Electrical Power for Astrophotography

Introduction

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:

Construction

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.

Summary

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

Introduction

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.

Review

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.

f-numberActualApproximateIdeal
210.2010.5310.74
323.37
23.70
24.16
441.81
42.14
42.94
565.51
65.84
67.10
694.48
94.81
96.62
7128.71
129.04
131.52
8168.21
168.54
171.78
9212.98
213.31
217.40
10263.02263.35268.40

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.

Installation

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.

Summary

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

Introduction

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.

Derivation

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,

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

or

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

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,

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

or

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

Approximation

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.

Results

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″.

f-numberActualApproximateIdeal
210.2010.5310.74
323.37
23.70
24.16
441.81
42.14
42.94
565.51
65.84
67.10
694.48
94.81
96.62
7128.71
129.04
131.52
8168.21
168.54
171.78
9212.98
213.31
217.40
10263.02263.35268.40

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.

Summary

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.