Jump to content

Narrowband

MTF of a telescope


Recommended Posts

@alex_stars

It looks like I'm right about time scaling when edge is tilted at an angle.

Here is what I've done - I generated two edges, one vertical, one diagonal - convolved both with PSF generated from clear aperture and differentiated both in X direction.

Then I took crop of each 1px tall and wide enough (around 400px each) and I performed FFT on both. I scaled result and printed on the same graph - this is what I got:

image.png.3b490f6e4acc19230c25896d7b620bab.png

Now, if I'm right - cutoff frequency between these two graphs should differ by ~1.41 (square root of two). We have one being at about 127 and other being at about 90.

127/90 = 1.4111111 - that is actually very good match for eyeballing numbers of the chart.

This means that curved edge that is averaged is going to produce issue - it will average MTFs with different scaling factors. I think that the end result is just "averagely" scaled MTF since FT has property of linearity (so FT of average of functions is average of FT of functions) - in any case, this makes cut off frequency inaccurate if line is at an angle.

In above example where you had different cut off frequency, did your software tilt the edge?

Link to comment
Share on other sites

It looks like I was right about under sampling as well

I'm not sure that I fully understand this graph - I was expecting different kind of cut off, but here is result:

image.png.ee20b5a047c9ef19084e5802fcc19f91.png

This graph is created in following way - I took edge, convolved it with PSF that is just properly sampled, differentiated it and then I binned x2 the result which would make it under sampled and did FFT.

Graph no longer hits the 0. I was not expecting it to keep the shape (fact that it has two sides is just due to line for profile - I did not bother to start at center - I just measured across the whole image).

If this is so - then I don't think we have viable method for amateurs to use - scopes that are F/6 for example would need ~1µm pixel size to properly sample without a barlow - and there are no such cameras.

  • Like 1
Link to comment
Share on other sites

9 hours ago, vlaiv said:

If this is so - then I don't think we have viable method for amateurs to use - scopes that are F/6 for example would need ~1µm pixel size to properly sample without a barlow - and there are no such cameras.

Interesting point you catch up on. Look just for the sake of argument and as you put in sooo much energy to prove things, I decided to run my real world edge data without super-resolution.

Here is the aligned edge data, you can see it gets quite nicely aligned, so the 1D FFT is valid, it is a 1D problem.

for_vlaiv_08.png.16d36fefd5bf8a2523a2d8aae02bd34f.png

I do the whole processing without super-resolution and without any interpolation whatsoever (happy?) So we  we get this graph for the MTF.

for_vlaiv_07.png.b5d3657cc4bc7534dc9191a2e47b34b5.png

The green one is completely correct, I have even re-assessed my pixel scale of my camera, so that is spot on where theory tells us the MTF should be. To be correct I had to switch to 600 nm wavelength as this is the wavelength my camera has the highest QE, so just being fair to the sensor.

As you can see the measured MTF eventually goes down to zero. As it should, BUT. More importantly it does so at a different location than the theoretical one.

And now comes the really important part for us amateur astronomers. When we take images with our cameras, we sample the world with the sensors we put on the back of our scopes. They HAVE way to coarse pixel dimensions  to sample an MTF completely.

As you finally seem to agree with me, the red curve from about X=0.25 onward to the left is under-sampled (thus quite useless), because our sensors (even the fancy ones with about 2 mu-m pixels) are way too bad to sample the full spectrum.

How does this translate to our scopes, their design and central obstructions?

Well in my case it does not matter if I image with my Mak or with a 125 mm unobstructed APO, I will be able to sample about the same scales properly. The really fine details I always undersample. Not because  the scope is bad, it's because of the camera I have.

And now you might as, whats about the fancy images one sees with a C14?

I will show you in my next post.

 

 

Link to comment
Share on other sites

While following the broad outline of your discussion I have not reviewed the details.

However, the recent comments on sampling reminded me that formally the MTF only applies to "shift invariant systems" and as I am sure you both know CCD detectors are not shift invariant as the result depends on where the image fall even with Nyquist sampling.

Regards Andrew 

  • Like 1
Link to comment
Share on other sites

50 minutes ago, alex_stars said:

Here is the aligned edge data, you can see it gets quite nicely aligned, so the 1D FFT is valid, it is a 1D problem.

With that image, here is what I got for MTF:

image.png.b025bd9f1d23d0a76af9ec9c584c85f8.png

I did it the same way I've done it every time so far:

- take image, convert to 32bit (in this case since it is 8bit)

- run differentiation filter

- crop to important bit

image.png.3cdc6dd5ecd682d3db967a435a383f88.png

Then I run 2D FFT on that and get this as a result:

image.png.d3d854062165b68b8e9bf72ac4821599.png

According to theory, at 600nm and 3.75µm pixel size, optimum sampling rate (provided that you used ASI224 in your signature and that you used all pixels in 600nm - not just red channel) is F/12.5. Your scope at F/15 is properly sampled and it shows from MTF.

  • Like 1
Link to comment
Share on other sites

49 minutes ago, jetstream said:

Do you lose detail this way? at what f ratio are you sampling and what are you imaging?

Somewhat, as we have discussed, we definitely loose contrast. My main point is that we have a hard time utilizing the really high spatial resolutions when we image, so we might not have to worry too much what happens in the different scope designs at the very right side of the MTF graphs. Something like that.

The image I used has been taken at f/15 of my Mak, so at about 2700 mm. I am aware of the fact that I could increase the pixel scale, use a barlow and such... But I just wanted to make a point about possible sampling of the MTF when we use a scope in real life.

I took an image of a black edge on white background, so a high contrast target (I posted the image earlier) and that was 170 m away of the scope, across a meadow in early morning, to keep atmospheric disturbance small.

  • Like 1
Link to comment
Share on other sites

22 minutes ago, andrew s said:

However, the recent comments on sampling reminded me that formally the MTF only applies to "shift invariant systems" and as I am sure you both know CCD detectors are not shift invariant as the result depends on where the image fall even with Nyquist sampling.

Thanks for reminding us on that. I think it was not mentioned yet in the discussion.

Link to comment
Share on other sites

1 minute ago, vlaiv said:

I wonder why we keep getting different results? Although, we did get the same curve from synthetic data, right?

Do we? I think we are converging with our results. Which I appreciate. Let me post a graph of my MTF with pixel scale soon. Today its late and I won't be online until Monday, but I will post the graph then.....

Link to comment
Share on other sites

On 06/02/2021 at 20:26, alex_stars said:

Do we? I think we are converging with our results. Which I appreciate. Let me post a graph of my MTF with pixel scale soon. Today its late and I won't be online until Monday, but I will post the graph then.....

Well, this last one is pretty similar except for two things.

Your is slightly more noisy (which is strange since we use the same data) and "overshoots" critical sampling. Mine is right up to critical sampling.

Btw, distance between mirrors in Maksutov system alters effective focal length (so it might be operating on slightly lower FL) and also can introduce spherical aberration. Not sure where focal point of Mak180 is placed (optimized for 1.25" or 2" diagonal) but since this is close focusing - mirrors will be further apart than usual?

I was thinking of doing the same with my ST102 SkyMax102.

Use Ha filter and ASI1600 (with 3.8µm pixel size) and shoot both straight edge and do Roddier test with artificial star (at the same distance so I get comparable results even if they contain some SA due to close focus).

Edited by vlaiv
  • Like 1
Link to comment
Share on other sites

Well, I'm planing a test on my SkyMax 102 - to both measure and verify this method with straight edge - not sure when I'll have both time and means to do it (hopefully soon).

Anyone wanting to try this method at home - I can walk them thru ImageJ usage - or even do it for them if they post their results here.

Recording part is straight forward - take your scope, find high contrast very straight edge at some distance (say minimum x20 focal length of your scope). Make sure edge itself is not blurred but very sharp and very straight and capture some images of it. If you can - use dedicated camera, if not, maybe even mobile phone at eyepiece could work?

I did not even think of that - but it would be interesting to see MTF of complete combination - scope + eyepiece. One just needs phone adapter to snap image.

Use high power eyepiece (does not need to be wide field) to have good sampling rate so that we don't loose high frequency portion of MTF due to under sampling. Take another shot of anything that we can use to calculate sampling rate. Maybe shoot ruler and also measure distance to the target (as precisely as you can).

Ok, so here is complete idea:

- Take straight sharp edge target (it can be just printed on a piece of paper). It is important that edge is high contrast and of uniform color (black / white), that edge is very sharp with no blurring of its own and that it is straight.

- measure distance to target as best as you can

- Take image of the target with high power eyepiece and your mobile phone (use adapter as any shake will void results) - also make sure your phone has good focus

- Take additional image in same configuration (same distance, same eyepiece, etc ...) of something of known length - maybe a good ruler or similar - so we can calculate sampling rate in given configuration.

From that data we can derive actual MTF or your scope + eyepiece and compare it to theoretical scope MTF?

  • Like 2
Link to comment
Share on other sites

5 hours ago, vlaiv said:

did not even think of that - but it would be interesting to see MTF of complete combination - scope + eyepiece. One just needs phone adapter to snap image.

I'm waiting for the TC Fonemate... I am very interested in seeing actual whole system MTF,extremely interested. Distance is from the calculator as discussed Vlaiv?

Link to comment
Share on other sites

37 minutes ago, jetstream said:

I'm waiting for the TC Fonemate... I am very interested in seeing actual whole system MTF,extremely interested. Distance is from the calculator as discussed Vlaiv?

Phone at eyepiece is not as easy to calculate. You want sampling rate to be able to produce accurate MTF (properly scaled for cut off frequency - general shape will be the same), and you also want to make sure you are not under sampling but rather oversampling (in this test it is ok to over sample).

Issue with phone is that you don't have phone lens focal length and often you don't have pixel size of your mobile phone - that leaves us with only measuring sampling rate by shooting object of known dimensions at known distance.

Otherwise, for spherical aberration - same rules apply - you need to place it at large enough distance for spherical to be minimized. You don't have to do it - you can test with that spherical term, if you want to see close focus performance of your scope or you can make comparison ideal MTF to contain spherical term as well - just to compare things (but again - you can't tell how much spherical to introduce without measuring).

I think I'll get myself that phone adapter as well. There is another project where I might need it - EEVA with smart phone thing.

  • Like 1
Link to comment
Share on other sites

2 minutes ago, vlaiv said:

I think I'll get myself that phone adapter as well. There is another project where I might need it - EEVA with smart phone thing.

Excellent!

I wish you better luck in acquisition than me Vlaiv. I have a long list of dreams atm (camera, etc etc) with no hope in site.

Link to comment
Share on other sites

Forgot to post.

For anyone interested in playing around with scope parameters and generating MTF - there is Aberrator: http://aberrator.astronomy.net/

It will pretty much do automatically what I do in ImageJ - given set of parameters it will generate various things for you:

image.png.5edae2bbde442a4690873324ed89ed66.png

One of the reasons I'm interested in all of this is to make modern version of Aberrator (last version is 3.0 from 2002 if I'm not mistaken)

  • Like 2
Link to comment
Share on other sites

22 hours ago, vlaiv said:

Ok, so here is complete idea:

- Take straight sharp edge target (it can be just printed on a piece of paper). It is important that edge is high contrast and of uniform color (black / white), that edge is very sharp with no blurring of its own and that it is straight.

- measure distance to target as best as you can

- Take image of the target with high power eyepiece and your mobile phone (use adapter as any shake will void results) - also make sure your phone has good focus

- Take additional image in same configuration (same distance, same eyepiece, etc ...) of something of known length - maybe a good ruler or similar - so we can calculate sampling rate in given configuration.

From that data we can derive actual MTF or your scope + eyepiece and compare it to theoretical scope MTF?

SO I see you are now recommending the edge detection method for estimating the MTF. Great! Mission accomplished. 😀

Is there anything left for us to sort out?

I don't think it is very interesting for everybody to continue the discussion of our curves, I can scale mine to look exactly like yours and that is not very amazing. Actually expected. If people code their programs in Python, because they can or if they use ImageJ is beside the topic of this thread, don't you agree?

I look very much forward to see your results from the 102 Skymax and how it compares to theoretical curves.

Since you use ImageJ, I was wondering if you are aware of the plugin that exists which performs that task. Never tried it myself, but looks decent.

Slanted Edge MTF ImageJ

I prefer to code in Python....

Edited by alex_stars
  • Like 1
Link to comment
Share on other sites

On 04/02/2021 at 15:58, jetstream said:

How much is that optics testing camera set up Andrew?

Well I did get a quote of the Skack Harrtmann telescope setup of €4700 to which you have to add import duty and VAT so out of my league.

Pity regards Andrew

  • Like 1
Link to comment
Share on other sites

1 hour ago, alex_stars said:

Is there anything left for us to sort out?

Well, I would like to explore what sort of results do we get from under sampled data.

There is well known drizzle algorithm that deals with this in imaging, but I believe it is often misused since people don't have control over dither step and I don't think it works good for random dither (original Hubble documentation implies that telescope is precisely pointed for dithers of a fraction of pixel - like 1/3 pixel dithers)

In this case - we can use edge at an angle to give us wanted consistent dithering step - but we need to compensate for the fact that edge is tilted.

I'm wondering if you implemented drizzle bit - or anything similar in your python code?

Method that I proposed above with afocal and mobile phone - will mix in both optical properties of eyepiece and phone lens (although not sure how much at that scale will be picked up) - but it will provide wanted sampling rate. Camera in prime focus is likely to under sample.

If we want a method that is reliable and easy for amateurs to use - we need to explore both options.

  • Like 1
Link to comment
Share on other sites

@alex_stars

I think that we are not yet close of having proper working method for this.

For your test data from few posts ago, this is what you got:

for_vlaiv_07.png

This is what I've got with 2D fft approach:

image.png.d4acba4af428cb883ca9c7310f6a5abd.png

and this is what ImageJ plugin that you linked above produces (plugin is a bit buggy - sometimes it works and sometimes it does not - not sure if selection size has something to do with it):

image.png.b2347e0ce6192634d818619aebc3b871.png

Their curve is much smoother and much more sagging.

 

Link to comment
Share on other sites

I figured out why plugin was not working - it requires dark side of edge to be located on left side of the image.

Here are results of perfect PSF for clear aperture at edge of sampling frequency - synthetic data, it should be the same, but it is not:

image.png.782a980dcec9386d80523fa34dd45ca2.png

Top one is plugin, bottom one is standard approach that I've been using (directly derived from math).

  • Like 2
Link to comment
Share on other sites

5 hours ago, andrew s said:

Well I did get a quote of the Skack Harrtmann telescope setup of €4700 to which you have to add import duty and VAT so out of my league.

Pity regards Andrew

I wonder if the the test results from one would be held in high regard? I'd buy one if I could test a few scopes to pay for it and I could have my own fracs tested by an optician I know, for comparison and reference with regards to accuracy. The exchange rate is in the wrong direction for me...

Does this set up do mirrors?

  • Like 1
Link to comment
Share on other sites

Create an account or sign in to comment

You need to be a member in order to leave a comment

Create an account

Sign up for a new account in our community. It's easy!

Register a new account

Sign in

Already have an account? Sign in here.

Sign In Now
  • Recently Browsing   0 members

    • No registered users viewing this page.
×
×
  • Create New...

Important Information

We have placed cookies on your device to help make this website better. You can adjust your cookie settings, otherwise we'll assume you're okay to continue. By using this site, you agree to our Terms of Use.