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joshdaskew
26-Oct-2009, 07:19
Hi, Was just hoping that someone out there could help me.. From reading a couple of posts, I have a rough idea about diffraction and that your images can get softer if using small apertures. As a rough guide, it seems that f22 seems to be this limit and then using smaller apertures than this (f32, f45) can soften the image. I also read in another post that someone was getting soft images shot with a 75mm lens at f22 and that this was apparently past the diffraction limit for that focal length. So I guess my question is, does the diffraction limit depend on the focal length or is it more format based? I am using a Rodenstock GRANDAGON 75mm f/6.8, Schneider Super Angulon
90mm f8, Rodenstock 135mm Sironar-N, Rodenstock Apo Sironar-N, Caltar 210mm II-N and a Nikon M 300mm. If someone could suggest the diffraction limits for each of these lenses that would be greatly appreciated!

Also, I am planning on printing a folio with the dimensions of 34 cm ( length ) x 28 cm ( width ) and was just wondering if diffraction would play a part in print sizes that small (even if closed right down to f45) compared to an image that was shot within diffraction limits.. Also, at that size, would there be any difference between the lenses I currently own and the latest offerings from Schneider, Rodenstock etc etc..

Ok, thanks so much, much appreciated! Best Regards Josh.

P.S Am not particuarly technically minded so please keep this in mind when answering. Thanks again.

ic-racer
26-Oct-2009, 07:26
In general it is 'format based' because the smaller formats are usually enlarged more to match the larger formats final print size.

You can also compare a 4x5 contact to an 11x14 contact, but you need to decide if they will have the same viewing distance, as the viewing distance influences the acceptable Airy disks sizes.


More info here: http://www.largeformatphotography.info/fstop.html

N Dhananjay
26-Oct-2009, 08:00
Diffraction depends upon the f stop. However, the sweet spot for sharpness in a photograph depends upon a tradeoff between diffraaction limitations and aberrations in a lens. Typicall, the larger the aperture, the aberrations tend to be high while diffraction limitations are low. Smaller apertures tend to reduce certain aberrations but increase diffraction limitations. So, the sweet spot is when you have stopped down enough to reduce aberrations significantly but not so much that diffraction becomes a huge issue. The idea of being diffraction limited is that beyond this point, lens aberrations are not decreased sufficiently to compensate for the diffraction costs. So, you would imagine that a lot depends upon lens design etc and saying something like 'f/22 is the sweet spot for all lenses' might be a bit of a sweeping generalization. But others have argued that manufacturers aim at that spot in their design.

I would suggest using the ground glass as the final arbiter. You shouold also keep in mind that we are dealing with different kinds of unsharpness, differences that you might care about. The diffraction limitation argument holds for whatever is in sharp focus. That is, if you were photographing a brick wall, what sort of aperture would give you the best sharpness? In reality, there are further trade-offs, the most prominent being depth of field (DOF). Diffraction affects the resolving power of a lens - it shows up a softening of the entire image. Shallow DOF shows up most prominently in the out-of-focus areas. Certain kinds/styles of photographs suffer more from lack of DOF than diffraction. For example, if you make portraits where you want the sitter in focus but would like to throw the background out of focus, you would probably tend towards larger apertures. You may still want to stop down some to reduce aberrations, but not so much that DOF includes background. At the other extreme, if you are shooting a landscape where you want near, middle and distance in sharp focus, you may have to use small apertures for sufficient DOF. That is, the slight softening of detail overall may be preferable to having some parts in focus and other parts blatantly blurred.

All of this also needs to be tied to what size print you are making, whether you are working in B&W or color etc. For e.g., color images typically need less sharpness than B&W to look similarly sharp (I'm talking about subjective sensations here) because the human eye-mind combination interprets color as information. On the other hand, getting colors of different wavelengths to focus on the same spot is also a fiendishly difficult problem for lens designers. Similarly, if one is contact printing, diffraction is much less of an issue - if it looks adequately sharp on the GG and negative, it should look adequately sharp on the print. When enlarging, you need to consider the fact that the diffraction blurs (and the aberration blurs) are being enlarged. At some point, they will be large enough to be unacceptable.

So, in practice, I think it makes sense to marry all this knowledge with how you want your photograph to look. It probably makes sense to aim at using the sweet spot, but sometimes conditions dictate otherwise. In other words, try to use movements so that you can work around the sweet spot, but also be prepared to make the tradeoff, when required. I enjoy learning about all this but I have concluded that it is all in the wash and one is better served by concentrating on visual concerns (while having the knowledge for those occasional situations that warrant it).

Cheers, DJ

Rick Olson
26-Oct-2009, 09:05
Hello Josh,

Does diffraction exist? The physics of optics says "yes." Do I see it in my 5 x 7 black and white negatives? No. I just developed several 5 x 7 sheets where I needed f32 and f45 to achieve some deep focus. I checked them with a 10x magnifier and they were tack sharp to me, as expected. I used to get all wrapped up in this "best f-stop" mentality and did whatever I could to stay at f22 or less for razor-sharp images. I was not able to achieve what I wanted so I ventured into the "risky waters" of lens diffraction. Didn't see a difference. Maybe my 1960s vintage, single-coated and scratched Fuji 210 lens is a supreme example of optical excellence and sharp at all f-stops. Anyway, I doubt I would see any diffraction effects when contacting printing, but maybe some can.

Use the f-stop you need to achieve the results YOU want and enjoy!


Rick

Bob Salomon
26-Oct-2009, 09:18
Hello Josh,

Does diffraction exist? The physics of optics says "yes." Do I see it in my 5 x 7 black and white negatives? No. I just developed several 5 x 7 sheets where I needed f32 and f45 to achieve some deep focus. I checked them with a 10x magnifier and they were tack sharp to me, as expected. I used to get all wrapped up in this "best f-stop" mentality and did whatever I could to stay at f22 or less for razor-sharp images. I was not able to achieve what I wanted so I ventured into the "risky waters" of lens diffraction. Didn't see a difference. Maybe my 1960s vintage, single-coated and scratched Fuji 210 lens is a supreme example of optical excellence and sharp at all f-stops. Anyway, I doubt I would see any diffraction effects when contacting printing, but maybe some can.

Use the f-stop you need to achieve the results YOU want and enjoy!


Rick

What kind of fine detail did you check at the edges, corners and the center? Were they equally sharp?

Brian Ellis
26-Oct-2009, 10:15
The effects of diffraction show up as an overall softness of the image caused by the fact that when a photograph is made some of the light passes through the lens aperture directly to the film without striking the aperture blades. The rest of the light first strikes the edges of the aperture blades and is bent ("diffracted") by them before the light strikes the film. The higher the proportion of bent light to direct light the greater the diffraction. And the smaller the aperture the greater the proportion of bent light to direct light. Which is why the effects of diffraction become more apparent as the aperture gets smaller.

N Dhananjay's explanation is very good and tells you about all you need to know. I'd add only a couple things to what he's said. While the size of the aperture controls the degree of diffraction regardless of film format or lens focal length, diffraction isn't a practical problem IMHO with 4x5 and larger film unless the print is enlarged beyond about 5x. Usually the effects of insufficient depth of field will be much more noticeable in the print than the effects of diffraction with LF film. So I agree with Rick. It's better to stop down as far as you need to go to get the depth of field you want than it is to worry about diffraction with LF film.

The situation is entirely different with smaller formats, especially 35mm, because smaller formats are typically enlarged much more than LF. That's why the smallest aperture on most 35mm lenses is f22 or even f16, whereas most LF photograhers are just getting started at apertures that wide.

The effects of diffraction aren't going to be any different in the edges or corners of film or a print than in the center. Diffraction might exacerbate differences that otherwise exist. But the differences are caused by lens optics or something else, not by diffraction because the effects of diffraction show up as an overall softness, not a softness in any particular area of the film or print. At least that's my understanding, someone more knowledgeable about the science involved can correct me if I'm wrong.

aduncanson
26-Oct-2009, 10:20
A note on usage:

"Diffraction limited" is a term used to describe telescopes and, less frequently, lenses meaning that the effects of the residual aberrations on lens resolution are masked by the maximum resolution allowed by diffraction for a perfect lens.

What are those maximum resolution limits? A complete answer is beyond my comprehension and attention span, but a useful rule of thumb is that the Max Resolution (in lp/mm) = 1600/ F-No. The actual limits depend on wavelength, position off the optical axis and whether resolution is measured radially or tangentially. However, the rule of thumb above can be used as an upper bound, or max value, for diffraction limited resolution under ideal conditions.

To tabulate those upper bounds:

f/16 - 100 lp/mm
f/22 - 71 lp/mm
f/32 - 50 lp/mm
f/45 - 35 lp/mm

As stated by several posters above, whether or not these diffraction limits will affect you, depends on the magnification of your print and the conditions under which you will inspect it. If the eye can resolve 6 lp/mm, you can use f/45 and make a 6X enlargement (24x30 inches) from your 4x5 and probably get by just fine (assuming everything else in your enlarging chain is working perfectly. ;)

Daniel_Buck
26-Oct-2009, 10:24
I've done some fairly lax tests on this to satisfy my own curiosity, and for me and my tolerances, I've not seen much 4x5 and practically none on 8x10 at print sizes less 20" wide and smaller. Granted I haven't tried any f90+ exposures, but at f32 and f45 (as stopped down as I would ever really need to go) I've not noticed anything soft enough that would make me not want to stop down that much.

Do a few quick tests, and you'll probably find out quickly if you can or can't tolerate shooting f45 or even f64 at your film and print size.

Rick Olson
26-Oct-2009, 10:25
Hello Bob,

I was shooting some abandoned railroad equipment this weekend in Chama NM on the Cumbres and Toltec railroad. The fine detail checked in the lower edges/corners was track ballast (rocks/gravel), rails and ties. Tilted to get this area sharp. Nearby was a track switch-stand at about 8' tall and some railroad cars down the track. Had to get those in focus. Behind that in the distance was a strand of tall trees that extended to the top of the image. Had to get that in focus also, so I adjusted the focus plane about mid-way up and stopped down. I tried a similar shot like this before at f-22 and it didn't cut it. This time, I shot at f-45 and it was sharp from the track ballast, a few feet in front of me (image edge/corner), the switch-stand and railroad cars (image center), to the tops of the trees. My 10x lupe certainly presented a sharp negative at an equivalent print size of 50" x 70", so I think my 5" x 7" contact print should look pretty good!

Rick




What kind of fine detail did you check at the edges, corners and the center? Were they equally sharp?

Bob Salomon
26-Oct-2009, 10:35
Hello Bob,

I was shooting some abandoned railroad equipment this weekend in Chama NM on the Cumbres and Toltec railroad. The fine detail checked in the lower edges/corners was track ballast (rocks/gravel), rails and ties. Tilted to get this area sharp. Nearby was a track switch-stand at about 8' tall and some railroad cars down the track. Had to get those in focus. Behind that in the distance was a strand of tall trees that extended to the top of the image. Had to get that in focus also, so I adjusted the focus plane about mid-way up and stopped down. I tried a similar shot like this before at f-22 and it didn't cut it. This time, I shot at f-45 and it was sharp from the track ballast, a few feet in front of me (image edge/corner), the switch-stand and railroad cars (image center), to the tops of the trees. My 10x lupe certainly presented a sharp negative at an equivalent print size of 50" x 70", so I think my 5" x 7" contact print should look pretty good!

Rick

Now, have you ever compared the sharpness, contrast, color, saturation, distortion and overall performance with a modern lens with modern coatings at the same magnification?

aduncanson
26-Oct-2009, 10:46
OK, just as a point of information and I am admittedly treading dangerously close to the limits of my comprehension here, but I believe that the explanation of diffraction limits as a due to the proportion of light rays bent by grazing the edge of the aperture is a misunderstanding arising from the way that diffraction is introduced in elementary physics classes - that is as an effect that takes place at an edge. Rather the diffraction limits to lens resolution are an inherent characteristic of the aperture size. Consider a radio telescope array made up of scores of dishes, or the sophisticated antennas used on the US Navy's Aegis radar with a great many small apertures. If the limiting issue were really only the fraction of rays bent at the edges of the individual apertures then the resolution would not be enhanced by using these large arrays. Yet increased resolution is absolutely one of the reasons for using arrays of small apertures. The arrays exhibit a resolution that can approach the theoretical limits for a single aperture the same size as the array.

Again, this point is not really of much interest to photography, but is a corrective to how you might think about the question.

Rick Olson
26-Oct-2009, 10:56
Bob,

I also own a Schneider 210 Apo Symmar-L lens, but my old Fuji 210W lens has the 80 degree angle of view and I really needed that for the type of photography I did this weekend. I love both lenses and the images they produce are outstanding. I have not compared the specifics you note lens-to-lens, but I am unable to tell which I used when looking over my contact prints. Photography is more fun than analytics to me, and pursue my hobby this way now.

Rick




Now, have you ever compared the sharpness, contrast, color, saturation, distortion and overall performance with a modern lens with modern coatings at the same magnification?

Paul Kierstead
26-Oct-2009, 11:17
Consider a radio telescope array made up of scores of dishes, or the sophisticated antennas used on the US Navy's Aegis radar with a great many small apertures.

Those are phased arrays, which get better information by using multi-phase transmission and extremely sophisticated signal processing. Not really analogous.

Emmanuel BIGLER
26-Oct-2009, 11:39
An answer to the original post by JoshDaskew :

Hello from France !
I have both the 75 mm and 90mm 6.8 grandagon-N. Both are extremely sharp lenses.
The problem with wide-angle lenses is that you demand an homogeneous image quality across the whole field up to 90° and above (6-element grandagons cover 102°) , hence the constraints are slightly different if compared to a standard lens covering only 70-75°.
In principle you should not stop down short focal lengths as much as long ones.
For the 75 and 90 you can use them at f//11 with an excellent image quality at the center but you will not keep this quality across the whole field. So Rodenctock recommends f/22 for those lenses but at the center you'll slightly loose sharpness due to diffraction if compared to f/11.

When a lens is stopped down beyond the recommended f-stop, the image quality decreasas very slowly and the subsequent softness is compensated by a more homogeneous image quality in depth (depth of field continues to increase somewhat). If compared to an ordinary out of focus image, I would say that diffraction softness can pleasant and "smooth" whereas unwanted out-of focus blur is irritating and frustrating !
So, do not hesitate to stop your lenses down beyond the f-stop recommended by the manufacturer, you'll see what happens and decide whether it is acceptable for your work or not.

For the same series of classical standard lenses like the sironar-N, the best f-stop can be estimated for different focal lengths by the approximate formula :
best f-number = focal length (in mm) divided by 8.
For example for a clasical 150 : best N = 150/8 = 19 = between 16 and 22 ; for a 300 mm of the same kind and same vintage 300/8 = 38 the best f-stop will be between 32 and 45.

For more recent top-notch standard lenses like the apo-sironar S and competitor apo-symmar L, the formula would be closer to f(in mm) /11 i.e. theire best f-stop is one f-stop wider.

Armin Seeholzer
26-Oct-2009, 11:40
With so small prints I think you are totaly on the save side atleast up to f 45 on 4x5.

Cheers Armin

aduncanson
26-Oct-2009, 13:25
Those are phased arrays, Yes


which get better information by using multi-phase transmissionYes


and extremely sophisticated signal processing. Yes


Not really analogous.Why not?

Do they not form a very narrow beam using many small apertures which individually would not be capable of doing so?

Do they not illustrate that diffraction is far more than just a matter of the relationship of the perimeter to the area of an aperture?

Do they not illustrate that the extent of the array is a large determinant of the ability to form a narrow beam, not the individual aperture size?

Paul Kierstead
26-Oct-2009, 14:05
Do they not form a very narrow beam using many small apertures which individually would not be capable of doing so?


They could also make a very narrow beam using many large apertures, so not your statement is not correct. The aspect that allows the narrow beam is the "many" and the phase control, not the size of the aperture, which is simply a matter of buildable/deployable size.



Do they not illustrate that diffraction is far more than just a matter of the relationship of the perimeter to the area of an aperture?


No, they do not. They illustrate that system performance is far more then just a matter of aperture or diffraction. In fact, they would likely work better with larger aperture.



Do they not illustrate that the extent of the array is a large determinant of the ability to form a narrow beam, not the individual aperture size?

They show that a large array is a method of achieving a narrow beam. They do not provide a conclusion w.r.t. to aperture and its relationship to beam size, nor do they provide a conclusion about diffraction.

In addition, beam size is not analogous to resolution issues in the sense it is being discussed here. It would be more analogous (though still an approximation) to narrowing the field of view and stitching for a panorama. There are a variety of antenna designs that allow narrowing the beam, but a phased array allows a real-time variably beam which alone would merit its likely use regardless of its 'absolute' resolution.

timparkin
26-Oct-2009, 14:31
I've made three prints of a 4x5 close up at f22, f32 and f45. There was visible softening at the f45 (although amazingly, more depth of field!). The print was a crop but would have been 24x30"... and it was a 150 Sironar S

Tim

Brian Ellis
27-Oct-2009, 00:00
OK, just as a point of information and I am admittedly treading dangerously close to the limits of my comprehension here, but I believe that the explanation of diffraction limits as a due to the proportion of light rays bent by grazing the edge of the aperture is a misunderstanding arising from the way that diffraction is introduced in elementary physics classes - that is as an effect that takes place at an edge. Rather the diffraction limits to lens resolution are an inherent characteristic of the aperture size. Consider a radio telescope array made up of scores of dishes, or the sophisticated antennas used on the US Navy's Aegis radar with a great many small apertures. If the limiting issue were really only the fraction of rays bent at the edges of the individual apertures then the resolution would not be enhanced by using these large arrays. Yet increased resolution is absolutely one of the reasons for using arrays of small apertures. The arrays exhibit a resolution that can approach the theoretical limits for a single aperture the same size as the array.

Again, this point is not really of much interest to photography, but is a corrective to how you might think about the question.

Actually what I wrote about bent light vs direct light and diffraction is what I learned from one of Ansel Adams books - The Camera, The Negative, or The Print, I forget which one. It didn't come from a physics class.

Emmanuel BIGLER
27-Oct-2009, 06:26
that is as an effect that takes place at an edge.

yes this elementary explanation is correct and can even yield some sophisticated computations named "geometrical theory of diffraction" : using this theory you can compute diffraction effects by adding the coherent amplitudes of ordinary, geometrical rays (or waves), with some "diffracted rays" re-emitted from the edges of the aperture.

In a simple academic case, this approach works really nicely, it is the case a parallel beam of ligth diffracted by a very thin and perfectly straight metallic knife-edge, what is transmitted behind the knife edge is the sum of the ordinary, geometrical, incident beam abruptly cut by the edge, casting a perfect shadow, plus a diffracted wave emitted by the edge itself. This diffracted wave will actually bring some light in the geometrical shadow, and the addition of the two waves is coherent, hence yielding some interference fringes.

But here in photography we are dealing with a very special case of diffraction effects, known as Fraunhofer diffraction effects or diffraction that occur at the image plane behind a lens.
In this situation, diffraction effects can be computed from the diffracted light distribution around the center of curvature of a perfect spherical wave representing a perfect converging geometrical light beam for a single point source -> single point image.

Since we are dealing with ordinary, incoherent light, there are some special rules to get a good model for the global image which will be blurred by diffraction effects but those details are not useful to the photographer, one only needs to know the order of magnitude of the effect for a given f-stop.

In a thick compound lens, when the iris is reasonably stopped down to the working aperture, the simplest model for diffraction effects neglecting geometrical aberrations is given by a perfect spherical wave alone, without any glass, the wave being abruptly cut by the edges of the exit pupil of the lens. In a sense for diffraction effects there is no difference with a perfectly thin lens element stopped down at its center. It happens that the solution, within reasonable approximations, can be computed by hand.

And the diffraction limit in this model, expressed in terms of the cut-off period (one period = one white space plus one black bar) in the image is simply : p_cut = N_eff . lambda
where lambda is the wavelength of light (0.7 microns being the actual worse-case limit for most silver halide films) and N_eff is the effective f-number as seen from the image plane, N_eff = (distance to pupil) / (pupil diameter).
If the distance is equal to one focal length, N_eff is the f-number defined as usual, when d = 2f like in macro work at 1:1 ratio, N_eff = 2 N.

No need for Airy disks at all, no need fro diffracted rays at the edges of the aperture ;-)

From a mathematical point of view the model is extremely simple at the center of the field,no need for sophisticated simulations to derive the cut-off period and even the whole diffraction-limited MTF curve.

More tricky is what happens in the corners of the image given by a wide angle lens, but the effective f_number can help us as well : the distance to the pupil increases and seen from the corners the pupil looks oval and no longer circular.
As seen from the corners of the image the effective f-number increases, the oval shape of the pupil yields a separation between two different values of p_cut for sagittal and tangential line pairs in the image.
Globally the cut-off period is bigger with respect to the center, diffraction effects degrade the image quality in the corners even for an hypothetical perfect wide-angle lens with no aberrations.

What happens when de-focusing is combined to diffraction is explained in a technical article written by Jeff Conrad, to be downloaded from Tuan's companion large format web site.

Robert Hughes
27-Oct-2009, 11:54
Here's a question - if diffraction is caused by an abrupt transition caused by the iris edge, could diffraction be eliminated by having a "soft" edge - if the iris faded from transparent to opaque over a distance greater than the wavelength of light? This could be tested by photographing an out-of-focus circle or light source, with the negative substituted for an iris.

What do you think? Would it make a difference?

Jim Michael
27-Oct-2009, 15:47
You could experiment with this by shooting a LED laser pointer at the fuzzy edge you create and compare the diffraction pattern with one you get when you shine the laser on the edge of a razor blade.

Mike1234
27-Oct-2009, 16:39
Robert, When it comes to the irsis I would think diffraction problems would be better reduced by lazer-sharp edges (coming to razer-sharp edges) rather than bunted or soft ones. However, unless the difference between blunt and sharp were extreme I doubt it would be noticible. I've been wrong many times though.

Hmm... this begs to raise the old "round iris" verses "less round iris" debate again, doesn't it?

N Dhananjay
27-Oct-2009, 19:48
The explanation that works better for me (than light grazing the edge of an aperture) is the following. Think of dropping a pebble in water. Waves (ripples) now radiate from that spot. Imagine these waves approaching a concrete wall or embankment. Imagine there is a small slit in that concrete embankment with water flowing through the slit into another water body. The wave does go out into the other water body as a chopped off wavelet. Instead. the slit acts like another point where a stone was dropped - that is, the ripples now radiate from the slit into the other water body. Tried uploading some AASCI art to illustrate this but it didn't take - if it is unclear, I'll try scanning a pencil sketch or something.

The other simple way to think of this is that the more you stop down, the closer you are to a pinhole - that is, you are using practically none of that expensive glass you purchased.

Hope that helps.
DJ

stealthman_1
27-Oct-2009, 20:51
Interesting reading. But I do have one question. I have a hundred year old Goerz, Berlin, Doppel Anistigmat, 12 inch brass lens that I finally got around to making a lens board for. It stops down to f384 (marked stops are at 6,12,24,48,96,182, and 384), which still yields about a 3mm opening. Now I know older lenses were stopped down more because they had far less control of aberrations, but with everything mentioned here shouldn't this lens be pretty fuzzy at such an aperture?

Jack Dahlgren
27-Oct-2009, 22:42
Interesting reading. But I do have one question. I have a hundred year old Goerz, Berlin, Doppel Anistigmat, 12 inch brass lens that I finally got around to making a lens board for. It stops down to f384 (marked stops are at 6,12,24,48,96,182, and 384), which still yields about a 3mm opening. Now I know older lenses were stopped down more because they had far less control of aberrations, but with everything mentioned here shouldn't this lens be pretty fuzzy at such an aperture?

The markings may not be f/ stops. On a 12" lens, f/384 would be very very small. Not 3mm.

N Dhananjay
28-Oct-2009, 05:46
Interesting reading. But I do have one question. I have a hundred year old Goerz, Berlin, Doppel Anistigmat, 12 inch brass lens that I finally got around to making a lens board for. It stops down to f384 (marked stops are at 6,12,24,48,96,182, and 384), which still yields about a 3mm opening. Now I know older lenses were stopped down more because they had far less control of aberrations, but with everything mentioned here shouldn't this lens be pretty fuzzy at such an aperture?

As mentioned, this representes other systems of marking apertures. The f number that we are familiar with represents the size of the aperture as f/x, where f is the focal length and x are the f-number series we are familiar with (4, 5.6, 8, 11 etc). Basically, proceeds in a progression of sqrt of 2 or about 1.414. Why sqrt of 2 - because it halves the amount of light from the previous stop. The actual numbers are sort of rounded off to make them easy to remember. Other systems that have been popular include the US (uniform stop) system, Zeiss system etc. See the table near the bottom of the page at http://en.wikipedia.org/wiki/F-number for detils of some of these systems and their comparisons against the system we are used to today. The specific lens referred to here is using the Goerz system.

Cheers, DJ

Brian Ellis
28-Oct-2009, 07:40
The explanation that works better for me (than light grazing the edge of an aperture) is the following. Think of dropping a pebble in water. Waves (ripples) now radiate from that spot. Imagine these waves approaching a concrete wall or embankment. Imagine there is a small slit in that concrete embankment with water flowing through the slit into another water body. The wave does go out into the other water body as a chopped off wavelet. Instead. the slit acts like another point where a stone was dropped - that is, the ripples now radiate from the slit into the other water body. Tried uploading some AASCI art to illustrate this but it didn't take - if it is unclear, I'll try scanning a pencil sketch or something.

The other simple way to think of this is that the more you stop down, the closer you are to a pinhole - that is, you are using practically none of that expensive glass you purchased.

Hope that helps.
DJ

You really find it easier to understand your water example that to just know that bent light produces a soft image, light is bent when it strikes the edges of the aperture blades, and the smaller the aperture the more light is bent?

stealthman_1
28-Oct-2009, 08:09
See the table near the bottom of the page at http://en.wikipedia.org/wiki/F-number for detils of some of these systems and their comparisons against the system we are used to today. The specific lens referred to here is using the Goerz system.

Cheers, DJ

Thank you guys, that was very helpful. So I really have a lens with an aperture range of f7.7 to f64. That makes a tad bit more sense...:)

aduncanson
28-Oct-2009, 08:25
Clearly I have not been successful in convincing many people that the size of the aperture, not the length or character of its perimeter, is responsible for the limits to resolution imposed by diffraction. I really believe that physicists like to talk about diffraction at hard thin edges because it is a limiting case and is relatively easy to analyze, not because a hard thin edge is necessary for diffraction. Diffraction is a wave phenomenon. DJ’s model of a wave on a pond encountering a small slit is entirely appropriate, but remember that a lens at f/22 has an aperture that is on the order of 20,000 wavelengths of light and as Emmanuel pointed out, the wave front that encounters the slit is spherical and converging. Which is difficult to conceive of in the case of a wave on a pond.

I imagine that if overcoming the diffraction limit could be done by simply substituting an aperture with a soft edge transition, then the makers of process lenses would have marketed such a solution 4 or more decades ago. Trying to use a negative to create a gradual transition at the aperture’s edge will not be successful because the film grains are effectively opaque and are much larger than the wavelength of light so what you will have done is to create an aperture with much, much more perimeter than the corresponding circle or polygon would have. So by the theory that the length of the perimeter is critical, this would make for far worse diffraction.

My understanding, to the contrary, is that it is the size of the aperture that determines the size of the airy disk and hence the maximum theoretical resolution. Fiddling around with the character of the edge, (except conceivably in some very special cases analogous to a fractal antenna) would most likely affect only higher order (small size and low amplitude – essentially not observable) features of the diffraction pattern and not in any significant way, the gross size of the airy disk.

Rodney Polden
28-Oct-2009, 14:47
...... remember that a lens at f/22 has an aperture that is on the order of 20,000 wavelengths of light ....................

Wouldn't that number depend on the focal length AND aperture of the lens, rather than just the aperture? It seems to me that it's the area of the aperture rather than the f stop, that will determine how many photons will pass through it in a given length of exposure, no? And that in any case, the numbers of photons involved may well reach into the billions/trillions/who knows?

Something that I personally cannot understand wrt diffraction, is that surely (given the extremely small size of those photon wavelengths) the actual percentage of photons that _strike_ the edge of the diaphragm blades (out of the total number that pass during the exposure time) must be quite tiny, and not significant in proportion to all the other image-forming light rays that flow through the "open" area of the aperture. Even at small apertures, relative to the size of a photon's path, that is one HUGE hole.

I know there is some obvious explanation to this, but I haven't figured it out yet. Having said which, I still don't use f45 to f280, even though they're available...... I know very well that diffraction occurs, of course.

aduncanson
28-Oct-2009, 15:37
Wouldn't that number depend on the focal length AND aperture of the lens, rather than just the aperture? Sure does, good catch! That 20,000 estimate was for a 210mm lens at f/22.

It seems to me that it's the area of the aperture rather than the f stop, that will determine how many photons will pass through it in a given length of exposure, no? And that in any case, the numbers of photons involved may well reach into the billions/trillions/who knows?
Not sure that I believe in photons myself. :p

Something that I personally cannot understand wrt diffraction, is that surely (given the extremely small size of those photon wavelengths) the actual percentage of photons that _strike_ the edge of the diaphragm blades (out of the total number that pass during the exposure time) must be quite tiny, and not significant in proportion to all the other image-forming light rays that flow through the "open" area of the aperture. Even at small apertures, relative to the size of a photon's path, that is one HUGE hole.Here we go again. Try not to think of the cause as waves (or photons) grazing the edge, but rather as the summed contributions of all of those infinitesimal wavelets on DJ's pond. To achieve a diffraction free image requires an infinitely large aperture. The airy disk arises due to the missing contributions from the wavelets not present in the infinite plane surrounding the aperture.

pocketfulladoubles
29-Oct-2009, 13:21
...and to make it more complicated, the ripple in the pond represents only one wavelength of the fundamental propagation for an unbounded half-space with a pure point source (although higher orders may travel as well, but keep it simple for just the first order). Light consists of a continuum of wavelengths that will diffract accordingly. So, the question is then, and I don't know myself, is the blurring coming from the separation of frequencies, or maybe due to total internal reflection within the glass due to large angles from the diffraction? Also, WRT to Fraunhofer diffraction - isn't this assuming that the source is sufficiently far away to estimate that the incident spherical wave is essentially planar. What about focusing on close objects, and where is the cutoff when Fresnel diffraction comes back into play?

JoeV
29-Oct-2009, 16:00
I recall reading in a Photo Techniques magazine from years ago that diffraction is an artifact of the physical size of the aperture, not necessarily of the focal ratio (f-number), thus f/16 on a short lens (like a 50mm lens for a 35mm camera system) is about a 3.125mm aperture, whereas a 3.125mm aperture on a 150mm lens (for 4"x5") would yield a focal ratio of around F/48. Hence the "Group F/64" dictum isn't a proscription for diffraction, since a lens like a 300mm (for 8"x10") at F/64 would yield an aperture size of around 4.7mm in diameter, larger still than the F/16 on the 50mm lens.

Conversely, I've thought recently about diffraction and aperture sizes on subminiature digital sensor formats; for instance with the micro-4/3'rds format the 20mm f/1.7 Panasonic Lumix lens would already be at a 3.125mm aperture at just f/6.4, so it makes me wonder how much image quality is degraded by what would have been mere moderate apertures in larger formats.

~Joe

rdenney
29-Oct-2009, 16:43
Rather than delve into the details already being discussed, I would like to go back to the original question and make a statement of principle:

Diffraction t'ain't no big thang.

I would never choose an aperture based on diffraction.

1. When I want the background to be fuzzy, I use a large aperture.

2. When I want the background to be sharp, I use a small aperture.

3. If the background isn't sharp when it should be, the enlargability of the image, even if it is acceptable in a contact print (which it might not be), will be much more limited than it would be because of diffraction.

Thus,

4. Choose the aperture that provides the required depth of field, after adjusting the tilts to establish the proper focus plane. Get this step wrong, and the image is probably unusable at any enlargement. Get it right, and at worst diffraction will limit print size slightly. If the diffraction effects are intolerable by the time acceptable depth of field has been reached, then the image desired is photographically impossible and a different visualization (or print size expectation) is needed.

Further obsession about diffraction is motivated either by scientific curiosity (which is, of course, wholly acceptable) or by those who confuse precision with accuracy.

Rick "preferring accuracy" Denney

N Dhananjay
29-Oct-2009, 18:23
I recall reading in a Photo Techniques magazine from years ago that diffraction is an artifact of the physical size of the aperture, not necessarily of the focal ratio (f-number), thus f/16 on a short lens (like a 50mm lens for a 35mm camera system) is about a 3.125mm aperture, whereas a 3.125mm aperture on a 150mm lens (for 4"x5") would yield a focal ratio of around F/48. Hence the "Group F/64" dictum isn't a proscription for diffraction, since a lens like a 300mm (for 8"x10") at F/64 would yield an aperture size of around 4.7mm in diameter, larger still than the F/16 on the 50mm lens.

Conversely, I've thought recently about diffraction and aperture sizes on subminiature digital sensor formats; for instance with the micro-4/3'rds format the 20mm f/1.7 Panasonic Lumix lens would already be at a 3.125mm aperture at just f/6.4, so it makes me wonder how much image quality is degraded by what would have been mere moderate apertures in larger formats.

~Joe

This is the way physics textbooks typically describe diffraction - as the physical size of an aperture. But diffraction patterns are angular projections and so, in photography, it depends upon both the physical size of the aperture as well as the distance between the aperture and viewing screen (or film), which in photography is the f stop. In other words, while the physical aperture of f/8 is larger (lower diffraction) than the f/8 on a 50mm lens, there is a greater distance travelled by the less diffracted light from the 300mm lens (compared to the 50mm lens) and the resultant circle of confusion is thus as bad.

In other words, larger formats need smaller f stops for the same depth of field. This means more diffraction. However, large formats are enlarged less, so the blur circles are enlarged less. Thus, in reality, the only cost for larger formats is speed.

Cheers, DJ

Brian Ellis
29-Oct-2009, 19:01
Clearly I have not been successful in convincing many people that the size of the aperture, not the length or character of its perimeter, is responsible for the limits to resolution imposed by diffraction. . . .

I haven't read all the responses but anyone who doubts that it's the size of the aperture that affects the degree of diffraction is wrong. It clearly is the size of the aperture because the size of the aperture affects the proportion of bent light to "direct" light and it's that proportion that controls the degree of diffraction visible in the print. I'm not aware of any issue or dispute about that, it's like Photography 101.

sanking
29-Oct-2009, 21:07
I haven't read all the responses but anyone who doubts that it's the size of the aperture that affects the degree of diffraction is wrong. It clearly is the size of the aperture because the size of the aperture affects the proportion of bent light to "direct" light and it's that proportion that controls the degree of diffraction visible in the print. I'm not aware of any issue or dispute about that, it's like Photography 101.


Leslie Stroebel in View Camera Technique, 5th edition 1986, gives a formula for diffraction limited resolution as R = 1800/f–N, where R is the resolution in lines/millimeter, 1800 is a constant, and f-N is the f-number.

This is an approximation and would be different for Red, Green and Blue light. Other formulas exist for specific light wavelength.

However, from the Stroebel formula it is clear that it is not the absolute size of the aperture that determines diffraction limited resolution, but the focal length of the lens and the aperture.

For example, if we apply the Stroebel formula lenses of 200mm and 400mm would both have diffraction limited resolution of 112 lines/millimeter at f/16, but at f/16 the diameter of the aperture of the 400mm lens would be 25mm, that of the 200mm lens 12.5mm.

Sandy King

Kirk Fry
29-Oct-2009, 23:44
I did an unscientific test. I made pictures in my back yard on Tmax 100 with a 19in Artar at f22, f32, f45 and f64 and looked at the results with a microscope. I could only see minor diffraction effects at f64. I figure you would need to optically print at the size of a bill board and examine it with a loupe to see it even at f64. After that I decide not to worry about. KFry

Rodney Polden
30-Oct-2009, 00:05
I did an unscientific test. I made pictures in my back yard on Tmax 100 with a 19in Artar at f22, f32, f45 and f64 and looked at the results with a microscope. I could only see minor diffraction effects at f64. I figure you would need to optically print at the size of a bill board and examine it with a loupe to see it even at f64. After that I decide not to worry about. KFry

............so maybe the f/64 Group were for real, and not some wry comment about diffraction at all!

The curious thing about this discussion is that, having read it all and thought about it some, I find myself back at exactly the same state of mind that I encountered at the end of the previous discussion regarding diffraction on this forum.

Confused about diffraction? You bet (at least in the area of practical results vs. theory).

aduncanson
30-Oct-2009, 11:09
If you are only interested in making good photographs (And there is nothing wrong with that.) then you have no reason to read this post. It is written for those who do want to understand the origin of diffraction and those contemplating making some sort of aperture plate with a gentle transition from transparent to opaque in order to improve lens performance at small apertures.

Brian, Your conception of diffraction as a phenomenon that occurs at the edges of the aperture is exactly what I am arguing against. Sometimes one learns in Physics 107 that the explanations you were taught in Photography 101 are not so much gospel, as they are a teaching tool useful for silencing questions from, not too, enquiring minds.

Back to DJ’s very handy pond and the idea (attributed to Christiaan Huygens) that the wave front can be modeled as a line of infinitesimal points every one of which is a source of waves radiating concentrically. The waves radiating from that infinite number of sources add together (at every point in the field) to create the diffraction pattern observed on the other side of the slit. Now here is THE MIND BLOWING PART: Every point along that line at the slit in the wall CONTRIBUTES EQUALLY to the spreading of the beam that we call diffraction. Go back to the model and consider how it works. All points along the line are equally strong. They all spread their energy omni-directionally in the forward plane. The contributions of each source are summed equally, that is without weighting the sources near the edge more heavily than those in the center. Conclusion: They must contribute equally to the spreading.

All that it takes to eliminate this spreading is to replace the concentric waves that are missing along the line of the slit where the incident wave front is blocked by the concrete wall. A larger aperture better controls the spreading simply because this sum of the contributions of all the infinitesimal sources over the larger aperture produces a tighter pattern. To obtain perfection, just replace all of those infinitesimal sources out an infinite distance on either side of the slit. (Please do not waste too much time on this exercise.) :)

If you want to maintain that the waves grazing the edge of the aperture are especially bent, then you need some sort of explanation for this bending. What is it? It is not gravity; it does not depend on the density of the aperture material. It is not magnetism; the aperture material need not be magnetic. It is not refraction; it occurs in a vacuum just as surely as in air. It is not some perverse reflection at the edge; the edge need not be reflective. Another question to be answered is, "Why would the edge rays be bent more when the aperture is smaller?" If the light not near the edge is not bent, then the larger aperture should have a brighter central core, but the diffraction pattern should be the same diameter. In fact the diffraction pattern does become smaller in diameter as the aperture is made larger. Conclusion: the light at the edge is not especially spread or bent any more than the light passing through the center of the aperture.

Now, why would St. Ansel enshrine this misunderstanding in his highly esteemed textbook? I can only speculate that his resource on the physics of diffraction was some physicist (or worse an engineer) whose specialty was not optics or radar, and whom Ansel encountered over cocktails at a reception, and who was far more interested in getting Ansel’s opinion on the best camera than in straitening the famous man out on a subject that he never enjoyed and only dimly remembered.

N Dhananjay
30-Oct-2009, 18:02
If you want to maintain that the waves grazing the edge of the aperture are especially bent, then you need some sort of explanation for this bending. What is it? It is not gravity; it does not depend on the density of the aperture material. It is not magnetism; the aperture material need not be magnetic. It is not refraction; it occurs in a vacuum just as surely as in air. It is not some perverse reflection at the edge; the edge need not be reflective. Another question to be answered is, "Why would the edge rays be bent more when the aperture is smaller?" If the light not near the edge is not bent, then the larger aperture should have a brighter central core, but the diffraction pattern should be the same diameter. In fact the diffraction pattern does become smaller in diameter as the aperture is made larger. Conclusion: the light at the edge is not especially spread or bent any more than the light passing through the center of the aperture.



Interesting argument. Without prolonging the confusion too much (too late...!)...

I have read an explanation for the bending around the perimter of the aperture. The idea is that propogating wavefronts are 'balanced' in some way - that is, every wavelet is balanced by other wavelets around it. I cannot think of a better way to describe this than the term 'balanced' - if you think of the usual way waveforms are visualized, this has to be the case. Now when a beam of light is cut off by the obstruction of the edge of the aperture, there is an imbalance created. The waves in the center of the beam are still balanced by the waves on their sides. But for the wave at the edge, which just grazed the aperture - this one has lost the wave beside it which was 'supporting/balancing' it (that wave got blocked by the aperture).

Getting theory to match empirical evidence is a fascinating game but it is a constantly shifting playground. The ability to invent stories to account for the extant empirical evidence is only limited by human imagination - it is perfectly possible to have conflicting theories that cannot be falsified by the extant available data. The empirical evidence for diffraction and the math predicting those are reasonably straightforward, even if the reasons for light waves behaving the way they do is less straightforward.

But it makes for interesting reading and speculation... :-)

Cheers, DJ

percepts
31-Oct-2009, 08:25
LOL.

So the aperture in your camera has thickness and its edge has a profile which is indeterminate in any of your damned theories. The maths simply ignores this fact which is why real world evidence does not match theoretical limits in your typical camera lens. That aperture profile not only creates the theoretical diffraction, but it also reflects light all over the place in indeterminate directions. Common sense if you actually think about it. That reflected light, some of which is going to hit the film, is going to form a larger percentage of total light hitting the film as your aperture gets smaller. When the aperture becomes small enough, the reflected (not diffracted) light becomes more significant than other lens aberations. The calculations simply do not account for this because the aperture edge profile is indetrminate.

Why do pinhole cameras use gold leaf to create the best pinholes? Because it's thinness gives sharper images. But why do they do that? Is diffraction different for different thickness of aperture? What if the pinhole has a vertical edge 1mm thick. You know the answer. Light bounces off that edge just like it does in a lens aperture and that bouncing is not the diffraction which gives the theoretical limits for lens diffraction. That thickness ( edge profile ) blurs the image with light that has not followed the path you want it to.

So in conclusion there is diffraction which is theoretically calculatable and there is diffusion which is not predictable in your average camera lens but which is not significant until apertures become small. The thinner your aperture blades, the smaller the aperture you can use without suffering from aperture edge diffusion.

Rodney Polden
31-Oct-2009, 11:47
.....in which case, a Waterhouse stop, being circular, will result in less scatter of light and diffraction than a conventional bladed diaphragm, since it can be made both thinner and shorter in circumference for a given aperture area.

That might be of interest for those of us who have barrel lenses with a slot for Waterhouse stops. A bit fiddly, I will admit, but then, if you can't take fiddly, you probably won't dig large format anyway;)

percepts
31-Oct-2009, 12:13
.....in which case, a Waterhouse stop, being circular, will result in less scatter of light and diffraction than a conventional bladed diaphragm, since it can be made both thinner and shorter in circumference for a given aperture area.

That might be of interest for those of us who have barrel lenses with a slot for Waterhouse stops. A bit fiddly, I will admit, but then, if you can't take fiddly, you probably won't dig large format anyway;)

The problem with gold leaf is that it's so fragile. For pinhole cameras its doable if you have something to support the leaf and a means of punching the hole without destroying the leaf. But if you have a 6mm aperture the edge of the leaf would just move around so you need something more rigid which means thicker.

Nathan Potter
31-Oct-2009, 17:49
For photographers Sandy Kings explanation is of great practical merit. Photographers are interested in the smallest spot size that can be imaged on the film surface. This size limit is determined by diffraction effects (as well as the quality of the optics of course). People dealing with optics call this smallest resolvable spot an Airy disc and its' diameter D is simply D= 2.44(lambda)N where lambda is the wavelength of light and N is the f/no. of the aperture. This is just a different form of what Sandy has said. Since N is the ratio of the diameter of the aperture to lens focal length both the diameter of the opening and the focal length are relevant. It's easy to compute the Airy disc diameter for example for any f/5.6 lens at say 500 nm (0.5 um) lambda. It is 2.44 X 0.5 um X 5.6 which = about 7 um. At f/64 we have 2.44 X 0.5 X 64 + about 78 um. This relation holds provided the optics of the lens is sufficiently well corrected to be able to image the 7 or 78 um spot of detail from the subject. Also the lens would have to be able to image all the visible light spectrum at the same point and that would require an apochromat type lens if we want our spot to contain that whole spectrum.

The bottom line here is that in practical LF field use resolution on film is hard to achieve in the under 50 um Airy disc size (10 lp/mm) without real attention to detail and critical focusing.

This diffraction effect from a circular aperture is the result of ray bundles from a common subject source transversing a different path length through the lens to the film. Those rays along the optical axis have a shorter path than those near the edge of the lens in reaching the film. The thickness of the edge of the aperture has nothing to do with this physical effect. However if the aperture is of a finite thickness then edge reflections are possible which will contribute reflective artifacts in the image.

The question of an edge that is graded in density came up and what would that effect be. The diffraction pattern would be blurred depending on the width of the gradation.

Modern microfabrication techniques allows us to make almost infinitely small openings using for example gold films that are very thin - say 0.1 um in thickness. This is done by depositing the gold film on a carrier layer say a 5 um layer of polyimide resin. A resist mask is applied and photolithographically exposed and developed then used as a mask against a gold etch which etches through the thin gold film. Then the polyimide is etched using the same applied mask making a hole all the way through. The polyimide can be over etched leaving the gold film overhanging the polyimide hole very slightly. Thus we have a tiny pinhole - as small as modern microfabrication will allow us to make - which can be submicron.
Now we can pose a real physics question. If the pinhole diameter is smaller than the wavelength of light what kind of diffraction pattern results?

Nate Potter, Austin TX.

percepts
31-Oct-2009, 19:58
Never mind the theoretical physics, at what point does the reflective property of the aperture edge become more siginificant than the diffraction and other lens aberations in a typical large format lens.
I'd guess at about 6mm aperture diameter but I have no way of proving it. And I guess no one here has actually measured all these theories in typical large format lenses. They have only measured resulting resolution and not actual airy disc size or proofs of theory. i.e. they have only proved that the theory doesn't hold true and not what typical reality is.

Jack Dahlgren
31-Oct-2009, 23:19
The problem with gold leaf is that it's so fragile. For pinhole cameras its doable if you have something to support the leaf and a means of punching the hole without destroying the leaf. But if you have a 6mm aperture the edge of the leaf would just move around so you need something more rigid which means thicker.

I made pinholes with brass sheet, dimpled it and sanded the dimple until it was quite thin and poked it with a needle. I can't imagine that moving from that to micro-machined gold leaf would improve the quality of the image much.

percepts
1-Nov-2009, 15:12
I made pinholes with brass sheet, dimpled it and sanded the dimple until it was quite thin and poked it with a needle. I can't imagine that moving from that to micro-machined gold leaf would improve the quality of the image much.

Well at least you've tried to make it as fine an edge as possible with material which is not too fragile.

Emmanuel BIGLER
2-Nov-2009, 03:11
Hello All !
Coming back to this technical discussion after several days...

from Robert Hughes
could diffraction be eliminated by having a "soft" edge -

In fact not. The effect is subtle. When the iris is a conventional one with sharp edges, the image of a single point source exhibits some ripples around the main disk, like in the Airy disk. In real photography in white light this image of a single source point is always blurred because different wavelengths generate different ripples of different diameters that overlap and blur each other.
An iris with a soft edge is something I am not aware of in photography, but this has been used in some optical instruments like spectrometers. When the aperture has soft edges, you can suppress the ripples in the image of a single point source of monochromatic light, but you do not cancel diffraction in the sense of this image has a certain width like an Airy disk.

Somebody mentioned that iris with sharp edges are easier to model and the calculation is easier ; in fact (see next remark)...

...From " pocketfulladoubles"
Also, WRT to Fraunhofer diffraction - isn't this assuming that the source is sufficiently far away to estimate that the incident spherical wave is essentially planar.

Yes, but Fraunhofer diffraction also includes all phenomena thar occur near an image.
Imagine that you focus your image at the focal plane. In this plane you get the image of what is located at infinity in front of the camera. When the iris is stopped down to a small aperture, much smaller than any other lens mounts, you may consider that the optics itself generates the perfect geometrical image of a diffraction pattern located at infinity.
Hence, diffraction effects in the focal plane and diffraction effects at infinity are exactly the same. It is more difficult to justify why in fact the same Fraunhofer model holds for any kind of image even at 1:1 ratio in macro...

The Fraunhofer diffraction image is computed by a mathematical model called : Fourier transform, and with modern computer techniques, you can Fourier-transform anything in a snap, not only a rectangular slit or a circular aperture !
And regarding an aperture with soft edges, the best mathematical model would be a gaussian transmission factor for the iris, you could generate this, painfully in practice, with a miniature graded filter of suitable darkening law to the egdes. In this case you would get no ripples at all in the image of a single point source, the Airy disk with additional ripples would be replaced bay another Gaussian intensity distibution.

Hence : soft edge means : no ripples and probably very smooth bokeh, but diffraction would not be canceled.

from SanKing
Leslie Stroebel in View Camera Technique, 5th edition 1986, gives a formula for diffraction limited resolution as R = 1800/f-N,

I have Stroebel's book which is, IMHO (for the English-speaking world) the reference for all of our readers who want to learn beyond the basic use of a view camera without being bored by too much maths.

We can re-interpret Stroebel's formula as follows : if the resolution limit in line pairs per mm is equal to 1800/N, then the cut-of period, 1/R, is equal to N/1800 millimetres i.e. 0.55 x N microns.

0.55 microns is the wavelength of light at the centre of the visible spectrum, this is the wavelengh of maximum sensitivity for the humen eye. If we accept to be slghtly more conservative and extend the visible spectrum to 0.7 microns, where the sensitity of the human eye drops to zero, then we get a worst-case estimation for diffaction effects : 1/R = 0.7 x N in microns, for a resolution limit of 1400/N cycles per mm.

I prefer the formula 1/R = diffraction cut-off period = 0.7 x N in microns because I know by heart how to multiply by 1.4 or 0.7 the usual series of f-numbers ;-)
We can directly compare this cut-off period to the period of the sampling grid in a digital sensor. In an ideal world with as many independant fine pixels as possible on the sensor, there would be no moiré / aliasing effects in digital images, we would always use at least two digital samples for one cut-off period of diffraction...
This is already close to be achieved in Sony's last camphone sensor with 12 Mpix stuffed in a tiny sensor with a diagonal of 7 mm. The sampling period in this miracle of technology is 1.4 microns, minimum image period according to the samplng theorem is 2.8 microns, this corresponds (using the 0.7 N microns as our rule of thumb) to a diffraction-limited lens @f/4.


From "percepts"
So the aperture in your camera has thickness and its edge has a profile which is indeterminate in any of your damned theories. The maths simply ignores this fact which is why real world evidence does not match theoretical limits in your typical camera lens....When the aperture becomes small enough, the reflected (not diffracted) light becomes more significant than other lens aberations.

Interesting suggestion about the influence of scattered / diffuse light in a photographic lens.
"veiling glare" (as defined in the ANSI standard PH3615-1980) or "flare" is a phenomenon for which lens manufacturers do not say much.
Source of flare are multiple and certainly parasitic reflection on the edges of the iris do contribute. Flare actually makes small details less visible by adding a background to the main image, but this background does not suppress the visibility of fine details. Whereas diffraction exhibits an absolute cut-off period. When stopped down to f/64 with a cut-off period of about 45 microns, nothing smaller than 45 microns can be perceived. With flare only an no diffraction, the contrast of small features of 45 microns in size would be reduced but the features could still be visible.

Hence : When the aperture becomes small enough, the reflected (not diffracted) light becomes more significant than other lens aberations
I disagree here. Sure, with a poorly-designed pinhole for a lens-less cameras, you get scattered ligth, and you cannot reach a total field of 120° ; but the diffraction cut-off period is still absolute, although we do not deal here with Fraunhofer diffraction. When a coated (even single-coated) lens like an apo-ronar is stopped down to f/128, fine details are blurred by diffraction, not by flare. Incidentaly, there is suprisingly very little flare in a 4/4 dialyte design like the apo ronar : fewer lens elements and restricted available image field being the reason for this.

Regarding diffraction versus parasitic flare.
In the case of imaging with a Fresnel zone plate, the actual f-number of the zone plate gives you the size of the tinest details that you can record, the Fresnel zone plat is... diffraction-limited ; unfortunateley, most home-made zone plates are plagued by so much scattered ligth that the benefits of a smaller diffraction cut-off period due to the wider effective aperture is almost cancelled by the presence of the unwanted background of light directly transmitted. But small details are actually there, this has been proved, for example, by various experiments in microscopy with soft X rays, no lenses being available in this part of the spectrum. Scientist have used Fresnel zone plates instead of lenses and the actual resolution limit is as expected, although parasitic light levels are high.

Regarding how the simple mathematical model for Fraunhofer diffraction matches or not real-world lenses, I have handy the FTM curves for the apo ronar series ; @f/22 the lens at the center of the field is incredibly close to a diffraction-limited lens. @f/32 no surprise, the diffraction-limited model applies in its simplicity, up to a field of about 40° !

GPS
2-Nov-2009, 08:07
Hello All !
Coming back to this technical discussion after several days...
...

Source of flare are multiple and certainly parasitic reflection on the edges of the iris do contribute.

... !

Good grief, let's stay on earth ! Flare from reflection on the edges of the iris is a red herring - there is no surface to speak of and the direction of rays is not prone to a reflection either. If not, we could also speak (with much more reason but the same lack of realism) about flare from reflections on lens blackened edges or - why not, staying in the fishing industry - about light reflected of dust particles present in the space around the aperture...:) ;)

aduncanson
2-Nov-2009, 09:32
Thanks Emmanuel, I appreciate your informed, enlightening contributions. I was not aware of the use of the Fourier Transform to analyze diffraction at an arbitrary edge or aperture. But I was thinking about instructors of undergraduate physics and photography classes, not engineers trying to solve real world problems when I suggested that the diffraction at a simple sharp edge is easier to model. A Fourier Transform will get you results, but it may be a little too much of black box to be of great teaching value at an introductory level.

Rodney Polden
2-Nov-2009, 13:37
I did an unscientific test. I made pictures in my back yard on Tmax 100 with a 19in Artar at f22, f32, f45 and f64 and looked at the results with a microscope. I could only see minor diffraction effects at f64. I figure you would need to optically print at the size of a bill board and examine it with a loupe to see it even at f64. After that I decide not to worry about. KFry

The science is interesting.......... but then so are the real-world applications in our craft of the information that science can provide us, regarding this issue of diffraction.

I understand fully that many posters are focussed on gaining a deeper insight into how exactly it is that diffraction occurs, and it is in that spirit that I am following the discussion here. Yet there does seem to be such an enormous discrepancy between the automatic assumptions that any small aperture (below f22 according to some, below f32 according to others, and not until f64 according to others) will result in degraded sharpness apparent on film, and the post from Kirk Fry quoted above.

Since the apertures that most of us commonly shoot at lie in this same range f22 to (gasp) f64, it seems to me it would be useful to be able to define for a given focal length exactly what is the aperture at which diffraction will be even detectable to the microscopic gaze, and indeed to the viewer/buyer of the resulting image.

For myself, I'm not really clear at this point if there is a definite consensus about whether focal length alters the aperture at which diffraction will be detectable. Some of the evidence seems to indicate that, but others seem to be disagreeing, yes? no? I'm not wishing to create acrimony or dissension on this, but "confused about diffraction?" certainly seems to invite clarification on issues such as this.

The difference even between f32 and f45 will be a hugely significant step in the series of trade-offs and balances that make up the movements used and the choice of exposure length and aperture, prior to releasing the shutter. (These apertures were chosen with 8x10 in mind, but the equivalents for your own format are equally applicable of course.) That may determine whether to re-compose to leave out elements that cannot be brought into focus, and so on. Or alternatively, to accept a different rendition of water, foliage etc.

In the end, the whole process rests upon a set of choices or trade-offs. Where something like film speed is concerned, there is a certainty that's broadly definable as, say, within half to one stop of manufacturer's rating. With film choice, a certain grain structure must be accepted (give or take small improvements from processing technique, developer choice etc). Where DoF is concerned, there is a fairly clearly visible change from unsharp to sharp, when a good loupe is used. With a certain choice of shutter speed, movement or blur can be predicted or eliminated.

In the case of diffraction from small apertures however, there seems to be much less certainty than with these other elements of the process. If we cannot confidently say, yes, at f/so-and-so this lens will inevitably be reduced from the sharpness to be had at one stop wider an aperture, then I am left feeling that the certainty that "ought" to be available has not yet been arrived at.

If we were talking about a 28mm lens on a 35mm camera, I would likely never use f16 unless I had no alternative. (It may be that f11 is actually an issue, maybe f8, but I haven't experienced diffraction per se at f8. Who knows?)

But this is LF, so what are the equivalent apertures for a 65mm lens, a 90, a 135, a 180, a 210, a 250, a 300, a 360, a 480, a 600? And let's assume for the sake of argument, that we're talking about a 6x enlargement, say.

Maybe in this way, we can move away from sensing a dark and possibly unwarranted cloud of assumed diffraction hanging over quite innocent and usable apertures. Or maybe we won't, but the discussion is sure to be thought-provoking.

rdenney
2-Nov-2009, 13:54
For those who still have an enlarger, there is a way to explore these issues. Just put a grain focuser under the enlarger, and look at different apertures through it. The effects of diffraction will be plain to see at the smallest apertures, as will the effects of lens faults at the widest apertures. Even at f/45, I never saw any loss of resolution from my ancient enlarging lens enough to mask the visible grain structure of the film.

One might do the same thing with a very fine ground glass and a very strong magnifier--maybe 20x. One would need a strongly lit subject to make viewing possible, but it's not something we'd need to do for every image, of course. It's just a way to calibrate our experience. I would make the comparison not only with subjects at the plane of sharp focus, but with subjects not focused but (hopefully) within the depth of field, to see where depth of field stops and diffraction begins. For most practical subjects, I suspect that diffraction will turn out to be a pretty minor effect compared to depth of field.

I have a cheapie Radio Shack 30x microscope. I guess I'll have to try my own experiment to see if it really works. Looking through a 30x microscope to a 4x5 ground glass would be like looking closely at a 10x12-foot print made from that film. If it works, I'll report back.

Of course, if I can't see the effects of diffraction in a 10x loupe on the ground glass, then I won't see them on a 40x50" print (from 4x5) looked at without aid.

If we are designing systems (or if we just like thinking about it in those terms), we need the science. If we just want to make good usage decisions, the empirical approach may be easier than trying to understand the science.

Rick "realizing that most practitioners are probably not comfortable with the mathematics of the frequency domain" Denney

aduncanson
2-Nov-2009, 15:12
In terms of the practical application I thought that there had been a pretty strong consensus. The size of your negative and your desired print gives the resolution you need in the negative, typically by something like 6 or 8 lppmm X the magnification in the print; and some rule of thumb like 1400/F-No, 1600/F-No or 1800/F-No tells you the best resolution that a particular aperture can deliver. If you want to be pretty conservative you might choose to use 8 lppmm for the print resolution and 1400/F-No as safe choices. For my typical 3-4X magnification prints (from 4x5 or 5x7), that allows me to stop down to f/45. To make an occasional 5X print (assuming I still intended to view it from as close as my bifocals will allow), I should probably respect a limit of f/32.

On the other hand, If I wanted to make a 12X print from a 35mm negative then I have keep the aperture faster than f/16, and I have to hope my lenses and film can resolve 96 lppmm under the prevailing conditions.

Finally, even if the performance of your enlarging set up matches that of your taking set up, you will get something worse through the two processes in series, so you should probably stay inside of the aperture limits calculated above by one or even two whole stops.

Barrie B.
2-Nov-2009, 23:01
Greetings all, I come in late to this discussion.
The 'f' stop on a lens, any lens , eg. f8 the diameter of the hole is one eighth the focal length of the lens. Therefor
a 50mm for 35mm camera has approx 6mm aperature @ f8.
a 150 mm lens for 4X5 @ f8 has approx. 18.5mm hole.
a 300mm lens for 8X10 @ f8 has approx. 37.5mm hole.
a 450mm lens for 'any film format' @ f8 has approx. 56mm hole.
Compact digital lenses 8mm or less VERY SMALL HOLE.

It is my belief that the size of the hole , NOT the number of the 'f' stop is what determines ' defraction '.

A large format lens with an f2 aperature would have a 150mm hole if it were a 300mm focal length , an expensive and very heavy piece of glass and a very large shutter if it were to be in the lens .
cheers Barrie B.

Peter K
3-Nov-2009, 01:11
The 'f' stop on a lens, any lens , eg. f8 the diameter of the hole is one eighth the focal length of the lens.
Only if the diaphragm is in front of the lens. In any other cases the f stop isn't a real diameter but the diameter of the lightbeam that can pass through the lens. If the diaphragm is placed between the lens the diameter of the incident beam is greater as the 'hole'.

The f-stop cannot measured directly by measuring the 'hole'. With most lenses the 'hole' diameter is more or less 30 per cent smaller as the f-stop, f/focal-lenght.

Cheers
Peter

rdenney
3-Nov-2009, 01:25
It is my belief that the size of the hole , NOT the number of the 'f' stop is what determines ' defraction '.

I once thought diffraction was governed by objective truth that didn't require belief, only agreement, and then I read the inner workings of this thread. I'm still sure there's objective truth in there, but it seems to be known by a smaller group than I once thought.

In any case, the f-number includes both the absolute diaphragm diameter and the focal length. f/5.6 is indeed bigger on a longer lens, but then that longer lens also magnifies the image more. That increase magnification enlarges the smaller diffraction effect. So, it's an approximate wash, apparently, leaving us with just the f-number.

Rick "glad the practical math ends up being simple" Denney

Emmanuel BIGLER
3-Nov-2009, 01:59
It is my belief that the size of the hole , NOT the number of the 'f' stop is what determines ' diffraction '.

Hello from the other side of the Earth (France)

Depends on which quantity you measure for the effects of diffraction

- if you consider the angular resolution limit in object space, then you are right, the absolute aperture diameter is the relevant quantity ; the angular resolution limit for an aperture "a" is lambda /a (in radians).
For the human eye if we take lambda = 0.5 to 0.6 microns (maximum of sensitivity of the retina to the solar light) and an iris diameter of 2 mm (during day time), we get an angular resolution between 0.25 and 0.3 milliradians ; one second of arc is about 0.29 milliradian, this is consistent with experimental tests of visual acuity ; at least for jet fighter pilots, my visual acuiy is probably closer to 2 seconds of arc, this is what I use for computing my home-made Depth of Field tables ;-)

- if you consider the linear details (in millimeters or in microns) recorded in the image plane, hence the f-number is the relevant quantity, not the absolute aperture diameter, and as mentioned above, the formula is extremely simple, the absolute cut-off frequency is equal to N. lambda. N = f/a

Both approaches are of course identical, depending on your application, since the connection between the angular resolution in the object space and linear resolution in the image plane for distant objects is simply :
(linear resolution in the focal plane) = (focal length) x (angular resolution in object space)

BTW this is the best definition for the focal length of any thick compound lens system, the focal length transforms a certain feature of angular size "alpha" in radians into a linear detail in the focal plane of size "f . alpha" in millimeters or microns (of course, lenses engraved in inches do the same, but in mils on output ;-) )
This definition allows to escape endless discussion about the position of principal or nodal planes of a thick asymmetrical system ;-)

Struan Gray
3-Nov-2009, 03:53
Emmanuel, shouldn't there be a 'tan' in there too?

i.e. D = f*tan(alpha) for rectilinear lenses.

Emmanuel BIGLER
3-Nov-2009, 05:08
Emmanuel, shouldn't there be a 'tan' in there too?

Yes, Struan, but for a small detail smaller than one degree of arc, sine = tangent = arc in radians ...

BTW and not kidding, I tried to check the focal length of my 360 Tele-Arton by measuring the rotation angle required for a distant object to cross the image field (about 10 cm) ; the precision is poor with a Gitzo 3-way head with graduations every 5 degrees. However one could imagine to connect some long rods to the rotating tripod head an measure the displacement of the rod at the end ;-)
(some of my favourite test targets at infinity are here, easily accessible from my home : http://www.besancon.fr/gallery_images/site_1/257/263/22394/quaivauban.jpg)

Struan Gray
3-Nov-2009, 05:34
Don't get me started on the photographic industry's neglect of the Vernier scale :-)

That said, even 'precision' lab mounts don't pretend to be accurate to anything beyond 0.1° if they're manually actuated. As you said, a long lever arm is better.

Orion works pretty well as an angular target for longer lenses - if you can fix the weather. Aussies and the like can use the Southern Cross instead. Otherwise you're back to that other perennial discussion, the location of infinity.....

Emmanuel BIGLER
3-Nov-2009, 06:03
neglect of the Vernier scale...

Shame on me ! No Vernier scale on my tripod head !
[OFF-TOPIC]Did you know that Pierre Vernier, the inventor of the Vernier scale was a true franc-comtois, born in Ornans, Courbet's city, close to home ! ;-)

Struan Gray
3-Nov-2009, 06:38
I know enough to capitalise "Vernier", but to my shame, that's about it.

Diffraction matters less than you might think because the Airy function is leptokurtic - it's more sharply peaked than the familiar Gaussian normal curve. That means it doesn't spread things out nearly as much as would a Gaussian with the same 'width', and it defeats easy formulations in terms of vaguely-defined 'resolution limits'.