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Understanding diffraction


timarmes

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Hi,

 

I'm not sure where to post this question. We're missing

a "Technical" forum. Since this question regards lenses, which are

indeed camera equipment, this forum seems the best choice of a bad

bunch.

 

Can someone please explain to me why, exactly, diffraction is related

to the f/stop and not to the physical size of the aperture. I

understand that diffraction is due to light passing through a hole,

and will be more prominante for smaller holes. However the size of

the aperture at, for example, f/8 on a 200mm is entirely difference

to that of a 22mm yet the diffraction will be the same. Physically,

why is this?

 

Thanks,

 

Tim

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.

 

I LOVE this technical stuff - it's so much easier to resolve, so to speak, than "real" photography! ;-)

 

 

Diffraction is NOT due to light passing through a hole, but rather to light passing over the sharp edges of a hole.

 

"Diffraction" itself is related to f/stop or aperture in that the GREATER the f/stop or aperture, the greater the edge surface area over which the light passes, and the GREATER the diffraction. The circumference is all that matters when calculating the potential diffraction.

 

But few people are concerned about diffraction on it's own. What is important is the amount of diffraction COMPARED to the amount of image forming light.

 

Diffraction is more prominent at smaller f/stops or apertures NOT because there is more diffraction -- because there isn't, there's LESS diffraction at smaller f/stops / apertures -- but due to the even smaller amount of image forming light getting through. What we observe at decreasing f/stops / apertures is actually an increase in the diffraction to "signal" ratio. That is, as we decrease our f/stop / aperture, even though the total diffraction goes down, at the same time the total amount of image-forming light is going down at an even greater rate at smaller f/stops / apertures. So the ratio between them changes in favor of the diffraction at smaller f/stops / apertures.

 

In ANY group of common activities, there tends to be abbreviations and resulting jargon -- which is intended to increase the speed and accuracy of communication between initiated members. However, this "coding" actually inhibits accurate communications with the uninitiated and thereby limits the growth and penultimate success of the group. What you have been hearing people say is probably, "... diffraction increases at smaller apertures ..." when what they should have been saying is, "... the total effect of diffraction increases at smaller apertures ..." or, "... diffraction-to-signal ratio increases at smaller apertures ..." That would have been more accurate if more time consuming.

 

Was this helpful?

 

Click,

 

Love and hugs,

 

Peter Blaise peterblaise@yahoo.com http://www.peterblaisephotography.com/

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It's just the other way round. Diffraction is related to the PHYSICAL dimensions of the aperture (or rather the circumference of the aperture). Any aperture of same diameter (but different f-stop number depending on the focal length of the lens) will give the same amount of diffraction. The light rays passing through the lens do not know about the focal length (and the focal length to aperture diameter ratio, AKA known as f-stop number) but only know an amount of circumference where diffraction happens.

 

That's, BTW, one of the reason why people still use large format (4x5inch and above). They can use much higher f-stop numbers (like f/64) but still do not get more diffraction than with a 35mm format lens stopped down much less.

 

Most 35mm lenses perform best around f/11. At higher f-stop numbers, diffraction dominates although you cut a smaller center piece out of the lens diameter (and thus reduce most of the abberations which are related to the distance between light rays and optical axis). When using larger formats (and lenses with much longer focal length), you can stop down much more and still get an acceptable amount of diffraction.

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<i>It's just the other way round. Diffraction is related to the PHYSICAL dimensions of the aperture</i>

<p>

Wrong.

<p>

Diffraction effects at the film plane are a function of the focal ratio. This is because the amount of diffraction that occurs as the light passes through the aperture is only half the story. The deflected rays then spread out as they travel toward the film, and they spread out further the longer the focal length. It's easiest to think of this as a pinhole a certain distance (the focal length) from the film. But it works the same for lenses.

<p>

The reasons people get away with using very slow f-stops in large format photography is that the degree of magnification from the negative to the print is less, so the negative needs to be less sharp.

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In fact diffraction is extremely dependent on the size of the aperture. However, it isn't the diameter of the aperture, but rather the angular size of the aperture as seen from the film plane that determines diffraction.

 

An f/8 aperture for a 200mm lens has a diameter of 25mm. Viewed from the film plane, a 25mm aperture 200mm away subtends 7.15 degrees.

 

In a 22mm lens, the f/8 aperture is 2.75mm, but because it is nine times closer to the film it subtends the same angle, 7.15 degrees, when viewed from the film plane.

 

(This geometry also explains, in a graphical way, why a given f/ number always produces the same illumination on the film regardless of the focal length of the lens.)

 

Since diffraction is a result of the light interacting with the edges of the physical aperture, and is (for practical purposes) not affected by the glass elements, then the total diffraction depends ONLY on the angle subtended by the aperture as viewed from the film. Since that angle is the same for a given f/stop in any lens, diffraction is always the same for a given f/stop.

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In any elementary physics textbook, you'll usually see a formula

for <em>angular</em> diffraction expressed as a function of the

hole diameter (or slit width; physics textbooks often study

the problem in 2-d). The <em>angular</em> diffraction of

a given wavelength is indeed inversely related to the hole diameter.

<p>

But photographers are rarely concerned directly about how wide

an angle the point source spills out into. They are more likely to

be concerned with how large the diffraction halo becomes at the

film plane. In other words, how much it effects resolution as

measured in lines per millimeter. To convert the angular spread

to a size at the film plane, you must multiply by the distance

between the diaphragm and the film plane, or in other words, the

focal length.

<p>

Since diffraction at the film plane is inversely related

to hole size, and directly related to focal length, it's

easy to show it's directly related to

(focal length)/(aperture diameter). And that is precisely the

formula for the f-number that photographers use.

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Hi all,

 

Thanks for your answers. Alan, your answer was particularly helpful to me, however I'm still not quite there...

 

When I draw out the situation you describe, with effectively two similar triangles, and it seems to me that the light that diffracts as it passes through the aperture at 200mm will have spread out further from the focus point than the light that deffracts at the 22mm mark, because it has further to travel before hitting the film. I would therefore expect more deffraction from the 200mm lens.

 

What am I missing?

Tim

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Diffraction occurs whenever any wavefront passes an edge, be it in a circle, square, or slit. The wavefront need not be electromagnetic radiation but can be associated with a particle. It is always a direct function of the wavelength involved, and inversely related to the size of any aperture or slit in the system. Diffraction at an edge is a little more complicated, but there are many good treatises which discuss the subject and give examples. Diffraction isn't always something to but minimized, but can be put to good use in gratings and grizms.
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<i>Diffraction is NOT due to light passing through a hole, but rather to light passing over the sharp edges of a hole.</i>

<p>

Actually it IS due to light passing through a hole.

<p>

Sharp edges certainly are not necessary. If they were, the optical performance of a lens could be improved by making the edges less sharp. Suppose we constructed an aperture and instead of a diaphragm we used a piece of glass, clear in the center and continuously, progressively darker toward the outside, until it was opaque. No edges. It isn't done because it would be a waste of time -- you'd still have diffraction.

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<I>...it seems to me that the light that diffracts as it passes through the aperture at 200mm will have spread out further from the focus point than the light that deffracts at the 22mm mark, because it has further to travel before hitting the film.</I><P>

OK, I don't like trying to understand diffraction myself, because frankly it requires more math than I want to deal with in what is supposed to be a "fun" hobby! That may explain my tendency to try to reduce things to a qualitative understanding rather than insisting on numerical precision. Which of course makes things tougher to explain, even when I think I sort of understand what's going on...<P>

We can probably agree on a gross description of what diffraction (for our purposes) is: when a beam of light (i.e., parallel rays from a point at infinity) passes through an aperture, the beam leaving the aperture is no longer quite parallel, but instead some of the light rays are spreading out. This is the phenomenon called diffraction.<P>

It turns out that the ANGLE to which the light is diffracted is inversely dependent on the physical size of the aperture. Smaller aperture equals larger angle of diffraction. (So, the occasional photon that might [in theory] make it through an infinitely small aperture could go any direction at all, since the Airy disc for an infinitely small aperture will be infinitely large...)<P>

So, yes, the smaller physical aperture in a 22mm lens will diffract the light to a greater angle than will the same f/number in a 200mm lens. However, since the 22mm lens is much closer to the film, the diffracted light rays get less time to spread out (as it were.) While the light from the 200mm lens does have more distance to travel, the diffracted rays are spreading at a narrower angle. In fact, the angular diffraction and the extra distance exactly cancel out, so the resulting Airy disc (the area that contains about 83.8% of the light that came through the aperture) is the SAME DIAMETER for either lens (at the same f/stop.)<P>

When you toss it all into a bag and shake it up, what falls out is that the f/number alone is needed to calculate the diffraction effects that we need to worry about. Everything else cancels out.<P>

Useful documents abound online. <A HREF="http://www.mellesgriot.com/pdf/001.20-1.22.pdf">HERE'S ONE.</A>

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Many thanks, especially to Alan Davenport for his pithy answer. I suddely understand a lot more about this than I did a minute ago.

 

However, several other answers raise a question for me. Some of you said that it is related only to the circumference of the aperture (as seen from the film), but my understanding was that it's related to the ratio of the circumference to the area.

 

 

That is, the light passing an edge is diffracted, while the light passing through the middle is not. With a smaller aperture, the light passing edges make up a larger percentage of the total light because the circumference is proportional to the radius while the area is proportional to the square of the radius, so diffraction effects will be more noticable with smaller apertures.

 

Is there any truth to that, or am I blowing smoke?

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.

 

First off, I'd like to say how much I really enjoy these discussions. I imagine that in moments, hours, at most, days, we are collecting an international group of people sharing insights and information that years ago took months if not years to happen. If Isaac Newton and Albert Einstein were alive today, they'd be happy and proud.

 

Secondly, I also enjoy our process. Some of us respond quickly with extemporaneous thoughts "off the top of our heads", and then the same or others respond with incredible research, experience and insights.

 

Thank you all!

 

I'm reminded of my childhood with a gang of boys huddled near the radio, listening to the game, discussing sports statistics and player's performances and skills. We haven't changed much, have we? But, where are the girls? Do any of us have any compatriots of the female persuasion who may pitch in on and expand these exchanges, or have we relegated ourselves to yet another "boys club"?

 

= = = = = = = = = =

 

Earlier on this thread: "... Useful documents abound online. HERE'S ONE...."

 

Peter Blaise responds: Since I at least read these threads in print, NOT on the web, the revealing of links is very helpful.

 

"HERE'S ONE" = http://www.mellesgriot.com/pdf/001.20-1.22.pdf from a greater volume from Melles Griot, this 3 page section entitled "Fundamental Optics, Diffraction Effects", covers circular aperture, slit aperture, energy distribution table, and gaussian beams, and is replete with formulae. Be aware that is is designed to support their business success, not define terms on their own, so they ONLY deal with diffraction in optical systems. Though this is appropriate for us, we may have to go a step further back to define our terms themselves and then apply them to our optical experiences here. Let's explore an example:

 

= = = = = = = = = =

 

Earlier on this thread: "...Actually [diffraction] IS due to light passing through a hole..."

 

Peter Blaise responds: Can anyone please tell me how a ray of light "knows" it's passing through a hole?

 

Presumably the "hole" is larger than at least a couple of rays of light otherwise it would not be much of a hole, right? Then, presumably, one "ray", say, one particular ray on the left side of the bunch ... well, how would it get information from a ray on the right side of the bunch, saying, "Hey, guys, this is a HOLE! Everyone on the periphery get ready to behave differently -- DIFFRACT"? What? Is there some sort of inter-light-ray/photon communication system that is sharing information about the media surrounding those light rays/photons? A communication system that moves information FASTER than the speed of light within the light ray/photon beam? If Isaac Newton and Alfred Einstein were alive to day they'd be spinning in their graves!

 

In order for the light rays/photons to take different action depending on passing through a hole or not, they would have to "see" in advance and then make their plan conditional in such information and then "spread the word" amongst themselves, "hole ahead, those on the periphery get ready to diffract". Otherwise, if they only assessed the hole once they were in it, then, at the speed of light, they'd already be at the image plane before they could respond.

 

No, it's the edge effect and the edge effect only. That fact that the edge is shaped like a hole is interesting to us as photographers with circular lenses, but it is not of much interest to the light rays/photos themselves, which behave as predicted by edge effect science, not hole science, if there were any!

 

= = = = = = = = = =

 

Earlier on this thread: "...Sharp edges certainly are not necessary..."

 

Peter Blaise responds: I put it to you that an edge is ALL any one particular light ray/photon "sees". See above for an exploration of the shared presumption * of a lack of a "super light speed inter light ray/photon communication system" that would inform one or more light rays/photons to behave otherwise due to remote environmental media information "observed" by one group of light rays/photons, information otherwise not immediately accessible to the first group of light rays/photons.

 

= = = = = = = = = =

 

Earlier on this thread: "...the optical performance of a lens could be improved by making the edges less sharp. Suppose we constructed an aperture and instead of a diaphragm we used a piece of glass, clear in the center and continuously, progressively darker toward the outside, until it was opaque. No edges. It isn't done because it would be a waste of time -- you'd still have diffraction..."

 

Peter Blaise responds: Isn't done? Oh, yes it HAS been done, and is commercially available today. The Minolta AF 135mm f/2.8 [T4.5] STF Smooth Trans Focus lens does take advantage of such a apodized "filter" within it's lens element system and aperture control system. It was the source of my first conversation here at photo.net with Philip Greenspun over how to calculate T value, "true" light transmission value. We don't have to go far - this lens is reviewed right here at photo.net:

 

http://www.photo.net/equipment/minolta/lenses

 

"...[Minolta] STF 135mm/f2.8 [T4.5] ... For those who think Minolta doesn't make exotic special-purpose lenses, here's a doozy. When it came time to fill the gap left by their long-discontinued 135mm/f2.8 ... the folks at Minolta decided to build a high-tech siege gun designed to wage war on the out-of-focus areas of your pictures, particularly portraits. I'd never heard of an apodization filter before, but it's there, along with a second ten-blade aperture designed to give precise control over aperture (the two features together are responsible for the T-stop designation). The goal is to produce a very smooth transition between in-focus and out-of-focus areas in your pictures, and reduce or eliminate distracting background effects ... this is the easiest-to-focus lens I've ever used, period... "

 

Trivia: it's also the ONLY electronic A-mount lens Minolta made that's MANUAL FOCUS only!

 

= = = = = = = = = =

 

* Perhaps we should define our terms more precisely at the beginning of our threads before we get off on a wild goose chase through our mis-meanings of them. Here, for our archives, from Google, the simple lookup: [define:diffraction] -- these aren't necessarily right or wrong, just already "out there" in the popular domain for our reference.

 

Definitions of diffraction on the Web:

 

* The bending of light around objects, such as cloud and fog droplets, producing fringes of light and dark or colored bands.

http://www.wrcc.dri.edu/ams/glossary.html

 

* A phenomenon exhibited by a light?s wave front when passing the edge of an opaque object (one that does not allow light to pass through it). The light becomes modulated, causing a redistribution of the light?s energy within the wave front. You will see it at the edges of the object?s shadow, in the form of minute dark and light bands. The edges of the shadow have a fuzzy appearance. Think of ripples meeting a rock in a pond. They go around the rock in a new series of ripples that can be seen on the sides

http://photographytips.com/page.cfm/1601

 

* Diffraction, the deviation of light from rectilinear propagation, is a characteristic of wave phenomena which occurs when a portion of a wave front is obstructed in some way. When various portions of a wave front propagate past some obstacle, and interfere at a later point past the obstacle, the pattern formed is called a diffraction pattern.

http://www.physics.nwu.edu/ugrad/vpl/glossary.html

 

* Change in direction and intensity of light as it passes by an obstacle or through an aperture.

http://www.thebeerchair.com/html%20documents/astronomy%20dictionary.htm

 

* Energy redistribution due to an obstruction or change in the surface over which it is passing. Diffuse 1. To pour in different directions. 2. Spread out or dispersed, not concentrated.

http://www.yourwebassistant.net/glossary/d6.htm

 

* The process whereby RF [radio frequency] signals or sound waves are, in certain circumstances, deflected from their normal straight-line path by physical objects.

http://www.audiotechnica.com/glossary/

 

* A type of distortion due to multi-path resulting in the spreading out or ?smearing? of the received signal. It occurs when identical signals arrive via different paths and have different time delays.

http://www.bluewaveantenna.com/technical/glossary.html

 

* The spreading of light as it passes a sharp edge of an opaque object.

http://sohowww.nascom.nasa.gov/explore/glossary.html

 

* The bending of a wave front around an obstacle in the sound field. [3]

http://www.keithyates.com/glossary.htm

 

* The bending of light as it passes through a small slit or opening. When we study the diffraction of sunlight, we see a rainbow of colours.

http://www.ontariosciencecentre.ca/school/clc/visits/glossary.asp

 

* The tendency of waves to bend around corners. The diffraction of light establishes its nature as a wave.

http://astronomy.nju.edu.cn/astron/AT3/GLOSS_D.HTM

 

* scattering of X-rays (in this case) from a crystal. It depends on the "long- range" order in the crystal. More disorder means poorer diffraction especially at higher resolution.

http://adelie.biochem.queensu.ca/~rlc/work/teaching/definitions.shtml

 

* The modification of white light as it breaks up into the color spectrum.

http://secretsofthegemtrade.com/glossary.htm

 

* when light waves bend around an obstruction, i.e. [id est, "that is"] suspended particle, and move in a new direction.

http://www.serc.si.edu/labs/phytoplankton/primer/definitions.jsp

 

* A fundamental and inescapable physical phenomenon where, in all light beams, some energy is spread outside the region predicted by rectilinear propagation.

http://www.navitar.com/zoom/zoom_glossary.htm

 

* is the breaking up of white light causing spectral colours.

http://www.costellos.com.au/opals/glossary.html

 

* The process by which the direction of radiation is changed so that it spreads into the geometric shadow zone of an opaque or refractive object that lies in a radiation field. Diffraction is an optical ?edge effect,? differing only in degree from scattering. Diffraction becomes more evident when dealing with particles similar to, or larger than, the wavelength of the radiation. In meteorological optics, important diffraction phenomena include the aureole, Bishop's ring, corona, iridescent clouds, etc. The principle of diffraction may also be applied to the propagation of water surface waves, as into the sheltered region formed by a barrier

http://amsglossary.allenpress.com/glossary/browse

 

* The deviation in the path of a wave that encounters the edge of an obstacle.

http://www.fisicx.com/quickreference/science/glossary.html

 

* The change in the direction of a wave train at the edges of objects.

http://www.physchem.co.za/Common%20Files/Glossary.htm

 

* the scattering of light from a regular array of points or lines, producing constructive and destructive interference

http://www.learnchem.net/glossary/d.shtml

 

* An effect on wavefronts passing though an aperture. Wavefronts passing by the edges of the telescope pupil are bent and result in fringe patterns in the resulting image.

http://cfao.ucolick.org/EO/steinb/education_outreach/demoweb/home/glossary.html

 

* the spreading or bending of light that occurs when light passes around an edge.

http://www.icknowledge.com/glossary/d.html

 

* The spreading of a wave motion, such as light as it passes an obstacle and expands into the region that is behind the obstacle. Differentiation See magmatic differentiation, planetary differentiation, and sedimentary differentiation.

http://imnh.isu.edu/digitalatlas/glossary/letter.asp

 

* Deviation of a ray from a straight course when partially cut off by an obstacle, or when passing near the edges of an opening.

http://www.pqcorp.com/technicalservice/Glossary.asp

 

* bending of wave, i.e. light and sound, around obstacles in their path. Diffraction effects are common in microscope systems where apertures are used to help measure very small samples.

http://www.harricksci.com/infoserver/GLOSSARY/glossary.cfm

 

* when light passes sharp edges or goes through narrow slits the rays are deflected and produce fringes of light and dark bands

http://wordnet.princeton.edu/perl/webwn

 

* Diffraction is the apparent bending and spreading of waves when they meet an obstruction. It can occur with any type of wave, including sound waves, water waves, and electromagnetic waves such as light and radio waves. Diffraction also occurs when any group of waves of a finite size is propagating; for example, a narrow beam of light waves from a laser must, because of diffraction of the beam, eventually diverge into a wider beam at a sufficient distance from the laser. http://en.wikipedia.org/wiki/Diffraction

 

= = = = = = = = = =

 

Earlier in this thread: "... the light passing an edge is diffracted, while the light passing through the middle is not. With a smaller aperture, the light passing edges make up a larger percentage of the total light because the circumference is proportional to the radius while the area is proportional to the square of the radius, so diffraction effects will be more noticeable with smaller apertures..."

 

Peter Blaise responds, finally (oh, yeah, when did I EVER go "final" on any discussion?!?): THANK YOU! Now please re-read my FIRST reply at the top of this thread. Thanks for the paraphrase. At greater apertures, the total amount of accurate image forming light overwhelms the recording of diffraction effects at the image plane, even though there's more total diffraction due to there being more total edge surface to the aperture. At smaller apertures, the total diffraction is smaller due to the smaller total edge surface of the aperture. But even smaller still is the proportion of accurate image forming light remaining which can no longer overwhelm the diffraction effects from being recorded as a higher percentage of the light striking the image plane.

 

It's not "diffraction" per se that we're concerned about, it's "diffraction to signal ratio".

 

Apparently the effects of diffraction are made worse or lessened only by:

 

Relative aperture size:

 

- Wider apertures = greater diffraction, but lesser diffraction effects reaching the image plane as a portion of the total image forming light.

 

- Smaller apertures = lesser diffraction, but greater diffraction effects reaching the image plane as a portion of the image forming light.

 

Distance from the image plane to the aperture:

 

- Greater distance from image plane to aperture = lesser diffraction effects being "recorded" due to some diffracted light being bent away from the narrow angle to the image plane.

 

- Shorter distance = greater diffraction effects being recorded due to greater amount of diffracted light included in the wider angle to the image plane.

 

Any examples? After all, we can include pictures here at photo.net!

 

Click!

 

Love and hugs,

 

Peter Blaise peterblaise@yahoo.com http://www.peterblaisephotography.com/

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.

 

Add the word RECORDED above and below. Again, more or less diffraction is less important than the ratio of REDORDED diffraction to the RECORDED image forming information at the image plane:

 

It's not "diffraction" per se that we're concerned about, it's RECORDED "diffraction to signal ratio".

 

Apparently the RECORDED effects of diffraction are made worse or lessened only by two criteria:

 

One: Relative aperture size (that is, aperture edge "length" or circumference relative to aperture area):

 

- Wider apertures = more edge surface area over which light will defract = greater total diffraction, but lesser diffraction effects reaching the image plane as a portion of the total RECORDED image forming light.

 

- Smaller apertures = less edge surface area over which light will defract = lesser total diffraction, but greater diffraction effects reaching the image plane as a portion of the REDORDED image forming light.

 

Two: Distance from the image plane to the aperture:

 

- Greater distance from image plane to aperture = lesser diffraction effects being "recorded" due to some diffracted light being bent away from the narrow angle of approach to the image plane.

 

- Shorter distance from image plane to aperture = greater diffraction effects being "recorded" due to greater amount of diffracted light included in the wider angle of approach to the image plane.

 

Endless editing, eh?

 

Click!

 

Love and hugs,

 

Peter Blaise peterblaise@yahoo.com http://www.peterblaisephotography.com/

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The confusion about diffraction seems to alot on photo.net . One wants a lens to be diffraction limited; this is perfection. A Diffraction limited design is the ULTIMATE in perfection. Optics speaks of diffraction by arc angle; OR a distance resolved on a plate; film or sensor; for a given focal length lens. For a telescope; aperture in inches/millimeters is what matters for resolving arc angle with double stars; not f stop. With an object that can be magnified; photo lenses have diffraction limits that varies with f-stop. A diffraction limited lens at F8 can resolve twice a diffection limited lens at f16. Most/many lenses increase in resolving power when stopped down a couple of stops; then drop some when further stopped down. Many photo books and sites water/dumb down diffraction; consult an optical book. Most folks have camera shake; miss focus; etc that really limit the resolving power of their systems.
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It was suggested that diffraction could be reduced or eliminated by getting rid of the sharp edges in the aperture diaphragm (and also in the shutter blades in a between-the-lens shutter). This is true and practical in a few applications. This is known as Apodizing. It could be made from a graded filter with maximum transmission in the center with built-up density to a maximum at the periphery, according to a specific formula. It will sightly increase the width of the first maximum, but get rid of much of the fringes. Unfortunately, it would seldom seem practical when a variable aperture is required.

 

My experience in apodization was with optical spectrometers where scattered light was often a bane to good performance. Apodizing masks were applied to the diffraction gratings to minimize the secondary maxima.

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Apodizing masks are sometimes used with amateur reflectors; with mirrors somewhat not perfect in the hand done parabolic process; off of a spherical. Here a 6 inch might be tried with a 5.5; 5; or 4 inch mask; cut with a star cuttout. One can observe double stars with known arc separations; and trial and error make a custom mask.
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<B>Previously, on <U>Understanding Diffraction</U>:</B><P>

<I>Apparently the effects of diffraction are made worse or lessened only by:<P>

Relative aperture size:<P>

- Wider apertures = greater diffraction, but lesser diffraction effects reaching the image plane as a portion of the total image forming light.<P>

- Smaller apertures = lesser diffraction, but greater diffraction effects reaching the image plane as a portion of the image forming light.<P>

Distance from the image plane to the aperture:<P>

- Greater distance from image plane to aperture = lesser diffraction effects being "recorded" due to some diffracted light being bent away from the narrow angle to the image plane.<P>

- Shorter distance = greater diffraction effects being recorded due to greater amount of diffracted light included in the wider angle to the image plane.</I><P>

=============================<P>

This is simply incorrect -- exactly the opposite of what the math tells us about diffraction! Diffraction is greater for smaller apertures, less for large apertures. The circumference of an aperture is not mentioned in any of the formulas that define diffraction, only the DIAMETER of the aperture.<P>

The AMOUNT of diffraction, if we need a quantity, is determined by the diameter of the spot formed (by diffraction) at the image plane. (Note that this is <U>not</U> referring to the "circle of confusion" that we use when discussing depth of field.) The diameter of the Airy disc for a particular wavelength of light can be given by the following formula:<P>

<B><I>y = 2.44 * lambda * f#</I></B><P>

where <B>lambda</B> is the wavelength, <B>f#</B> is the numerical f/stop of the aperture, and <B>y</B> is the diameter of the Airy disc.<P>

It's worth commenting at this point, that the resulting value will ALWAYS be larger than the physical diameter of the aperture: we can never escape diffraction.<P>

Recall that the f# is, by definition, the focal length divided by the physical diameter of the aperture. Using "D" for the focal distance and "d" for the aperture diameter, our <B>f/#</B> becomes <B>D/d</B> and our formula for the Airy disc becomes:<P>

<B>y = (2.44 * lambda * D) / d</B><P>

For purposes of this discussion, we don't care about a particular wavelength of light, nor for that matter the precise diameter of the Airy disc. So we can throw out the wavelength and the constant and come up with:<P>

<B>Diffraction [is proportional to] D / d</B><P>

What this tells us is that a wider aperture ("d" is larger) the amount of diffraction is LESS, not more. And that for a longer focal length ("D" increases; the aperture is at a greater distance from the image plane) the diffraction will increase.<P>

For any given scene, there is an optimum f/stop. "Optimum" being defined as the f/stop that will produce the best definition on the film over the required depth of field. If the aperture you choose is too large, defocus effects will predominate and you will lose definition. If the aperture is too small, diffraction will overwhelm the image and you lose definition.<P>

I'll stop now.<P>

For a much more concise discussion of the science than you'll get from me, see the <a href="http://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/diffracon.html#c1">hyperphysics page on diffraction,</a> and pay particular attention to the link to <a href="http://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/cirapp2.html#c2">Circular Aperture diffraction,</a> which is of course what we're talking about.

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