diffraction limiting?

[Tom Hoskinson]

I prefer Highland Park, Ed - but that's a different story.

 

[glbeas]

I was trying to say that the study of light - and diffraction was *far* more complex than the scope of APUG would allow.

Thats an understatement for sure.

It is *not* as simple as "The image is only formed by the straight rays..."

For practical purposes concerning pinhole cameras it is. Diffraction is the interference that limits how small you can make a pinhole for optimum sharpness. We aren't dealing with fancy diffraction lenses like is used on X-ray telescopes. The propogating sphere of light illuminating the surfaces is interfered with by the pinhole which allows a tiny spot through which is stopped at the film surface. Simple geometry suggests how the imaging takes place from this point.

I'll suggest the book ... that I quoted verbatim et literatim:

A.C.S. van Heel
C.H.F. Velzel

What is Light?

Translated from the Dutch
by J.L.J. Rosenfeld

World University Library
McGraw-Hill Book Company
New York Toronto

(c) mrs. H.G. van Heel and C.H.F. Velzel 1968
Translation (c) George Weidenfeld and Nicolson Limited 1968
Library of Congress Catalog Card Number 67-24448
Phototyped by BAS Printers Limited, Wallop, Hampshire, England
Printed by Officine Grafiche Arnoldo Mondavori, Verona, Italy.

Another sample (struck with a sudden masochistic urge fro typing:

"Until now we have used as a model for the propagation of light the principles of Huygens, which we define as follows. One can imagine a wave front to originate out of the previous one by supporting each point in the latter to be a secondary source of spherical waves. The envelope of these spherical waves forms the new wave front. Notice that here, in contrast to our previous formulation of Huygens' principle, we are talking in the language of waves (italics mine -E.S.). But we have in the meantime discovered that waves show interference. Fresnel's addition to Huygens' principle consists, as we shall see in the following, in this, that he takes account of these interference phenomena. We should add a word about the range of validity of Fresnel's theory. The electromagnetic theory of light, which we shall describe later on, explains diffraction effects in an unforced manner and is, on deeper examination more precise. But Fresnel's theory of diffraction does, in most instances give the correct explanation even of details, and for this reason is considered by opticians to be a good working tool."

OK, class ... close your books. Time for a pop quiz...

Hmmm... another passage:
"This can be described as follows. It is unfortunatey a somewhat long and complicated tale, but it cannot be shortened and is most easily understood with the aid of a recipe, Think of a sphere about P which just touches V at Q and call the distance QP, l. Imagine further other spheres with P as centre whose radii are respectively ..."

No more ... Is Jim beam a good remedy for typer's (and brain) cramps?

Looks like interesting reading. I wish I had time to delve into all the interesting sources I've encountered here. You've supplied some of the best.
I'm not saying you're wrong about anything Ed, just that you're overcomplicating the issue unneccesarily. Sometimes you need to drop to the simpler levels for the sake of clarity.
Jim Beam is great for those cramps purely on a medical basis. ;-)

 

[Helen B]

So, this all started so simply. I disagreed with the statement that a pinhole would not create an image if there was no diffraction. Do we all agree that the principal way in which a pinhole creates an image can be described by geometric optics, with the limit set by diffraction? Does that suit all parties?

And didn't Lord Rayleigh do well, getting a similar answer to Sayanagi (which is the same result I quoted, after assuming lambda, in case no-one had noticed). There are many ways to formulate the behaviour of light - the trick is to know which one is appropriate for the case under consideration.

Best,
Helen

 

[Tom Hoskinson]

Amen Helen! I think this particular horse is well and truly dead.

 

[Ole]

Amen Helen! I think this particular horse is well and truly dead.

...and full of holes as well

 

[Ed Sukach]

...and full of holes as well

I ... I ....

No!! I'm going to keep my big mouth shut and (hopefully) stay out of trouble.

A couple of web sites:

http://www.mrpinhole.com/index.php

http://users.erols.com/njastro/barry/

http://www.mines.edu/~mmyoung/PHCamera.pdf

I hope they all work.

 

[glbeas]

The PDF was a goldmine Ed, thanks! It explains what you were talking about, that diffraction effects can induce a sharper image when the Airy disk has the outer rings the weakest, causing a "focal length" to the pinhole. This works in conjunction with the classic pinhole description. From what I read about it it's detectable with resolution charts and if you know what you are looking for it might be seen in a pinhole photograph. I think though most people except the diehard purists wouldn't even be concerned by it though it's nice to know about.

 

[Ole]

I was going to write just about what Gary said, but got distracted by (ugh) work.

As I understand it, by making the first dark ring (1st extinction zone) overlap the edge of the "geometric" hole-image, the resolution will be increaset beyond what the geometric model would predict. Neat!

 

[Murray@uptowngallery]

I, too, found the Matt Young article to be perhaps the best explanation of pinhole imaging I've seen, but apparently I need to read it again because I couldn't explain it to my a couple of girl scouts in my wife's troop...

thanks for the extended discourse.

Murray

 

[127]

Based on the Young article I was prompted to do some simulations... (aahh digital! - no digicams though - all software). Thanks for putting me on to that, as it's been really usefull.

One interesting result is that to accuratly sample the wavefront passing through a pinhole you would need to sample it at intervals of lamba/2 (Nyquist theory - is there nothing it can't do!). For a diameter of d that gives 2d/lamba samples. You can't have any information in the image thats not in the pinhole samples, so that gives a maximum number of "pixels" available of 2d/l or d/l lines (spread over 180degrees). If you drop this into Young's equations in place of the Airey disk stuff it matches his results, give or take a small scale factor!

In other words the reason (or at least a valid interpretation of why) we get diffraction is simply a pinhole is too small to fit that much information through, so the image has to get blurry!!!

Ian

 

[Struan Gray]

For my money, the strange thing is not that light passing through a hole spreads out, but that light propagating in a straight line does not.

The point is that when you have a straight wavefront the waves spreading from the left cancel the waves spreading from the right. If you place an obstruction so that the waves on the right get absorbed or reflected away, those on the left are now free to spread themselves. And they do - not because they feel a mysterious compulsion to do so, but simply because they can. This is what Huygens' construction is all about.

One of the photographs I most want to take is of the light patterns formed by the sun shining through the double row of trees outside our flats. Depending on the sizes of the gaps beween the leaves on each side you get a mix of pinhole images of the sun, pinhole images of the first row of trees, shadows of both rows and all possible convolutions of the two. Add that the southernmost row loses its leaves first in the Autumn and you have the makings of a wonderful series. Sadly, the best patterns are at 1430, when I'm least likely to be able to get away from work. One day.

 

[jjstafford]

For contact printing diffraction should never be a problem.

Diffraction limited resolution varies according to color of light but can be approximated by the following formula.

R = 1500-1800/f-N, with R resolution in lppm, f = aperture of lens. The figure varies from 1500 - 1800 because of different resolution with color of light.

For example, a 355 G-Claron used at an aperture of f/90 would have a diffraction limited resolution of between 17 - 20 lppm, depending on color of light. This is considered more than adequate for contact printing since the human eye is said to have maximum resolution of about 15 lppm at a viewing disance of 10 inches.

For projection printing the limits are more stringent since the negative will most likely be enlarged. For example, a 2X magnification of a 5X7 negative made with a lens aperture of f/90 would result in an effective resolution of only 8-10 lppm on the print, less than the maximum resolution of *some* people at a viewing distance of 10 inches.

Sandy

Close. Keep in mind that the enlarging process further degrades accutance (specifically contrast and resolution). But still, in the case above, you still get a good print.

 

[jjstafford]

[...] One of the photographs I most want to take is of the light patterns formed by the sun shining through the double row of trees outside our flats. [...]

Indeed! It would be a great study. I was fortunate enough to experience an eclipse of the sun at a university in the upper midwest a several years ago and the apertures caused by the trees' leaves showed remarkably clear images of the partially eclipsed sun. It was gratifying to see the students understand what was happening all at once; a real Wow factor.

 

[Struan Gray]

We had that partial eclipse too. The tree shadows had horrible bokeh

 

[Murray@uptowngallery]

They must not have been Japanese Maples :O)

 

[Struan Gray]

The best bokeh is to be had from the famous '0' Tannenbaums from deep in valleys of the the Kaisergebirge. The only thing that comes close would be an original Wunderbaum, but those are so pricey and exclusive they're not a practical recommendation. Don't be fooled by the cheap Japanese imitations.