What really causes "diffraction blur" ?

[Harold Gough]

Perhaps I can take this off at a tangent (I nearly wrote "a slight tangent", an oxymoron ).

This all seems to be to do with conventional lenses.

Would either of the following, generic designs, offer better performance, due to the mirror components, if they could be made as a macro version? (Their history shows that making wide aperture versions is challenging and aperture rings cannot be incorporated).

Harold

[mgoodm3]

And there is no chromatic aberration in a mirror.

[rjlittlefield]

This all seems to be to do with conventional lenses.

Diffraction blur doesn't have anything to do with the lens, only the light that comes out the back of the lens. A mirror lens with the same angular aperture would have the same amount of diffraction blur.

And there is no chromatic aberration in a mirror.

And there are short-focus mirror lenses, called "reflecting objectives", that offer long working distances at large apertures. An example is the Ealing Catalog Number 25-0506, specified as 15X and NA 0.28 at WD 24.5 mm. See pages 4 and 5 of the pdf file HERE.

All these aspects combined to give me very high expectations about how useful such a lens would be for high magnification stacking. I was delighted when I was able to snag a used one on eBay.

My delight disappeared when I received the lens and started testing it. The quality of image was inferior to an inexpensive 10X NA 0.25 achromat, there were significant changes in perspective with focus that caused problems for stacking, and with open illumination, it was very difficult to baffle the lens to prevent stray light from getting past the mirrors. After several iterations of "try this, try that", I gave up and returned the lens for refund -- I believe only the third time in my life I've done that.

I'm sure the lenses are great for their advertised purposes ("Ideal for laser beam delivery"). And it's certainly possible that the unit I received had degraded over the years, say through warping of the mirror block. But for my purposes the experience turned out to be such a waste of time that I won't be exploring that route again.

--Rik

[mgoodm3]

Upon further refelction, the aperture edges must have at least a partial effect upon the resulting Airy disc.

The reason for me is that a laser shot through an aperture causes an Airy disc. Since laser light is very nearly parallel as it hits the aperture there will be very little interference associated with convergence of light at various angles.

[Harold Gough]

Rik,

Interesting! I seem to have led a sheltered life!

Trying desperately to remember what little I once knew about microscope optics: would those have been designed (calibrated) to work only through a glass coverslip?

Harold

[rjlittlefield]

mgoodm3, it might help at some point to go slog your way through the earlier thread. The thread starts HERE with a discussion of scale bars (!), but soon goes off-topic into an extended discussion of what causes the blurring effect. It's a long read, and what you'll see is that most everybody (myself included) has trouble getting a good grip on how to think about the phenomena.

Anyway, someplace near the end of that thread, Graham links to this illustration: http://www.cmmp.ucl.ac.uk/~ahh/teaching ... node4.html. The illustration shows the Huygens-Fresnel principle of wave propagation, as it applies to a plane wave (think laser beam) passing through an aperture.

The Huygens-Fresnel principle itself is described in more detail in a Wikipedia article.

In very brief and paraphrased form, the principle states that you can think of a arbitrary wavefront as being replaced by a set of infinitesimally small sources, each of which emits a spherical wave. The evolution of the original wavefront is then equal to the sum of the evolutions of the spherical waves.

If you start with a plane wave in free space (no aperture), the contributions of all those tiny spherical waves turns out to add up to just another plane wave, happily propagating "in a straight line".

When you impose an aperture, you remove from the sum all of those contributions that would otherwise have come from outside the aperture.

The removal of those contributions makes the result be no longer a simple plane wave. Instead, it is something that looks very much like a plane wave close to the aperture's center, but is obviously an interference pattern near the aperture's edges.

The farther back from the aperture you make the observation, the more obvious it becomes that in fact the whole thing is an interference pattern. As you move far behind the aperture, that pattern resolves itself into something that we recognize as the Airy disk.

Here are the results of a simulation that illustrates this effect. It shows what happens when a plane wave, moving downward, strikes an aperture.



It is important to note that this simulation does NOT involve sines, cosines, angles, spherical wavefronts, or any other obviously wave-related mathematics.

Instead, it simply iterates over and over again the following set of additions and subtractions:

Code: Select all

        for (int ix = 1; ix < gridNX-1; ix++) {
            for (int iy = 1; iy < gridNY-1; iy++) {
                d2u[ix][iy] = k[ix][iy] * ( + u[ix-1][iy]
                                            + u[ix+1][iy]
                                            + u[ix][iy-1]
                                            + u[ix][iy+1]
                                            - 4*u[ix][iy] );
            }
        }
        for (int ix = 1; ix < gridNX-1; ix++) {
            for (int iy = 1; iy < gridNY-1; iy++) {
                du[ix][iy] = du[ix][iy] + d2u[ix][iy];
                u[ix][iy] = u[ix][iy] + du[ix][iy];
            }
        }

These additions and subtractions are nothing more -- and nothing less -- than a direct numerical solution to the wave equation. The fact that the result ends up looking like interfering waves simply reflects the fact that waves and interference are a natural way of thinking about the solutions to this equation.

Getting back to mgoodm3's words,

the aperture edges must have at least a partial effect upon the resulting Airy disc.

The reason for me is that a laser shot through an aperture causes an Airy disc

I hope it's clear at this point that the edges of the aperture do not cause the Airy disk.

What causes the Airy disk is the removal of all contributions outside the edges of the aperture.

If you observe close behind the aperture, then the effects are definitely more obvious near the edges. But that is simply because you are paying attention to an area where the weight of various contributions is changing quickly. Farther back, the weights become more equal, and the classic Airy disk appears.

--Rik

Edit: to tweak phrasing.
Edited 11/2/2021 to fix formatted of code block after upgrade of forum software

[rjlittlefield]

Trying desperately to remember what little I once knew about microscope optics: would those have been designed (calibrated) to work only through a glass coverslip?

They vary. Some are optimized to be used with no coverslip, some with a coverslip, some with no coverslip but immersed in water, and some immersed in oil. For immersing in oil, it doesn't matter much whether there's a coverslip or not, because the refractive indices of immersion oil and coverslip glass are very close to identical. Likewise for low magnification objectives, but that's more because they have small NA's -- relative to high magnification objectives, that is. My beloved Nikon CF N Plan Achro 10X NA 0.30 objective is specified for 0.17 mm coverglass, but there's no obvious difference with and without.

--Rik

[mgoodm3]

I should have stuck with what I had going previously

So, I'm thinking that everything comes down to interference of light waves. An image is an summation of interference patterns caused by the convergence of light by the lens.

So the aperture doesn't directly cause the effect of diffraction, it changes it nature by filtering out portions of the light.

[rjlittlefield]

So, I'm thinking that everything comes down to interference of light waves. An image is an summation of interference patterns caused by the convergence of light by the lens.

So the aperture doesn't directly cause the effect of diffraction, it changes it nature by filtering out portions of the light.

That's a pretty good summary........at this point.

The problem is, if someone had written those words about 500 lines ago, they wouldn't have made any sense to you then.

After all, filters are things that change colors, and darken skies, and add starbursts. What could filtering possibly have to do with diffraction blur?

--Rik

[Harold Gough]

After all, filters are things that change colors, and darken skies, and add starbursts. What could filtering possibly have to do with diffraction blur?

--Rik

"Filter"? Now, there's misused term.

If I look through ads for photographic accessories, I find close-up and macro supplementary filters, mulitimage filters, soft focus filters, etc

Take mensicus filters for close-up work. They are graded in diopters. As I type this, I am wearing spectacles fitted with varifocal filters. It seems I have been mis-sold, as I clearly recall paying for lenses.

[Harold Gough]

This link to another thread may be of interest:

http://www.photomacrography.net/forum/v ... 7376#37376

Harold

[Harold Gough]

And for those who still thirst for more:

http://www.cambridgeincolour.com/tutori ... graphy.htm

Harold

[rjlittlefield]

Thanks for adding that link, Harold. The cambridgeincolour page has been linked several times in months and years past, but it's an excellent presentation and deserves be kept visible.

There is one peculiarity of the page to watch out for. In the section titled "VISUAL EXAMPLE: APERTURE VS. PIXEL SIZE", the graphic is interactive but the user interface is unusual. Rather than requiring a mouseclick to select a setting, the graphic runs entirely on mouseover. If you want to lock in a particular setting for aperture or camera type, the trick is to hover over that selection and then move left or right to get out of the column. Also it's not the box that counts for selection, but only the text, so watch for the highlighting. The interface is really fast and convenient after you get used to it, but I remember getting pretty frustrated before I figured it out.

--Rik

[Harold Gough]

I didn't think I had seen it and I don't trust the forum search engine for other than single words. It seems a good idea to collect relevant information in one place.

I'm used to mouseover since I installed my e-mail verification software. It uses it for showing certificates for individual messages. Something similar also works in the feedback posting software on eBay, to show details of a transaction.

Harold

[rjlittlefield]

I'm used to mouseover also, but all the other mouseover actions that I'm familiar with are transient. You mouse over and the information appears; you mouse away and it disappears.

That cambridgeincolour page is the only one I've seen where mouseover has a lasting effect and mouseclick gets ignored. That's what makes it a bit tricky to use. Perhaps you've run into other interfaces like this.

About the link, it is absolutely not a problem to post a relevant link even if it's been posted before. The added posting simply adds evidence of the value of the linked page.

At some point the search facilities may get good enough to use that evidence. ('Show me the most frequent links from posts containing the word "diffraction".')

In the meantime, they are useful hints & reminders for us humans.

--Rik