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I think that it actually changes the focal length - I just don't know which way. Here is two lens formula: d is separation between lenses. In mak, secondary is negative but is oriented "backwards" - so I have no idea what are the signs for focal lengths (in regular lens - positive lens is + and negative lens is -, hence the names).

I just have one question - are you sure that creating larger separation between mirrors is going to shorten focal length? In fact - I'm even not sure if focusing closer is done by making separation between mirrors larger (it's just a hunch that I have).

I think so, here are examples: modded webcam (Logitech c270): QHY-5IILc - which is same specs as ASI120 camera only USB2.0 version: Both taken with 130mm F/7 newtonian on EQ2 mount.

Over sampling is not just about empty resolution - it is about loss of SNR as well. We all want to get better image in set amount of time or get equal image in shorter time. Imaging at 0.77"/px vs imaging at for example 1.3"/px - which is much more realistic is deliberately choosing to image for x2.85 less time - or rather SNR equivalent.

I found it rather easy to do - but using particular method that requires CMOS camera (original is with DSLR - whatever is sensitive and has fast download times). Here is tutorial that I followed - only difference being way I measured defocus in corners - I used FWHM tool in SharpCap with my ASI1600 rather than bahtinov mask (which I do have but find completely useless next to FWHM/HFR readings and even eyeballing star size in the image). https://deepspaceplace.com/gso8rccollimate.php

I forgot - it gives rather nice FOV on galaxies with ASI1600:

Well, I'm sort of biased on that one Yes, that is my TS RC8" steel OTA version in action side by side to ST102 in guide scope role here. I like that setup and it works very good for me, but only after I've spent considerable amount of money (almost the price of scope) in improving my mount and some additions for the scope itself. I tuned it, replaced bunch of bearings, did belt mod on it, changed puck/clamp for vixen/losmandy combo one from Geoptik and finally changed tripod for Berlebach planet short version. Now mount guides at 0.5" RMS if conditions are good and you need them to be good to fully exploit 1"/px that 1624mm and ASI1600 bin x2 give you. I still believe that I'm oversampling most of the time and I'll be adding reducer / flattener at some point. You might have a bit less issues with EQ6 but make sure your mount runs smooth and guides good. I use OAG with above scope now. Scope will need change of focuser for best performance. Stock monorail 2" is decent focuser but does not offer threaded connection. I switched to 2.5" R&P version from TS - this one: https://www.teleskop-express.de/shop/product_info.php/info/p5769_TS-Optics-2-5--Rack-and-Pinion-Focuser---holds-Acc--up-to-6-kg---travel-95-mm.html

Indeed, I guess wholesale prices can't be that different. I just saw pack of M12 hex nuts - 100 pcs for £7.59 online. Rest is just price of running the business and wages in UK are a bit higher than over here

I've got craving to do some light weight wide field imaging - just a simple DSLR on a tracker from my back yard (not the best location but I'll take it ). Since I still have not ordered wedge and counter weight for AzGti to go in EQ mode - for this little exercise I decided to go with what I have on hand. At first I thought to just go without counter weight, but then I realized that I have L bracket and camera (Eos 750d) and 55-250 Canon IS STM lens and I'll be shooting stuff near zenith right past meridian - all that weight will be hanging at almost 90 degrees - almost horizontal - like the worst place to hang weight without having counter weights. Wedge will be simple Ball head for photography, and hopefully I'll manage polar alignment with simple finder scope (I'll aim for Polaris itself - that will give me just enough error to have sub pixel trailing at 55mm FL for one minute exposure). I had everything sorted except for counter weight. Where could I get it on a short notice at a reasonable price? It turns out that it was less expensive than I even hoped. Here is the unit "assembled" I purchased threaded rod - M12 - one meter long - ~ 1.3 euro (you can even save some money if you can get 20-25cm M12 screw threaded full length and you are happy with that length of CW shaft). Three M12 hex nuts - two regular ones and one with rubber thingy that I used as nice end cap ~ 0.7 euro total 15 pieces of slightly oversized washers - larger than M12 but small enough so they can still be held in place with M12 nut ~0.75 euro total Assembly - well, one just needs to cut off a piece of threaded rod - long enough to be decent counter weight shaft - I used hand saw and it took me something like 5 minutes to do it? Then assemble as per image above. Balancing is achieved by loosening and moving nuts and washers and then tightening them back up. It would perhaps be better idea to use one nut with counter screw as above can become loose on rotation - like when screwing everything into mount head. Btw, each washer is about 40g so 15 of them will be roughly 600g - enough to balance DSLR and lens but probably not scope + camera. Either more washers would be needed for that or something else for counter weight. Total cost ~2.75 euro. I don't see it being cheaper than that

Either doubles or if one wants different type of feature, we could take two small craters on the Moon next to each other to be resolved as two features or maybe two mountain peaks - what ever needs to be actually resolved - or determined there are two things. Problem with artificial stars is to make one that has proper separation. Two artificial stars that are 1" apart need to be ~0.4mm at a distance of 100m. For longer distances we probably need stronger light sources and for closer distances we have issue with separation. Most telescopes also need barlow for camera to properly sample so one might always argue that we are not measuring optics itself and that barlow somehow "impeded" perfect optics. Another obstacle that we need to consider is sharpening of photographic results. Any sharpening that we often do in planetary imaging is effectively giving us better resolution than the scope is capable of. By sharpening, we are effectively restoring resolution that has been lost in area I marked in above graph. We can't sharpen past highest frequency as these are effectively cut off - zero so no way we can determine what they were before, but for any non zero value - we can restore it to some extent.

As far as I understand, neither of these two statements should be called into question with respect to talk about resolving power of the optics. Zeta Herculis had angular separation of about 1.3" back in 2013, right? Dawes limit is 4.56/D which for 120mm scope translates to 0.9652" angular separation. Rayleigh criteria places that at ~1.07" for light at 510nm. Both are smaller than said 1.3". Sirius is 3" at smallest separation if I'm not mistaken (11" at largest) - again this is not related to resolution but rather to difference in magnitude and scattering of light. Vallis Alpes and Saturn rings represent something else and again are not related to resolving power of telescope. These are linear features and similarly to single stars - continue to show regardless of resolution loss imposed by aperture - they just end up having less contrast in smaller apertures (to the point of blending in with surroundings).

ASI1600 is perfectly capable of doing what you are asking. There are better cameras but for different reasons (I can explain those as well). We really need to first understand FOV / pixel scale and galaxy size in the image and how all of those fit together. Let's take M63 as our case study, although you won't be imaging that galaxy for another half of the year (it will be positioned appropriately come springtime). I just fired up Stellarium and did very quick measurement of extent of this galaxy - it is about 15 minutes of arc or 900 arc seconds. Given that you have EQ6 mount and that average skies are as they are and so on and so on (we can discuss that as well but it is rather technical discussion) - you need to sample at about 1.2"/px (in reality I would advocate for 1.2-1.4 but you already have scope that samples at 1.43"/px). Let's say you go for 1.2"/px. How large would that galaxy be when looking at it at 100% zoom level (1:1 or one image pixel to one screen pixel) - only 750px wide. Here it is: This is it - look at this image at 1:1 (if you have larger computer screen and you are not reading this on your phone - you should be able to see it displayed at 1:1 on web page). You can't get closer than that. You can - but: 1) there is no point, you wont capture any additional detail 2) you will waste your SNR because light will be spread over more pixels and each pixels will get less signal overall - less signal means lower SNR. This is why you don't want to over sample. Very important point number one - when you have your pixel scale set - galaxy image at 1:1 will always look the same size regardless of the scope and camera used to capture it. Now look at this: This compares field of view between two very different setups. First is ASI290 with 80ED and matching x0.85 FF/FR giving resulting focal length of about 510mm - sampling resolution ~1.2 (I rounded it up it is just a bit shy of 1.2 at 1.17"/px but that is not important for what I'm trying to show here) vs Skywatcher 130PDS newtonian at 650mm focal length and ASI1600 - again sampling at 1.2"/px We have seen from rule number one that galaxy image will have the same size when viewed at 1:1 - it will be ~750px across. On the other hand, these two setups have very different FOVs. How come and what does it mean? Explanation is really simple - ASI1600 has 4656px in width while ASI290 has only 1936px. If each pixel covers same area of the sky - ASI1600 will simply cover more of the sky. Remember - galaxy size on the image when viewed at full size / 100% zoom / 1:1 will look the same. Very important point number two - think of FOV in terms of sky covered by certain number of pixels at given resolution. More pixels you have - more sky is covered. You can crop away empty sky that does not contain target for better framing. If in above image you crop away empty pixels of ASI1600 and leave only central 1936 pixels - you will get same image as with ASI290! Same FOV and same galaxy size when viewed at 1:1. Only issue with having a large FOV is when image is viewed at "screen size" - that means whole FOV is scaled so it can fit on screen. If you have more pixels in your image than there are pixels on the screen that you are using to view the image - image will be shrunken down and galaxy will look smaller. More additional / empty FOV you have in this case - galaxy will look smaller and smaller. Now very important point number three Since galaxy of interest is only 750px wide and most other galaxy targets are of similar size or frequently smaller than that, 4656px that ASI1600 provides is much more than you need. To solve this you can either crop or you can bin. It is waste of sensor area to capture empty space around galaxy so perhaps better solution is to bin. What is binning? It is taking group of 2x2 pixels and making them act as single pixel. In fact, you can take groups of 2x2 or 3x3 or 4x4 pixels and so on... Let's examine ASI1600 with pixels binned 2x2 - what does it mean for us? First, you'll no longer have 4656px in width, you'll now have 2328px in width (similarly half of pixels in height as well). Much less wasted space around the galaxy 750px wide. Second thing that happens is that your pixels now "grow". They are no longer with their sides 3.8um - they now have twice as much - 7.6um. This in turn means that you can use twice as long focal length and still have 1.2"/px. We no longer need 650mm, we can now look at scopes that have 1300mm of focal length. This in turn has very important consequence - longer focal lengths also mean larger apertures - more light gathered and faster imaging. Very good! Here is another example of galactic imaging setup and its FOV: This is 1370mm with ASI1600 and 6" aperture. This is 6" RC scope (also available as GSO, AltairAstro and TS branded scope. This scope is made out of mirrors only and does not require much in terms of correctors / reducers and such. Problem is that it is reflector - needs collimation and many people find collimating RC very intimidating - but it's not that hard really. Just to address your post from the beginning - could C9.25 EdgeHD be good galaxy imaging scope? Only if you use it correctly. You want to sample at 1.2"/px or there about as I doubt that your mount/guiding and skies will allow for more. What sort of FOV can you expect with ASI1600? Ok, not bad, but you have 2350mm of focal length, how do you get 1.2"/px with ASI1600? Well, if you bin your camera 4x4 - you will get 1164 x 880px camera and sample at 1.33"/px - which is to be expected, after all above FOV is pretty tight and if galaxy with its extent is 670px (sampled at 1.33"/px - same 900" but less pixels as pixel covers bigger part of the sky - rule #1) - then there is only something like 250px left on each side of empty sky. Your images will be small by today's standards when everyone has 1920x1080 or higher res screen, but you will have very fast system that has 9.25" of aperture to collect photons. In the end, what camera is better than ASI1600 in the light of above rules? - One that is larger - it allows for larger scopes / larger aperture while still retaining same FOV / resolution (if properly binned). For example ASI6200 paired with 16" RC will deliver same FOV as ASI1600 paired with 8" RC. It has about x2 more pixels in both width and height and binning those pixels can make same resolution as binning ASI1600. Since all else can be made equal, we are left with 16" of aperture collecting light vs 8" of aperture collecting light - that is x4 increase in light. Which setup do you think is faster Hope this helps a bit when choosing a telescope. I think I would go for either 1300mm (which means binning x2 and 2300x1700 image size) or 2000mm (which means binning x3 and images that are roughly 1500 x 1100 px in size). You can go for 650mm scope and crop empty sky - in fact, you already have 550mm scope. Just take one of your images with smaller target and crop away empty sky and see how you like different FOV (this won't change details in the image - target will still be the same size when viewed at 100% - or 1:1).

Given the mount you will be using and camera you will be using, any scope with focal length over 700mm will be either over sampling or will need to bin pixels to get to good sampling rate. 700mm with 3.8um pixel size of ASI1600 will give you 1.12/px. That is really high sampling for most scopes under 8" and in principle with EQ6 class mount - you should consider that to be your upper limit (in fact - it would be closer to 1.2-1.4"/px). 127mm F/7.5 triplet would there fore be ideal scope. You are used to refractors, and with good x0.75 FF/FR (Riccardi reducer / flattener), that scope could operate at 714mm. If you are willing to get a newtonian - 6" F/5 with good coma corrector will give you 750mm. Next option would be to double focal length and use x2 binning. Something in 6"-8" in RC domain would not be a bad choice?

I agree with dip size being a continuous monotonic function as PSFs get closer. As such, dip will hit 0 at some distance between PSFs centers - monotonic function does not cross origin and it won't hit zero only as distance between centers hits zero. Precisely, dip will hit 0 once height of PSF is at half maximum at the point where PSFs meet (provided that intensities of sources are equal). There is some separation of stars where there is no dip any more. If you look at last image I posted - third case still shows separation between PSF centers and there is no dip in function. We will take this point to be limit of resolving. It will have some numerical value associated with it. This value will depend on aperture of telescope and no observer can claim to see the dip if stars are at this separation or closer. No matter how good their optics. This was my point. There is physical limit to what certain aperture can resolve. Take larger aperture and it will show the dip because PSFs themselves will be narrower - Airy disk will have smaller diameter. Yes, I would like that. It is very interesting claim and I simply can't figure out where it is coming from - but would like to know what sort of reasoning lead to it.

I don't think we necessarily disagree. Indeed it is, we can create other criteria based on actual MTF and call those rules. Maybe one I suggested - when stars are separated at twice FWHM - as that leaves no dip in curve. What is important is that both criteria have same underlying physical reality (I know that in the light of what you have pointed out this is up for discussion and I will address it below) - there is maximum spatial frequency and it depends on diameter of aperture. Quite correct, but this is "one way" street - they can undershoot but they can't overshoot - they can't see what is not there. If we take above criteria where there is no dip in the graph - well, then no one can see the dip. Psychological reasons excluded. I totally agree, but we can derive a criteria where they don't have to judge anything being certain percent lighter or darker or whatever. We can do basic thing - test of equality. If two stars are separated so that space between them is at one point as dark as surrounding empty space - we will call that resolved (or clean split - as it is often called). Ok, now I see what you mean - I totally missed that, but I wonder where is it coming from? My concentration is lacking at the moment, so I can't really tell where is it coming from except that it is from comparison graph of 32% CO and 10% larger aperture with 1/4 wave spherical. My question is - why does such graph show first minima in Airy pattern to be in the same place when it should be 10% inward for larger aperture (or 10% outward for one with central obstruction)? If we do Fourier optics simulation - we will get results consistent with dashed red line in right graph. Based on what theory / math / whatever do we need to consider this claim that maximum spatial resolution increases with central obstruction?

I have now and I'm well aware of central obstruction "boost" in high frequencies. I'm failing to see what this has to do with pushing "premium" optics beyond theoretical limits. Even rather large central obstruction creates very small boost in high frequencies over perfect unobstructed aperture. We can easily show that central obstruction reduces peak intensity of airy PSF compared to unobstructed, and hence difference in peak and dip is even more pronounced (contrast loss - harder to see).

We can say that having separation of 0.81 of airy disk diameter rather than 1.0 airy disk diameter is certain not to produce dip at all, right? (0.42 lambda is sigma of intensity based gaussian approximation, so at FWHM would be at 0.42 * 2.355 = 0.9891 which is 81% of 1.22 lambda) In that sense - there is a hard limit that premium optics can't out resolve.

No it is not. I think you are confusing things here. Look at this image: I think you are thinking in terms of dashed lines here but you need to look at their sum rather than individual Airy patterns. At some point, when patterns are close enough, their sum is larger than the dip formed by individual patterns and dip disappears.

I'm not sure how this could happen. If we have correct protocol - i.e. Call them split if and only if you detect .... How can someone see what is not there?

Only objection to this very nice explanation that I have is that it can be misleading to anyone knowing anything about pixels Pixel is often considered to be a unity / single quantity / binary object. It is either lit or not. It is a dot that can either be seen or not. If you compare detail in a telescope to something like that, there is a chance that people will think something along the lines: "if feature is smaller than telescope resolving capability - it will not be seen" (it's smaller than single pixel). Or, as the opposite of that - I'm seeing this thing (let's say crater on the moon) it does look like a featureless blob (not resolved - you can't even tell it is crater it is just dark "dot") but I know it is crater that is smaller in size then what my telescope is supposed to resolve - therefore my telescope "resolves beyond theoretical limit". This is not how telescopes and resolution works - every star that we observe in our night sky is smaller than what our telescope can resolve / smaller than a single pixel - yet we see each of them. Probably best way to "remedy" this pixel analogy would be to explain that pixel will be "lit up" even if there is something very small inside that pixel. Whole pixel will be lit up. And when we increase magnification - we won't see actual pixels - like little squares

@John you are actually saying that according to some reports, people are resolving more than theoretical limit for perfect aperture of a given size? Can you quote / link single example of such claim?

I think so, but am happy to be proven otherwise.

As far as I know, these are just there to help cool the primary mirror. If you have your scope permanently mounted in observatory at ambient temperature, you probably don't need to use them at all.

That's how I would see it as well if I had scope with fans on primary (my RC8 does not have those, and probably does not need them for its size).

You can tell the difference in 24h - planet will move compared to where it was yesterday but you won't be able to see it at eyepiece - night is too short to notice any real movement. For example, Mars does something like 17' per day at the moment (speed will depend on relative position of earth and planet in their orbits). That is 42.5"/hour. Well, if you have background star in your FOV and you observe for an hour or two - you should be able to see those two move relative to each other, but Mars certainly won't leave FOV due to that in said hour or two.