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Sure is. We often use short FL eyepieces for planetary to get enough magnification. Rarely anyone uses less than say x70-x80 to view the planets. That would mean lowest mag EP would be something like 15mm. Even wide field 15mm EP will have relatively small field stop - like 20ish mm. At 10 mm away from optical axis at focus point, illumination diagram looks like this: Again not 100% - but that is closer to say 80% vignetting at lowest power wide field planetary eyepiece.

Yet it has only 22% CO - meaning 33mm. If secondary is placed so that focus point is say 200mm away from focal plane secondary mirror (about 90mm to the edge of the tube and another 110mm for focuser and drawtube), then converging beam at secondary will be 25mm or comparable in size. I think that around 19mm away from central axis illumination drop off will be 50%! That is eyepiece with field stop of 38mm. Even field of 1.25" is not fully illuminated. Intersection of two - converging beam and secondary mirror at edge of 1.25" field look like this:

Indeed, however, you will find that most 6" F/8 newtonians come with 1.25" focusers while most 4" F/10 achromats come with 2" focusers. Limitation on 6" F/8 newtonian comes from the size of secondary mirror / central obstruction. To be general purpose scope, CO is often around 25%. That means 1.5" in diameter (a quarter of aperture size 6/4 = 1.5). You can't effectively illuminate 2" field with 1.5" secondary mirror - you will get a lot of vignetting, and compromise is to use only 1.25" eyepieces. Do another comparison between the two scopes - one using max field stop EP in 2" variety and other using something like 32mm plossl (which has largest field stop in 1.25" version).

Only if you use F/5 newtonian instead of F/8. Two different instruments.

Out of interest, what is the purpose of this inquiry? Are you looking to get yourself a new scope and wander which way to go or something else? We have not discussed all the other things that go with owning a telescope - like size, mounting options, portability, storage and so on ... Are these relevant for this discussion?

LP signal is made out of photons, right? Those photons always behave the same. Regardless if they are coming from the target or from LP, which means that they have associated noise - Poisson noise. LP Signal itself is very easy to remove. It is usually either constant or in form of a linear gradient (in some cases it can be higher order polynomial, but in any case - easy to model and remove). What you can't remove is Poisson shot noise tied to that LP signal and it is this noise that adds to total noise in the image. Since both read noise and this LP shot noise have zero correlation - they are added like linearly independent vectors - or square root of sum of squares. We can easily calculate increase in LP noise given the "swamp factor" - or how many times LP noise is larger than read noise. Say that we have some read noise X and we have x5 larger LP noise. Total noise will be: sqrt(X^2 + (5*X)^2) = sqrt( X^2 + 25 *X^2) = sqrt(26*X^2) = X * sqrt(26) = 5.099 *X In another words - if we have LP noise that is x5 larger than read noise it is the same as having LP noise that is 5.099 / 5 = 1.0198... or ~2% (1.98....%) times larger and no read noise at all. By choosing suitable sub duration we can ignore read noise of the camera by assuming we have 2% more of the light pollution noise. That 2% might seem like significant value - but in reality it is far from it. Over the course of the evening, due to target changing position we can have its apparent magnitude change by 0.05 most of the time (atmospheric attenuation). That translates into ~5% change in signal level and consequently more than 2% change in SNR, so you see 2% increase in noise happens just because earth spins and is not something you'll notice in the image. Hear me out . What I'm saying is not my personal opinion. I'm just listing verifiable facts. I've seen people often mention this video, and I think it will benefit you to watch it as well: https://www.youtube.com/watch?v=3RH93UvP358

I also took their test once and "failed" (actually score was above maximum measured by their test). I decided to play "hard to get" and did not become a member (although they really wanted me to). True story.

4" F/10 achromat is completely different instrument. Mine, although cheap mass produced item (SW Evostar 102) showed me views of Jupiter and Saturn one evening that are probably in top 5 views of all times of these targets that I had with any scope.

Well, here is one thing that you probably can't do with 6" F/8 newtonian: It has a bit more focal length, but main issue is the size of secondary mirror and if it will illuminate 47mm of field

Of what? I'm inclined to say that 6" F/8 newtonian of good optical figure would best 4" F/10 achromat on everything except wide field views.

At this point in time - I'm finding much easier to answer what drives me away from SGL rather than to it. It's become part of my life so I'm not thinking in terms of being drawn to it (much like you don't think what drives you to your family, it's your family, you know), however, there are things that I must actively combat against in order not to be driven away from it.

Why? If we look at weighing function up to N - sure, it will produce smaller result then all ones up to N, but if we include weighing coefficients above N which are greater than zero - why do you think that sums will be different in the limit where N tends to infinity? But when you are summing the series - you are doing the same, you are summing weighted numbers, except in this case weights are 1,1,1,1,1,1, .... ,0,0,0,0,0, ... I'm not sure that you are understanding weighing function properly. Let me show you with a graph Green is poorly drawn and it should look like this: There should be smooth transition at each ever higher N. For the most part - two weighing functions are roughly the same - only around N there is difference in how they transition the actual value of N - either discontinuous or smooth (which makes it analytical function). Both of above weighing functions would produce similar looking graphs when you plot calculated values against N like you suggested: Only difference is that when you apply rigorous mathematical framework of limits to some smooth weighing functions - you get converging result and for others result remains diverging (like in case of step function). Maybe it is best to think of it this way: let's solve X^2 = -4 If you try the "brute force" approach of finding square root of -4 - you might end up in infinite calculation without end (try any iterative method designed for positive numbers in order to calculate X). But if we write above expression a little bit differently - like this: X^2 = 4 * i^2 Then it is trivial to calculate that X = 2i - even if we use iterative method to calculate square of 4 - which will work in this case. You might say - but you used a trick! Sure, but it is valid, well defined mathematical trick that is consistent with the rest of the mathematics, so not much trickier than say checking if number is divisible by two by examining the last digit.

Brightness of the image does not depend on captured data but rather white point you use and brightness of the display device you use to show the image. Important metric is signal to noise ratio - or can something be detected above noise level. I've shown that, while in single image unbinned - there is no way to detect tidal tails as they are below noise floor (you need about SNR of 5 to have reliable detection) - then can easily be seen in binned image because of SNR being higher. Quite the opposite - they need to be truly random with zero correlation in order to add like that. If they were fully deterministic - they would add like normal numbers do - like signal does - just plain old addition. No comment

Signal does not need to swamp the read noise at all - and when imaging the faint stuff - it almost never does, at least not signal of interest - target signal. What is important when we talk about read noise is to swamp read noise with some other type of noise. Out of basic types of noise present when imaging - only read noise is "per exposure". All others are time dependent - that is dark current noise, light pollution noise and target shot noise. Since target signal is often weaker then read noise in single exposure - that is not our candidate. Neither is thermal noise (dark current noise). Only real candidate is light pollution noise. Noise adds like linearly independent vectors and if one is much bigger than the other - result will be very close to that larger one (think right angled triangle and one side being particularly short - that makes hypotenuse almost the same length as the other side). Histogram is just a distraction - it has almost zero value in astronomical imaging. Main thing it can tell us if there is some clipping - but we can see that from the stats as well, so no real reason to use histogram. When you want to calculate optimum exposure length - you should simply measure background signal per exposure - from that derive LP noise (which is square root of sky signal) and compare that with your read noise. This LP noise should be 3-5 times larger than read noise. Any exposure length longer than that is just bringing in diminishing returns (there is only 2% difference in SNR if one uses x5 swamp factor over single long exposure - and humans can't tell that difference in SNR by eye). This makes no sense - as I've shown above with the example of one sub. In that sub read noise is many times larger than signal in tidal tails - yet binning works just as fine. SNR impact of read noise depends on other noise sources and not on signal we are trying to capture. As long as we keep it (read noise that is) below some fraction of some other noise source - it is irrelevant regardless of how low our target signal is. Let me ask you a question like this: Say you have fast scope with large pixels and two different cameras, but cameras differ only by read noise. First camera has 1.5e of read noise, and second camera has 3e of read noise. Under which circumstances will you actually see decrease in SNR between these two setups? Full size well has nothing to do with bringing signal below read noise levels into view. Full well size of camera is largely inconsequential in astrophotography.

actual FPS will depend on several factors - but most important one is the size of frame you are downloading: Other is actual USB speed of computer and settings in capture software (there is something called usb speed or similar which regulates how much of usb bandwidth is hogged up by camera - raise that value to get better FPS but lower it if you start experiencing unresponsive camera / freezes or similar). @Dunc78 I concur it is probably ASI224. Given certain priorities - some other model might be better suited (for example, for lunar, size of sensor might be more important than max FPS as moon is rather stationary target that often needs larger FOVs, or for Ha solar due to fact 656nm wavelength is captured with Ha scopes that are often very high F/ratio - larger pixels are important factor in order not to bin the data)

It's not bad - it is just one of weighing schemes that indeed produces an infinity. Many different weighing schemes also produce infinity, but there are some that produce -1/12. I also think that you can't have arbitrary weighing scheme - only one that satisfies certain criteria. I'm not sure what that criteria is, but as far as I can tell - Terence Tao did research into that and probably proved that certain class of weighing schemes are equivalent. Perhaps one criteria is that weighing function needs to tend to 0 as one moves to the right of N at greater speed than the speed of N approaching infinity and similarly that weighing function needs to tend to 1 as one moves to the left from N (again going faster than N goes to infinity) - or some other requirement like that. My firm belief is that sum 1+2+3+4+5+.... of to infinity is one way of calculating certain value - but flawed way of doing that as it does not converge in classical sense. Which does not mean that actual number does not exist. Another way of calculating the same value would be by using different weighing function - and some of those weighing functions are not flawed and allow you to calculate the value in that way. Zeta function is yet another way to calculate the same value (which again works). Point is not in the infinite sum being equal to -1/12, but rather it is that we have some value that is -1/12 and that there are different ways to calculate it - one of which fails but we know why it fails and when we encounter this way of calculating - we know what the answer should be - regardless if we can't actually pull off that particular calculation. This is why it works in physics - we know that answer is right - it is just "algorithm" to calculate it that it is flawed, and above paper gives us better insight into why it's flawed and what are correct ways to calculate such values that we can use when we stumble onto a flawed way of calculating them.

I don't think it was aimed an anyone in particular - but in general notion that often repeats - advice is "get large newtonian" rather than "get large aperture telescope of any design type that suits you the best". Both will have the same speed at the same pixel scale, but other types might be, and often are, more manageable than large newtonian on several basis. First, they can often be used without corrective optics which often reduces strehl ratio of the telescope in center (to be able to correct over larger field). Second - they can be of a compact design which is of course easier to manage and mount. There are some drawbacks - like ease of collimation (which I think might be debatable) and soundness of construction - but that is just different type of discussion - bad vs good telescope execution. Newtonians also have one major thing going for them and that is price - they are often cheaper. There are some other smaller things in favor of folded designs - like better baffling, slower to dew up, easier to produce flat fields (less chance of light leak) and so on ..., but again, that might be better directed at bad vs good telescope execution rather than inherent design type.

Not only the aperture - it is aperture in combination with sampling rate - or "how much of the sky is covered by a single pixel" Actual formula would be aperture_area * area_of_the_sky = speed of the setup If you think about it - that is what "speed" of the telescope does in a sense (if we keep the physical pixel size the same): "faster" telescope = shorter focal length = more sky covered with single pixel (if we keep the physical pixel size the same) = faster speed because of "area_of_the_sky" part of above equation. However - we don't need to alter F/ratio of the system in order to cover more of the sky - we can simply use larger pixel (in physical size sense) - either by using camera with larger pixels in microns or by binning our existing pixels.

Ah, ok. This is because 8" F/8 telescope working at 1"/px will produce the same SNR image in the same imaging time as 8" F/4 telescope working at 1"/px. Both gather the same amount of light and spread it over the same amount of "pixel surface" - so resulting signal and thus SNR is the same. Fact that one is F/8 and one is F/4 is irrelevant - hence, speed of the scope is irrelevant once you set your working resolution. Makes sense?

Yes - you would produce the same quality image (in terms of SNR) in 1/4 of the time with Newtonian as you would with 100mm refractor. This is because you have x4 more light gathering area with 200mm of aperture versus 100mm of aperture. Second benefit is that given same sky, same mount, same conditions - 8" would produce very slightly sharper image than 4" - if both scopes are diffraction limited (which might not be the case if you use CC for newtonian or field flattener for refractor).

No, it really does not. While it is good to have the mount that can keep the target on sensor - I was able to do that with Eq2 mount with simple DC tracking motor that had potentiometer speed control (so I adjusted tracking rate in real time to keep the planet on sensor). Individual subs are so short that mount simply does not have time to make impact - it is virtually stands still for duration of ~5ms (actually - we can calculate it roughly if sidereal tracking speed is 15"/s then in 5ms - mount moves for 1/200th of that or about 0.075" - there is simply no "room" for it to make error or any sort of jitter that would show in single frame).

I like how they use rigorous mathematical framework to actually derive this identity in the video. Standard procedure for divergent series, or in fact any series is to define a partial sum up to certain N and then find a limit as N tends to infinity. We can see this as weighted summing where weights are 1, 1, 1, 1, ... (all the way up to Nth position) and then 0, 0, 0, 0, .... for the rest Now, if I got this right from the video, it was Terence Tao who showed some years ago that any distribution that starts of as 1 and then transitions to 0 around N can be used all the same as weights. When we examine different distributions we get that limit of the sum is in form of c * N^2 - 1/12 + .... some other stuff that we ditch as N goes to infinity. Some of distributions set c to 0 thus leaving us with 0 * N^2 -1/12 = -1/12 no matter how big N gets (it is still -1/12 in the limit as anything multiplied with 0 is still 0). And the final punch line is that symmetry dictates for which distributions c = 0 (think symmetry of physics - Noether's theorem rather than symmetry of distribution). This is why we can use this framework to normalize infinite sums in QFT (or at least there is general impression that two are deeply linked somehow - thus calculations work as they should although there are "infinites" involved).

Valid point - but you can always choose to let read noise have a bit larger impact by shortening individual subs. You might choose swamp factor of 3 over 5 or something like that and simply go with shorter subs if wind gusts are real concern. Alternatively - everyone likes lower read noise camera, so maybe they will keep reducing the read noise further

I indeed skimmed over that because there is no issue there really. Let me explain by using two points. First is - read noise in terms of CCD vs CMOS. CCDs used to have very large read noise - like 7-8e and sometimes even more (very few models had read noise as low as 5-6e). Modern CMOS sensors have read noise in 1-2e range. That is at least x4 less then CCD sensor - so one would need to expose for x16 loner with CCD to reach the same level of "overwhelm" with sky noise. Indeed, back in the day, exposures of 20 or more minutes very fairly common (even half an hour or longer for NB imaging). Now onto mounts and guiding. Most mounts have periodic error that is order of up to 10 minutes or there about. That is full period, and half period - where mount takes to go from peak to peak is half that. We could argue that "road" from peak to peak is either a) smooth - making RA drift same for first two and a half minutes as for second two and a half minutes - then if you can image/guide for 2.5 minutes - you should be able to image whole 5 minutes without issues and by extension whole worm cycle as it is the same road in other direction or b) one of two parts is significantly steeper - so it can't be guided - then you would loose every other sub to not being able to guide. If that is not the case - and you don't loose subs - then you should be able to guide whole RA period - and if you can guide whole RA period - what stops you from guiding 2 consecutive periods? In any case - I don't think that sub duration is very important issue. If one can't guide for 10-15 minutes, one should sort out that bit first before attempting to do close up galaxies.

For lunar and planetary (lucky type), aperture is king.