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How to calculate depth of vignetting?

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#1 astrovienna

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Posted 22 February 2020 - 10:37 PM

I've seen several online calculators that show whether vignetting will happen with a certain combination of f-ratio, sensor diagonal, distance from sensor and size of opening.  But I haven't found any tool to quantify that vignetting:  at what radius on the sensor does it begin, and how deep (% light loss) does it get on the edges of the sensor?  Does anyone know how to do this?

 

I'm trying to plan out an ASI6200 or QHY600 on a short-focus newtonian, and it would help me decide on a coma corrector and positioning of the other components if I could figure this out in advance.  Thanks.

 

Kevin



#2 TOMDEY

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Posted 22 February 2020 - 11:38 PM

I'm sure there are software aps that will do that prediction for you... but the fundamental starting point, that should capture most of the effect is what we optics guys call "cos fourth vignetting" ... You just draw Apparent Field lines from the center of your lens's exit pupil to various zones on your sensor and the illumination drops off as cos4 of that zone's apparent field angle. That's the lion's share; Simple as that.

 

BUT: There are myriad things that can exacerbate or mitigate that starting approximation:

 

>The exit pupil may morph/distort/shrink/enlarge/migrate as a function of field angle, which will boost or reduce vignetting impact

>Your sensor may be less sensitive to oblique flux. Especially true of CCD and CMOS comprising lenticular arrays, exacerbating vignetting

>Some lenses further comprise intermediate stops and element edges that clip objectionably-aberrated oblique rays, but exacerbating vignetting

>Coatings are less efficient at oblique angles, exacerbating vignetting

 

Stuff like that... Flats auto-address all of those, to the extent possible...

 

 apparent half-field       simplistic illumination

  seen by sensor               cos4 vignetting

 

       0 deg                               100%

       1                                      99.9

       2                                      99.8

       3                                      99.5

       4                                      99.0

       5                                      98.5

      10                                     94.1

      15                                     87.1

      20                                     78.0

      25                                     67.5

      30                                     56.2

      35                                     45.0

      40                                     34.4

      45                                     25.0

 

Image-space telecentric lenses entirely mitigate this by simply placing the exit pupil at infinity. Many lenses substantially mitigate this by distorting the exit pupil larger, as the image-space field angle becomes more oblique. Take a fisheye lens and hold it at arm's length as you tilt it; you will see the pupil bloom larger with angle.    Tom                          



#3 astrovienna

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Posted 23 February 2020 - 07:47 AM

Tom, thanks for the reply.  The effect I'm trying to calculate is for obstructions.  The imaging setup I'm looking at has constricted openings at various distances from the sensor.  For example, the front surface of the filters, with a 48mm opening (being optimistic), is 22.5mm from a sensor (IMX455) with a 43.3mm diagonal.  If I try to put an f/3.8 light cone through that path, my calculations show it will vignette since the maximum should be f4.79.  But I don't know to quantify the depth of the vignetting.



#4 vehnae

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Posted 23 February 2020 - 10:29 AM

Here is a sample of a f/3,8 light cone (f/4 mirror + ASA 0,95x corrector) being constricted by a M54 adapter on the filter wheel with 50,4mm of free aperture 42,3mm away from the sensor. I measured the extreme corners to have 50% vignetting. So once the mechanical vignetting kicks in it's fairly severe.

 

Since taking this picture I bolted my filter wheel directly to the camera and to my M68 tilt adapter, which got rid of all mechanical vignetting. But since the wheel was made by Atik it required a bit of creative drilling and tapping :-). According to my calculations I should be good up to f/3.

 

  ++ Jari

 

flat.jpg

 


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#5 astrovienna

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Posted 23 February 2020 - 01:21 PM

Jari, this is very helpful. What camera was this? And I’m guessing the corrector is the 3” ASA? BTW, if you squeezed that M68 tilt unit under an OAG guide port, please let me know how you did it. That’s another issue I’m trying to figure out.

#6 vehnae

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Posted 23 February 2020 - 01:46 PM

Jari, this is very helpful. What camera was this? And I’m guessing the corrector is the 3” ASA? BTW, if you squeezed that M68 tilt unit under an OAG guide port, please let me know how you did it. That’s another issue I’m trying to figure out.

Ah yes, the corrector is the ASA 3" and the camera is ASI6200MM. No OAG in my setup though, as I run the system unguided. The Gerd Neumann CTU that I use is fairly thick so not much space for one. My image train is a custom extra short ASA-M68 adapter (2.8mm), 5mm spacer, CTU (17.2mm), Atik EFW3 (21.8mm) and ASI6200MM (12.5mm). 

 

If you have the ASA corrector and want the OAG use the TS ASA3-M68 tilt unit (7.2mm), so ZWO OAG-EFW-ASI6200MM (50mm) and a 3mm thick filter (-1mm) will get you to 56.2mm. The optimal distance for f/4 is 58.5mm so add 2mm of spacer rings and you're good to go. Tilt adjustments can then be used to fine tune the distance if needed. 

 

  ++ Jari



#7 vehnae

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Posted 23 February 2020 - 01:50 PM

Oh wait, the OAG port might interfere with the tilt plate (see here) because the plate is larger than the corrector body. Better check that out from someone who has the kit, it's hard to estimate from pictures where the OAG stalk will end up when in focus.

 

  ++ Jari


Edited by vehnae, 23 February 2020 - 01:50 PM.

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#8 freestar8n

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Posted 23 February 2020 - 05:27 PM

I've seen several online calculators that show whether vignetting will happen with a certain combination of f-ratio, sensor diagonal, distance from sensor and size of opening.  But I haven't found any tool to quantify that vignetting:  at what radius on the sensor does it begin, and how deep (% light loss) does it get on the edges of the sensor?  Does anyone know how to do this?

 

I'm trying to plan out an ASI6200 or QHY600 on a short-focus newtonian, and it would help me decide on a coma corrector and positioning of the other components if I could figure this out in advance.  Thanks.

 

Kevin

I have seen tools out there to calculate filter vignetting - but for many scope designs you need to be aware of the size and location of the exit pupil in image space - or the calculation will be very wrong.  Here is a write up and link to the online tool:

 

https://www.cloudyni...tting-with-app/

 

A follow up thread is here:  https://www.cloudyni...ting-revisited/

 

The exit pupil is particularly important for dslr's and sct's with reducers because it completely changes how the cone of light enters the sensor near the edge of the field where vignetting happens.

 

But for a Newtonian with no field corrector everything is simpler.  The pupil is just the mirror itself and simple geometry will tell you how much drop off there is due to the secondary size.

 

And one thing to keep in mind: you can always reduce vignetting by making the secondary larger, but at the same time you will be losing light in the center of the field.  As long as your main object is near the center of the field and as long as your flat fielding works well - you are probably better off with some amount of vignetting so you have max light in the center.  And with flats you won't notice the drop off toward the edge except as a slight increase in noise.

 

Any tool out there that doesn't explicitly mention the role of the exit pupil size and location will be wrong unless it is dealing with a simple Newtonian or refractor.

 

Frank



#9 jhayes_tucson

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Posted 23 February 2020 - 08:51 PM

I'm sure there are software aps that will do that prediction for you... but the fundamental starting point, that should capture most of the effect is what we optics guys call "cos fourth vignetting" ... You just draw Apparent Field lines from the center of your lens's exit pupil to various zones on your sensor and the illumination drops off as cos4 of that zone's apparent field angle. That's the lion's share; Simple as that.

 

BUT: There are myriad things that can exacerbate or mitigate that starting approximation:

 

>The exit pupil may morph/distort/shrink/enlarge/migrate as a function of field angle, which will boost or reduce vignetting impact

>Your sensor may be less sensitive to oblique flux. Especially true of CCD and CMOS comprising lenticular arrays, exacerbating vignetting

>Some lenses further comprise intermediate stops and element edges that clip objectionably-aberrated oblique rays, but exacerbating vignetting

>Coatings are less efficient at oblique angles, exacerbating vignetting

 

Stuff like that... Flats auto-address all of those, to the extent possible...

 

 apparent half-field       simplistic illumination

  seen by sensor               cos4 vignetting

 

       0 deg                               100%

       1                                      99.9

       2                                      99.8

       3                                      99.5

       4                                      99.0

       5                                      98.5

      10                                     94.1

      15                                     87.1

      20                                     78.0

      25                                     67.5

      30                                     56.2

      35                                     45.0

      40                                     34.4

      45                                     25.0

 

Image-space telecentric lenses entirely mitigate this by simply placing the exit pupil at infinity. Many lenses substantially mitigate this by distorting the exit pupil larger, as the image-space field angle becomes more oblique. Take a fisheye lens and hold it at arm's length as you tilt it; you will see the pupil bloom larger with angle.    Tom                          

 

Tom

While it true that the cos4 falloff has been called "vignetting" in some circles, it is not vignetting--and many of us "optics guys" actually don't call it "vignetting."   The cos4 falloff in irradiance across the field is due to radiometry, which is why it is more correctly called "radiometric falloff".  It is due to three effects:  1)  The change in apparent illuminating aperture, 1/r2 irradiance fall off with distance, and oblique illumination on a flat image surface.

 

Vignetting occurs when an aperture in the system cuts into an off-axis marginal ray bundle.  Irradiance fall off in an image is due to both vignetting and radiometric falloff.  Mis-named terms make it hard to clearly discuss things and there are enough of these in the amateur astronomy community that I hate to see this one added to the stack.

 

John


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#10 TOMDEY

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Posted 23 February 2020 - 10:10 PM

Tom

While it true that the cos4 falloff has been called "vignetting" in some circles, it is not vignetting--and many of us "optics guys" actually don't call it "vignetting."   The cos4 falloff in irradiance across the field is due to radiometry, which is why it is more correctly called "radiometric falloff".  It is due to three effects:  1)  The change in apparent illuminating aperture, 1/r2 irradiance fall off with distance, and oblique illumination on a flat image surface.

 

Vignetting occurs when an aperture in the system cuts into an off-axis marginal ray bundle.  Irradiance fall off in an image is due to both vignetting and radiometric falloff.  Mis-named terms make it hard to clearly discuss things and there are enough of these in the amateur astronomy community that I hate to see this one added to the stack.

 

John

Hi, John! Yeah... I'm suspecting that may be era or school variant? Doug and Rudolf called it "cos fourth vignetting" 1970s, possibly casually ... but I'll bet the Tucson guys may have used different wording. Maybe Jim would know, being that he was/is deeply immersed at both schools. Lots of seasoned engineers got bent when some insisted on changing "optics" to "photonics". Hard to keep up with, and acceptable nomenclature seems to change every time a standards committee convenes. I painfully recall the time Duncan docked me an entire half-letter grade because I used millionths (of an inch), rather than microns. I was working at B&L, at the time, where they insisted on millionths. A rose by any other name could care less. The school-marms just never succeeded in thrashing compliance into me. And... as Frost put it... "That has made all the difference"... for better and worse!   Tom


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#11 astrovienna

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Posted 24 February 2020 - 12:18 AM

Oh wait, the OAG port might interfere with the tilt plate (see here) because the plate is larger than the corrector body. Better check that out from someone who has the kit, it's hard to estimate from pictures where the OAG stalk will end up when in focus.

 

  ++ Jari

Yup, that's exactly the problem.  BTW, as far as I can tell the 3" ASA corrector is no longer being produced.  But Teleskop Service has a bunch of Wynne variants, including a 3" 1x short barrel with a bit more backfocus.

 

Kevin


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#12 freestar8n

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Posted 24 February 2020 - 02:14 AM

 Doug and Rudolf called it "cos fourth vignetting" 1970s, possibly casually ... but I'll bet the Tucson guys may have used different wording. 

I am in complete agreement with John on distinguishing vignetting from cos^4 - and not because I also have a Tucson background.  The two forms of falloff are completely different mechanisms.

 

But the main thing to keep in mind for this thread - it has nothing to do with what the OP is asking about.

 

As for Rudolf, here is a line from Lens Design Fundamentals:

 

 

Vignetting is one of the reasons why the illumination on the film in a camera falls off at increasing transverse distances from the lens axis.  Other reasons are (a) cos^4 law, (b) distortion of the pupil...

So there are many reasons illumination may drop off - and it won't strictly obey cos^4 in a real system anyway.  So it is important to keep vignetting separate from the other causes for drop off.

 

Kevin is asking specifically about a Newtonian with a particular Wynne corrector.  Fortunately the link he provides has a nice ray diagram of the corrector and you can tell that the cones of light arriving on the sensor are nearly parallel - which means the system is telecentric in image space and the exit pupil is near infinity.  That should help gauge how much vignetting there might be with a given camera, filter and oag.  Some shadowing by the OAG is ok and should be fixable with good flats but you also want the oag to be on the narrow side of the sensor if the sensor isn't square.

 

I'm not clear exactly what the image train being planned is - but there is a lot of info to go on.

 

Frank

tskorw3-backfokus.jpg



#13 TOMDEY

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Posted 24 February 2020 - 06:30 AM

I am in complete agreement with John on distinguishing vignetting from cos^4 - and not because I also have a Tucson background.  The two forms of falloff are completely different mechanisms.

 

But the main thing to keep in mind for this thread - it has nothing to do with what the OP is asking about.

 

As for Rudolf, here is a line from Lens Design Fundamentals:

 

"Vignetting is one of the reasons why the illumination on the film in a camera falls off at increasing transverse distances from the lens axis.  Other reasons are (a) cos^4 law, (b) distortion of the pupil..."

 

So there are many reasons illumination may drop off - and it won't strictly obey cos^4 in a real system anyway.  So it is important to keep vignetting separate from the other causes for drop off.

 

...

Hi, Frank; sure, semantics, no problem there. But, keep in mind... Rudolf, with his Kodak hat, was working for a company that, above and beyond else, made cash-cow film and cameras. And the camera specialists called it "cos fourth vignetting". e.g. >>>

 

"Cos4 vignetting describes the natural light falloff caused by light rays reaching the sensor at an angle. The light falloff is described by the cos^4(θ) function, where θ is the angle of incoming light with respect to the optical axis in image space. The drop in intensity is more significant at wide incidence angles, causing the image to appear brighter at the center and darker at the edges."

 

And the word vignette originated in the most general pre-optics context of artwork, where the edge of a (typically circularly-formatted portrait) image is intentionally-feathered / darkened. Later, the camera and optics guys gleaned the word and eventually claimed exclusivity.

 

So, I'm just preferring a term that the artists and photographers used and use... no one right or wrong, just different contexts. And appending the cos4 to the term makes it overtly unambiguous. As Alan Wertheimer was wont to say, out in the lab, "We seem to be is a state of violent agreement!"

 

I did a lot more than just lens design, much "non-image-forming geometrical optics", lots of that lighting design for GE, ITT, Volkswagen, smalls... So that same illumination falloff (trying to uniformly illuminate the road or desktops from above) had cosNs in there, and the targeted inverse correcting function we called "batwing". Semantics tends to be parochial to ones background, like local dialects. Diversity is good!   Tom



#14 astrovienna

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Posted 24 February 2020 - 06:31 PM

Jari and Frank,

 

The vignetting Jari's image shows isn't what I would expect from his setup.  The tool developed by Frank indicates that only the outer ~1mm in each corner should vignette.  Another tool here gives a similar result.    And while I don't know how to calculate the expected depth of the shadowing, the actual light loss of 50% seems surprisingly large.

 

Do Jari's results surprise you?  Jari, did the vignetting really drop to zero after you went to the M68 adapter?  I've heard from two sources that the ASA Wynne should start to vignette at 14mm off axis, regardless of the mechanical setup.

 

Kevin


Edited by astrovienna, 24 February 2020 - 06:35 PM.



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