An Introduction to Field Derotation
Altitude-azimuth (alt-az) telescopes cannot be used for long exposure astrophotography. To overcome this flaw in alt-az-mounted telescopes, Cheng-Yang designed and built a field derotator that removes this degree of freedom and enables alt-az telescopes to become astrophotography platforms.
Most telescopes used by amateurs for astrophotography are equatorially mounted. However, the more popular computer-controlled telescopes for amateurs are altitude-azimuth (alt-az) mounted and usually deemed unsuitable for astrophotography. The reason is that alt-az mounted telescopes have one more degree of freedom that is not corrected because it does not affect visual observations of celestial objects. Unfortunately, by leaving it uncorrected, alt-az telescopes cannot be used for long exposure astrophotography. In order to overcome this flaw in alt-az mounted telescopes, I designed and built a field derotator that removes this degree of freedom and thus allows alt-az telescopes to become astrophotography platforms.
INTRO TO ASTRONOMY
When I was a child—I think, like most Circuit Cellar readers—I looked up into the night sky and wondered how cool it would be to have a telescope to look at the stars and have an up close and personal look at them. I was also inspired by the Hubble Space Telescope photographs of nebulas and galaxies and wondered whether I could see those objects in a telescope with my own eyes and be filled with wonderment. And so, about 18 years ago, after a bit of research, I bought a classic Meade LX200 8″ telescope (see Photo 1). Advertised by Meade as a research-grade telescope for the amateur, the LX200 is considered a “go-to” telescope by members of the astronomy community. It has an onboard computer that enables it to focus on any stellar object after it is aligned with known stars.
When my LX200 arrived and I finally got my grubby little hands on it, I became that excited little boy again. I took it out on the first clear night to see those objects that I had always wanted to see. Unfortunately, I live 40 miles from Chicago and the sky glow prevents me from seeing really dim objects except for a few brighter ones. The two planets, Jupiter and Saturn are always impressive—especially, Saturn, with her rings, which I think is the prettiest object in the sky. However, in general, I was not impressed at all by what I saw. I think I had expected to see what Hubble saw (i.e., nice bright and colored nebulas and beautiful spiral galaxies). Unfortunately, what I saw was mostly small and gray, and with enough squinting and averted vision, I could just make out some colors. But most of all, I could not see most of the interesting objects that I had wanted to see, which was because of my observation site and also due to my unrealistic expectations.
Sadly, I gave up. It just took too much effort to drag out my LX200, set it up, align it, and then spend at most an hour looking at only a few objects before dragging it back into the house again. Although winter nights were the best for observing because of the calm sky, they were the worst for comfort. I just didn’t find it worthwhile to freeze my backside off just for an hour to see a few objects. Furthermore, the mostly cloudy skies here also did not help. The low duty factor and the short observation times took their toll on my interest. My LX200 became another toy that sat in my house and gathered dust for the next 17 years.
After a 17-year hiatus from my LX200, and one smaller ETX125 telescope in between, I decided one fine day to take up astrophotography so that I could resurrect my LX200. My thought process went something like this: I had a nice research-grade telescope with tracking. I figured I’d be able to add a camera to the LX200 and then start taking nice celestial pictures. And so, I fired up my trusty web browser, pulled out my credit card, and bought an SBIG STF-8300C camera, an ST-i guider camera, and an OAG-8300 off-axis guider optical assembly. Photo 2 shows the devices connected to my LX200.
So, after adding these new accessories to my LX200, I renewed my interest in astronomy again. Of course, there’s a little bit more to astrophotography than just snapping away at the object of interest. It involves pretty sophisticated software to guide the telescope and to take multiple exposures of the same object. When offline, these multiple exposures are composed together in a process called stacking and the result is then image processed to bring out the details of the object. And finally, a jpeg file is created that can be published for the world to see.
Photo 3 is one of my first attempts. It’s a photograph of the core of the Andromeda Galaxy (M31) that was taken on October 25, 2014. It consists of a stack of 15 frames of 240 s exposure each. On closer examination of the results, I can’t say that I am impressed with my work because the stars that are away from the core are obviously oblong and not round! This is clearly a problem, but why?
Of course, the first thing I did was to check the entire setup to make sure that there wasn’t anything loose. Well, that wasn’t it and thus there must be something fundamentally wrong with what I was doing. Before I identify the source of the problem, I’d like to digress a little bit to discuss the difference between alt-az and equatorial mounts.
EQUATORIAL VS. ALT-AZ
An example of an equatorially mounted telescope is shown in Photo 4. In this photograph, I have my ETX125 optical tube assembly mounted on an iOptron ZEQ25 computerized “go-to” equatorial mount. For the mount to work correctly, I have to point its right ascension (RA) axis at Polaris.
Since the Earth rotates around Polaris at a fixed angular velocity, the stars also rotate around Polaris at this angular velocity. Thus, any celestial object is tracked as it moves across the sky when the mount’s RA axis is pointed at Polaris and the telescope is rotated about RA at the same angular velocity. In fact, if the RA tracking motor is perfect, the image of the object of interest as seen by the camera does not move at all. Technically, an equatorial mount is an extremely simple piece of equipment that compensates the rotation of the stars by using only one motor. However, its simplicity belies its utter annoyance in its setup. I will discuss why this is the case after I describe the alt-az mount.
An example of an alt-az mounted telescope is my LX200 shown in Photo 5. Unlike the equatorial-mounted telescope that I have mentioned earlier, I don’t need to align the altitude (alt) and azimuth (az) axes to Polaris. The alignment procedure for the LX200 requires that I start at a predefined home position and then align it to two bright references stars and that’s it. The pointing accuracy of the LX200 is extraordinary and once I have performed the alignment procedure correctly, the LX200 has no problems finding any celestial object that I want.
Once I’ve found an object of interest, the LX200 tracks the object to keep it centered on the image plane of the camera. To me, the alt-az coordinately system is very similar to the Cartesian coordinate system if I approximate the small viewing area seen through a telescope as a plane. Moving the telescope azimuthally is similar to moving in the horizontal direction and moving it in the altitude direction is similar to moving in the vertical direction. Therefore, in contrast to equatorial tracking which rotates the telescope about Polaris, in alt-az tracking, the telescope moves up down and left right for tracking. Clearly, tracking an object in alt-az mode requires two motors, one that adjusts for altitude changes and one that adjusts for azimuth changes.
Now comes the naiveté part. I had thought that since an alt-az mounted telescope tracks as well as an equatorially mounted scope, astrophotography would work equally well, albeit tracking with an alt-az mount is technically more complex than an equatorial mount. Boy was I wrong, because there is an extra degree of freedom that is not taken care of in alt-az mounts.
EXTRA DEGREE OF FREEDOM
So where is this extra degree of freedom that I keep alluding to? The best way to see it is to examine how alt-az mounted telescopes track. For example, Figure 1 shows my alt-az mounted telescope tracking the center star, Alnilam, on Orion’s belt by moving the telescope up vertically and towards the west horizontally. As you can see, that despite perfect tracking, because Alnilam is always at the center of view, the rest of the stars of Orion rotate about Alnilam over time. This is the field rotation that all alt-az mounted telescopes suffer from. Field rotation is irrelevant for visual observation, but for astrophotography, it limits the exposure time because a star trail forms if the exposure time becomes too long. This is the reason why there are oblong stars in Photo 3.
Now, contrast this to equatorial tracking where the telescope rotates about Polaris, and thus all changes in the orientation of the stars with respect to the tracked star is compensated because the view seen through the telescope rotates as well. This is the reason why amateur astrophotography is done with equatorially mounted telescopes. (Refer to Larry McNish’s website—http://calgary.rasc.ca/field_rotation.htm—for an illustration of the difference between equatorial tracking and alt-az tracking and field rotation.)
I found the source of the problem, so what was next? Abandon my alt-az mounted LX200 and install the LX200 wedge option to make it into an equatorially mounted telescope?
My simplest option was to abandon the alt-az mount and adopt the equatorial mount like other amateurs do for astrophotography. I have to say that I do not like equatorial mounts and have found them to be most annoying to set up, align to Polaris and cumbersome to use. Besides my general dislike for equatorial mounts, there are major and perhaps more defensible reasons for why an equatorial mounted telescope is not for me. For example, in order to align an equatorially mounted telescope, I must be able to see Polaris. Unfortunately it is hard for me to see it at my location because of sky glow. And despite what most people think, Polaris is actually quite dim. Even if I can find Polaris visually, there’s another problem: with the addition of my camera, the optical tube assembly cannot be set in line with the fork arms that is required for Polar alignment. Photo 6 shows what I mean. The camera obstructs the ability of the optical tube assembly from getting to the home position for alignment to Polaris.
The above are just two problems that dissuade me from using an equatorial mount. In my opinion, unless I have a permanent pier to mount my telescope, so that I can Polar align once and do not need to do it ever again, the alignment and set up of an equatorial mount eats up way too much precious photography time to be useful for me. Thus, I am left with the alt-az mount option for astrophotography and I have to find a way to fix the field rotation problem.
In my quest to solve the field rotation problem, I found a device called a “field derotator.” However, I found a myth that perpetuates in the amateur astronomy community that field derotators are hard to use and are unreliable. In my mind, this myth may have been rooted in truth decades ago, but with the advancement of technology and the availability of cheap microcontrollers, I just cannot believe that field derotation can be that hard. In fact, I am confident that I can be that iconoclast who destroys this myth.
Anyway, it is interesting that the correction of field rotation is actually not new. It is, in fact, used on nearly all large telescopes because balancing an equatorially mounted heavy telescope with a heavy weight is impractical. A web search shows that Meade actually sold a field derotation device a long time ago, but it is no longer available for purchase. In my hunt for a solution, I found one manufacturer who is still in the business of selling derotators. Unfortunately, that device has a diameter of 5.8″ inches, which does not fit on my telescope because I have only 3.25″ in diameter to spare due to the JMI electric focuser. Therefore, the only avenue left for me was to design and build a smaller, lighter, and better field derotator from scratch. I hope that this device will also be useful for the astrophotography community as well.
THE FIELD DEROTATION FORMULA
The first thing I needed was the equation that tells me the angular velocity of the field rotation. It turns out that the formula is rather trivial:
ζ is the field rotation frequency. Ω is the Earth’s angular rotation frequency. (η0,x0) are the alt-az coordinates of the object at which the telescope is pointing. ϕlat is the latitude of the location of the telescope. This formula is deceptively simple and yet I have been unable to find a reference that derives it. In order to confirm Equation 1 to my own satisfaction, I derived it and wrote it up. Refer to my document, “An Analysis Of Field De-rotation For Alt-Az Mounted Telescopes” (https://github.com/cytan299/field_derotator/tree/master/field_derotator_formula).
OFF-AXIS GUIDING AND DEROTATION
Now, I don’t want to sound like by adding derotation, everything required to take good astrophotographs is solved. It is still necessary to guide the telescope so that it accurately tracks the motion of the stars as they move across the sky. Although the LX200 has very good tracking, there is still too much error for astrophotography. Therefore, corrections must be applied to the alt-az motors for accurate tracking. This correction process is called guiding.
The way guiding works is that a guide camera (not the imaging camera, but another camera, such as the ST-i shown in Photo 2) looks at a star that is chosen as the reference star. This star is set onto cross hairs of the guide camera and a feedback loop is set up so that commands are sent to the alt-az motors to keep the reference star fixed on the cross hairs.
There are two ways of mounting the guide camera for guiding. The first method attaches the guide camera and its optics to the optical tube assembly with mounting rings. Thus, during derotation, the imaging camera sees a rotated image with respect to the image seen by the guide camera. Therefore, any corrections applied by the guide camera feedback loop are incongruent with the corrections applied by the field derotator. This means that this type of guiding actually exacerbates the problem that I am trying to solve and is unsuitable for correcting field derotation.
The second method is called off-axis guiding. This is accomplished by setting a pick off mirror that is “off-axis” from the main optical axis of the telescope to divert a small part of the image seen by the imaging camera to the guide camera. In this case, both the imaging camera and the guide camera rotate together and thus corrections applied by the guide camera are consistent with the corrections applied by the field derotator. In fact, field derotation actually reduces the amount of correction that the guider feedback loop needs to apply. The proof of this statement can be found in “An Analysis of Field De-rotation for Alt-Az Mounted Telescopes.” Although field derotation and off-axis guiding improves tracking, there are inherent limits that I also discuss in that document.
The bottom line that should be taken away from this section is that for derotation to work, an off-axis guider must be used. This combination works even if the guide star is not the tracked star. (“An Analysis of Field De-rotation for Alt-Az Mounted Telescopes” for the explanation.)
With my motivation and an abridged discussion about derotation theory out of the way, I can start work designing a field derotator. It is natural to partition the field derotator into two parts: an electronic controller and a mechanical derotator.
I want the controller to act as the interface between my computer and the derotator. I added the requirement that the controller be able to control the derotator without a computer as well. My last requirement means that it must have an onboard microcontroller that is powerful enough to numerically evaluate Equation 1 in real time. This basically rules out small microcontrollers with limited memory and computing power. Being a lazy person, I didn’t want to design everything from scratch. A predesigned board that has a large choice of peripherals that I can buy off the shelf is ideal. A large, active community that supports both the hardware and software will certainly help with my development of the field derotator. After doing a bit of homework, I decided that the Arduino platform met my requirements. Arduino has a large ecosystem of both predesigned boards and software and will, in my opinion, make development quick and painless.
On the derotator side, its construction would have been a lot trickier if I had decided to design the field derotator a decade ago. Ten years ago, I probably would not have had access to a machine shop and I would have spent inordinate amounts of time scouring for parts and catalogs with long distance phone calls to shops. Thank goodness things have changed and most of the scouring involves searching the web for parts. Even better, online machine shops have sprung up that support hobbyists like eMachineShop and Ponoko. Without these online machine shops, building the mechanical hardware would have been a lot harder.
Everything came together and, finally, after six months of work that included electronics and mechanical designs, manufacture, assembly, software development on both the Arduino and my Mac, the field derotator was born. Photo 7 shows the field derotator before it is mounted on a telescope with an imaging camera and an off-axis guider.
All my effort building a derotator would have come to naught if it did not work. I waited with bated breath for a clear night to test it. My first opportunity to do so was on the evening of May 27, 2015 when the skies were clear enough for a test. I pointed my telescope at a globular cluster called M13 in the Hercules constellation. I took a picture of it with an exposure time of 480 s with the derotator off. Photo 8 shows the expected oblong stars from such a long exposure.
Then came the moment of truth. Did the field derotator work? I took the same picture of M13 for 480 s again, but this time with the derotator on. Photo 9 shows the results. It is obvious that the stars are no longer oblong. And on closer examination, the center of the cluster actually looks clearer than the one shown in Photo 8. I works!
In the next part of this article series, I will discuss how I built the field derotator. I will cover the design of the Arduino system that includes a controller module that talks to the derotator and LX200, Wi-Fi and serial line options that talk to the computer, and an algorithm that implements Equation 1. I will also show how I built the mechanical part of the derotator that has a driver module, how the gear sizes were chosen, and how I defined a mechanical home position that could be repeatedly found with accuracy. Finally, I will have a discussion on the user interface on the computer that I use to control the field derotator remotely via Wi-Fi or serial line.
Astronomy Forum, “Field-DeRotator for Altazimuth Telescope Mounts vs Wedge for Astrophotography?,” 2012, www.astronomyforum.net/astro-imaging-forum/131099-field-derotator-altazimuth-telescope-mounts-vs-wedge-astrophotography.html.
LX200Classic: A Website Dedicated to the Meade LX200 Classic Telescopes, www.lx200classic.com.
L. McNish, RASC Calgary Centre – Field Rotation with an Alt-Az Telescope Mount, http://calgary.rasc.ca/field_rotation.htm.
C. Y. Tan, “An Analysis Of Field De-rotation For Alt-Az Mounted Telescopes,” 2015, https://github.com/cytan299/field_derotator/tree/master/field_derotator_formula.
Arduino MEGA 2560
Arduino | www.arduino.cc
ZEQ25 Center-Balanced Equatorial Mount
iOptron | www.ioptron.com
MOTOFOCUS for Meade Cassegrain Telescopes
JMI | www.jimsmobile.com/buy_motofocus.htm#Meade
Meade Instruments | www.meade.com
Pyxis Camera Field Rotator
Optec | www.optecinc.com/astronomy/catalog/pyxis/pyxis.htm
OAG-8300 Off-Axis Guider, STF-8300C camera, and ST-i Guider camera
SBIG | www.sbig.com
Stark Labs | www.stark-labs.com
PUBLISHED IN CIRCUIT CELLAR MAGAZINE • APRIL 2016 #309 – Get a PDF of the issue