# Fraunhofer Diffraction - A Primer

Started by
mloffland
, Sep 01 2009 11:19 AM

8 replies to this topic

### #1

Posted 01 September 2009 - 11:19 AM

### #2

Posted 03 September 2009 - 12:15 AM

Nice article. Sure, Lord mask it is!

### #3

Posted 03 September 2009 - 09:12 PM

Very good article.

Are the angles of the "Y" 150°, 60°, and 150°?

Are the angles of the "Y" 150°, 60°, and 150°?

### #4

Posted 05 September 2009 - 07:46 AM

great article chris, thanks for posting it

### #5

Posted 17 September 2009 - 02:32 PM

What dimensions do you recommend for a 100mm f/2 lens. Of course I'll stop it down for photography, but for focusing purposes, I'll leave it at f/2.

Very nice article btw.

Very nice article btw.

### #6

Posted 26 January 2013 - 07:02 PM

Someone pointed me to Chris's article and suggested that I make one of these masks if they do indeed work better than Bahtinov masks. I made one with my laser cutter, and it didn't work nearly as well as the bahtinov mask that I made for my telescope (152mm achromat). I was fairly convinced by the article, but it appears that something is off in the calculations.

**Edit:**Has anyone else tried making one of these and comparing them to a Bahtinov (or other) focusing mask? I'd like to have some more data points.### #7

Posted 10 February 2013 - 11:49 PM

"So where is the entrance pupil? For most practical purposes it can be considered as lying immediately in front of the objective, and to have a diameter equal to the objective's clear aperture. In reality it either lies at infinity, or a considerable distance in front of the objective. Because star light entering a telescope from an astronomical object is parallel, the distinction in practice does not matter."

I don't want to get too picky with you guys but I need to make a correction here: the distinction does indeed matter. The entrance pupil is the image of the stop in object space. For a Newtonian (or simple refractor,) the stop is at the objective (the primary mirror surface or the lens) and the entrance pupil lies in the same location--not at infinity. Remember, the chief ray (which defines the maximum field angle) passes through the center of the stop and the pupils (both entrance and exit pupils). Telecentric systems have the stop imaged at infinity so that the chief ray is parallel to the optical axis. Simple telescopes are not telecentric. The exit pupil, on the other hand, is the image of the stop in image space. If you forget about an eyepiece and consider the intensity distribution in the focal plane, these calculations simply look at the effect on PSF for binary apodization of the exit pupil--assuming no wavefront errors.

One other thing to understand about these type of FFT calculation is that the results are only an approximation of what you will actually realize in an optical system. The results are close but there are aliasing and leakage effects (energy leaks from one Fourier period into surrounding periods) that cause small errors. If you know what to look for, you can see a lot of this stuff in these results (mainly because of the low sampling rate.) In order to show what these patterns will do as you add a lot of defocus, you need to use a near-field, Fresnel model. Far field computations can accurately model only a few waves (<5-10 ?) of defocus.

John

I don't want to get too picky with you guys but I need to make a correction here: the distinction does indeed matter. The entrance pupil is the image of the stop in object space. For a Newtonian (or simple refractor,) the stop is at the objective (the primary mirror surface or the lens) and the entrance pupil lies in the same location--not at infinity. Remember, the chief ray (which defines the maximum field angle) passes through the center of the stop and the pupils (both entrance and exit pupils). Telecentric systems have the stop imaged at infinity so that the chief ray is parallel to the optical axis. Simple telescopes are not telecentric. The exit pupil, on the other hand, is the image of the stop in image space. If you forget about an eyepiece and consider the intensity distribution in the focal plane, these calculations simply look at the effect on PSF for binary apodization of the exit pupil--assuming no wavefront errors.

One other thing to understand about these type of FFT calculation is that the results are only an approximation of what you will actually realize in an optical system. The results are close but there are aliasing and leakage effects (energy leaks from one Fourier period into surrounding periods) that cause small errors. If you know what to look for, you can see a lot of this stuff in these results (mainly because of the low sampling rate.) In order to show what these patterns will do as you add a lot of defocus, you need to use a near-field, Fresnel model. Far field computations can accurately model only a few waves (<5-10 ?) of defocus.

John

### #8

Posted 04 March 2013 - 04:42 PM

That explanation seems to agree with my experimental results. Thanks for adding to my understanding.

### #9

Posted 26 June 2015 - 02:28 AM

I just stumbled onto this article...

But I am not sure Chris L has understood the operation of the Bahtinov mask - there is no simulation at all of the pattern shown with slight but significant defocus. This is, of course, the crucial part - a small defocus should clearly show by the spikes not intersecting at one Point.

Here's how I see it: imagine a Hartmann type mask, with 3 fairly large holes, each on its own 120 deg sector of the aperture. You get 3 superposed images (each with an Airy disk more than 3 times as large as that of the unmasked, focused aperture). Off focus, they do not quite coincide, but this is hard to see.

So put a coarse grid over one opening - you get a (double) spike as wide as the Airy disk but long enough to be visible way off the focus. Put similar patterns over the other two openings, but with bars at different angles, and you get two more spike pairs. Only at best focus will they all intersect at one Point. Off focus, the middle spikes will look shifted WRT the crossing of the other two. But for this to work well, the 3 zones (hartmann mask holes) must occupy clearly separated sub-areas of the full aperture - I see no reason that the single Y pattern (or later intersecting 3-bar patterns) could be of much use for focusing (cf posting #6!).

Nils Olof

But I am not sure Chris L has understood the operation of the Bahtinov mask - there is no simulation at all of the pattern shown with slight but significant defocus. This is, of course, the crucial part - a small defocus should clearly show by the spikes not intersecting at one Point.

Here's how I see it: imagine a Hartmann type mask, with 3 fairly large holes, each on its own 120 deg sector of the aperture. You get 3 superposed images (each with an Airy disk more than 3 times as large as that of the unmasked, focused aperture). Off focus, they do not quite coincide, but this is hard to see.

So put a coarse grid over one opening - you get a (double) spike as wide as the Airy disk but long enough to be visible way off the focus. Put similar patterns over the other two openings, but with bars at different angles, and you get two more spike pairs. Only at best focus will they all intersect at one Point. Off focus, the middle spikes will look shifted WRT the crossing of the other two. But for this to work well, the 3 zones (hartmann mask holes) must occupy clearly separated sub-areas of the full aperture - I see no reason that the single Y pattern (or later intersecting 3-bar patterns) could be of much use for focusing (cf posting #6!).

Nils Olof