post. The result was two images of the nebula that were processed in Adobe Camera Raw and finished with Adobe Photoshop. Finally, the two images were selectively merged. The image created using the 5-second subs provided the core of the nebula and the image from the 30-second subs was used to provide the subtle nebulosity near the outer edges of the nebula.


In the future I will focus my efforts on one or two objects per night and try an array of exposure times, a number of subs, etc. rather than trying to acquire data for 5 or 6 objects. The time required to frame, focus, and take samples wasted a lot of time and in the end only resulted in two usable images.

You may notice that the shape of the stars in the image appears a bit triangular in shape. I believe this is due to a collimation error in my optical path. I have acquired a laser collimator and Hyperstar attachment and will use them to test my hypothesis and correct the problem if it exists. Hopefully, my next images will be better than those presented here.

Astrophotography: First Attempts


This post documents my first attempts at astrophotography with the Celestron CPC 1100 GPS telescope and the Hyperstar imaging system. My first targets were Markarian’s Chain and the Pinwheel galaxy (M101). Unfortunately, the targets were captured in an environment polluted by lights from a neighboring high school and multiple street lights. The remainder of this post describes the equipment used, the process used to capture and improve them and the images captured.


The main equipment used to capture Markarian’s Chain and M101 was a Celestron CPC 1100 GPS telescope, the Hyperstar 3 system and a ZWO ASI071MC Pro camera. In this configuration, the CPC 1100 becomes a 560mm focal length f/2 system. The telescope was mounted on the Celestron HD Pro Wedge which increased tracking accuracy allowing for longer exposures. The camera was connected via USB 3.0 to a laptop running Nebulosity 4 for image capture. The resulting images were processed using Photoshop.

Capturing and Pre-processing Images

Target images contain the desired signal as well as noise from several sources: bias, thermal and optical system imperfections. Bias noise represents the electronic signature of the camera. Thermal noise becomes more evident with long exposure times and warm sensors. Optical system imperfections include vignetting and other characteristics specific to a particular optical system. Many target and calibration images are taken, processed and combined to reduce noise. This section describes the images that are captured and the processing necessary to yield results.

Bias Frames

As previously mentioned, bias noise is created by the electronics of the camera used to capture the images of interest. By capturing short exposure images with the camera’s lens cap on, they contain little noise from thermal or optical issues. These images are collected with the same camera gain used to collect target images. The bias frames collected are averaged to create a master bias frame. How this master bias frame is used during processing will be described shortly. It is important to point out that every frame contains bias noise regardless of exposure time or how cool the sensor is kept.

Dark Frames

Dark frames contain both bias and thermal noise. They are acquired by placing the lens cap on the camera and taking exposures equivalent to those used to acquire the target images. It is ideal to have the camera at the same temperature, use the same gain and the same exposure times that were used to capture the target sub-images. Like bias frames, these frames are averaged resulting in a master dark frame.

Flat Frames

Flat frames contain bias noise as well as artifacts of the optical system. These artifacts include vignetting, dust on lenses, mirrors and sensors, and other optical system imperfections. While there are multiple ways to collect these frames, I use the t-shirt method. I place two layers of a white t-shirt over the aperture of the telescope and take numerous exposures. The focus and orientation of the camera to the optical system are kept consistent with those used when the target images were collected. The exposure times are controlled to give reasonable exposures.

Sub-Exposures or Subs

The sub-exposures, or subs, are the acquired images of the target object including the described noise and imperfections. The optimum exposure time for subs is a hotly debated topic in numerous forums. Too short and the images contain too much read noise to result in good quality finished products. Too long, in areas like mine, and they are washed out from light pollution. Exposure times between 2 and 20 minutes seem common with the average being in the 3-5 minute range. Given that this f/2 system is 8-10 faster than most others, I use exposure times considerably shorter.


The noise components of captured images cannot simply be subtracted resulting in a noise-free result, but the solution isn’t that much more complicated. One of the complications is that bias noise is contained in all captured frames. Let’s first consider the flats and the elimination of vignetting.

Flats contain data characterizing the optical issues of a particular system as well as bias noise. We begin by subtracting the master bias frame from each flat frame. The resulting flat frames have little thermal noise because they were acquired with short exposure times and the bias noise has been subtracted. The resulting frames are averaged to create a master flat frame.

The master dark frame, described above, is subtracted from each of the subs. The result is a set of images that contain target data and ideally no bias or thermal noise. Each of these frames is then divided by the master flat frame to remove the imperfections of the optical system. The result is a set of subs that ideally contain no noise or optical imperfections.

These subs are then de-mosaiced, converted to a full-color image, aligned, rotated and scaled using star images and averaged. The result is a single output image file with a much higher signal to noise ratio that can be post-processed to yield good results.

First Targets

The two targets of interest were Markarian’s Chain and the Pinwheel galaxy (M101). This section describes the subs taken and shows the results after post-processing in Photoshop.

Markarian’s Chain

The Markarian’s Chain sub-exposures were acquired using 50 second exposure times with a camera gain of 94 (unity gain). The figure to the right is one of the 110 sub-exposures. The most significant visual issue is the significant vignetting. In addition, these exposures are likely too long given the conditions. Future attempts will be made with more subs, but shorter exposure times.

Bias, dark and flat frames were collected and used to process these sub-exposure frames. The result was a single pre-processed image file that represented just over 1.5 hours of total exposure time. This image was processed using Photoshop resulting in my first finished product illustrated below.

The technical aspects of creating such an image are interesting to me, but in addition, I am always moved by the sheer immensity of space and the beauty of the creation. This image contains at least 10 galaxies each of which contains hundreds of millions of stars, that’s simply amazing and inspiring!

The Pinwheel Galaxy (M101)

The Pinwheel galaxy is located near the handle of the big dipper and was an enjoyable target to witness for the first time. Each sub-exposures was acquired with a 5 second exposure time with a camera gain of 200 and an offset of 50. The figure to the right is one of the 120 sub-exposures. The most significant visual issue is again the significant vignetting. In addition, there is significant noise due to the high gain used. In the future, I am unlikely to use gains greater than unity.

As with the Markarian’s Chain images, bias, dark and flat frames were collected and used to process the M101 sub-exposure frames. The result was a single pre-processed image file that represented 10 minutes of total exposure time. This image was processed using Photoshop resulting in the finished product illustrated below.

I look forward to targetting M101 again and experimenting with longer exposure times and perhaps capturing many more sub-exposures.


I am captivated by both the beauty of the universe and the technical aspects of capturing it. I can hardly wait for the next clear night and the opportunity that it will give me to capture more. I look forward to experimenting with more sub-exposures and varying exposure times. I look forward to experiencing the system in its f/7.5 configuration to increase magnification. While this will increase exposure time significantly, the challenge will be fun. Finally, I look forward to summer and fall and the new targets they’ll bring.

Electrical Power for Astrophotography


Telescopes that slew to, and track celestial objects do so through the use of electric motors that drive their axes of rotation. Portable telescopes, like the Celestron CPC 1100 GPS, depend on either alternating current (AC) line voltage or batteries for their power. In addition, camera coolers, dew heaters and other accessories require power. The remainder of this post describes power requirements of typical astrophotography equipment and the construction of a do-it-yourself (DIY) portable power supply.

Astrophotography Equipment

The equipment I use includes a telescope, camera and dew heaters:

This equipment and their power requirements are listed in the following table.

EquipmentMake and ModelOperating VoltageReported Current
TelescopeCelestron CPC 1100 GPS12 V1.5 A
CameraZWO ASI071MC Pro12 V3 A
Dew HeaterDew-Not DN01212 V1.57 A
Dew HeaterDew-Not DN00312 V350 mA
Dew Heater ControllerThousand Oaks Four-Channel12 VNegligible
Total6.42 A

The reported values were obtained from vendor web sites, while the measured values were observed during operation. The total required current has a maximum value of 6.42 Amperes. The remainder of this post will describe the construction of a DIY power supply to meet these needs.

Power Supply

This section describes the construction of a portable power supply that meets the needs of my astrophotography equipment. This system must be portable and supply 12 Volts at just over 6 Amperes for 4-5 hours. We’ll first list the items needed and then dive into the simple construction.

Tools and Parts

This project is very straightforward and requires very few tools and a handful, a heavy handful, of parts. You’ll need a 1.25 inch hole saw or drill bit, a couple of wrenches, and scissors or a utility knife. In addition to these tools you’ll need the following items or appropriate substitutes:


Lets start with the green utility box pictured to the right. Remove the inside dividers and then drill two holes in one of the ends. These 1.25″ holes will enable the mounting of the 12 Volt receptacles and can be placed wherever you’d like them. Then install and securely tighten the receptacles in place.

The next step is to make a secure location for the battery to sit in the box. Place a 1/2″ layer of closed cell foam in the bottom of the utility box. Then add two 1″ thick blocks of foam to each end with just enough space between them to squeeze in the battery. Then add 1″ thick foam on both sides of the box to hold the battery firmly in place. In the image to the left you can easily see the indentation in the bottom of the box intended to accept the battery.

The cigarette lighter power sockets include simple wiring harnesses that enable them to be easily connected to a battery. Connect each harness to the battery with two 1″ x 1/4″ bolts with associated nuts and washers. The socket end of the harness simply plugs into the blades protruding from the power sockets. Make sure you tie the positive socket terminal to the positive side of the battery! Once this is done you simply tuck the wires neatly under the power sockets, slip the battery in place and latch the lid closed.

You now have a portable source of 12 Volt power. When the battery needs recharging, you simply open the lid and charge it.


In this post we outlined the need for 12 Volt power for remote astrophotography and presented a simple DIY power supply to meet the need.


Get Focussed: Feather Touch 10:1 Focuser


In a previous post we discussed depth of focus and the difficulties obtaining good focus with fast optical systems. In this post we’ll discuss a solution to the problem, the Feather Touch 10:1 focuser for the Celestron CPC 1100 GPS telescope.

We’ll briefly review the challenge of focusing fast telescopes and then describe how the Feather Touch 10:1 focuser will help. We’ll conclude with the installation of the focuser on a CPC 1100.


In a previous post we derived three equations for depth of focus and presented a table illustrating the depth of focus for various f-numbers. This table is included below for convenience.


The most important conclusion that can be drawn from this data, for the discussion at hand, is that fast telescopes, such as those operating at f/2, have very narrow depth of focus. For example, an f/10 system has a depth of focus of approximately 263 microns, while an f/2 system’s depth of focus is only about 10.5 microns. These figures are for seeing disks with a diameter equal to the diameter of the Airy disk. In great seeing conditions where the seeing disk might be 2″, these figures would increase to approximately 543 microns and 21 microns respectively.

Clearly, for fast telescopes, such as those operating at f/2, the depth of focus is very narrow. These tight tolerances may make focusing these systems a challenge.

My Application

As previously mentioned, at f/10 in ideal seeing, the depth of focus is 263 microns while at f/2 this is reduced by 25x, resulting in a narrow band of only 10.5 microns. However, with diminished viewing and larger seeing disks these numbers will grow. The application that spawned this investigation was astrophotography with a Celestron CPC 1100 GPS in its f/2 configuration. The question that started it all was, is the standard focuser on the CPC 1100 adequate to deal with these tight tolerances. We know how fine the focusing must be. In this section we’ll determine whether the standard focuser is up to the task or whether we need to look at other options.

Standard Focusing Mechanism

The focusing mechanism that comes standard with the Celestron CPC 1100 is illustrated to the right. As the focus knob is rotated, the focuser either pushes or pulls a threaded rod, that is connected to the primary mirror, in or out.

The rod and the focuser have a thread pitch of approximately 0.8 threads per millimeter. In other words, each rotation of the knob moves the primary mirror in or out 0.8mm, or 800 microns.

In ideal seeing conditions, with this telescope in the f/10 configuration, we have a depth of focus of 263 microns. So the entire depth of focus can be traversed with just under 1/3 of a turn of the focus knob. With degraded, but great, seeing conditions where the seeing disk is 2″ in diameter, the depth of focus increases to 542 microns, or 2/3 of a turn of the focus knob. It seems reasonable to expect, and experience has demonstrated, that achieving focus with these constraints is straightforward.

However, when this system is configured to operate at f/2 the depth of focus under ideal conditions is reduced to just 10.5 microns. Even with a seeing disk of 2″ the depth of focus is only 21 microns. The entire depth of focus is traversed with 1/78 and 1/38 of a turn of the focus knob respectively. These are very tight tolerances that would make achieving focus very difficult.

Feather Touch 10:1

After some investigation, I decided to try and solve the focussing problem, identified in the previous section, by acquiring and installing a Feather Touch 10:1 focuser for the CPC 1100. This focuser has dual speeds, a 1:1 ratio focusing knob, black in the image, and a brass colored 10:1 ratio knob.

Recall from the previous section that our challenge is to focus a system with a depth of focus of 10.5 microns in ideal conditions and 21 microns in the best likely conditions. At a 1:1 ratio the entire depth of focus is traversed in 1/78 and 1/38 of a turn of the focus knob respectively. With a 10:1 ratio these tolerances increase to 1/8 and 1/4 of a turn respectively. While these are still tight tolerances, I believe focus will be obtainable.

In the next section I’ll quickly walk through the installation of this focuser. It was fairly straightforward and required few tools.


In this section we’ll walk through the installation of the Feather Touch 10:1 focuser for the Celestron CPC 1100 GPS telescope. There were three items in the box: the focuser, a stop and a small washer. The installation requires the reuse of four screws associated with the standard Celestron focuser.  You’ll need a 1/2 inch open end wrench and a medium sized Phillips-head screwdriver.

The first task is to position the CPC 1100 in a horizontal position, altitude of 0°, so the primary mirror does not move during installation. Then we turn to removing the standard focuser. After pulling the rubber knob straight off and removing the three visible screws holding the focuser to the rear of the telescope, we have something that looks like the image to the right. Hang on to the three screws as they will be used to install the new focusing mechanism.

You must now rotate the brass focussing assembly clockwise until you see the head of the Phillips-head screw hidden inside. It takes quite a few turns to move the mirror back and the screw head never emerges from the hole, but does become easily accessible. When you’ve removed the screw, remove the small washer and replace it with the new washer that came with the Feather Touch focuser. Retain this screw as it will be reinstalled shortly.

Now the brass assembly needs to be removed. Rotate it in a counterclockwise direction until it is detached. It takes quite a few turns to free it. When it is removed, take the stop off of the new focuser and thread it onto the threaded shaft far enough that a few threads of the shaft are exposed. At this point it looks something like the image to the right.

Now reinstall the screw, with its new washer, into the end of the threaded rod. Screw the Feather Touch focuser onto the exposed threads of the rod until it reaches the stop. Hold the stop with a 1/2 inch open end wrench and tighten the focuser against the stop. You can grasp the focuser easily by the 1:1 ratio focus knob. This must be tight!

Now rotate the focuser down the rod until its mounting plate is flush against the back of the telescope. It may be necessary to push the mirror slightly forward to get the Feather Touch to seat properly. Reinstall the three screws retained earlier, and you’re done. The finished product is illustrated to the right.

Now you are ready to focus normally with the black knob and with precision with the 10:1 ratio brass knob.


In this document we presented the depth of focus for various f-numbers and determined that focusing fast optical systems is problematic. Finally we presented a solution and described its installation.

Depth of Focus


Without diffraction and atmospheric turbulence, ideal telescopes would focus stars to points. However, there would also be a single focal point, plane or surface and everywhere else would be out of focus. Back in the real world, where diffraction, atmospheric turbulence and telescope flaws exist, stars are not imaged as points, but rather as Airy disks or seeing disks that are larger. This leads to a range where focus can be obtained. This range is called depth of focus and is the topic of this document.

We’ll first describe depth of focus in more detail. Afterwards, we’ll derive it mathematically and present an approximation and a simplification based on ideal seeing. We’ll then present data for various telescope configurations and discuss challenges with focusing fast optical systems.

Depth of Focus

Today’s telescopes are generally diffraction limited. This means that defects in design and construction are not the limiting factors in focusing a star to a point. The aperture of a telescope limits its ability to focus a star to a disk smaller than an Airy disk. Due to atmospheric conditions this limit is rarely achieved. Good seeing conditions result in disks as small as 2 arc-seconds (2″) in diameter.

The above figure depicts light from a star entering a reflector telescope from the left and being brought to a focus at the point labelled Focus. As this cone of light converges towards focus, its cross-sectional diameter decreases until focus is reached. Beyond focus its diameter again increases. When the cross-sectional diameter is as small as the Airy disk, or the minimum size disk obtainable due to seeing conditions, there is nothing gained by it being brought closer to the point of focus. The vertical red lines indicate the region within which the image is as small as conditions permit. The length of this region is the depth of focus.


The angle, \theta_{cone}, formed by the sides of the cone at the focus, is

    \[ \theta_{cone} = 2 \sin^{-1}(\frac{\text{Aperture}}{2 \times \text{Focal Length}}) \]

where \theta_{cone} is measured in degrees and the Aperture and Focal Length of the system are measured in meters. Recall that the focal length divided by the aperture of a system is its f-number. Thus,

    \[ \theta_{cone} = 2 \sin^{-1}(\frac{1}{2 \times \text{f-number}}) \]

As previously mentioned, the cross-sectional diameter of the cone decreases as the focus is approached. We are interested in the distance from the focus to where the cross-sectional diameter of the cone is equal to the diameter of the seeing disk. This is illustrated in the following figure.The distance from the seeing disk on the right to the focus on the left is,

    \[ \frac{1}{2}F_{depth} = \frac{\frac{1}{2}D_{size}}{\tan \frac{\theta_{cone}}{2}} \]


    \[ F_{depth} = \frac{D_{size}}{\tan \frac{\theta_{cone}}{2}} \]

where F_{depth} is the depth of focus in meters, D_{size} is the size of the seeing disk in meters and \theta_{cone} is the angle of the converging sides of the light cone at the focus, in degrees.

The size of a seeing disk is described by the following equation.

    \[ D_{size} = \frac{2\pi}{360} \theta_{disk} \times \text{Focal Length} \]

where D_{size} is the seeing disk size in meters, \theta_{disk} is the angular size of the seeing disk in degrees, and Focal Length is measured in meters.

Through substitution we obtain the result,

    \[ F_{depth} = \frac{\frac{2\pi}{360} \theta_{disk} \times \text{Focal Length}}{\tan (\sin^{-1}(\frac{1}{2 \times \text{f-number}}))} \]


    \[ F_{depth} = \frac{\frac{2\pi}{360} \theta_{disk} \times \text{Focal Length}}{\frac{(\frac{1}{2 \times \text{f-number}})}{\sqrt{1-(\frac{1}{2 \times \text{f-number}})^2}}} \]


By noticing that the ratio in the denominator of the above equation is approximately equal to \frac{1}{2 \times \text{f-number}} the above equation can be simplified.

    \[ F_{depth} = \frac{\frac{2\pi}{360} \theta_{disk} \times \text{Focal Length}}{\frac{1}{2 \times \text{f-number}}} \]

In addition, this result can be simplified and the units of \theta_{disk} can be converted to arc-seconds, to yield,

    \[ F_{depth} = \frac{4\pi}{360} \frac{\theta_{disk}}{3600} \times \frac{(\text{Focal Length})^2}{\text{Aperture}} \]

where F_{depth} is the depth of focus in meters, \theta_{disk} is the angular size of the seeing disk in arc-seconds, Focal Length is measured in meters and f-number is the numerical f-number of the system.

Ideal Seeing

Ideally a telescope with an aperture d can focus a star to a seeing disk with an angular diameter of an Airy disk. An approximation for the radius of an Airy disk is given by,

    \[ \theta = 1.22\times\frac{\lambda}{d} \]

where \theta is the radius of the Airy disk in radians, \lambda is the wavelength of light in meters and d is the diameter of the mirror or lens in meters. Manipulating this equation to yield a disk diameter in arc-seconds yields,

    \[ \theta = \frac{360}{2\pi} \times 3600 \times 2.44\times\frac{\lambda}{d} \]

where \theta is now in arc-seconds and represents the diameter of the Airy disk.

If we adjust \theta_{disk} to be equal to \theta, derived above for the given Aperture d, we obtain,

    \[ F_{depth} = \frac{4\pi}{360} \frac{\frac{360}{2\pi} \times 3600 \times 2.44\times\frac{\lambda}{d}}{3600} \times \frac{(\text{Focal Length})^2}{\text{Aperture}} \]

This simplifies quickly to,

    \[ F_{depth} = 2 \times 2.44\times\frac{\lambda}{d} \times \frac{(\text{Focal Length})^2}{\text{Aperture}} \]

Recalling that, for this ideal case, we constrained d and Aperture to be equal, this simplifies to,

    \[ F_{depth} = 4.88 \times \lambda \times \text{f-number}^2 \]

where \lambda is the wavelength of light in meters being observed or imaged and f-number is the numerical f-number of the system. F_{depth} can be adjusted for degraded seeing by multiplying it by the ratio of the width of the seeing disk to the width of the Airy disk for the chosen aperture.


The following table contains depth of focus values in microns for ideal seeing at various f-numbers using the derived equation, the approximate equation and the final equation based on ideal seeing. We’ll assume an aperture of 280mm as two of the three equations require focal length and aperture as parameters. The Airy disk diameter for an aperture of 280mm is 0.97″.


There are two important conclusions that can be drawn from the data in the above table. First, all three of the derived equations yield quite similar results. Second, the fact that the depth of focus is proportional to the square of the f-number is significant. This means that at f/10 the depth of focus is approximately 263 microns while at f/2 it is only about 10.5 microns. It is important to remember that these figures are for seeing disks with a diameter equal to the diameter of the Airy disk. In great seeing conditions where the seeing disk might be 2″, these figures would increase to approximately 543 microns and 21 microns respectively.

For fast telescopes, such as those operating at f/2, the depth of focus is very narrow. These tight tolerances may make focusing these systems a challenge.


In this post we described depth of focus and derived it mathematically. We then presented an approximation and a model that assumes ideal seeing. The ideal seeing model is routinely used by others and yields good results. Finally, we presented depth of focus figures for various f-numbers and determined that focusing fast optical systems may be problematic.


Field Rotation and Alt-Azimuth Mounted Telescopes


Telescopes can be mounted in a variety of ways. Two common telescope mounts are the altitude-azimuth, or alt-azimuth, and the equatorial mount. The alt-azimuth mount is easier to construct than an equatorial mount, but requires motion on both axes to accurately track celestial objects as they move across the night sky. Astrophotography using an alt-azimuth mounted camera system suffers from field rotation, whereas properly aligned equatorial mounted systems do not. The intention of this document is to describe field rotation and determine its impact on astrophotography. In addition, we’ll determine where astrophotography with a CPC 1100 GPS XLT system used in its f/2 configuration can be successful using its alt-azimuth mount.

Telescope Mounts

As previously mentioned, the two most common telescope mounts are the alt-azimuth and equatorial mounts. A system utilizing an alt-azimuth mount can benefit from the features of the equatorial mount with the addition of a wedge. This section describes these three mounts and briefly discusses their pros and cons.

Alt-Azimuth Mount

An alt-azimuth mount often consists of a pair of forks that stand vertically. These forks rotate around the vertical or azimuth axis. The telescope is attached to the forks and can pivot on the horizontal or altitude axis. This system is obviously quite simple to construct and operate, but to track celestial objects, in their apparent circular paths across the sky, requires nearly constant adjustment of both axes. The introduction of microprocessor-based control systems has made this tracking viable.

Equatorial Mount

An equatorial mount has two perpendicular axes. The first axis is aligned with the earth’s axis of rotation, right ascension. The second is perpendicular to the first, declination. The telescope is attached to the second axis. To track a celestial object using this mount, the telescope is pointed to the desired object, found at a specific right ascension and declination, and then a constant sidereal clock drives the right ascension axis to compensate for the earth’s rotation.

Open Fork Mount

An alt-azimuth fork mount can be configured to benefit from the features of an equatorial mount by aligning the azimuth axis with the earth’s axis of rotation, providing motion in right ascension. The telescope can then swing between the forks in declination.  The device used to align the fork’s axis with that of the earth is commonly referred to as a wedge. With the addition of a wedge, the alt-azimuth mount must only be driven in right ascension to track celestial objects.

Field Rotation

As a constellation rises, crosses the sky on an apparent circular arc and sets, you’ve likely noticed that it appears to rotate. For example, as the constellation Orion rises in the east it may appear to be leaning slightly to the left, at its highest altitude it may be upright and as it sets it appears to be leaning to the right. This is illustrated below.Let’s continue using the Orion constellation as our example. If you’re imaging with a system on an equatorial mount, the telescope and associated camera rotate in right ascension, as illustrated below. The gray rectangles in the figure represent the field of view of the imaging system. The camera retains its relative orientation to the celestial body being photographed. If the equatorial mount is accurately aligned with the earth’s axis, no field rotation occurs.

Unlike the previous example, if you’re imaging with a telescope on an alt-azimuth mount you will experience field rotation.  In the following illustration, the gray rectangles again represent the field of view of the imaging system. Over time the imaging system remains centered on the middle star of Orion’s belt, but the camera remains level with the horizon due to the orientation of the mount’s two axes of rotation.

Notice in the above figure that Orion appears to rotate in the field of view as time passes. If the gray boxes represent distinct times within a long exposure, the stars in the constellation would appear as arcs rotating in a clockwise direction around the center of the frame, in this case, the middle star of Orion’s belt. This is what is meant by field rotation and it is generally undesirable.

It should be clear that equatorially mounted systems do not suffer from field rotation issues. However, this is only true if they are well aligned with the earth’s axis of rotation. While alt-azimuth mounted systems typically suffer from field rotation, solutions have been developed that rotate the imaging system to counter the field rotation. While some of these solutions have been available to amateur observers in the past, it doesn’t appear that any commercial solutions are currently available. In addition, software can be used during post processing of images to remove some of the artifacts introduced by field rotation.

The above examples illustrate the basic issues related to field rotation and astrophotography. However, field rotation is more complex than first meets the eye. In the northern hemisphere when looking south, like in our example above, the field rotation is in a clockwise direction. Looking north we observe counterclockwise field rotation, and this complexity is just the beginning. In the next section, we’ll investigate the math describing field rotation and present associated graphs.

The Math of Field Rotation

As eluded to in the previous section, field rotation is more complex than our simple examples lead one to believe. It would be easy to believe that the rate of rotation is constant or that rotation continues in the same direction as observed bodies fall below the horizon, neither are true. In this section, we’ll introduce the math behind field rotation and illustrate graphically what this means. The rate of field rotation is defined as,

    \[ \omega_f = \omega_{earth} \times \cos latitude_{observer} \times \frac{\cos azimuth}{\cos altitude}  \]

where \omega_f is the angular velocity of the field rotation in degrees per second, \omega_{earth} is the angular velocity of the earth’s rotation in degrees per second, latitude_{observer} is the latitude where the observations are made, and azimuth and altitude describe the coordinates of the celestial body of interest, at the time of observation, in degrees.

There are a few interesting observations regarding this equation. First, if the observer is at either pole, the \cos latitude_{observer} will be zero resulting in \omega_f being zero. This is easily visualized if you imagine standing precisely on either pole and observing the movement of the stars. They will move around you with no change in altitude. This path is easily tracked by rotating around the azimuth axis of an alt-azimuth mount. Second, the field rotation is maximal at the equator where \cos latitude_{observer} is equal to 1. However, as illustrated in the following figure, the increase in field rotation from latitude 40° north to the equator, for any given azimuth and altitude, is only about 30%. In this figure the horizontal axis is latitude in degrees, where negative values represent latitudes in the souther hemisphere. The vertical axis is the value of \cos latitude_{observer}.

Second, if the \cos altitude is zero we have a divide by zero issue. This occurs at an altitude of 90°, the zenith, where field rotation is infinite and cannot be tracked by an alt-azimuth mounted telescope.

With regard to the field rotation equation, there are four variables of interest, namely \omega_f, azimuth, altitude and latitude_{observer}. Four dimensions are difficult to visualize so we’ll use my latitude of 40.3245° north and analyze the other three variables graphically.

The vertical axis of the above surface plot illustrates the angular velocity of the field rotation, in degrees per second, for various values of azimuth (horizontal axis) and altitude (depth axis). There are several interesting insights worth pointing out. First, at altitudes less than 65° the field rotation never exceeds 0.01° per second regardless of the azimuth chosen. Second, the field rotation never exceeds 0.01° per second for altitudes up to 75° for azimuths between 240° and 300° and 60° and 120°. In other words, looking due east or due west is far better than looking north or south. Finally, looking north or south results in high rates of rotation.

This section has illustrated the mathematical theory governing field rotation. While the math is fairly straightforward, the results are more complicated than one may have initially thought. In the next section, we’ll determine the impact field rotation has on astrophotography for our specific system and reexamine the surface plot above in terms of safe and ill-advised zones for various exposure lengths.

Impact on Astrophotography

For long exposures using imaging systems attached to alt-azimuth or poorly aligned equatorial mounts, field rotation is an issue that degrades image quality. In the previous section, we presented an approach to determine the angular velocity of the field rotation for a given latitude, azimuth and altitude. In this section, we’ll use that information to quantitatively determine how field rotation impacts image quality using systems with various characteristics.

Acceptable Field Rotation

Imaging system characteristics such as focal length, aperture, f-number, exposure length, sensor size and pixel size play important roles in astrophotography. The characteristics that determine the level of impact field rotation has on image quality are focal length, the size of the sensor and the associated pixels. The following figure is a representation of an image sensor made up of a two-dimensional array of pixels. The green, yellow and red disks represent seeing disks projected onto the sensor with angular sizes of 1″, 2″, 3″ and 4″ respectively. This is to scale for a sensor with a pixel size of 4.78µm and a system focal length of 560mm. The sizes of these disks are proportional to the focal length of the system as described below.

    \[ Size_{disk} = \frac{2\pi}{360°} \theta_{disk} \times Focal\;Length \]

where Size_{disk} is the size of the seeing disk on the sensor in meters, \theta_{disk} is the angular size of the seeing disk in degrees and Focal\;Length is the focal length of the optical system in meters. The four seeing disks illustrated on the sensor are approximately 2.71µm, 5.43µm, 8.14µm and 10.86µm in diameter.

While an image is being exposed, the field is rotating at an angular velocity \omega_f. For a specific exposure time, time_{exposure}, the angle of image rotation \theta_f can be computed as \theta_f = \omega_f \times time_{exposure}. While all objects in the field of view rotate around the center at the same angular velocity, those furthest from the center cover more distance. To ensure good image quality, the distance travelled must be less than a few pixels on the sensor. In the next section, we’ll try and quantify how much image rotation can be tolerated while still achieving esthetically pleasing results.

The Rule of 500

To determine just how many pixels can be traversed without significant impact, we’ll turn to the rule of 500 used by photographers to image the night sky. It should be noted that this rule was not developed to deal with field rotation, but rather to deal with star movement relative to a stationary camera. However, it does suggest the amount of movement that can be tolerated and still yield pleasing results. This rule of thumb suggests that the maximum length of an exposure, without significant star trails, is computed by dividing 500 by the focal length of the system measured in mm. The angular distance a star image travels across the sensor in this length of time is derived below.

    \[ \theta_{star} = \omega_{earth} \times time_{exposure} \]

where \theta_{star} is the angular distance in degrees traveled by a star in time_{exposure} measured in seconds given that the earth is rotating at the angular velocity of \omega_{earth} measured in degrees per second.

According to the rule of 500 an appropriate exposure time is 500 divided by the focal length of the optical system measured in mm,

    \[ \theta_{star} = \omega_{earth} \times \frac{500}{Focal\;Length} \]


    \[ \theta_{star} = \frac{\omega_{earth}}{2 \times Focal\;Length} \]

where Focal\;Length is now measured in meters. By determining the fraction of the sensor that \theta_{star} represents and multiplying it by the number of pixels, we’ll get the number of pixels traversed when applying the rule of 500. To start with we know that,

    \[ FOV = \frac{360°}{2\pi} \frac{Sensor\;Size}{Focal\;Length} \]


    \[ Pixel\;Count = \frac{Sensor\;Size}{Pixel\;Size} \]

where FOV is the field of view projected onto the sensor measured in degrees, Sensor\;Size is the size of the sensor in a particular dimension measured in meters, Focal\;Length is the focal length of the system measured in meters, Pixel\;Count is the number of pixels in the same dimension as mentioned above and Pixel\;Size is the size of one pixel, measured in meters.

Dividing \theta_{star} by FOV and multiplying by Pixel\;Count} we obtain,

    \[ \frac{\theta_{star}}{FOV} \times \frac{Sensor\;Size}{Pixel\;Size} = \frac{\frac{\omega_{earth}}{2 \times Focal\;Length}}{\frac{360°}{2\pi}\frac{Sensor\;Size}{Focal\;Length}} \times \frac{Sensor\;Size}{Pixel\;Size} \]

Simplifying we obtain,

    \[ \frac{\theta_{star}}{FOV} \times \frac{Sensor\;Size}{Pixel\;Size} = \frac{\pi}{360°}\frac{\omega_{earth}}{Pixel\;Size} \]

Finally, we recognize that \frac{\theta_{star}}{FOV} \times \frac{Sensor\;Size}{Pixel\;Size} is simply the number of pixels traversed by the seeing disk on the sensor, resulting in

    \[ Pixels_{traversed} =\frac{\pi}{360°}\frac{\omega_{earth}}{Pixel\;Size} \]

where Pixels_{traversed} are the number of pixels that can be traversed without leaving significant star trails according to the rule of 500, \omega_{earth} is the rotational velocity of the earth in degrees per second and Pixel\;Size is the size of each pixel in meters.

A sidereal day is 23 hours 56 minutes and 4.1 seconds or 86,164.1 seconds long. The earth rotates through 360° in this length of time resulting in \omega_{earth} being approximately equal to 0.00418° per second.

For a pixel size of 4.78µm, the rule of 500 suggests that 7.63 pixels can be traversed. We’ll round down to ensure better image quality. For the remainder of this work we’ll assume that if a seeing disk traverses 7 or fewer pixels across the sensor, due to field rotation, the image quality will be acceptable.

It is important to keep in mind that the rule of 500 has nothing to do with field rotation. However, photographers have used this rule to achieve good results shooting the night sky without significant star trails in their photographs. If stars traversing 7 pixels in these photographs are not objectionable, they shouldn’t be in our images either.

Acceptable Viewing

In the previous section we determined that star images traversing 7 or fewer pixels across the sensor would be acceptable. In this section we’ll investigate what impact we can expect due to field rotation and determine where in the night sky it is safe to image without having elongated stars in our photographs.

Given a rectangular image sensor, the distance an object travels in terms of rotational velocity and distance from the center of the sensor is described by,

    \[ D = \frac{2 \pi R}{360} \times \omega_f  \times time_{exposure} \]

where D is the distance in meters an object travels across the sensor at a distance R from the center of the sensor, R is the distance from the center of the sensor to the object of interest in meters, \omega_f is the field rotational velocity in degrees per second and time_{exposure} is the length of the exposure in seconds. Combining our initial equations for \omega_f with this equation we have,

    \[ D = \frac{2 \pi R}{360} \omega_{earth} \times \cos latitude_{observer} \times \frac{\cos azimuth}{\cos altitude}  \times time_{exposure} \]

where D is the distance an object travels across the sensor in meters, R is the distance from the center of the sensor to the object of interest in meters, \omega_{earth} is the angular velocity of the earth’s rotation in degrees per second, latitude_{observer} is the latitude where the observations are made, azimuth and altitude describe the coordinates of the celestial body of interest in degrees and time_{exposure} is the length of the exposure in seconds.

Let’s consider the characteristics of a specific CMOS sensor, the IMX071. This sensor is 23.6mm x 15.6mm with a 28.4mm diagonal. The pixel size of this sensor is 4.78µm and they are organized in a two-dimensional array that measures 4944 x 3284 pixels. While objects at the extreme corners of the sensor are not captured as they rotate through the field, their distance from the center is a good worst case measure since they travel further than anything else in the field for any given time_{exposure}.

If we assume the same latitude_{observer} of 40.3245° north as before and an exposure time of 10 seconds, we obtain the surface below. The vertical axis is the number of pixels traversed during a 10 second exposure, the other two axes represent the azimuth and altitude of the observed object.

For good image quality it is important to have as little movement as possible, but less than 7 pixels according to the rule of 500 discussed in the previous section. The following figure illustrates azimuths and altitudes that result in good 10 second exposures at a latitude of 40.3245° north.

The green area illustrates where pixel traversals of 7 pixels or less occur. The yellow areas have pixel traversals of 7 to 14 pixels and the red regions represent pixel traversals greater than 14 pixels.

For altitudes less than 75°, acceptable images can be acquired at any azimuth value. Between 70° and 110° azimuth and 250° and 290° azimuth, acceptable images can be obtained at altitudes up to 85°. There are few restrictions for 10 second exposures. Also recall that these values are based on the very corner of the sensor where field rotation has the biggest impact.

The next two figures illustrate azimuths and altitudes that result in good 20 and 30 second exposures at a latitude of 40.3245° north.

Exposure times of 30 seconds result in far more restrictions. The poles should be avoided above 45° and only due east and west are virtually unrestricted.

As stated earlier, there is no field rotation at the poles of the earth. The equatorial region suffers the most field rotation. The following figure illustrates azimuths and altitudes that result in good 10 second exposures at the equator, latitude 0°.As previously stated, moving from a latitude of ~40° to 0° has little impact on the effects of field rotation. There are no restrictions below 70° of altitude and almost no restrictions in the vicinity of due east and due west.

In this section we discussed and visualized the impact of field rotation on astrophotography and discussed where in the sky it is acceptable to image. In the next section we’ll discuss these results as they apply to a specific use case.

Celestron CPC 1100 GPS XLT

In the previous sections we have described field rotation and determined its impact on astrophotography in terms of azimuth, altitude, latitude and exposure time. In addition, we have hypothesized, using the rule of 500, that star images can cross 7 or fewer pixels on the image sensor without significantly degrading image quality. In this section, we’ll investigate how this impacts images captured using a Celestron CPC 1100 GPS XLT telescope on an alt-azimuth mount. Finally, we’ll determine under what circumstances this configuration can successfully capture images of deep space objects (DSO).

Specific Configuration

The system of interest is a Celestron CPC 1100 Schmidt-Cassegrain telescope mounted in its standard alt-azimuth mount. The system includes a Hyperstar 3 lens system and a ZWO ASI071MC Pro camera. The Hyperstar system replaces the secondary mirror of the telescope and results in an optically fast f/2 system with a focal length of 560mm.

The ZWO ASI071MC Pro camera uses the IMX071 sensor that measures 23.6mm x 15.6mm with a 28.4mm diagonal. The pixel size of this sensor is 4.78µm and they are organized in a two-dimensional array that measures 4944 x 3284 pixels.

Astrophotography Limitations

An f/2 optical system is quite fast, which allows shorter exposure times than used by astrophotographers using more traditional f5.6 or slower refractor telescope systems. In fact, an f/2 system is 8 times faster than an f/5.6 system. While there is much debate around the optimal exposure time of sub-exposures used in stacking, there are many who use 2 to 5 minute sub-exposure times with f/5.6 systems. Compared to an f/5.6 system, an f/2 system can collect the equivalent amount of light in 15 to 37.5 seconds.

Given my latitude of 40.3245° north, our use of the rule of 500 and the above information we can once again refer to the following figure. Again, the green area of this figure is where the field rotation results in fewer than 7 pixels being traversed at the corner of the sensor during a 30 second exposure. The yellow and red regions violate the rule of 500 for this long of an exposure.

On our f/2 system a 30 second exposure is equivalent to a 4 minute exposure on an f/5.6 system. This should be satisfactory for sub-exposure times for many DSOs. The green area in the above figure represents azimuths and altitudes where we can expect good results. We should have good results anywhere below an altitude of 45°. Since seeing is generally not ideal below an altitude of 30°, we should expect to find success at any azimuth between an altitude of 30° and 45°. We can also find success at azimuths from 55° to 125° and 235° to 305° for altitudes up to 65°. Due east and west we have virtually no limitations.

While the exposure times discussed above result in acceptable field rotation within a give sub-exposure, there will be significant field rotation over the set of sub-exposures that will be stacked during post processing. Removing this field rotation requires the stacking algorithm to align stars using both translation and rotation. Nebulosity 4 can perform star alignment using translation, rotation and scaling. I’m confident other tools can as well.


Alt-azimuth mounted telescopes used for astrophotography suffer from field rotation. Field rotation causes star images on the sensor to circle around the center of the field of view. To achieve acceptable results the amount of movement must be minimized. The rule of 500 suggests that if 7 or fewer pixels are traversed during an exposure, the outcome in terms of star trails will be acceptable. For 10 second exposures, there are few limitations on where in the sky an object can be photographed. As the exposure times increase to 30 seconds far more restrictions exist, but success can be found.

Several obvious things can be done to improve the likelihood of acquiring acceptable results. First, imaging where field rotation will result in 7 or fewer pixel traversals will help. These areas are identified in the previous graphs. Second, the shorter the exposure times the better. While 30 second exposures have a few unacceptable areas of the sky, 10 second exposures have virtually no limitations. Finally, since field rotation issues decrease as you move towards the center of the sensor, cropping acquired images will help.

For our Celestron CPC 1100 GPS XLT at ~40° north latitude operating in an f/2 configuration, there are few limitations when taking 10 second exposures. Since f/2 is 8 times faster than a typical f/5.6 refractor telescope used for astrophotography, 30 second exposures, or even shorter, will likely result in acceptable sub-exposures. Now it is time to collect data and see how accurate these findings are.

Astrophotography Camera Selection Notes


There are numerous issues to consider when choosing a camera for astrophotography. Consideration must be given to the type of astrophotography of interest, the specifications of the chosen telescope, and the camera style, technology and sensor specifications. This document addresses these issues in general terms and illustrates specifics based on an example telescope, a Celestron CPC 1100 GPS XLT.

Objects of Interest

The two types of astrophotography investigated in this document are planetary imaging and deep space object (DSO) photography. Planets and DSOs have unique characteristics that demand different approaches for capturing aesthetically pleasing images. The two characteristics that most influence the employed methodologies are apparent size and brightness.

The apparent size of celestial objects are measured in arc-seconds. The celestial sphere, like a circle, has an angular circumference of 360°, read as 360 degrees. Each degree can be subdivided into 60’, read as 60 arc-minutes, and each arc-minute can be subdivided into 60”, read as 60 arc-seconds. For reference the apparent size of our sun and moon are approximately 32’ or 1920”. The planets range in apparent size from Neptune at 2.21” up to Jupiter at 40.95”. In comparison DSOs in the Messier Catalog range in apparent size from M40 at 48” up to M31 at 10,680” or 178’.

The apparent brightness of celestial objects are measured in magnitude (m) as observed from earth. The brightness of an object can be measured in various wavelengths of the electromagnetic spectrum. We’ll restrict our interest to the visible spectrum where magnitudes are denoted mv. Brighter objects have lower magnitudes, it’s an inverse relationship. The brightest object in the sky is the sun at magnitude -27 or mv = -27. The magnitude scale is logarithmic. A difference in magnitude of 1 is equivalent to a change in brightness by a factor of \sqrt[5]{100} or approximately 2.512. The magnitudes of the planets range from Neptune at mv = 7.96 up to that of Venus at mv = -3.86. However, the most imaged planets range in brightness from Mars at mv = 0.56 up to Venus at mv = -3.86. In comparison the DSOs in the Messier Catalog range in magnitude from M91 at mv = 10.2 up to M45 at mv = 1.6. However the second brightest item in the Messier Catalog is M7 at mv = 3.3, illustrating that M45 is a bright exception.

With regard to astrophotography, the planets are very small and relatively bright objects, while DSOs are huge in comparison and very dim. These differences lead to different imaging strategies which in turn influence equipment configuration and technology choices.


There are many types and sizes of telescopes. This document will not attempt to describe the various types or their strengths and weaknesses. Instead, it will cover basic configuration parameters that impact the imaging of planets and DSOs. From the previous discussion it should be clear that a large field of view is important for imaging DSOs and high magnification is essential for photographing the planets. These are competing requirements in terms of telescope specifications.

The aperture of a telescope is the width of the primary mirror or lens. Larger apertures are capable of resolving finer detail and collecting more light, resulting in lower exposure times. The focal length is the distance from the primary mirror or lens to where the image is focused. Longer focal lengths result in more magnification and narrower fields of view. The f-number, or speed of the telescope, is determined by dividing the focal length by the aperture. For a given aperture, planetary imaging demands a large f-number where high magnification is obtained. For imaging DSOs a low f-number yields less magnification and a greater field of view.

Astrophotographers acquire telescopes with as much aperture as they can afford and physically handle. Those photographing DSOs tend to acquire moderately sized apochromatic (APO) refractor based telescopes with f-numbers in the f/5.6 to f/7 range. They often add a focal reducer to further decrease the effective f-number. Those photographing planets tend to acquire telescopes with longer focal lengths and employ Barlow lenses to increase the focal length by a factor of 2, 3 and even 5.

Telescopes like the Celestron CPC 1100 GPS XLT have a large 280mm aperture. The Schmidt-Cassegrain telescope (SCT) design results in a focal length of 2800mm and an f-number of f/10. This configuration results in a narrow field of view and relatively long exposure times for faint DSOs. The addition of a Barlow lens to this configuration results in a system that is ideal for planetary imaging. Fortunately, Celestron included a removable secondary mirror to the CPC 1100 system that can be replaced by a lens system called Fastar or Hyperstar. These systems convert the telescope from a relatively slow f/10 system to a fast f/2 imaging system. In this configuration the CPC 1100 has a focal length of 560mm and a huge field of view of just over 2.76°. This convertible feature makes the CPC 1100 useful for both planetary and DSO imaging.


There are many choices to be made when selecting a camera for astrophotography. These choices include the camera form factor, the sensor technology and detailed specifications such as sensor size, pixel depth and pixel size.

Camera Form Factors

While there are commercially available cameras specifically deigned for astrophotography, many photographers use modified DSLR cameras. The beneficial modification entails removing the infrared filter that sits permanently over the sensor of the camera. This renders the camera less than useful for regular photography, but allows the camera to be more sensitive to the wavelength of light produced by Hydrogen-alpha emission nebulae. These cameras may be used with nearly any telescope, but when placed in front of the optical path, using a system like Fastar or Hyperstar, the size and shape of the camera may block an unacceptable amount of light and introduce diffraction artifacts in captured images.

Many dedicated astrophotography cameras have better form factors that permit them to be connected within the optical path without negatively impacting the amount of light entering the system. In addition, many of these cameras are cooled, reducing sensor noise and increasing the quality of the finished results. However, these cameras have connected cables that introduce unwanted diffraction patterns in images.

Sensor Technology – CCD or CMOS

Commercially available astrophotography cameras are available with CCD and CMOS sensors. CCD sensors have an edge over CMOS sensors in image quality, but CCD sensors have slower read speeds. High read speeds increase the frames per second (fps) that can be acquired by a camera. High frame rates are particularly important in planetary photography using lucky imaging techniques. This methodology requires many frames per second be taken in the hope of collecting images, or portions of images, less distorted by atmospheric turbulence. CMOS sensors are better suited for this technique.

For DSO photography the read speed is less important, but can reduce the overall session time. The near infrared portion of the spectrum is important in DSO photography and CCD sensors are more sensitive than CMOS sensors in this area. However, CMOS sensors, found in modified DSLR and commercially available astrophotography cameras, are adequate in this area and cost far less for the same pixel count. The remainder of this document will focus on CMOS sensor based technologies.

Sensor Specifications

To determine necessary camera specifications it is important to understand what is trying to be imaged. The next sections will describe the imaging of stars and how this impacts camera sensor specifications.

Star Images

Stars are far enough away and small enough in comparison to their distances from earth to be considered points of light. Ideally, these points of lights should be focused to points within an optical system, but due to diffraction and atmospheric turbulence they are not.

Due to diffraction, the smallest point to which a mirror or lens can focus a point source of light is the size of what is known as an Airy disk. The Airy pattern, named after George Biddell Airy, has a bright central region, the Airy disk, surrounded by concentric bright rings. A graphical representation of an Airy pattern is shown to the right. As a mirror or lens focuses a star, it will appear as an Airy pattern to the observer. In this case the vertical axis represents the intensity of the observed star light and the horizontal axis is a measure of the dimeter of the Airy pattern.

There is a lower limit to the diameter of an Airy disk for a particular mirror or lens. An optical system that has reached this level of perfection is said to be diffraction limited. Reducing system imperfections beyond this point do not reduce the diameter of the Airy disk. The radius of the Airy disk is approximately described by the following equation:

    \[ \theta = 1.22\times\frac{\lambda}{d} \]

where \theta is the radius of the Airy disk in radians, \lambda is the wavelength of light in meters and d is the diameter of the mirror or lens in meters. Our example telescope (a Celestron CPC 1100 SCT) is diffraction limited and has an aperture of 280mm. In ideal conditions this optical system would produce an Airy disk with a diameter of 0.97” for visible light with a wavelength of 540nm. So an ideal 280mm diffraction limited telescope, without an atmosphere between it and the observed star, would produce an Airy disk with a diameter of 0.97”.

Our atmosphere distorts star light traveling through it. These distortions often occur more than 100 times per second. For long photographic exposures (greater than a few seconds) this movement of the Airy disk results in a larger disk know as a point spread function or seeing disk. This disk is similar in shape to the Airy disk, actually a two-dimensional normal distribution, and its width, generally defined as the full width at half maximum (FWHM), is a measure of the seeing conditions. The best seeing from high altitude mountain observatories is reported to be approximately 0.4”. Most observers seem extremely content with FWHM of 1”, happy with FWHM of 2” and 3” and stop work above 4”. In the next section we’ll use a FWHM equivalent to the diameter of the Airy disk to determine the sensor requirements to accurately represent images captured during perfect observing conditions. If seeing is worse than ideal, the chosen sensor characteristics will be more than adequate.

Sensor and Pixel Size

CMOS sensors are available in a range of sizes with each containing a different number of light collecting elements or pixels. The size of the sensor and the number of pixels determine the pixel size. Sensor size is important because it influences the field of view (FOV) of collected images. Pixel size is important to ensure that the light from each star strikes enough pixels to be sampled properly.

The field of view of a telescope and sensor combination is described by the following equation.

    \[ FOV = \frac{Sensor\;Size}{Focal\;Length} \]

where FOV is the real field of view in radians, Sensor\;Size is the size of the sensor in one dimension, measured in meters, and Focal\;Length is the focal length of the optical system also measured in meters. The field of view of a single pixel FOV_{pixel} is,

    \[ FOV_{pixel} = \frac{\frac{Sensor\;Size}{Pixel\;Count}}{Focal\;Length} \]

where Sensor\;Size is the size of the sensor in one dimension measured in meters, Pixel\;Count is the number of pixels in the same dimension and Focal\;Length is the focal length of the optical system in meters. The ratio of Sensor\;Size to Pixel\;Count is simply the pixel size, Pixel\;Size.

    \[ FOV_{pixel} = \frac{Pixel\;Size}{Focal\;Length} \]

Nyquist sampling indicates that we need at least two samples of the seeing disk, or the Airy disk in our ideal case, to accurately represent it. Two samples is what is required of one-dimensional signals like audio, but for a two-dimensional system, like the one at hand, it is more like 3.3. In other words, FOV_{pixel} should be 1/2 to 1/3 the diameter of the Airy disk. We’ll use 1/2 for the remainder of this work which is equal to the Airy disk’s radius.

    \[ 1.22\times\frac{\lambda}{d} = \frac{Pixel\;Size}{Focal\;Length} \]

Solving this equation for Pixel\;Size and recognizing that Focal\;Length divided by aperture   is equal to the \text{f-number} of the system results in,

    \[ Pixel\;Size = 1.22\times \lambda \times \text{f-number} \]

For an f/2 optical system at 540nm, the ideal pixel size is 1.32µm while the same system operating at f/10 would have an ideal pixel size of 6.59µm. It is unlikely the seeing conditions will ever approach the ideal and will more likely result in FWHM values of between 2” and 4”. At these values the ideal pixel sizes for an f/2 system would be 2.72µm and 5.44µm respectively. For an f/10 system they would be 13.59µm and 27.22µm respectively.

Three commercially available CMOS sensors include the MN34230, IMX294, and the IMX071. These sensors have pixel sizes of 3.8µm, 4.63µm and 4.78µm respectively. These sensor pixels are not quite small enough to offer the ideal sampling at f/2 with good seeing, are satisfactory for imaging in poorer conditions and are more than adequate for imaging at higher f-numbers. In addition, beautiful images can be obtained without reaching these sampling goals, which are often less important for aesthetically pleasing pictures than a large field of view. With a focal length of 560mm these sensors yield fields of view of 1.81°, 1.95° and 2.41° respectively.

Sensor Dynamic Range

Each pixel of a CMOS sensor can only collect so much light energy before it reaches its maximum value or saturation. This point is called full well capacity. When a pixel value is read, it returns the measured intensity of light that struck the pixel and a small error. This read error (and dark current noise) subtracted from the full well capacity represents the dynamic range of the pixel and associated sensor. We’re assuming here that for cooled astrophotography cameras the dark current impact is negligible. This may not be the case, but for comparison purposes it is a reasonable approximation. High dynamic range is a desirable feature.

ADC Capacity

When light strikes a pixel in a CMOS sensor it generates a voltage. This voltage is sampled by an analog to digital converter that translates the voltage into a binary number. The set of binary numbers representing all pixels on the sensor represent the collected image. The number of bits representing each pixel defines how well subtle tonal changes in a scene will be preserved. More bits representing each pixel will result in a final image that is a better representation of the original scene. Typical sensors use 8-14 bits to represent each pixel.

Read Speed

Typically the larger a sensor is in terms of the number of pixels, the slower the read speed. Some sensors permit partitioning allowing portions of the sensor to be read, increasing speed. Read speed is related to frames per second that can be captured. Planetary imaging using lucky imaging techniques require many frames per second. Typical large CMOS sensors have full sensor read speeds between 10 and 30 frames per second. Reduced resolution reads can be done much faster.

Commercially Available Cameras

While there are many commercially available astrophotography cameras from numerous vendors, this document will illustrate just a few. The following table illustrates the specifications for cameras based on the MN34230, IMX294, and IMX071 CMOS sensors. Two of the cameras are based on the same sensor, but have slightly different specifications. In the next section we’ll consider which characteristic of each camera is a best match for our application.

 ASI1600MC ProASI294MC ProASI071MC ProQHY168C
Resolution16MP 4656 x 352011.3MP 4144 x 282216MP 4944 x 328416MP 4952 x 3288
Pixel Size 3.8µm4.63µm4.78µm4.78µm
Sensor Size17.7 x 13.4mm19.1 x 13mm23.6 x 15.6mm23.6 x 15.6mm
Sensor Diagonal22.2mm23.2mm28.4mm28.4mm
Capture Speed23 FPS19 FPS10 FPS10 FPS
Read Noise1.2 - 3.6e1.2 - 7.3e2.3 - 3.3e2.3 - 3.3e
Full Well Capacity20000e63700e46000e46000e
Dynamic Range (no dark current)75 db79 db83 db83 db
ADC12 bits14 bits14 bits14 bits
FOV @ 560mm FL1.81° x 1.37°1.95° x 1.33°2.41° x 1.6°2.41° x 1.6°
FOV per Pixel @ 560mm FL1.4"1.69"1.75"1.75"

Our Application

In this section we’ll consider each CMOS camera illustrated in the previous table and how it fits our application. We desire a camera that will be useful for DSO imaging in conjunction with a Fastar or Hyperstar system connected to a CPC 1100 GPS XLT telescope. We would also like to use the same camera for planetary imaging connected to the same telescope in its f/10 configuration augmented with Barlow lenses to increase the f-number to f/20 or f/30.

Form Factor

Each of the four cameras are cylindrical in shape with diameters that are less than the diameter of the secondary mirror of the Celestron CPC 1100 telescope. In other words, none of the cameras obstruct the useful aperture and all have the same cabling, causing unwanted diffraction. These cameras will also connect fine in the f/10 configuration.

Sensor and Pixel Size

In the f/2 configuration, with perfect seeing, we could use a pixel size of 1.32µm, but with realistic expectations of FWHM of 3”, Nyquist requires a pixel size of 4.08µm. Only the ASI1600MC Pro has a pixel size that meets this requirement. In the f/10 configuration, all of the cameras meet Nyquist’s requirement. In fact, the large pixel size of the two cameras using the IMX071 sensor would meet the sampling requirement down to f/7, using a focal reducer, with perfect conditions, and lower under realistic seeing.

Dynamic Range and ADC

The larger pixels of the ASI294MC Pro, ASI071MC Pro and the QHY168C result in higher full well capacities that in turn result in potentially better dynamic range. This is particularly important when operating at f/2 when bright stars within the large field of view may quickly saturate some pixels. In addition, these three cameras also have 14 bit ADCs that may result in slightly more accurate images.

Read Speed

The four cameras range in speed from a low of 10 fps to a high of 23 fps. However, each is capable of higher speeds at lower resolutions. For example, the QHY168C is capable of frame rates as high as 130 fps for 240 lines of resolution and 30 fps for 1920 x 1080 HD. These rates should be adequate for useful planetary imaging in good seeing conditions.

Best Fit

In this section we’ll refer to data in the above table and point out meaningful characteristics that are best met by the associated camera. The camera with the best pixel size that approaches proper sampling is the ASI1600MC Pro. However, none of the cameras have small enough pixels to meet the demands of Nyquist’s sampling requirements for ideal seeing conditions. As previously stated, beautiful images can be obtained without reaching the Nyquist sampling goals and these goals are often less important than obtaining a large field of view.

Since the field of view is directly related to the sensor size, the ASI071MC Pro and the QHY168C are the big winners. Their fields of view are nearly 1/2° wider than the next best camera. In addition, these two cameras have better dynamic range and have the same size ADCs.

In comparing the ASI071MC Pro and the QHY168C, the ASI071MC Pro has a larger memory buffer made of DDRIII instead of DDRII memory. It also achieves a slightly cooler temperature which should further increase its dynamic range beyond that of the QHY168C. The ASI071MC Pro includes a 2-port USB 2.0 hub, is 60g lighter and insignificantly smaller. Finally, the QHY168C is currently $181 less expensive than the ASI071MC Pro.

The following table illustrates the components that are necessary to use the Celestron CPC 1100 GPS XLT telescope for astrophotography. Note that the additional $181 for the ASI071MC Pro adds only 5% to the total cost of the project. This seems reasonable given the slight feature advantages it has over its competitor.

 ASI071MC ProQHY168C
Celestron HD Wedge$350$350
Hyperstar 3$999$999
10:1 Focuser$275$275
Bahtinov Mask$35$35


The convertible feature of the Celestron CPC 1100 GPS XLT telescope makes the system useful for imaging planets in its f/10 configuration, while its f/2 configuration, using Fastar or Hyperstar, yields a massive 2.7° field of view for imaging DSOs. While none of the reviewed cameras have small enough pixels to satisfy Nyquist sampling requirements for theoretical seeing conditions in the f/2 configuration, two of the four are adequate and yield 2.4° fields of view. For planetary imaging these two cameras easily meet the sampling requirements and have fast enough frame rates to support lucky imaging techniques. While the cost of the ASI071MC Pro is slightly higher than the QHY168C, the ASI071MC Pro reaches cooler temperatures, has a USB hub that may reduce wiring congestion, is 60g lighter and is slightly smaller. Overall, the ASI071MC Pro is our best fit.