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Fixing the dreaded tilt and backspacing error in optical systems with objective analysis. The curse and blessing of modern CMOS cameras is that amateur astro-imagers have easy and relatively affordable access to extremely high resolution detectors but at the same time these tiny pixel, large chip cameras create challenges with optical systems when it comes to producing a well corrected field. The IMX455 is becoming more and more popular, and people are starting to realize that this sensor is a true torture test for optics. Even the smaller APS-C IMX571 has proven to be a challenge for most optical systems. To get the most out of these high resolution, large chip cameras it may require significant effort to dial in spacing and tilt. In the past I have always used aluminum foil to shim my image trains to correct tilt, and spacing was largely a trivial task as I used smaller sensors. (Optical systems are more forgiving of spacing error with smaller chips). With large chip, modern CMOS sensors you get a compounding effect of error where limited corrected fields of telescopes combined with tiny pixels as well as tilt create aberrated stars off-axis (further from center). The challenge here is that you might have several problems going on and it’s difficult to address as making adjustments can impact other error sources, and focus point can significantly confuse single frame analysis (more on this later). For this article we need to assume that your optics are well collimated. Of course, in reality any telescope can suffer from collimation error. Since these issues can be detected and in many cases corrected with collimation tools and eyepieces, I’m going to ignore this in order to focus solely on backspacing and tilt error. Please keep in mind that I am not claiming that I have developed anything here. I have simply spent countless hours exploring this topic to get the most out of my imaging system and thought that this information might be helpful to the Abin community. I welcome discussion, debate, comments, and constructive criticism.  Why do we care about tilt and spacing? When tilt or spacing error is present in an imaging system it results in aberrated stars that get worse as you get farther from the center of the frame. This visually results in elongated or mis-shapen stars in the corners of the image. It’s measurable using analysis tools like ASTAP. Above is the analysis of an image taken with a QHY268 and Astrophysics Stowaway Telescope. ASTAP measures the tilt effect at 10%. This is represented by the quadrilateral shape above. If it was a perfect square, there would be no tilt present. As you can see, stars get bigger as you move to the right side of the frame, and even more-so towards the lower right. The numbers at the corners are the HFD (Half Flux Diameter) measurements of stars across the frame. Below is the Pixinsight Aberration Inspector of this same frame:  As you can see, stars are not perfect in the corners of this image. This is a well corrected telescope with a large corrected field and a relatively small sensor (APS-C). Imagine how much more pronounced this would be with a larger sensor. You may have seen even worse stars in your images. I certainly have. In the past I would simply crop these out, or downsample the image so they were not as pronounced. But you don’t need to do this. Below is an image taken with the same telescope and camera, after tilt has been corrected.   So how do we get from a 10% tilted frame with obvious star issues in the corner, to a 0% tilted frame with nice round stars in the corners? First, lets take a look at how to objectively identify that you might have an issue. To do this, you perform a focus bracket analysis from intrafocus through extra focus and plot the HFD or HFR of the analyzed frames for the center and corners. As of this writing there are two ways that I know of to do this. You can capture the data manually and load it into ASTAP for analysis and then manually copy that data into excel for graphing, or you can use NINA Hocus Focus plugin to automatically capture and analyze the data. I’ll describe ASTAP first, just to explain how this works, however at this time I generally recommend NINA Hocus Focus as it is a much simpler method. In addition to capturing and analyzing the data, NINA will also output recommended adjustments for specific corners as well as spacing. The first step to performing this analysis is to capture a set of exposures (I recommend 10 to 13) through a set of focuser positions around critical focus. How far out of focus should you go? ASTAP recommends no more than 20 hfd for the analysis. So, do a little experimentation to determine how much out of focus you need to be to have slightly less than 20 hfd stars. With the system below I’m using an AP 130GTX with an Optec Quicksync focus motor and an IMX455 based camera. For my system I captured a set of data with the focuser position range of 27700 and 28800 steps, or about a range of 1100 steps. My focuser has a step size of 1 micron, so this represents about 1.1mm of focuser travel. I captured exposures for every 100 steps of travel with critical focus right in the middle and loaded them into ASTAP. (In ASTAP, click the sigma icon, then select the inspector tab. Then click browse to input your test captures.). Once your images are loaded into ASTAP, click on the Hyperbola curve fitting button. ASTAP will measure each frame and output an HFD value for stars based on focuser position for all four corners as well as the center of the frame. You can then take this data and copy and paste it into EXCEL to graphically analyze. (I’m not going to discuss how to graph this data in Excel. You can simply search for the topi cand find many tutorials for using Excel to generate various types of graphs.) Your copied data will look something like this in excel:  You will get a table that lists the HFD of each of the corners and center as well as the focus position. Focus position column is highlighted above. For my analysis I created separate tabs to house the graphical representation of this data. First, lets take a look at what a graph looks like that shows each of the corners and center HFD values for each focuser position:  I’m going to break this down so it makes more sense. What you are looking at is HFD on the Y axis and focuser position on the X axis. Each line represents a different corner along with the center. These 5 lines are labeled at the bottom. This is showing what the HFD of stars are at specific focuser positions for specific areas of the frame. What you need to know, is that in a perfect system that is tilt free, with perfect backspacing, each of these lines would stack together to form one single visual line. Because these lines don’t stack, it is a visual representation of tilt and backspacing error in the system. Lets separate some of these lines out to illustrate how the sensor is positioned relative to the optical axis of the telescope. First, lets take a look at the center curve, plotted with an average of the corner curves. Below you will see a graphical representation of backspacing error, or field curvature. Assuming that the optics are capable of producing a flat field for the sensor size you are using, you should be able to perfectly dial in spacing to achieve that flat field. This would be graphically represented as a perfect stacking of the lines of corner average and center HFD.  While these lines do look pretty close, it’s clear that the orange line (corners) is shifted slightly right of the blue line (center). In other words, the corners achieve optimal focus at a focuser position that is slightly further out than where the center achieves optimal focus. Remember, that a perfectly spaced system would achieve optimal focus for the center and corners at the SAME EXACT focuser position (and represented graphically by the lines stacking). So in the example above, there is backspacing error present. Roland Christen has published a guide to optimizing backspacing. In a nut shell, what he has said that if you 1) focus the center of your frame and find that 2) your corner stars exhibit field curvature that if you 3) move the focuser out slightly and corner stars improve that you need to reduce your spacing or 4) move the focuser in slightly and corner stars improve that you need to increase your spacing. What you see above is a graphical representation of Roland’s advice. In the case above, moving the focuser out improved corner stars, so backspacing needs to be reduced. Note the inverse relationship. If outfocus improves corner stars, you need to reduce spacing, and vice versa. So the last graph shows what backspacing error would look like. Lets take a look at some of the individual corners to understand how the sensor is tilted. The first graph showed all corners and center on the same graph, which does get a little bit confusing. When we isolate the bottom left and top right curves for example, its easy to see how the sensor is tilted.  It’s pretty obvious that these two points of the sensor do not arrive at the focal plane at the same focuser position. If they did, the lines would stack. The top right corner of the sensor is actually tilted closer to the Optics than the bottom left.  When we compare the bottom right to the top left we see that these two corners are pretty well aligned. The curves stack and optimum focuser position is the same. So the sensor is NOT tilted from the bottom right to the top left. These three graphs give us a pretty nice visual representation of how the sensor is tilted relative to the optical axis as well as how much backspacing error there is. Keep in mind that when I am describing a tilted sensor, that I am not suggesting that the camera is defective and has a tilted sensor. I am describing the position of the sensor relative to the optical axis. The source of tilt could be the camera, the filter wheel, the OAG, spacers, etc… It doesn’t really matter what the source of tilt is, they would all be represented by this type of graphical analysis. So what happens to the focus graphs for this equipment when we correct for tilt and backspacing? Once again, here is the original plot of all corners and center before correction:  And here is the graph after correcting for tilt using a Gerd Neumann CTU and reducing the backspacing by 2mm.  As you can see, the corrected result is much less cluttered! And the corrected backspacing graph is here:  Notice how these graphs stack, suggesting a much more accurate backspacing. Not only are all of these improvements seen graphically, but the improvements can also be seen in the stars. Before:  After:  I highly recommend that you take a look at ASTAP. It’s a wonderful piece of free software, authored by Han Kleijn and offers many more features than the two that I have briefly touched on here. You can also see the full documentation on his website to discuss how the field is evaluated for the image inspector tools. In addition to providing the hfd data in a table, there is an output of results that can be interpreted as a guide for you to square your sensor. Despite the power of ASTAP, at this time I am recommending a plugin for NINA to perform this analysis. I’ve been inundated with emails over the last few months by people striving to improve their images, and because NINA has a plugin that automatically captures, analyzes and outputs sensor plane adjustments… it’s just MUCH easier for me to refer them to that software. The NINA plugin Hocus Focus, performs all of this automatically. Simply connect your gear, slew to an area of the sky where there is decent density of stars and initiate an autofocus run. Hocus Focus will then output a graph of the curve analysis (the same thing I created manually in Excel) as well as a table showing the focuser position delta between each corner and the center and an output of backspacing error. The graph is a great visual representation of whether your sensor is orthogonal to the optical axis, but the table is where the magic is. If the corresponding number is positive it tells you that you need to increase the backspacing for that corner, I fit is negative you need to reduce the backspacing for that corner. The numbers themselves are derived by calculating the difference between optimal focuser position (in steps) for center and corners. The numbers in this chart are optical differences based on the specific backspacing that you are using. So if it says 20 microns, that is not telling you that you need to move only 20 microns, but rather use this as a RELATIVE value when compared to the other corners. Use the positive and negative assignment as your guide. Below you can see the output of analysis for My AP 130GTX with the QTCC Reducer and IMX455. This first output was run without any tilt adjustments made and an approximate backspacing estimate.  As you can see, the graph is a bit cluttered. Its obvious by looking at the graph that there is tilt and backspacing error. When you look at the table below you can clearly see that there is guidance on which direction to move each sensor. It’s suggesting that I move the top left out, the top right out by a smaller amount, the bottom left in and the bottom right in by a larger amount. If the system was tilt free and backspacing optimal, all of these values would be very close to zero. Zero representing, no difference in HFR measurement between the corners and the center. There is also a suggestion directly below the graph that states I need to move the sensor away from the optics. Pretty straight forward. I made an adjustment with my tilt device and ran the focus analysis again. After several iterations, I was able to achieve the result below.  As you can see in this second image, the curves all stack nicely, corresponding to optimal spacing and tilt, and the table below has numbers very close to zero. The nice thing about NINA Hocus Focus, is that it will allow you to objectively achieve a result that is the best your optical system can achieve. There is no guesswork on where to make an adjustment. If you have ever sat out under the stars and tried to adjust a tilt device through trial and error you have no doubt experience the frustration of confusing and conflicting results when looking at a single in-focus frame. Now, you can simply execute a focus run and follow the guidance of Hocus Focus to dial in your equipment. Hocus Focus was written by George Hilios and is a fast evolving plug-in that continues to offer additional features as well as settings so you can refine your focus runs to achieve your specific goals. There are several tilt devices available on the market and depending on how much backspacing you have available in your image train as well as your budget you can decide if any will work for you. I’ve personally used the ZWO tilt plate, the Gerd CTU and the Octopi. The ZWO tilt plate is very crude. It will get you there, but you need to be very careful with your adjustments. There are three points for collimation with a push/pull grub screw design. The Gerd CTU is an excellent device. It has a high resolution three point collimation system that allows 200microns of precision with every screw rotation. It costs about $300, and the only downside is that it takes up 17.3mm minimum of backspacing. The Octopi is the gold standard in my opinion. It’s pricey at about $800, but has a high resolution four point collimation system that allows 125microns of precision with every screw rotation. It only takes up 3.5 to 5mm of backspacing and offers a 5mm range for precision backspacing adjustment. Since there are 4 points to adjust you can align them with the sensor corners, and this makes the process extremely easy. If you are using very fast optics such as Epsilon or RASA, this is definitely the best choice. Whether you manually evaluate your data with ASTAP or automatically with NINA, both tools will allow you to objectively achieve the best result your optics and sensor combination will allow. I’ve described the logic and process here, and tried to keep things simple. There are additional considerations however that are worth discussing, such as how to use single frame ASTAP analysis as a guide, and what to watch out for as well as considerations on how to best approach dialing in a field where the sensor is larger than the corrected field and what compromises can be made depending on your goals. I have so far dialed in my QHY268 and QHY600 on multiple refractors with and without reducers, and will soon be dialing in my QHY600 on a newly acquired Tak Epsilon 160ed. I'll share my progress for that here as I use Hocus Focus to refine backspacing and tilt using the Octopi. I hope this information is helpful. Please let me know I need to clarify anything or if anyone has a questions. I’m happy to go into more depth on anything here as well as answer questions you may have about implementing this process with your own equipment. |
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| Incredible article - thank you Chris ! |
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| I am both thrilled an depressed by this superb piece of work... thrilled that it finally looks like an approach I can understand and the tools I can use (ASTAP and NINA) to tackle what is the bane of imagers... depressed because with all my tweaking over the years I've rarely reached even your starting point and would have thought wow that's close enough... damned perfection tempting me, and just when I'm trying to start imaging with an SCT and stars like those above are a distant and fond dream at the moment ;-) |
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I am both thrilled an depressed by this superb piece of work... thrilled that it finally looks like an approach I can understand and the tools I can use (ASTAP and NINA) to tackle what is the bane of imagers... depressed because with all my tweaking over the years I've rarely reached even your starting point and would have thought wow that's close enough... damned perfection tempting me, and just when I'm trying to start imaging with an SCT and stars like those above are a distant and fond dream at the moment ;-) Don't be depressed! Everything looks better when viewed in low resolution on the internet. Looking at high resolution files at 1:1 definitely looks worse! My stars were not as perfect as they look in the "Before" shots. After, they were indeed nice and round to the corners. The good news, is that this method (in particular NINA) makes it easy to at least approach the issue. Otherwise, its a lot of trial and error which in itself can be frustrating. I'll be dialing in my e160ed soon (just waiting on a focus motor) which will be interesting as that is a really fast scope. Upper right and lower left show the worst stars. I have a little bit of tilt and backspacing. Its tricky when 1/10 of a mm matters! But I'm not stressed now that I know how to do it.  |
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Great write-up! Looking forward to hearing your experiences with the e160-ED. I am about to jump into the same field work after my current project wraps up. |
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This is great info, thanks. Anyone know... Is there an easy way to tell the top from the bottom of a QHY268 sensor? I ran the Hocus Focus analysis and have some numbers but I'm not sure which corner is which. |
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Great write-up! Thanks! We can compare notes. Would be a nice addition to the epsi specific forum thread you've started. |
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Jason Doyle Sr: Jason, With mine, when viewing it from behind the camera, the usb port is on the left side of the chip, the filter wheel port is on the right. |
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Jason Doyle Sr: My odds of getting it right just doubled. Thanks Chris 🙂 |
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I am both thrilled an depressed by this superb piece of work... thrilled that it finally looks like an approach I can understand and the tools I can use (ASTAP and NINA) to tackle what is the bane of imagers... depressed because with all my tweaking over the years I've rarely reached even your starting point and would have thought wow that's close enough... damned perfection tempting me, and just when I'm trying to start imaging with an SCT and stars like those above are a distant and fond dream at the moment ;-) Worth noting and stating that the field there on the Epsilon is pretty darn good as is. Will Chris get it dialed in even better? Of course he will, no doubt, but I would not cry over that field as-is, with the big IMX455 chip that is pretty solid. |
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Chris, I can't thank you enough for this post, I've been battling with this for the past few weeks by trial and error, and while I've seen improvements, it's still not where it all should be! I'll be trying your guide as soon as I possibly can! Clear skies, --Aleks |
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Aleksandar Todorovic: His guide is like awesome maple syrup. Once you try it, you won't use anything else.  |
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| Excellent piece if write up, Chris! Thank you very much for this!!! |
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Worth noting and stating that the field there on the Epsilon is pretty darn good as is. Will Chris get it dialed in even better? Of course he will, no doubt, but I would not cry over that field as-is, with the big IMX455 chip that is pretty solid. I think I have an unhealthy obsession with getting perfect stars.  |
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Aleksandar Todorovic: Share your results here! I hope that this can be an interactive thread where I and others can share their experience to help the broader community. This is especially important as so many people are adopting APS-C and FF sensors with tiny pixels. It takes effort to get the best stars your optics can produce. (Note that there is no guarantee that your optics can support these chips. There are very few scopes out there that can perfectly support IMX455 chips to the corners, and they are $$$$$) |
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I thought I would add a section on single frame analysis. Has anyone out there used a single frame to evaluate their field? I have! There are pitfalls that you should be aware of, and I'm going to expose them here to hopefully help you avoid some of the frustration that I have experienced in the past. If you take a single frame and look at the corners, then make an adjustment, then look at the corners and things unexpectedly got worse... you are not alone. If you then go in the other direction, and things still get worse... well, that is a recipe for CONFUSION! Now you've spent potentially hours with a trial and error method of adjusting spacing or tilt and things seem no better than they were when you started. Plus, because of inconsistent results after adjustments, now you really dont know which way to fix it. Why does this happen? The answer FOCUS. Focus plays an interesting role in this process. It has the ability to mask, mitigate and even invert the results you get after making an adjustment. It becomes absolutely critical to focus exactly the same way with the same precision, in between adjustments. This is easier said than done. I've used many different focus methods out there, including full field focus from SGP, NINA, Voyager as well as single star focusing with Voyager. The problem is, if you run two focus runs back to back... you might not get the same exact result. This is especially true with full field focusing. Depending on how robust the algorithm is the results might be quite different. I'm not talking about whether a frame is in focus or not, I'm talking about a slight variability in focuser position as the software attempts to find the best fit focus position for the entire field. With my 1 micron step focuser that can result in over 50 steps of variability if I run the focus routine back to back. Thats why when creating filter offsets for focusing, you take the average of several focus runs. This small amount of variability might not be immediately apparent, but off-axis (towards the corners) this variability can interact with field curvature and produce some unexpected results. Take for example the concept that you can use focus position to improve corner stars when backspacing is not perfect. You can run a focus routine, end up with a step position of 30,000 and notice elongated stars in the corners. Simply by moving the focuser 50 steps to 30,050 position you notice that the corner stars become round. OK. So you then reduce your backspacing a little bit and run the test again. Now your stars look even worse! This could be because of focus position variability. The same phenomenon can make tilt look worse, even though you might have actually improved it with an adjustment. As you move through the critical focus position, field aberrations from tilt and spacing actually invert. Thats why it is so confusing. If you are slightly intra focus the problem looks like it might be in the lower left, but then when you are slightly extra focus the problem is in the upper right. Well, with tilt... the problem is indeed in both places but if you have the wrong assumptions it can lead you down the wrong path. By the way, fixing the lower left would also fix the upper right. A tilted sensor does not have independent corners. When you adjust one corner, you are adjusting all corners. You just need to know how this interaction occurs to know that you are still moving in the right direction. Here is a visual example. The first is 100 steps inside focus and the second is 100 steps outside focus.   Notice something interesting? The tilt model inverts as you pass from inside focus to outside focus. If you are not using an autofocus routine that can precisely achieve the same exact focus position (within say 10 or 20 microns) then this could be a reason why single frame analysis (whether with ASTAP or visual) is confusing you. The only method of focus that I have found to be repeatable enough for single frame analysis is Voyager's single star method. I can reliably get close enough to the same focus position where I get consistent results for single frame analysis. This is why I am recommending the focus bracket analysis, in particular the NINA Hocus Focus Plug-in for this kind of work. It doesnt matter how consistent the focus routine is, because you are analyzing a full focus range for determining how to adjust your sensor. It is a far more robust model than the more confusing single frame approach. That said, now that you know what to look for and why you might get inconsistent results, you might find the single frame approach more useful. Before George wrote Hocus Focus, I got pretty adept at using the single frame approach, however now... I just use Hocus Focus. It's so much easier, and it's free so there is no reason not to give it a try. ***Special consideration. The scenario above is particularly relevant when your sensor size and resolution is pushing up against (or exceeding) the corrected field of your telescope. If you are using a small sensor relative to your corrected field, you might not have too many issues getting your system dialed in. But for those of you using IMX455 or IMX571 chips, there is a good chance this is why you are struggling. ***Another note... I suggest precision to within 10 or 20 microns when repeating focus runs. This is really kind of an arbitrary suggestion. 10 to 20 microns might be literally NOTHING to an f10 system, but at f2... it could be massive. So what I should have stated was that you need to have enough repeatable focus precision for YOUR system to make the single frame analysis method effective. |
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Thank you very much for the detailed write up, Chris! I am about to try and eliminate the tilt on my ASI2600mm after I return from my holiday. I've been putting it off for too long and this article is exactly what I need! Been scratching my head after examining single frames in ASTAP and getting different results. Now it's clear, why... Just one question: do you remove the original tilt plate when using either Octopi or Gerd Neumann's CTU? I'll go with the latter, don't fancy fiddling with the original ZWO tilt plate. So, should I remove it? Thank you again! Jure |
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| Following. Thank you. |
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Hi Chris, Thank you for posting this. Now I hope Astrobin has bookmark function for articles. |
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Jure: You might need to keep the tilt plate installed. It's been a while since I've has a zwo camera in my hands and I can't recall if there are other ways to connect accessories. I believe the zwo filter wheel can connect without the plate in place. Are there threads on the face of the camera? In any event with the zwo tilt plate installed you just lose backfocus spacing. Keep in mind though, that any and all accessories can contribute to tilt. I measured a zwo tilt plate that was 100 microns thicker from one edge to the other. A source of tilt. Don't feel bad, qhy adapters are equally as variable. Both companies need to do a better job with QC. You can buy a micrometer on Amazon for under $50. They come in very handy. |
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You might need to keep the tilt plate installed. It's been a while since I've has a zwo camera in my hands and I can't recall if there are other ways to connect accessories. I believe the zwo filter wheel can connect without the plate in place. Are there threads on the face of the camera? In any event with the zwo tilt plate installed you just lose backfocus spacing. There is a way to connect the ASI2600mm without the tilt plate directly to the ZWO EFW but since backspacing will not be critical I'll first try with it installed. And buy me a micrometer, indeed! Thank you again, Chris! |
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Jure:You might need to keep the tilt plate installed. It's been a while since I've has a zwo camera in my hands and I can't recall if there are other ways to connect accessories. I believe the zwo filter wheel can connect without the plate in place. Are there threads on the face of the camera? In any event with the zwo tilt plate installed you just lose backfocus spacing. I'd ditch it. Less space between the camera sensor and filters is better. Plus the zwo tilt plates are suspect for adding tilt in my experience. I'm not the only one that has reported this. |
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Roland Christen has published a guide to optimizing backspacing. In a nut shell, what he has said that if you 1) focus the center of your frame and find that 2) your corner stars exhibit field curvature that if you 3) move the focuser out slightly and corner stars improve that you need to reduce your spacing or 4) move the focuser in slightly and corner stars improve that you need to increase your spacing. Hi Chris, For what Roland said, I am wondering if it applies to all flattener/reducer systems? Or just flatteners? Just flattener/reducer on refractors? Or also flattener/reducer for RC? How about Newtonian coma correctors? |
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Wei-Hao Wang:Roland Christen has published a guide to optimizing backspacing. In a nut shell, what he has said that if you 1) focus the center of your frame and find that 2) your corner stars exhibit field curvature that if you 3) move the focuser out slightly and corner stars improve that you need to reduce your spacing or 4) move the focuser in slightly and corner stars improve that you need to increase your spacing. It should apply universally although it's been a few years since I had a newt and I've only been working on this type of testing for the last 8 months or so. Think back to the focus curves though with NINA. Optimal backspacing is achieved when the apex of the corner curves and center curves are either stacked (or at least vertically aligned). If they don't align an adjustment is necessary and the inverse relationship between the focuser position for center and corners apply. I know that the NINA guidance for backspacing has worked for reflector users, I just can't personally confirm it yet. Roland and NINA are saying the same thing. I'll confirm this when I test my epsilon in the very near future. |
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| I believe that's a universal approach to any optical system. |
