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Microlens diffraction effect explained

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#1 spokeshave

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Posted 07 October 2018 - 06:34 PM

I thought my camera was immune to this effect since after two years of use, I had never encountered it, despite imaging some very bright stars, including Alnitak. But alas, I was struck by the microlens diffraction affliction while imaging gamma cass:

microlens.jpg

In this case, there are some very interesting aspects to the pattern. Very clearly, there are concentric diffraction rings in each of the diffraction spots - as if they were out-of-focus stars. I had not seen this before. This is an integration of 206 600-second Ha subs so the data is pretty clean.

Another interesting aspect is that the pattern is so consistent between subs, despite a heavy dither. If this were a reflection artifact from the microlenses, one would expect the artifacts to move around as the star falls in the microlenses differently after each dither. So, my conclusion was that it is a diffraction artifact, not a reflection artifact.

So I did some literature searching and found the answer. This is, in my opinion, the Talbot effect, first observed by Henry Talbot in 1863. Talbot observed that when light is incident upon a diffraction grating, the image of the grating repeats at a distance (or multiple of) called the Talbot length defined as:

Zt = 2a^2/lambda

Where "a" is the grating spacing and "lambda" is the light wavelength. As applied to microlenses, here is my take. The Talbot effect would form a reflected Talbot image the Talbot length in front of the sensor. In my case, the "grating" spacing is 3.8u or 3800nm and lambda is 656nm. The Talbot length is then 44,000nm or 0.044mm. So, the Talbot effect is forming an image of the microlenses about 0.044mm above the sensor plane. Another Talbot image is created at every additional Talbot length between the sensor and the cover glass. These images are then reflected off of the sensor cover glass and imaged by the pixels. However, these images are out-of-focus by the distance from the Talbot image, reflected off of the cover glass and back to the sensor. So, the Talbot image closest to the cover glass forms the smallest artifact, and those closer to the sensor form the larger ones.

At least that's my take on it. I need to do some more research on the Talbot effect, but I think this is the right track. In fact, there is a paper that I am studying now that discusses the Talbot effect on microlenses:

https://www.suss-mic...onal_Talbot.pdf

So, at least we now have a name for it.

Tim
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#2 TOMDEY

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Posted 07 October 2018 - 07:02 PM

Microlens array allows the chip-makers to claim a nearly 100% "Fill Factor" and then high QE. But, it comes at a price: >>>

 

Yep! Some people (most of us?!) almost entirely forget that those microlenses are ON there! ... until we see artifacts.

 

Another, also oft unnoticed effect is that, if you try to feed the array with a Too-Fast Feed... It will reject the fast/oblique edge rays to adjacent elements or entirely away. Once you go faster than F/4... it becomes problematic / diminishing returns / increasing stray light.

 

As with all this stuff, I point out Emmy Noether's Theorem. No free lunch! In this case, you can't increase the fill-factor without Having To (proportionally) restrict the usable F#. It's Not a design failure; it's dictated by Nature!  Tom

 

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#3 Der_Pit

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Posted 08 October 2018 - 07:02 AM

The only objection I'd have after a quick glance would be that the Talbot effect is for a plane wave, i.e., parallel light, whereas we are in the focal plane.  So you would at least expect deviations from the formula as to where the talbot planes are located.

 

But definitely a nice investigation/finding  waytogo.gif



#4 sharkmelley

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Posted 17 November 2018 - 01:43 PM

I've only just noticed this thread.  Tim, your image is the best example of this microlens diffraction pattern that I've ever seen!  It's a very useful observation you make that "there are concentric diffraction rings in each of the diffraction spots - as if they were out-of-focus stars."

 

I hadn't heard of the Talbot effect before but it seems to be a self imaging  effect of a 1D or 2D array.   In that sense it does have a similarity to this microlens diffraction artifact, which might also be a kind of self imaging effect.

 

But there is a very important difference.  The Talbot effect causes a self image at the same spacing as the original or a smaller spacing than the original.  Instead of this, the image we are seeing with this microlens diffraction has a hugely magnified spacing.   It is not simply an out of focus version of one of the images at a multiple of the Talbot length.

 

In short, I find it impossible to bridge the gap between the Talbot effect and the greatly magnified version we see in this microlens diffraction effect.

 

Mark


Edited by sharkmelley, 17 November 2018 - 06:52 PM.

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#5 Mike Clemens

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Posted 20 November 2018 - 09:43 PM

...2060 minutes of the Gamma Cass nebula is on the way?!?



#6 spokeshave

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Posted 20 November 2018 - 10:57 PM

...2060 minutes of the Gamma Cass nebula is on the way?!?


Final version:

get.jpg?insecure

Tim
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#7 sharkmelley

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Posted 21 November 2018 - 01:05 AM

Final version:

 

That's a beautiful final version!

 

Astrobin indicates you used the Tak FSQ106EDX4.  Was it at the native focal length of 530mm and at f/5?  Does the H-alpha filter restrict the effective aperture in any way?  The QHY163M has a pixel pitch of 3.8microns - you already said that.

 

Knowing this will allow the spacing of the diffraction pattern to be calculated.  Given your excellent diffraction pattern above, this can be done a lot more accurately than attempts with previous microlens diffraction patterns.

 

Mark


Edited by sharkmelley, 21 November 2018 - 01:07 AM.

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#8 evan9162

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Posted 21 November 2018 - 01:57 AM

Here's my Gamma Cass diffraction pattern:

 

GammaCas.jpg

 

Celestron C80ED, Teleskop Express 0.79x reducer (for 480mm F/6), Astronomik 6nm Ha filter, ASI 178mm-c (2.4um).  19x600s@gain 200

 

The filters are fairly close to the camera (25-30mm sensor to filter).  Not sure if that has any impact on this effect at all...

 

 


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#9 spokeshave

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Posted 21 November 2018 - 08:00 AM

That's a beautiful final version!
 
Astrobin indicates you used the Tak FSQ106EDX4.  Was it at the native focal length of 530mm and at f/5?  Does the H-alpha filter restrict the effective aperture in any way?  The QHY163M has a pixel pitch of 3.8microns - you already said that.
 
Knowing this will allow the spacing of the diffraction pattern to be calculated.  Given your excellent diffraction pattern above, this can be done a lot more accurately than attempts with previous microlens diffraction patterns.
 
Mark


Mark:

This is at the native 530mm, f/5. The H-a filter is 5nm and 36mm. There should be no vignetting or effective aperture reduction.

Tim

#10 sharkmelley

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Posted 21 November 2018 - 06:15 PM

Here's my Gamma Cass diffraction pattern:

 

attachicon.gif GammaCas.jpg

 

Celestron C80ED, Teleskop Express 0.79x reducer (for 480mm F/6), Astronomik 6nm Ha filter, ASI 178mm-c (2.4um).  19x600s@gain 200

 

The filters are fairly close to the camera (25-30mm sensor to filter).  Not sure if that has any impact on this effect at all...

Interesting.  The overall pattern is much more widely spaced - probably because of the smaller pixel pitch.  Some of the "discs" that form the pattern are quite elliptical, which is something I haven't noticed previously.

 

Mark



#11 evan9162

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Posted 21 November 2018 - 08:19 PM

In my image, Gamma Cass is near the lower right of the frame.  I don't quite have the correct spacing for my focal reducer, so there is still some residual field curvature - I bet that's the cause of the elliptical shape of the reflections...



#12 sharkmelley

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Posted 22 November 2018 - 02:35 PM

I've done a bit more work on this and I can now explain the geometry of the examples from both Tim (spokeshave) and evan9162.

 

The answer is a combination of the work that I did in a couple of previous threads. 

 

Here are the most relevant posts from those threads:

https://www.cloudyni...tion/?p=7542880

https://www.cloudyni...n-6d/?p=6951276  (Note the hyperbolae in the diagram)

 

I developed the mathematics from first principles (I graduated in maths from a top UK university) but I was very pleased to find out later that I was simply re-inventing the wheel.  As it happens, the theory is very similar to Laue X-ray diffraction.  Laue X-ray diffraction has similar hyperbolae, which you can see in diagram 6-2(5) on this page:

https://www.iucr.org...text/principles

But in our case we are dealing with a much longer wavelength (light instead of X-rays) and a much larger grid (CMOS/CCD pixel array instead of an atomic structure).

 

It's about time I got round to doing this because there still isn't a full explanation that I can find elsewhere.  I'll use diagrams, a bit of maths and a lot of intuition. Be patient while I prepare the explanation.  I'll even provide some PixInsight PixelMath code so you can generate your own hyperbolae.

 

Why am I talking so much about hyperbolae?  It's because the one line explanation of this microlens diffraction effect is that we are seeing a whole load of overlapping very-out-of-focus stars laid out on a hyperbolic grid.  The geometry of the grid is defined by the pixel spacing, the wavelength of the light (usually H-alpha) and the height of the reflective cover slip above the sensor plane (usually a fraction of a millimetre).

 

Stay tuned!

 

One word of warning though - even though we might end up understanding the geometry, I still can't predict when it will happen.  Using identical cameras many folk rarely (if ever) see this artefact.

 

Mark


Edited by sharkmelley, 22 November 2018 - 02:39 PM.

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#13 freestar8n

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Posted 22 November 2018 - 04:36 PM

I've done a bit more work on this and I can now explain the geometry of the examples from both Tim (spokeshave) and evan9162.

 

The answer is a combination of the work that I did in a couple of previous threads. 

 

Here are the most relevant posts from those threads:

https://www.cloudyni...tion/?p=7542880

https://www.cloudyni...n-6d/?p=6951276  (Note the hyperbolae in the diagram)

 

I developed the mathematics from first principles (I graduated in maths from a top UK university) but I was very pleased to find out later that I was simply re-inventing the wheel.  As it happens, the theory is very similar to Laue X-ray diffraction.  Laue X-ray diffraction has similar hyperbolae, which you can see in diagram 6-2(5) on this page:

https://www.iucr.org...text/principles

But in our case we are dealing with a much longer wavelength (light instead of X-rays) and a much larger grid (CMOS/CCD pixel array instead of an atomic structure).

 

It's about time I got round to doing this because there still isn't a full explanation that I can find elsewhere.  I'll use diagrams, a bit of maths and a lot of intuition. Be patient while I prepare the explanation.  I'll even provide some PixInsight PixelMath code so you can generate your own hyperbolae.

 

Why am I talking so much about hyperbolae?  It's because the one line explanation of this microlens diffraction effect is that we are seeing a whole load of overlapping very-out-of-focus stars laid out on a hyperbolic grid.  The geometry of the grid is defined by the pixel spacing, the wavelength of the light (usually H-alpha) and the height of the reflective cover slip above the sensor plane (usually a fraction of a millimetre).

 

Stay tuned!

 

One word of warning though - even though we might end up understanding the geometry, I still can't predict when it will happen.  Using identical cameras many folk rarely (if ever) see this artefact.

 

Mark

Hi Mark -

 

Yes almost all that is being seen is consistent with Laue diffraction - but you can even demonstrate most of the effects without assuming anything about diffraction and instead just see how light from a small sub-array of coheren point emitters creates a pattern on a screen some small millimeters away.  That's what I show in those threads - and it captures the hyperbolic appearance, color dependence, and the growing ellipticity and so forth.  It certainly isn't the Talbot effect for many reasons - the main one being what you pointed out - that if the array imaged itself all you would see is a uniform glow - because the light is falling back on the pixels exactly.  Another reason is that with only a small spot illluminated, any pattern would disappear after travelling only a few microns.

 

And for people who haven't seen the other threads - the entire effect is happening within the sensor itself and its coverslip - and doesn't involve other filters.  In contrast, big halos around stars are caused by filters - but that happens within the filter itself - and doesn't involve a bounce from the sensor to the filter.  So the distance to the filter doesn't matter there either.

 

Here is a company that simulates microlens diffraction - including wavefront aberrations:

 

https://www.lighttra...-apertures.html

 

and you can see the overall pattern matches what you get just with a small array of point emitters - though aberrations affect things slightly.

 

So the core effect should be no mystery at all.

 

But there are details that are hard to simulate - the main one being the f/ratio and the pupil shape.  And I'm not sure what is causing the appearance of two overlapping patterns of very different sizes.  If anyone can simulate those things I would be interested in seeing the results.  I attempted to do it by simulating the pupil illuminating a small array of emitters, which then project to a screen - but integrating over the pupil is tricky because the phase changes so rapidly.

 

Frank



#14 sharkmelley

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Posted 22 November 2018 - 06:08 PM

 

So the core effect should be no mystery at all.

 

But there are details that are hard to simulate - the main one being the f/ratio and the pupil shape.  And I'm not sure what is causing the appearance of two overlapping patterns of very different sizes.  If anyone can simulate those things I would be interested in seeing the results.  I attempted to do it by simulating the pupil illuminating a small array of emitters, which then project to a screen - but integrating over the pupil is tricky because the phase changes so rapidly.

 

Frank

Hi Frank,

 

I already know you have a very good understanding the basic geometry of this.

 

Now regarding the f-ratio, we assume that the primary image of the star is in focus at the sensor.  But if the light could pass straight through the sensor to a screen beneath it, we would see an out-of-focus star image whose diameter would be determined by the f-ratio multiplied by the extra distance travelled.  The same happens at the intersections of the hyperbolae.  At each intersection, all the wavefronts arrive in phase and therefore create an image at that point.  Each image is a duplicate of the primary image of the star but is defocused by the extra distance travelled.

 

So why do we have larger discs overlapping smaller ones?  It is clearly because the light has travelled a greater distance before reaching that point i.e. it is reflecting off a surface which is not the underside of the cover slip.  I strongly suspect this is caused by light entering the glass of the cover slip and being reflected back by the upper glass boundary instead of the lower glass boundary.

 

Mark


Edited by sharkmelley, 22 November 2018 - 06:12 PM.


#15 sharkmelley

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Posted 22 November 2018 - 06:38 PM

For the ASI178 image, here are the hyperbolae whose intersections mark the centres for the smaller discs:

 

ASI178_Hyperbola1.jpg

 

The only information required was the pixel pitch of 2.4 microns and the wavelength of H-alpha light 0.65 microns.

I then had to estimate the position of the reflective surface, which came out to be 530microns above the sensor i.e. just over half a millimetre.  So the light has to travel an extra distance of over a millimetre before it hits the sensor again.

 

Then I had to estimate the position of a second reflective surface for the large discs. It turned out to be 860microns above the sensor.  I've added the relevant hyperbolae here:

 

ASI178_Hyperbola2.jpg

 

What I don't fully understand is why the discs further from the centre of the pattern become elliptical.  I guess it is due to the shallow angle at which the in-phase wavefronts arrive at the sensor to form this disc.  At least I think that makes sense.

 

The size of the discs (or ellipses) is governed by the focal ratio of f/6 in this case, multiplied by the extra distance travelled by the light bouncing off the reflective surface and arriving at each intersection.

 

By the way, I particularly like this image as an example of the effect because the smaller pixels and slower f-ratio have the effect of spreading out the diffraction pattern and isolating the various elements a bit better.

 

Mark


Edited by sharkmelley, 22 November 2018 - 07:02 PM.

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#16 freestar8n

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Posted 22 November 2018 - 07:34 PM

Hi mark. Yes it makes sense the larger ones are going farther - but I don’t know what the other surface would be.

As for ellipticity and size of spots - that all happens without any reference to the pupil size or shape. It happens just with a small array of emitters and as the array gets bigger the spots get smaller.

The f ratio and pupil shape clearly plays a role since you often see holes in the spots from the secondary. So the two factors must be working together.

One way to view the ellipticity is that for a point in the image off a diagonal the array will appear foreshortened in distance but it will remain wide. And the wider array of emitters will make a narrower diffraction pattern in that dimension. But there is no round pupil involved in that - just a round array of emitters corresponding to the star spot on the sensor.

Frank

#17 jhayes_tucson

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Posted 22 November 2018 - 10:08 PM

I agree that the second, larger pattern is coming from a reflection off of the outer surface of the cover glass, which is 330 microns thick.  Refraction within the cover glass is probably causing that second, larger patterns to be elliptical.

 

John


Edited by jhayes_tucson, 23 November 2018 - 12:02 AM.


#18 sharkmelley

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Posted 23 November 2018 - 01:20 AM

I agree that the second, larger pattern is coming from a reflection off of the outer surface of the cover glass, which is 330 microns thick.  Refraction within the cover glass is probably causing that second, larger patterns to be elliptical.

 

John

To be more precise, the thickness of the cover glass is not 330microns (860-530) but the thickness is such that when adjusted for its refractive index gives an equivalent optical path of 330 microns in air. So the glass needs to be quite a lot thicker than 330 microns (I think!).

 

The ellipses are not caused by refraction within the glass because their positions are explained by reflection off the inner surface of the cover glass without any refraction involved.  I believe they are simply caused by the way the cone of light strikes the sensor at a shallow angle.  I know that's a "light ray" explanation of the effect rather than an explanation based on a superposition of wavefronts but I'm pretty sure we can formalise the argument.

 

I'll be able to produce more diagrams over the weekend and hopefully we'll be able to fully explain the main features of both diffraction pattern examples in this thread.

 

Mark


Edited by sharkmelley, 23 November 2018 - 01:35 AM.

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#19 freestar8n

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Posted 23 November 2018 - 01:53 AM

To be more precise, the thickness of the cover glass is not 330microns (860-530) but the thickness is such that when adjusted for its refractive index gives an equivalent optical path of 330 microns in air. So the glass needs to be quite a lot thicker than 330 microns (I think!).

 

The ellipses are not caused by refraction within the glass because their positions are explained by reflection off the inner surface of the cover glass without any refraction involved.  I believe they are simply caused by the way the cone of light strikes the sensor at a shallow angle.  I know that's a "light ray" explanation of the effect rather than an explanation based on a superposition of wavefronts but I'm pretty sure we can formalise the argument.

 

I'll be able to produce more diagrams over the weekend and hopefully we'll be able to fully explain the main features of both diffraction pattern examples in this thread.

 

Mark

The elliptical shapes happen directly just from the way a finite array of emitters interfere with each other on a screen some distance away.  I show it here:

 

https://www.cloudyni...g-and-examples/

 

That simulation makes no assumptions about diffraction or pupil or anything.  It just sums up the amplitude and phase from each emitter in a round star spot on the pixel array.

 

I'm not sure what the coverslip geometry involves - but yes you need to factor in its reduced thickness due to its refractive index.

 

The bottom of the coverslip needs to be far enough away from the microlenses to form the diffraction pattern on reflection - while the top of the coverslip forms the pattern with the larger spots.

 

I don't know of a cross section view that lets you see how these things are laid out.

 

Some sensors don't show the larger secondary image - so it seems to be sensor dependent.

 

Frank


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#20 sharkmelley

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Posted 23 November 2018 - 01:58 PM

The elliptical shapes happen directly just from the way a finite array of emitters interfere with each other on a screen some distance away.  I show it here:

 

https://www.cloudyni...g-and-examples/

 

 

I had forgotten about that thread - it's really useful. 

 

It gives me an idea actually.  Think of a sheet of rubber on which we print a rectangular grid with a circle at each intersection.  If we now stretch that sheet in a non-uniform manner to create the hyperbolae, then the same distortion will also generate the ellipses. 

 

Mathematically this is simply a coordinate transformation.  It's probably the breakthrough I need ...

 

Mark


Edited by sharkmelley, 23 November 2018 - 01:59 PM.

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#21 jhayes_tucson

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Posted 23 November 2018 - 03:20 PM

To be more precise, the thickness of the cover glass is not 330microns (860-530) but the thickness is such that when adjusted for its refractive index gives an equivalent optical path of 330 microns in air. So the glass needs to be quite a lot thicker than 330 microns (I think!).

 

The ellipses are not caused by refraction within the glass because their positions are explained by reflection off the inner surface of the cover glass without any refraction involved.  I believe they are simply caused by the way the cone of light strikes the sensor at a shallow angle.  I know that's a "light ray" explanation of the effect rather than an explanation based on a superposition of wavefronts but I'm pretty sure we can formalise the argument.

 

I'll be able to produce more diagrams over the weekend and hopefully we'll be able to fully explain the main features of both diffraction pattern examples in this thread.

 

Mark

Mark,

I was in a hurry.  Yes, I agree that 330 microns is the optical thickness of the window; not the mechanical thickness.  I completely agree that the geometry that creates the hyperbolas plays a role in the shape of the patterns; but, because of the large angles of incidence, I believe that if you ray trace the reflection off the outer surface of the window, you'll find that the index plays a role as well.  Maybe it's a small effect but I haven't done any serious analysis so I can't say for sure.  I look forward to seeing what you come up with.

 

John


Edited by jhayes_tucson, 23 November 2018 - 03:21 PM.


#22 sharkmelley

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Posted 24 November 2018 - 09:41 AM

At last, here are the results (split across two posts).

 

Firstly the ASI178. 

 

Here are the Laue diffraction hyperbolae and the defocused stars for the reflection that we assume comes from the lower surface of the cover slip:

 

ASI178_Diffraction1.jpg

 

 

The geometry is determined by the pixel pitch (2.4microns), the wavelength of H-alpha (0.65microns).  The height of the cover slip (520microns) had to be determined to fit the pattern.  The size of the discs formed by the defocused stars is determined by the focal ratio of the optics i.e. f/6.

 

The pattern for the larger discs comes from a reflector 850microns (optical equivalent) above the sensor - probably the upper surface of the cover slip:

 

ASI178_Diffraction2.jpg

 

 


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#23 sharkmelley

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Posted 24 November 2018 - 09:43 AM

I've done the same for the QHY163 from the original post. Firstly I halved the scale to get it back to 1:1 scaling.  Here's the pattern for the smaller discs, which come from the lower surface reflection:

 

QHY163_Diffraction1.jpg

 

 

Here I've added the pattern for the larger discs, which come from the upper surface reflection:

 

QHY163_Diffraction2.jpg

 

The parameters used were:

  • pixel pitch:    3.8 microns
  • wavelength:  0.65 microns
  • focal ratio  f/5
  • cover slip surface heights: 600 microns and 1025 microns

 

You'll notice that the red pattern is slightly offset from the green pattern for both this and the ASI178 patterns.  This makes complete sense if the star was off-centre in the image and therefore the primary ray was not orthogonal to the sensor.

 

I generated those patterns using PixInsight.  Here's the code for generated the green pattern for the ASI178 image:

Attached File  MicrolensDiffractionCode.txt   3.96KB   42 downloads

 

Open the PI script editor, create a new JavaScript Source File and paste this code into the window.  It can be executed by pressing the "red lightning" icon in the script editor - it will prompt you to save the .js file first.

 

If you don't have PixInsight then it's still worth looking at the code, it's surprisingly straightforward.

 

Mark


Edited by sharkmelley, 24 November 2018 - 09:47 AM.

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#24 jhayes_tucson

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Posted 24 November 2018 - 10:41 AM

That's outstanding Mark!  Very well done.

 

John


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#25 freestar8n

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Posted 24 November 2018 - 06:24 PM

I've done the same for the QHY163 from the original post. Firstly I halved the scale to get it back to 1:1 scaling.  Here's the pattern for the smaller discs, which come from the lower surface reflection:

 

 

 

 

Here I've added the pattern for the larger discs, which come from the upper surface reflection:

 

 

The parameters used were:

  • pixel pitch:    3.8 microns
  • wavelength:  0.65 microns
  • focal ratio  f/5
  • cover slip surface heights: 600 microns and 1025 microns

 

You'll notice that the red pattern is slightly offset from the green pattern for both this and the ASI178 patterns.  This makes complete sense if the star was off-centre in the image and therefore the primary ray was not orthogonal to the sensor.

 

I generated those patterns using PixInsight.  Here's the code for generated the green pattern for the ASI178 image:

 

 

Open the PI script editor, create a new JavaScript Source File and paste this code into the window.  It can be executed by pressing the "red lightning" icon in the script editor - it will prompt you to save the .js file first.

 

If you don't have PixInsight then it's still worth looking at the code, it's surprisingly straightforward.

 

Mark

Hi Mark-

 

Nice work - that looks good.  And it answers my question on how f/ratio plays a role.  What I was doing was looking at the pattern formed by a single point in the pupil - and much of the pattern and hyperbolic shape emerges directly from that - but you don't see the shape of the pupil.  I had tried integrating over the pupil coherently - but you are effectively showing an incoherent image formed by the diffraction from all points in the pupil - which actually makes sense.  So I will see if I can modify my code to do that extra integral.

 

Can you explain the 1+4*fratio^2 term in your radius expression?  The 1 doesn't make a big difference at f/6 but I'm not sure why it's there.

 

Frank




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