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Spot diagrams for RASA, Epsilon and Sharpstar


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Does anyone have a feeling for what a good spot diagram should look like?

I think @vlaiv  have suggested that the RASAs are not diffracton limited and referred to a spot diagram. Still I am impressed with the resolution of my RASA 8, an example of which is the Tadpole nebula that I recently posted, a resolution which even impressed @ollypenrice.

So this rainy Sunday afternoon I started googling spot diagrams and found them for RASA 8, RASA 11, Tak Epsilon 180, Sharpstar 150 and 200. In addition I found some for Tak Apo refractors for comparison. Starring at these spots actually gave me a headache as I found them difficult to figure out and compare. The fact that Tak and Sharpstar put their spots into 40, 50 or 100 um squares while Celestron use 18 um squares did not make a straight visual comparison easy. I think my preliminary conclusion is that the RASAs are quite comparable to the Epsilon, if anything they have smaller spots. The Sharpstars have bigger spots as far as I can tell. What surprised me the most was that the spots of the Tak Apos did not seem to be much smaller than these mirror astrographs, but I am probably missing something here. I could not easily find any spot diagrams for the very expensive Riccardi Honders astrographs.

Comments most welcome, not the least from someone less ignorant about spot diagrams than me.

Cheers, Göran

RASA 8 f/2:

810478636_RASA8Spotdiagram.thumb.png.362b0d3c29c749db4d1a5ebf79a92ce0.png

RASA 11 f/2.2:

2103573679_RASA11Spotdiagram.thumb.png.cd05028ea82e6ac7074a366a378aded3.png

Epsilon 180 f/2.8

24615005_Epsilon180Spotdiagram.thumb.png.e21c77c02b6438cc733bf7fd442e011c.png

Sharpstar 150 f/2.8

582696280_Sharpstar150Spotdiagram.thumb.png.4225deb4b3b0536e1a65fbf4bfcc9c4e.png

Sharpstar 200 f/3.2

19382231_Sharpstar200Spotdiagram.thumb.png.4917fc769df21b01dc206f528ae1c6c9.png

Tak FSQ 106 f/5

1237309952_Tak106FSQSpotdiagram.thumb.png.a5333d6822fc130abd7bf9a2a216003a.png

Tak FS & TSA 102 f/8

934819856_TAKFSTSA102Spotdiagram.thumb.png.c4ef6f0b43b82f71d01c7ae2a6c12857.png

 

Edited by gorann
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The RASA8 appears to list a spot diagram only up to 11mm from the centre point, the others present information on double this distance or more.  Some boxes are 50, some are 100, some are 18, some are 40!  Very hard to make a quite judgement on the images.

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4 minutes ago, tooth_dr said:

The RASA8 appears to list a spot diagram only up to 11mm from the centre point, the others present information on double this distance or more.  Some boxes are 50, some are 100, some are 18, some are 40!  Very hard to make a quite judgement on the images.

Yes, the others have a wider image circle. In the case of RASA 8 a wider image circle would mean that a bit too much of the 8" front lens would be centrally obstructed. About the RASA 8 Celestron/FLO says "whilst ~22mm diagonal is optimal the RASA 8 can also be used with larger sensors up to 32mm diagonal, including the APS-C sized sensors, though some compromise must be expected at the image periphery." With my ASI2600 that has a diagonal of 28 mm the corners are quite acceptable.

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I was just thinking about this and I'm not sure that spot diagrams matter that much for imaging as long as you are aware of what they mean and what you can expect.

First a bit of background - what are spot diagrams?

They are produced by geometrical casting of rays in optical system - as designed (not as manufactured). Ideal telescope will not have spot diagram - it will have single spot and that spot will be in center of a circle representing Airy disk.

Here is an example for parabolic newtonian that is perfect design on optical axis (and as soon as you start going away from it - there is coma):

image.png.9aae407bcf9437019b6d720f2dc099ae.png

Look at bottom row - this simply means - any ray that you cast will end up in single point. That is perfect optical performance, but it does not mean that such telescope will have infinite resolution. There are still laws of physics and interference and ultimately all those rays produce an airy pattern - that is denoted as little circle (when stated so).

Often quoted term diffraction limited optics - simply means that all rays cast will end up in circle that marks Airy disk. This does not mean that such scope has the same performance as one with perfect optics - as again laws of physics play a part and once all interference happens - there is additional blurring over perfect design.

What we can do when examining spot diagrams is few things:

- understand spread of spots in relation to Airy disk diameter - if there are spots outside this diameter - we call optics not diffraction limited. If all are inside - we say, optics is diffraction limited. Diffraction limited just means - telescope will give acceptable high power views of the planets (but by no means best possible - and this even does not touch on diffraction effects - like issues with central obstruction).

- we can see if diagram is symmetric or not. Asymmetry in diagram causes more issues than symmetric diagrams - symmetric diagrams (especially rotational symmetry) tend to produce round stars or more pleasing stars when seeing is added (think coma as being totally asymmetric, then astigmatism being more symmetric and just regular star bloat as being completely symmetric).

- we can see how star shapes change over the field of view / photographic field - this is important if we want to use sensor of certain size.

- we can see how star shapes change over range of wavelengths - important for narrowband imaging and any chromatic effects

- we can asses equivalent aperture of a telescope that is diffraction limited. Even if telescope is not diffraction limited as such - there is equivalent smaller aperture for which such spot diagram would be deemed diffraction limited.

Let's examine spot diagram of RASA 8" posted above. It is common to draw a little circle to denote diameter of airy disk of a telescope.

First let's see if that is the case here. Big box is 18µm, and small square is 1.8µm on its side. Circle at 700nm looks to be exactly two squares in diameter. At this wavelength, 8" scope will have airy disk size of 1.76" or 3.4µm at this focal length. That is close enough to 2 x 1.8µm = 3.6µm

This telescope is clearly not diffraction limited - even on optical axis - except for 500nm wavelength where it is on edge to be diffraction limited. It does however have rather symmetric spot diagram across the board - which is good. If we take largest spot diagram of interest at 700nm and "measure" its spread - we get about 6 squares to be diameter - or 6 x 1.8µm = 10.8µm

That is equivalent as 50mm F/8 telescope - or rather 50mm F/8 telescope that is diffraction limited will produce the same sharpness as RASA 8"

Is 150 F/2.8 sharp star better or worse than RASA 8"?

According to it's spot diagram - in worst case, geometrical radius is the worst in field 3 (that is 14mm away from optical center) and it equals 12µm - only tiny fraction larger than 10.8µm of RASA".

I would say that these two scopes perform similarly with respect to sharpness. Btw, what level of sharpness is that? Keep your sampling rate above 2"/px with these scopes - as it is very unlikely that you'll have FWHM below 3.5-3.6" with them.

 

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Spot diagrams are the result of ray tracing using geometric optics and don't  therefore takes account of diffraction.

Things to consider would be:

Are the spots  larger than the diffraction limit or not.

How to they compare to your pixel size.

How do they compare to you guiding accuracy and or local seeing.

What use do you want to put it to.

I see @vlaiv has given a comprehensive account while I was typing.

Regards Andrew 

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11 minutes ago, vlaiv said:

I was just thinking about this and I'm not sure that spot diagrams matter that much for imaging as long as you are aware of what they mean and what you can expect.

First a bit of background - what are spot diagrams?

They are produced by geometrical casting of rays in optical system - as designed (not as manufactured). Ideal telescope will not have spot diagram - it will have single spot and that spot will be in center of a circle representing Airy disk.

Here is an example for parabolic newtonian that is perfect design on optical axis (and as soon as you start going away from it - there is coma):

image.png.9aae407bcf9437019b6d720f2dc099ae.png

Look at bottom row - this simply means - any ray that you cast will end up in single point. That is perfect optical performance, but it does not mean that such telescope will have infinite resolution. There are still laws of physics and interference and ultimately all those rays produce an airy pattern - that is denoted as little circle (when stated so).

Often quoted term diffraction limited optics - simply means that all rays cast will end up in circle that marks Airy disk. This does not mean that such scope has the same performance as one with perfect optics - as again laws of physics play a part and once all interference happens - there is additional blurring over perfect design.

What we can do when examining spot diagrams is few things:

- understand spread of spots in relation to Airy disk diameter - if there are spots outside this diameter - we call optics not diffraction limited. If all are inside - we say, optics is diffraction limited. Diffraction limited just means - telescope will give acceptable high power views of the planets (but by no means best possible - and this even does not touch on diffraction effects - like issues with central obstruction).

- we can see if diagram is symmetric or not. Asymmetry in diagram causes more issues than symmetric diagrams - symmetric diagrams (especially rotational symmetry) tend to produce round stars or more pleasing stars when seeing is added (think coma as being totally asymmetric, then astigmatism being more symmetric and just regular star bloat as being completely symmetric).

- we can see how star shapes change over the field of view / photographic field - this is important if we want to use sensor of certain size.

- we can see how star shapes change over range of wavelengths - important for narrowband imaging and any chromatic effects

- we can asses equivalent aperture of a telescope that is diffraction limited. Even if telescope is not diffraction limited as such - there is equivalent smaller aperture for which such spot diagram would be deemed diffraction limited.

Let's examine spot diagram of RASA 8" posted above. It is common to draw a little circle to denote diameter of airy disk of a telescope.

First let's see if that is the case here. Big box is 18µm, and small square is 1.8µm on its side. Circle at 700nm looks to be exactly two squares in diameter. At this wavelength, 8" scope will have airy disk size of 1.76" or 3.4µm at this focal length. That is close enough to 2 x 1.8µm = 3.6µm

This telescope is clearly not diffraction limited - even on optical axis - except for 500nm wavelength where it is on edge to be diffraction limited. It does however have rather symmetric spot diagram across the board - which is good. If we take largest spot diagram of interest at 700nm and "measure" its spread - we get about 6 squares to be diameter - or 6 x 1.8µm = 10.8µm

That is equivalent as 50mm F/8 telescope - or rather 50mm F/8 telescope that is diffraction limited will produce the same sharpness as RASA 8"

Is 150 F/2.8 sharp star better or worse than RASA 8"?

According to it's spot diagram - in worst case, geometrical radius is the worst in field 3 (that is 14mm away from optical center) and it equals 12µm - only tiny fraction larger than 10.8µm of RASA".

I would say that these two scopes perform similarly with respect to sharpness. Btw, what level of sharpness is that? Keep your sampling rate above 2"/px with these scopes - as it is very unlikely that you'll have FWHM below 3.5-3.6" with them.

 

Thanks a lot Vlaiv! It clarified several thing, not the least that diffraction limited means that the spots should be within the airy discs. I assume the circles in the Sharpstar diagrams are not airy discs, but the circles for the RASA 8 may be airy discs.

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4 minutes ago, gorann said:

Thanks a lot Vlaiv! It clarified several thing, not the least that diffraction limited means that the spots should be within the airy discs. I assume the circles in the Sharpstar diagrams are not airy discs, but the circles for the RASA 8 may be airy discs.

Indeed, for RASA8 - they are of proper size (and change with wavelength), but for SharpStar are way too large to be airy disks.

Sometimes people put circles in these spot diagrams - as a marketing trick - see that circle? See complete pattern inside that circle? Must be a good (diffraction limited) scope :D

It is for that reason best to actually check using math if circle drawn corresponds to airy disk. You can use this formula for that:

http://www.wilmslowastro.com/software/formulae.htm#Airy

image.png.6213f3baa25f52aba8368976cd529bf2.png

Also be careful of the scale of squares used - for example Sharpstar F/2.8 may look like tighter spot diagrams over Sharpstar F/3.2 - but check the actual numbers - diagram for F/2.8 is 100µm in size while that for F/3.2 is 40µm.

Good thing is that there are actual numbers for each spot diagram (very useful feature).

image.png.208c3162e413758602496e56f1a76eac.png

This is for SharpStar F/3.2. Note that Geo radius - which just means further extent seems rather big, but for actual sharpness it is RMS radius that counts more and although we would say that 9.852µm is radius that we use to determine corresponding equivalent diffraction limited aperture - actual performance will be closer to what RMS radius gives.

I just realized that in my analysis above I used 12µm in the wrong context - it is radius not diameter. Sharpstar F/2.8 has lower resolution than RASA8" not comparable one.

Let's try to figure out equivalent aperture of SharpStar F/3.2 by using RMS radius instead and paying a bit more attention to what it all means.

RMS radius will be equivalent to Sigma for Gaussian distribution and we can use Gaussian approximation for Airy disk to compare it with. First let's go ahead and convert it to arc seconds as that is more related to actual resolution rather than to pixel size used.

At 640mm 4.38µm is equivalent to 1.41". That is sigma of gaussian distribution. According to Wiki Sigma relates to Airy disk like this:

image.thumb.png.bab1504e5ceabce7727dfc380826cb08.png

From that we have that Airy disk radius is 4.23" which is equivalent to 30.3mm of aperture.

In outer field SharpStar 200 F/3.2 is as sharp as 30.3mm of aperture.

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"In outer field SharpStar 200 F/3.2 is as sharp as 30.3mm of aperture. "

30 mm aperture is like a small handheld binocular.  It cannot be that bad so I must miss something here about what aperture here means. Also, what about the Tak apos, their airy disks did not seem much smaller than those of the mirror scopes.

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15 minutes ago, gorann said:

30 mm aperture is like a small handheld binocular.  It cannot be that bad so I must miss something here about what aperture here means. Also, what about the Tak apos, their airy disks did not seem much smaller than those of the mirror scopes.

30mm of aperture in terms of resolution - not in terms of light gathering power. That is really not that bad resolution when we talk about long exposure imaging.

Sure, such telescope would not produce excellent images of Saturn or Jupiter - more something along this lines:

image.png.bb03d1cf75a548bf03d6945e1996304b.pngimage.png.f30e52c3439b5d64e4d9b797515eb1f5.png

This got me thinking - what is equivalent aperture of resolution when we add in the seeing?

image.png.3095ef4c2c1324489d71497c52ad99e1.png

Left is actual perfect aperture expressed in mm in 2" seeing and 1" RMS guide error - right is equivalent aperture - pure resolving power (again in mm).

As you can see, perfect 80mm scope in 2" seeing and 1" RMS guiding will resolve the same as 33.1mm of aperture with no atmosphere influence and with perfect tracking. 250mm scope won't resolve much more as with 2" seeing and 1" RMS guiding - we are entering domain that is seeing/guiding limited.

With Tak apos - actual airy disks are about twice as big as airy disks of 200mm scopes - since they are only ~100mm in diameter. Same spot diagrams means that in case of Taks - they are twice "as condensed" with respect to perfect aperture.

In order to fully compare spot diagrams of two scopes in terms of resolution - you need to scale them to same Airy disk size and express them in angular units. Longer focal length scope will have larger spot diagram in microns - not because it is of lesser quality - but because it magnifies more.

 

 

 

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3 minutes ago, vlaiv said:

30mm of aperture in terms of resolution - not in terms of light gathering power. That is really not that bad resolution when we talk about long exposure imaging.

Sure, such telescope would not produce excellent images of Saturn or Jupiter - more something along this lines:

image.png.bb03d1cf75a548bf03d6945e1996304b.pngimage.png.f30e52c3439b5d64e4d9b797515eb1f5.png

This got me thinking - what is equivalent aperture of resolution when we add in the seeing?

image.png.3095ef4c2c1324489d71497c52ad99e1.png

Left is actual perfect aperture expressed in mm in 2" seeing and 1" RMS guide error - right is equivalent aperture - pure resolving power (again in mm).

As you can see, perfect 80mm scope in 2" seeing and 1" RMS guiding will resolve the same as 33.1mm of aperture with no atmosphere influence and with perfect tracking. 250mm scope won't resolve much more as with 2" seeing and 1" RMS guiding - we are entering domain that is seeing/guiding limited.

With Tak apos - actual airy disks are about twice as big as airy disks of 200mm scopes - since they are only ~100mm in diameter. Same spot diagrams means that in case of Taks - they are twice "as condensed" with respect to perfect aperture.

In order to fully compare spot diagrams of two scopes in terms of resolution - you need to scale them to same Airy disk size and express them in angular units. Longer focal length scope will have larger spot diagram in microns - not because it is of lesser quality - but because it magnifies more.

 

 

 

Very interesting comparison Vlaiv. If I get it right, the Tak FSQ 106 f/5 has about the same resolving power that the RASA 8 f/2, but then needs 4 times longer to gather the same amount of photons (counting aperture area) or even 6-times as counted from f-value. They weigh the same but the FSQ 106 costs 3.3 times more.

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8 minutes ago, gorann said:

Very interesting comparison Vlaiv. If I get it right, the Tak FSQ 106 f/5 has about the same resolving power that the RASA 8 f/2, but then needs 4 times longer to gather the same amount of photons (counting aperture area) or even 6-times as counted from f-value. They weigh the same but the FSQ 106 costs 3.3 times more.

Ok, now we have to be careful. If you want to see if Tak will have the same pure resolving power - you need to scale their spot diagrams accordingly.

Let's go and do that for better understanding. First - we need to scale diagrams in to same units:

We need to enlarge Tak spot diagram by factor of 100/18 = 5.555 because of scale of things - it has size of square 100µm while Rasa one has 18µm.

Then we have to reduce size of Tak spot diagram by factor of 530 / 400 if we want to adjust for focal lengths and convert to angles. We need to enlarge it to 419%.

At 11mm it has about 20% larger red (~700nm) spot diagram:

image.png.af587022e7af700017c755d421affcc6.png

So yes, it has about the same resolving power - without impact of atmosphere and guiding. If you throw that into the mix - it will only even things out further. Just remember - these are design specifications, not manufacturing ones. Which one has the reputation for better manufacturing of optics (to a higher standard - closer to the actual specs?).

Is it really slower than RASA? Depends on what you want to image. RASA8" will accept about 22-23mm imaging circle (I know it says up to 28 - but let's go with "sharp" field - for the sake of argument). Tak will illuminate 44mm diagonal.

If you are imaging very wide target - the will have the same speed. Tak has about 1/4 of light collecting surface, but RASA will need 2x2 mosaic. If you match sampling rate - they will be roughly the same in "speed". Rasa will image each panel 1/4 of the time with x4 higher light gathering.

If you image just narrower field of view provided by 22mm of RASA8" - then RASA is indeed about x4 faster.

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56 minutes ago, vlaiv said:

Ok, now we have to be careful. If you want to see if Tak will have the same pure resolving power - you need to scale their spot diagrams accordingly.

Let's go and do that for better understanding. First - we need to scale diagrams in to same units:

We need to enlarge Tak spot diagram by factor of 100/18 = 5.555 because of scale of things - it has size of square 100µm while Rasa one has 18µm.

Then we have to reduce size of Tak spot diagram by factor of 530 / 400 if we want to adjust for focal lengths and convert to angles. We need to enlarge it to 419%.

At 11mm it has about 20% larger red (~700nm) spot diagram:

image.png.af587022e7af700017c755d421affcc6.png

So yes, it has about the same resolving power - without impact of atmosphere and guiding. If you throw that into the mix - it will only even things out further. Just remember - these are design specifications, not manufacturing ones. Which one has the reputation for better manufacturing of optics (to a higher standard - closer to the actual specs?).

Is it really slower than RASA? Depends on what you want to image. RASA8" will accept about 22-23mm imaging circle (I know it says up to 28 - but let's go with "sharp" field - for the sake of argument). Tak will illuminate 44mm diagonal.

If you are imaging very wide target - the will have the same speed. Tak has about 1/4 of light collecting surface, but RASA will need 2x2 mosaic. If you match sampling rate - they will be roughly the same in "speed". Rasa will image each panel 1/4 of the time with x4 higher light gathering.

If you image just narrower field of view provided by 22mm of RASA8" - then RASA is indeed about x4 faster.

When you say the RASA will have to make a 2x2 mosaic, then I get a bit confused. Do you mean that you have a camera with a 44 mm diagonal on the Tak, so a full frame APS? Then, taking the FL into account the FOV is still not that different. Here is a comparison of the Tak with an ASI6200 (44 mm diagonal) and the RASA 8 with an ASI2600 (28 mm diagonal):

Skärmavbild 2020-12-20 kl. 19.38.32.png

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Just now, gorann said:

When you say the RASA will have to make a 2x2 mosaic, then I get a bit confused.

Except I used 22mm that are fully corrected according to Celestron and we have comparing spot diagram of. Allow for 10% in overlap with mosaic and that is roughly the same FOV - Tak and FF sensor vs RASA8" 2x2 4/3 sensor

image.png.f53ea937cec51f9900cc6aa755690b8d.png

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Not sure what fully corrected means here - the spot diagrams suggest to me that is a rather arbitrary concept. In any case, if you turn the ASI1600 90° then two panels would approximately cover the same FOV, and 4 panels would certainly cover much more.

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33 minutes ago, gorann said:

Not sure what fully corrected means here - the spot diagrams suggest to me that is a rather arbitrary concept. In any case, if you turn the ASI1600 90° then two panels would approximately cover the same FOV, and 4 panels would certainly cover much more.

You are probably right. In any case - RASA8" seems like greater value - maybe only limited by the fact that camera needs to be in front and mono with filters would be awkward to use.

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2 minutes ago, vlaiv said:

You are probably right. In any case - RASA8" seems like greater value - maybe only limited by the fact that camera needs to be in front and mono with filters would be awkward to use.

Yes Valiv, the RASA is cetainly aimed for use with a OSC for RGB or when the moon (or light pollution) is an issue with a OSC and either a dual (or triple?) band filters or a filter slider for NB.

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