Can you image small DSOs with a Mak?

[pointedstick]

Hello again!

You crazy people have succeeded in getting me completely hooked on astronomy. I've been spending night after night under the stars alone, or with my kids too. We're learning the constellations and how to locate the major stars by sight. Now they're also into it and are asking for their own telescopes. I hope you're happy!

While I've managed to get decent views of the Jupiter and Saturn (and of course the moon) with a 6" SCT that technically belongs to my father (one day I assume he will want it back lol), all of the DSOs I've seen have been disappointing even under fairly dark skies. And the smaller planets and Venus are mostly not visible or are just boring little dots. With the equipment I already have, I feel like I'm running out of interesting targets, at least for this time of year. But from what I can tell, there is a nearly endless assortment of fascinating, beautiful deep sky objects visible year-round--yet most of them will be underwhelming smudges when seen with the naked eye unless I get a truly giant telescope and bring it to someplace extraordinarily dark.

So I'm thinking that astrophotography might be a more rewarding long-term entry point. I'm a fairly technical guy and putting in a lot of research and performing many fussy esoteric technical tasks to get better results is up my alley. I think I'll start with a small-ish APO refractor as is typically recommended. But when I catalogue a list of targets I'd like to see, and plug them into https://astronomy.tools/calculators/field_of_view/ using some of the telescopes I'm looking at, I notice that a lot of them are actually quite small in the sky compared to a short focal length refractor's field of view. I'm not sure if one of these small scopes would get enough resolution on very small targets like M51 (Whirlpool Galaxy) or NGC 7635 (Bubble Nebula) especially without a camera that has a monster imaging sensor, which I don't yet have. I will be starting with an older Olympus E-500 micro 4/3 camera with an 8MP sensor, which I realize is kind of rubbish for the task, but it's what I've got for the moment.

So here is my question: is it realistic to do DSO imaging of these sorts of small targets with a Mak instead? I'm attracted to MCT scopes because of their simple bulletproof designs and how their very narrow fields of view and clear optics make them suitable for solar-system visual observation as well, because I don't want to totally lose the ability to look at the planets and the moon in fine detail. Is this an insanely stupid idea because their excessive f ratio?

If a Mak is out, what is the recommended way to take nice pictures of the really small DSOs? Just use the refractor with a 26MP camera sensor and crop out 95% of the final image?

[Craney]

Hi there,

Imaging with a long focal length is definitely a viable option for small DSOs.   In fact, most planetary nebula and quite a few thousand NGC galaxies (!!!   ) require in excess of 1000mm focal length to get enough detail.  We are talking 8inch SCT, 8 inch RC , SW 180mak territory.

The problem you are going to encounter with any of these is getting a high enough level of tracking accuracy to make the results worthwhile.  Telescope / Camera quality is one thing, but you really have to invest in a decent mount.  Read reviews and pay special attention to the imaging payload.

On the back of this, Maks have very high focal ratios... F13+  and so the time you need to expose an object to get a good signal to noise ratio begins to rack up..especially if you have an uncooled DSLR.

Tie long exposures in to any border line specs on a mount and you may start to lose more subs than you really want ... and start to pull your hair out.

I would start with bigger objects and with wider tolerance on the equipment.

Here are a couple of shots I took using an OMC 140   (FL=2000mm >>>> 0.67x reducer to get 1360mm ish.)

 

Regards,

Sean.

 

 

[Clarkey]

Just to add a couple of extra points to Craney's comments above.

Firstly at the sort of FL you are looking at you will really need to be guiding - which for a Mak I guess would be a OAG and new camera

Secondly you need to consider pixel scale - it is not all about the FL. If you have a long FL and small pixels as typically found in DSLR's you will be greatly over-sampling.

To be honest the main reason people recommend a small refractor is that it is relatively easy to guide (or use unguided) and is more forgiving on the mount tracking errors. I use an RC8 at 1600mm with an AZ-EQ6 which is probably the limit for the mount. Fortunately I have managed to get the RMS to around 0.3 so it is OK.

Finally AP is great - but it is expensive and addictive. The n+1 rule no longer applies. It becomes n+N and an enormous load of kit you never realised you 'needed'😂.

[pointedstick]

22 hours ago, Craney said:

Here are a couple of shots I took using an OMC 140   (FL=2000mm >>>> 0.67x reducer to get 1360mm ish.)

 

Regards,

Sean.

 

 

Lovely!

Using that reducer to achieve 1300mm focal length at f/9.6, it seems like you basically turned your Mak into an SCT. I am starting to get the sense that an SCT or a Ritchey Chretien is going to be the superior choice for this due to its faster focal ratio. Is there any major reason why this would not be the case?

[vlaiv]

Focal length is not really that important.

You should really consider everything in arc seconds per pixel (sampling rate). Here are couple of rules to help you out:

1. You won't manage to image on lower resolution than about 1"/px - without oversampling. That is just fact of life - or rather consequence of atmospheric seeing. Consider this to be upper limit.

2. Over sampling is bad for you - it lowers SNR that you can achieve in set amount of time

3. Your mount should be able to do at least half of your imaging resolution in terms of RMS - accurately measured. Say you want to image at 1.2"/px - well you should really make sure your mount guides below 0.6" RMS (accurately measured). You won't be able to accurately measure 0.6" RMS with finder/guider scope with say 160mm of FL. If you want to go high res - you really need to think in terms of OAG rather than guide scope

4. You can recover from oversampling by use of binning. However - you must be aware of read noise and its impact on single sub duration. Slow scopes require longer individual exposures that are later stacked.

5. Maksutov scopes are OK, but RC scopes are better for imaging. Larger corrected field, no dew issues - no moving primary mirror (although you can "lock" mirror in Mak), etc ...

6. Achieved resolution in part depends on scope aperture. I would not consider going high res without at least 8" of aperture.

Here is example of Bubble nebula done at 1"/px in narrowband:

This was taken with 8" RC scope

[pointedstick]

Thanks for the information. I think I understand that the smaller the pixels in your imaging sensor, the harder the rest of the equipment has to work to actually make use of the high resolution. Do I have that right?

However, I'm not sure I follow when you say that focal length is not really that important. Please correct me if I'm wrong, but if you stay within the 1-2 arc-seconds per pixel guideline and use a low focal length scope where the object is small in the image frame, won't the object occupy fewer pixels compared to using a high focal length scope where the object will be larger in the frame and occupy more pixels?

FWIW dew is never going to be a problem where I live. The only time it ever gets wet enough for there to be condensation outdoors, the skies are cloudy so you can't do any astronomy anyway.

What is "OAG"?

[Nerf_Caching]

Just now, pointedstick said:

Thanks for the information. I think I understand that the smaller the pixels in your imaging sensor, the harder the rest of the equipment has to work to actually make use of the high resolution. Do I have that right?

However, I'm not sure I follow when you say that focal length is not really that important. Please correct me if I'm wrong, but if you stay within the 1-2 arc-seconds per pixel guideline and use a low focal length scope where the object is small in the image frame, won't the object occupy fewer pixels compared to using a high focal length scope where the object will be larger in the frame and occupy more pixels?

FWIW dew is never going to be a problem where I live. The only time it ever gets wet enough for there to be condensation outdoors, the skies are cloudy so you can't do any astronomy anyway.

What is "OAG"?

Off-axis guider. It is when you have a guide camera sharing the same scope as the imaging camera using an OAG to reflect some of the incoming light to the guide camera.

[vlaiv]

11 hours ago, pointedstick said:

Thanks for the information. I think I understand that the smaller the pixels in your imaging sensor, the harder the rest of the equipment has to work to actually make use of the high resolution. Do I have that right?

Up to a point. At some point - no matter how hard you try - atmosphere is limiting factor and you simply won't make use of smaller pixels.

Here is simple formula to help you calculate sampling resolution:

sampling rate = 206.3 * pixel_size(in µm) / focal_length(in mm)

With modern cameras we now have pixel sizes that are around 4µm. If we put in rule of 1"/px as limit in above equation, we will get:

1"/px >= 206.3 * 4 / focal_length

focal_length <= ~825mm

There you go - you really don't need longer focal length than about 800mm with modern sensors and small pixels.

That does not mean that you can't use longer FL scope. I'm using 1600mm FL scope, but then I have to be careful and process my data accordingly - I bin x2 or x3 depending on sky conditions on particular night with that scope.

11 hours ago, pointedstick said:

However, I'm not sure I follow when you say that focal length is not really that important. Please correct me if I'm wrong, but if you stay within the 1-2 arc-seconds per pixel guideline and use a low focal length scope where the object is small in the image frame, won't the object occupy fewer pixels compared to using a high focal length scope where the object will be larger in the frame and occupy more pixels?

This is where you need to factor in that for given conditions - you won't resolve more detail.

Say you have object that is 3 arc minutes in size. If you sample it with say 1"/px - it will be 180px large in the image. Can you make it be 360px large? Sure - you can do it in two different ways:

- you can use longer focal length and sample at 0.5"/px

- you can sample at said 1"/px and simply enlarge the image (resample it in software).

You will now say - well, what is the point in enlarging the image - I'll just get larger image with no detail, and I'll say - same thing will happen if you image at 0.5"/px - you will get larger image with no detail (and more noise).

This is very important to understand - there is a limit to what you can resolve and if you push that limit - you'll get larger blurry image - same as if you enlarged image on computer, but only with extra noise because you are spreading light over more pixels and signal part is getting lower in SNR equation (there is limited amount of light that you capture with given setup).

There is a good exercise that you can do - examine people's images posted here on SGL - note their sampling resolution and look at high resolution image of object by Hubble or such and compare them.

I'll get you started with some examples - one of my captures:

This image is presented at 1"/px here. However - this image is not 1"/px resolution image - it is lower resolution image. You can't tell that by just looking at the image above, but let me show you in couple of examples.

First I'm going to take that same image, and I'm going to reduce it to 50% of its original size in software - thus making it 2"/px

Now, to my eye - this version is properly sampled - you can see that by the size of stars and detail in the image (look at dark features in the bridge between galaxies).

I'm now going to enlarge this small version back 200% to be the same as before:

Can you spot any difference in this and original image (except for noise grain - I'm talking about detail in the image - is there anything that is more blurry in this second version - not as sharp)?

Now compare that image - to same sampling rate from Hubble:

Now this is resolution that 1"/px can display - it is much more detailed than my image above.

In the end, I'd like to point out that there is difference between - resolution that you need to capture all detail available in the image and all detail that particular resolution can show. This is very complex topic, it goes into Fourier domain, Sampling theorem, modulation transfer functions of telescopes and so on ... I'm saying that so you don't get discouraged by looking at peoples images and HST images. HST images show what can be displayed on certain resolution and that is a bit more than other case

By the way - look at this, I'm going to compare my image at 2"/px to hubble image at 2"/px:

Now they are getting very close in detail and with a bit of sharpening (frequency restoration or difference between those two cases above - sampling rate needed to capture all detail available and available level of detail at particular sampling rate) they would look even more similar.

I added a bit of sharpening. Look at bridge and left galaxy - almost the same now. Stars are still much smaller in Hubble image though.

Ok, hope this helps a bit with understanding resolution / sampling rate and all of that.

[ollypenrice]

The resolution in arcsecs per pixel which Vlaiv, rightly, makes the benchmark for discussion is controlled by the focal length and the pixel size. You can pair a shorter focal length with smaller pixels or a longer focal length with larger pixels and get the same sampling rate. My experience is that the advantage of a very large scope with large pixels over a much smaller one with smaller pixels is far less than one might expect. (I'm not talking about going to professional-sized instruments but, in my case, I'm comparing a 14 inch ODK and a 5.5 inch refractor.)  Added to that, large pixels are becoming scarce with the CMOS revolution and the sensitive new cameras have small pixels.

But may I suggest a step back from this high resolution brink? 🤣

You seem to be going into deep sky imaging with a shopping list of targets from the visual world. If you do that you will land in advanced imaging territory with all the problems that brings. Small targets, high res imaging train, precise guiding, etc etc. Why not start imaging the objects which best lend themselves to small setups? These are often not visual targets at all. They are too large for the eyepiece and too faint for the eye. Indeed, the fact that they cannot be seen visually adds to their charm. On top of that, the sky is full of them!

Olly

Edited June 3, 2021 by ollypenrice

[pointedstick]

Thank you everyone, this is super helpful. Let's see if I understand:

Say I have a 600mm focal length f/6 telescope and I pair it with a camera with 3um pixels, for a value of 1.03 arc-seconds per pixel.

If I also get a 1200mm focal length f/6 telescope and I pair it will a second 6um pixel camera, they will reach the same 1.03 arc-seconds per pixel.

Am I correct that combination 1 will (theoretically) produce images of the exact same detail because its twice-as-long focal length is exactly cancelled out by its twice-as-large pixels, and the focal ratio is no better? And, since the telescope in combination 2  would need a much larger aperture to reach f6 at that focal length, wouldn't it already be worse since it would be larger and heavier and require a beefier mount?  Or alternatively, if it kept the same aperture size but had a slower focal ratio of f/12 like the MCTs I was originally asking about, wouldn't it simply be worse in a different way, requiring 64 times longer exposures to catch the same amount of light?

I think I'm starting to understand why people recommend refractors for astrophotography. It seems like you basically need a 3-4um pixel camera with the largest sensor/highest resolution you can afford, and a 600mm focal length telescope with the largest aperture you can afford that can be carried by your mount, keeping in mind the 1/2 weight rule. So can anyone tell me why this 4.35kg 610mm focal length f/4 classical Newtonian isn't the perfect do-it-all astrophotography telescope for cameras with pixel sizes of between 3 and 4um? Is it just things like build quality, collimation annoyances, and difficulty of balancing the optical train because of the Newtonian design? Or something else? Or is this really actually a great choice?

 

6 hours ago, ollypenrice said:

But may I suggest a step back from this high resolution brink? 🤣

You seem to be going into deep sky imaging with a shopping list of targets from the visual world. If you do that you will land in advanced imaging territory with all the problems that brings. Small targets, high res imaging train, precise guiding, etc etc. Why not start imaging the objects which best lend themselves to small setups? These are often not visual targets at all. They are too large for the eyepiece and too faint for the eye. Indeed, the fact that they cannot be seen visually adds to their charm. On top of that, the sky is full of them!

Olly

Oh yes, I know that my skill level won't let me get those tiny targets anytime soon, and that starting with easier things is a better idea. I'm just doing my research now to try to understand the options and constraints so I can spec out a set of initial equipment that will all match and work well together. Knowing the physical limitations at play is useful so that I don't accidentally buy something that's too much or too little for things that can't be changed, such as atmospheric conditions. Camera pixel size will get smaller over time, but the atmosphere won't become more forgiving, so it makes sense to hold that as a constant and optimize around it. This seems like quite an expensive, equipment-driven hobby, so I'd like to avoid as many costly mistakes as possible. Besides, half the fun of a hobby for me is learning new technical information, so I'm already having fun for free!

[ollypenrice]

3 minutes ago, pointedstick said:

 

Oh yes, I know that my skill level won't let me get those tiny targets anytime soon, and that starting with easier things is a better idea. I'm just doing my research now to try to understand the options and constraints so I can spec out a set of initial equipment that will all match and work well together. Knowing the physical limitations at play is useful so that I don't accidentally buy something that's too much or too little for things that can't be changed, such as atmospheric conditions. Camera pixel size will get smaller over time, but the atmosphere won't become more forgiving, so it makes sense to hold that as a constant and optimize around it. This seems like quite an expensive, equipment-driven hobby, so I'd like to avoid as many costly mistakes as possible. Besides, half the fun of a hobby for me is learning new technical information, so I'm already having fun for free!

I think it's equipment-driven up to a point, but only up to a point. If we take the example of any equipment setup, fix it and call it 'observatory x,' what variables remain?  Ooooh, lots and lots. What target do you go for? How do you lay siege to it? Will it be a mosaic? What filters will you use? How will you blend them? How will you process the data? The million dollar question!

So I don't think AP is equipment-driven, I think it is processing-driven. 

Olly

[vlaiv]

11 minutes ago, pointedstick said:

Am I correct that combination 1 will (theoretically) produce images of the exact same detail because its twice-as-long focal length is exactly cancelled out by its twice-as-large pixels, and the focal ratio is no better? And, since the telescope in combination 2  would need a much larger aperture to reach f6 at that focal length, wouldn't it already be worse since it would be larger and heavier and require a beefier mount?  Or alternatively, if it kept the same aperture size but had a slower focal ratio of f/12 like the MCTs I was originally asking about, wouldn't it simply be worse in a different way, requiring 64 times longer exposures to catch the same amount of light?

If you set your working resolution, like in your example - then as far as speed of system is concerned - aperture wins. Speed can be defined as aperture at resolution.

If both scopes are F/6 and both sample at same 1.03"/px - larger scope will be faster. In fact, in your proposed case it will reach same SNR in 1/4 of the time.

If you change F/ratio of one scope and use F/6 scope with smaller pixels and F/12 scope with larger pixels - they will reach same SNR in the same time - because they have same aperture size.

Other than that - there is plethora of things to consider when choosing a telescope - size and weight (thus mounting requirements) are just part of the story.

What about spot diagrams? Is telescope diffraction limited and over what field? How big is fully illuminated field? Is telescope mechanically sound / rigid? Is it well baffled for stray light? How well does it tolerate temperature changes?

16 minutes ago, pointedstick said:

. So can anyone tell me why this 4.35kg 610mm focal length f/4 classical Newtonian isn't the perfect do-it-all astrophotography telescope for cameras with pixel sizes of between 3 and 4um? Is it just things like build quality, collimation annoyances, and difficulty of balancing the optical train because of the Newtonian design? Or something else? Or is this really actually a great choice?

Well, you answered question yourself.

As is F/4 classical newtonian is going to have very small diffraction limited field. It will require coma corrector. Coma corrector while corrects for coma - enlarges star sizes, depending on type of corrector introduces spherical aberration on axis and so on. Such fast system is very sensitive to collimation and sensor tilt.

Even if you account for everything - you'll get maybe 24-25mm imaging circle.

Part of achieved resolution depends on telescope size. You can take 80mm apo scope that has very good field and is mechanically sound and everything - but you can't image with it at 1"/px with it as airy disk size of such scope is 3.21". No way that you are going to achieve 1"/px with so small aperture - best that you can hope to is about 2"/px.

150mm scope has 1.71" airy disk size and can image in 1.4-1.5"/px range at best.

[pointedstick]

Okay, new terms for me to learn: "airy disk" and "diffraction limited field".

If it's possible for two f/6 scopes to have different "speed", what does the focal ratio mean? It is mostly useless for astrophotography?

[vlaiv]

Just now, pointedstick said:

If it's possible for two f/6 scopes to have different "speed", what does the focal ratio mean? It is mostly useless for astrophotography?

F/ratio or F/speed is mostly term from daytime photography and while it is somewhat useful in astrophotography - it does not have the same significance. I'll explain.

In daytime photography, we are operating in light dominated regime - there is simply plenty of light and signal to noise is well defined with light level. In astrophotography, things are not so simple as we are operating in photon starved domain - many other noise sources start to be important and have impact on SNR - therefore simple rule like F/ratio change means certain exposure change simply no longer hold.

Another thing is that F/ratio in daytime photography is usually used in context of same camera. You swap F/2 lens for F/1.4 lens or you set aperture on your lens and change it from F/5.6 to F/4. Pixel size remains the same and does not change.

In astrophotography, pixel size is important variable and determines speed of the system - you have a choice of camera to put on a telescope as well as choice of telescope itself.

We have seen how change of both focal length and pixel size can make F/6 telescope be the same speed as F/12 telescope. What we did not say there is FOV aspects of that gymnastics.

If you have twice as large pixel on one camera versus another - you'll have to juggle sensor size as well. 3000 x 6µm is 18mm and 4000 x 3µm is only 12mm. If you set your working resolution - field of view that you get will be determined by number of pixels. You better make sure that you have enough pixels to cover the target - that your sensor is large enough and that your scope can produce image that large in focal plane.

Here is a spot diagram of Celestron RASA scope. It shows field definition - or how ideal star will look like when imaged. In each of these boxes there is small circle. That is airy disk.  If you have perfect scope with no aberrations - it will still not produce pin point result - it will produce this:

Star / pin point source will actually be little circle / disk when magnified and there will be rings around it. Smaller the aperture of the scope - larger that disk is. That is known as airy disk and it impacts resolution of telescope. It is in part what blurs the image that telescope produces.

Above spot diagram is simulation of what actual image of pin point source looks like thru given telescope - and there is reference circle representing ideal telescope. Btw, airy disk depends on wavelength of light as can be seen in above diagram - circles for red are larger than for blue part of spectrum. In any case - diffraction limited telescope is one where all (or majority) of these dots on spot diagram land inside airy disk. Above scope is clearly diffraction limited only in green light and only in central portion of the field - up to 5mm away from optical axis (or 10mm diameter).

Such scope can only be used as wide field imaging instrument where resolution wanted and achieved is significantly smaller than aperture of telescope would suggest.

 

[pointedstick]

So I found a diffraction limit chart and used that to generate a table of arc-second resolution limits for various telescope apertures to reach the full visual spectrum:
- With a 175mm telescope:  resolution is limited to 1 arc second
- With a 150mm telescope:  resolution is limited to 1.4 arc-seconds
- With a 125mm telescope:  resolution is limited to 1.6 arc-seconds
- With a 100mm telescope:  resolution is limited to 1.9 arc-seconds
- With a 90mm telescope:   resolution is limited to 2 arc-seconds
- With an 80mm telescope:  resolution is limited to 2.5 arc-seconds
- With a 70mm telescope:   resolution is limited to 2.8 arc-seconds

Basically, to actually achieve that atmospherically-limited 1 arc-second per pixel resolution across the visible spectrum, it seems like you need a minimum aperture of 175mm.

Then I used that to generate a table of minimum camera pixel sizes for the achievable resolution in arc-seconds with various telescope designs/apertures/focal lengths. My impression is that it's fine to have smaller pixels than these, but any larger and you lose out on potential resolution.

Refractor:
- 70mm / 350mm: 1.69um * 2.8 arc-seconds diffraction limit = 4.75um max pixel size
- 72mm / 420mm: 2.03um * 2.8 arc-seconds diffraction limit = 5.70um max pixel size
- 80mm / 480mm: 2.32um * 2.5 arc-seconds diffraction limit = 5.81um max pixel size
- 80mm / 560mm: 2.71um * 2.5 arc-seconds diffraction limit = 6.78um max pixel size
- 100mm / 714mm: 3.46um * 1.9 arc-seconds diffraction limit = 6.57um max pixel size
- 125mm / 975mm: 4.72um * 1.6 arc-seconds diffraction limit = 7.56um max pixel size
- 150mm / 1216mm: 5.89um * 1.4 arc-seconds diffraction limit = 8.25 max pixel size

Classical Newtonian:
- 130mm / 650mm: 3.15um * 1.6 arc-seconds diffraction limit = 5.04um max pixel size
- 150mm / 750mm: 3.63um * 1.4 arc-seconds diffraction limit = 5.08um max pixel size
- 200mm / 1200mm: 5.81um * 1.0 arc-seconds diffraction limit = 5.81um max pixel size

Astrophotography-focused Newtonian:
- 150mm / 420mm: 2.03um * 1.4 arc-seconds diffraction limit = 2.85um max pixel size
- 150mm / 610mm: 2.95um * 1.4 arc-seconds diffraction limit = 4.14um max pixel size
- 178mm / 500mm: 2.42um * 1.0 arc-seconds diffraction limit = 2.42um max pixel size
- 200mm / 800mm: 3.87um * 1.0 arc-seconds diffraction limit = 3.87um max pixel size

Richey-Chretien:
- 150mm / 1370mm: 6.64um * 1.4 arc-seconds diffraction limit = 9.29um max pixel size
- 200mm / 1625mm: 7.87um * 1.0 arc-seconds diffraction limit = 7.87um max pixel size

Classical Cassegrain:
- 150mm / 1836mm: 8.90um * 1.4 arc-seconds diffraction limit = 12.46um max pixel size
- 200mm / 2400mm: 11.63um * 1.0 arc-seconds diffraction limit = 11.63um max pixel size

Schmidt-Cassegrain:
- 150mm / 1500mm: 7.25um * 1.4 arc-seconds diffraction limit = 10.1um max pixel size
- 200mm / 2000mm: 9.69um * 1.0 arc-seconds diffraction limit = 9.69um max pixel size

Maksutov-Cassegrain:
- 127mm / 1540mm: 7.46um * 1.6 arc-seconds diffraction limit = 11.94um max pixel size
- 150mm / 1800mm: 8.74um * 1.4 arc-seconds diffraction limit = 12.20um max pixel size

RASA:
- 200mm / 400mm: 1.93um * 1.0 arc-seconds diffraction limit = 1.93um max pixel size

 

Does this look broadly accurate to you? If not, can you tell me where I went wrong?

If it is (broadly) correct, I also understand that field flatness and coma become important too because you want a clear image across the full field of the sensor. The larger the sensor, the flatter and more coma-free the image has to be, right?

[vlaiv]

48 minutes ago, pointedstick said:

So I found a diffraction limit chart and used that to generate a table of arc-second resolution limits for various telescope apertures to reach the full visual spectrum:

Ah, ok, this probably only includes diffraction limit of aperture. I'm going to show you full math physics of things (brief). There is critical sampling rate or pixel size for any aperture / focal length there.

That is fairly simple calculation.

https://en.wikipedia.org/wiki/Spatial_cutoff_frequency

Or if rearranged a bit

f = aperture / (lambda * focal_length)

Critical sampling rate is twice sampling frequency (Nyquist theorem) and that means

pixel size = lambda * focal_length  /  (2 * aperture)

where all three are in millimeters. Factor of two is there because pixel needs to be half of wavelength.

Say you have 180mm aperture 2700mm FL MCT telescope - what size pixels should you use? We can take lambda to be 0.00051mm (that is 0.51µm or 510nm - center of spectrum - or you can go for blue if you wish at 400nm - slightly different result).

pixel size =  0.00051 * 2700/ 2 * 180 = 0.003825 = 3.825µm

This is so called critical sampling and is used for planetary imaging. It does not have much to do with deep exposure imaging that is dominated by seeing.

For that, we need to look at some other formulae.

First is - resolution of the image is determined by PSF. PSF in long exposure image is simply image of single star - since stars are point sources. Stars are mostly (in absence of serious aberrations) just Gaussian (or Moffat in large telescopes) shape. Gaussian shape is characterized by either sigma or FWHM - there is simple relationship between the two: sigma * 2.355 = FWHM.

FWHM of the star in the image that you'll get from diffraction limited optics is convolution of three different blurs:

1. seeing blur

2. mount tracking error blur

3. Airy disk blur (same as above where we discussed only diffraction limited case - without points 1 and 2).

Seeing blur is usually expressed in FWHM in arc seconds. Most of the time seeing FWHM is 2" - 1.5" is considered very good. 1.2" is exceptional. Values below 1" usually don't happen in regular observing sites. You can get the idea of what you can expect for your location if you look at seeing forecast - found here:

https://www.meteoblue.com/en/weather/outdoorsports/seeing/albuquerque_united-states-of-america_5454711

(make sure you put your actual location)

Ok - this just proved me wrong - it forecasts 0.4" seeing in Albuquerque in next two days. That just never happens to the rest of the world

Look here is forecast for my town:

Although seeing columns are green - values are around 2"

In any case - that is the seeing - it is hard to predict and it is variable quantity.

Next is guiding performance - that you take your total RMS that your mount is usually capable of. Stock Chinese mounts like HEQ5 / EQ6 guide at about 1" RMS. Tuned and modded will go down to 0.5-0.6" RMS. High end mounts go in 0.2"-0.3" RMS range.

In the end we need Gaussian approximation to Airy disk - found here:

https://en.wikipedia.org/wiki/Airy_disk#Approximation_using_a_Gaussian_profile

That is 0.42 * lambda * F_ratio in millimeters or

angular sigma = 180 * arctan(0.42 * lambda / aperture) * 7200 / PI

or if we use small angle approximation that tan(alpha) = alpha for small angles

airy_sigma = 173.26 * 0.51 / aperture = 88.364 / aperture

where aperture is in millimeters.

In the end we get total_sigma = sqrt ( seeing_sigma^2 + guide_sigma^2 + airy_sigma^2).

Let's do example. Say that you image with 8" scope and 0.5" RMS mount in 1.5" FWHM seeng - what is resolution that you can expect?

First - let's see what sort of star FWHM you can expect.

8" scope is 200mm so airy_sigma = 0.44182

0.5" RMS just means guide_sigma = 0.5"

1.5" FWHM seeing means that seeing_sigma = 1.5 / 2.355 = ~0.637"

We can calculate total sigma as being sqrt(0.1952049124 + 0.25 + 0.405769) = ~0.9225 and corresponding FWHM 2.1725"

Ok, now we have FWHM of Gaussian PSF - last thing we need is proper sampling rate. Here we need to do approximation - as Gaussian profile is only approximation. Fourier transform of Gaussian is Gaussian - so there is no clear cutoff frequency for that. We can adopt that once frequencies get attenuated to 10% or below - that will be our cut off point.

That happens at sampling rate equal to FWHM / 1.6, so our proper sampling rate in this case will be 2.1725 / 1.6 = 1.36"/px

From all of this - you can see that 1" requires perfect conditions and large aperture and good guiding. That is not something that will happen often. That is why I said that you need at least 8" of aperture and very good mount and steady skies to even attempt going at 1"/px. In reality - most of the time amateur setups are limited to maybe 1.2-1.4"/px or even less than that if seeing is not good.

Now this only holds for diffraction limited scopes - any imperfection in optical system will lower max resolution still - however, that is pretty hard to asses - maybe spot RMS for particular scope could be used instead of gaussian approximation to airy disk - but that is just off the top of my head, that would need verification (and not many systems have proper spot diagrams, and spot diagrams are best case scenario   - in reality scopes don't perform that good).

 

 

Edited June 3, 2021 by vlaiv

[pointedstick]

Oh I get it. The more performance or precision you demand of a system, the more something else becomes the weakest link and prevents you from reaching the desired level. It's about stacking the variables in your favor:

- Living in a place with generally good seeing and going out on a night that actually has good seeing (it's 100% cloudy tonight so I'm stuck indoors doing research instead of looking up at the sky)

- Using an 8" aperture scope so you are less likely to be diffraction-limited by your level of seeing

- Using a mount with a guiding error less than the other two

- Achieving that guiding performance using a guide scope system, periodic error correction, encoders, etc.

...And so on. Definitely seems like it would be easier to start with cheaper equipment that tops out at an achievable resolution of 2 arc-seconds rather than chasing 1 immediately. So again I see why the small refractors are recommended for beginners. It seems like they make it easy to get pretty good results for large targets with entry-level mounts.

I think you've helped me understand that trying to image small dim faraway objects with a small Mak is likely to be a frustrating and unsatisfying experience, at least at the beginning

 

Anyway thanks for explaining all the math. I think I'm going to need to upgrade from a text file to a spreadsheet. Ultimately I think I will probably end up taking the conventional advice of "mount, mount, mount, camera, telescope" and get as good a mount as my budget allows with a small refractor. Upgrading the camera and telescope later is likely to be cheaper. Famous last words, right...

[ollypenrice]

4 hours ago, pointedstick said:

Oh I get it. The more performance or precision you demand of a system, the more something else becomes the weakest link and prevents you from reaching the desired level. It's about stacking the variables in your favor:

- Living in a place with generally good seeing and going out on a night that actually has good seeing (it's 100% cloudy tonight so I'm stuck indoors doing research instead of looking up at the sky)

 

Don't confuse seeing with transparency. They are not the same by any means. 'Seeing' refers to the optical stability of the lightpath through the atmosphere. Does a beam from the object get stirred up on its way through? If so the information arrives in an already-blurred condition.  The finer your sampling rate in arcseconds per pixel the more damage this does and it can very quickly become your weakest link. (Fast frame solar system imagers fight back by taking hundreds of very short subs and retaining/combining just the lucky ones which enjoyed a moment of stability.)  Transparency, though, is self explanatory. It's very common indeed to have the best seeing on nights of imperfect transparency.

Factors influencing seeing include warm air rising from houses/ tarmac, the elevation of the object (the higher the better), wind (which often causes different layers of atmosphere to have different temperatures) and the time of night. (Usually seeing improves, though not always.)

Olly

[pointedstick]

OK I have one final question on this subject: Would it be largely pointless to put a focal reducer on a Mak because the extra theoretical field of view you'd gain would be exactly offset by a reduction in the image circle?

For example this Alter MK 503 f/10 Mak has a focal length of 1270mm. If one added a 0.5x focal length reducer, it would double the field of view but halve the image circle and therefore you wouldn't actually be able to make use of the larger field of view, right? It would "see" the same thing? So in this case, am I correct that the only possible advantage of doing that would be if you have a small sensor that will still fit in the smaller image circle and want a lower focal ratio to reduce your exposure times?

[vlaiv]

1 hour ago, pointedstick said:

OK I have one final question on this subject: Would it be largely pointless to put a focal reducer on a Mak because the extra theoretical field of view you'd gain would be exactly offset by a reduction in the image circle?

For example this Alter MK 503 f/10 Mak has a focal length of 1270mm. If one added a 0.5x focal length reducer, it would double the field of view but halve the image circle and therefore you wouldn't actually be able to make use of the larger field of view, right? It would "see" the same thing? So in this case, am I correct that the only possible advantage of doing that would be if you have a small sensor that will still fit in the smaller image circle and want a lower focal ratio to reduce your exposure times?

Quite right.

If you have large enough sensor to capture whole illuminated and corrected circle - you don't need reducer. You can achieve same sampling rate by binning x2 instead of using x0.5 reducer.

However, if you have small sensor that won't cover whole circle - then yes, reducer will help to capture whole field.

[pointedstick]

OK great, thanks!

Actually this makes me realize I have a further related question related to how it interacts with a non-fully-illuminated image circle. If you have a telescope setup where the image circle is not fully illuminated, will a focal reducer crop out some or all of the non-fully-illuminated area, or will it simply scale down the whole thing so that you still end up with a non-fully-illuminated area, only smaller?

Also is there a way to calculate the size of the illuminated area if the manufacturer doesn't provide that data?

[vlaiv]

1 minute ago, pointedstick said:

Also is there a way to calculate the size of the illuminated area if the manufacturer doesn't provide that data?

No - you need to know geometry of telescope in order to do that - size of baffle tubes, diameters of openings, size of optical elements and so on.

That is usually done with computer in CAD type software.

It is really easy to measure it though, in fact - it is standard part of imaging process. It is called flat fielding / flat calibration. We take so called flat exposures - uniform light is shone on aperture and exposure is taken (can even be sky light with T shirt over telescope aperture - but best results are achieved with flat box). With such exposure you can precisely measure percentage of light hitting the sensor. It is also used to correct for the vignetting.

Problem is not in vignetting - that gets corrected with flats. Problem is that you lower your SNR in outer parts of the image - light blockage means less signal and less signal means lower signal to noise ratio. If you have 50% vignetting - it's like you exposed edges of the image only half of total imaging time (while center receives 100% of imaging time). Noise in outer parts will be noticeable.

6 minutes ago, pointedstick said:

Actually this makes me realize I have a further related question related to how it interacts with a non-fully-illuminated image circle. If you have a telescope setup where the image circle is not fully illuminated, will a focal reducer crop out some or all of the non-fully-illuminated area, or will it simply scale down the whole thing so that you still end up with a non-fully-illuminated area, only smaller?

Maybe simplest way to think of focal reducers is that they "compress" already existing field into smaller size. Say you have x0.8 reducer and you have 28mm original field. Now you'll be able to image with 28 mm * 0.8 = 22.4mm diagonal sensor - whole 28mm field.

If you use 28mm sensor - then you'll in fact image 28 / 0.8 = 35mm diameter. If such 35mm diameter field is vignetted and aberrated - that will end up on your 28mm sensor as well.

In fact - most reducers if they are not specially designed like Focal reducers / field flatteners made for particular type of scope, will introduce additional vignetting and aberrations. They have smaller clear aperture and that can cause additional vignetting, and aberrations are inherent in some of their designs.

For example, simple x0.5 reducer will make perfect stars into little astigmatic streaks at the edge of the field:

(here spot diagram is presented in angular units rather than millimeters from optical axis, source: https://www.telescope-optics.net/miscellaneous_optics.htm)

This is very important to understand and take into account. For example here is reducer that is often recommended for one of my scopes - RC8" scope:

https://www.teleskop-express.de/shop/product_info.php/info/p8932_TS-Optics-Optics-2--CCD-Reducer-0-67x-for-RC---flatfield-telescopes-ab-F-8.html

It is x0.67 focal reducer and works for flat field telescopes of F/8 or higher. RC8" is flat field telescope and F/8 one - so it's "no-brainer" to pair those two together. But there is a catch!

If you look at the specs for telescope:

https://www.teleskop-express.de/shop/product_info.php/info/p5222_TS-Optics-8--Ritchey-Chr-tien-Pro-RC-Telescope-203-1624-mm-OTA.html

they say that field is usable as is for up to 30mm diagonal sensors. In reality, even APS-C will struggle somewhat with 27-28mm diagonal.

Now if we take those 28mm and apply x0.67 reduction - we will compress that field into only 18.76mm. That is smaller than even micro 4/3 format (about 22-23mm diagonal). Most people find this reducer much better working at x0.75 (with some reducer designs you can vary their reduction factor by changing their placement / working distance to sensor).

If we take again 28mm and apply now x0.75, we get 21mm - you can clearly see why x0.75 is working for people who have 22mm diagonal sensor.

Using such reducer of telescope that has excessive field curvature or is fast is likely to result in very prominent aberrations.

[pointedstick]

Thanks again Vlaiv.