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murrayatuptowngallery
Posted: Tue Mar 11, 2008 6:58 pm
Joined: 09 Jul 2005 Posts: 38 Location: Michigan
Hello:

I am curious about diffraction's role in photographic imaging, if any.
That's my background, with some physics from an engineering
curriculum. SO I hope to understand replies, just lack enough
education to my question myself. I'm not in the sci.optics filed, so I
realize there is some inherent ignorance in my questions.

I noticed in a few classic optics texts that a chapter on diffraction
appears to be the starting point for imaging. The simplest example of
interest to photographic imaging is the circular aperture. It and the
slit are apparently the only things simple enough to attempt a
rigorous text derivation of with minimal assumptions and
approximations.

Rayleigh may have used the phrase 'Imaging without refraction or
reflection' in his paper on resolution limits.

This leaves only diffraction. To me, it's intuitive that diffraction
is the only reason a pinhole image is produced that is much wider than
the pinhole aperture. The index of refraction is the same on either
side of a pinhole aperture. A pictorial image is just a more complex
situation than a laser demonstrating diffraction with an aperture.

It occurred to me that many photographers are obsessed with and
misunderstand diffraction. They lust for 'diffraction-limited' optics,
and thus assume by judicious use of their equipment they can avoid
diffraction 'effects'. I also hear pinhole photographers talk of
avoiding diffraction or "too much" diffraction. I believe this should
only be relevant to a loss of resolution from too small an aperture

I am getting to my question...it occurred to me that I remembered a
lens or an aperture both act as (or at least can be modeled/explained
as) a Fourier transformer. The aperture function is present in both a
lens (whether is has an iris or it's own clear diameter inherently
limiting it as an aperture) and in a circular pinhole aperture.

Is it not the case, then, that diffraction is the method by which
imaging occurs in a 'lens-based' optical system as well? ...and
refraction provides the bending, focusing and improved resolution as
an 'improvement' on the fundamental effect of the aperture and
diffraction?

Or is diffraction really a minor effect in an optical system using a
large enough aperture to avoid resolution loss from diffraction?

Lastly, regarding the fact that a simple lens and a pinhole aperture
both invert an image, is either diffraction or the Fourier transform
the common factor causing the inversion. (I'm notentirely comfortable
with this question, as the phenomenon existed before the 'name'
Fourier transform became available...and thus may only be a model or
explanation for the phenomenon.

Thanks

Murray Leshner
Holland MI
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Philip McCulloch
Posted: Wed Mar 12, 2008 10:19 am
Guest
Murray,

You're asking an awful lot here. A message board is a difficult place
to cover several lectures worth of material regarding physical optics.

One statement I can quickly clarify is in regards to a photographer's
hunt for diffraction limited optics. The diffraction limit of an
optical system defines the smallest point that can be formed at the
image plane. The derived equation for the diameter of this
fundamental spot is 2.44 * (wavelength) * F/# . It can be derived
from fourier optics techniques and wave theory (if you consider the
two topics to be separate). 88% of the energy that would form this
point is contained within this circle.

So why do photographers care about the size of a diffraction limited
spot, or if a system is diffraction limited at all? An optical system
can create distortions in the image (the general term we use is
aberrations, and distortion is a particular type of aberration). A
diffraction limited system is one that is free of all aberrations and
is therefore producing the best images possible limited only the
barriers of physics. In a scenario where the pixels of your detector
are small enough (say 1/2 the size or less of the diffraction limited
spot) the diffraction limit directly defines the resolution an imaging
system is capable of.

You may recall back to the early days of Hubble. The optics weren't
tested properly initially which led to improper manufacturing which
created a terrible amount of spherical aberration. The images were
blurry until additional optics were put in place to reverse the
effects spherical aberration and restore the telescope to diffraction
limited imaging quality, and thus maximizing the resolution of the
system.

If you in Ann Arbor and want to talk optics over a beer I'm around. I
think there is also an active OSA group here too but I haven't
attended their meetings.

Cheers,
Philip
Salmon Egg
Posted: Wed Mar 12, 2008 1:33 pm
Guest
In article
<4efc8d32-bce7-49bb-943e-27be6fcdfbc2@u72g2000hsf.googlegroups.com>,
murrayatuptowngallery@yahoo.com wrote:

Quote:
I am curious about diffraction's role in photographic imaging, if any.
That's my background, with some physics from an engineering
curriculum. SO I hope to understand replies, just lack enough
education to my question myself. I'm not in the sci.optics filed, so I
realize there is some inherent ignorance in my questions.

<snip>

You ask many good questions that I cannot and will not answer in this
kind of a forum. It is something you have to lern for yourself with
possibly some guidance in this forum.

The diffraction theory of imaging is described in books like Born and
Wolf. It uses wave physics and mathematical methods, especially those of
integral calculus. It is not a description of only diffraction effects.
It includes geometrical (ray) optics (no diffraction) but also
describes the diffraction effects sitting on top of the geometrical
optics.

Good luck. Have fun.

Bill
murrayatuptowngallery
Posted: Wed Mar 12, 2008 9:34 pm
Joined: 09 Jul 2005 Posts: 38 Location: Michigan
OK, sorry.

It was a long-winded question. I was kind of looking for an answer
like:

A) I oversimplified a complex subject.
B) Yeah, I nailed it.
C) I misunderstood and made too many assumptions.

It's not for a class, by the way. I couldn't sleep the other day and
that's what I was thinking about. I figured the best kind of Dr. to
talk to about that problem would be here. Born & Wolfe was one of the
books I was reading a year or so ago. I got the big picture but not al
lthe details.

Really all I wanted to know (maybe I can make it fit category A B or
C), were the following, which might better be asked in a photo forum
but for all the old wive's tales, urban legends & krap that gets
passed around there. :O)

1) Am I correct in insisting that pinhole photography works for all
practical purposes solely BECAUSE of diffraction?

2) If Q1 is true, is diffraction fundamental to image formation with a
lens or is it reduced to merely an undesirable side effect to be
controlled like aberrations (I believe diffraction is not an
aberration).

I hope that's more acceptable. If not, I'll keep reading here & there.

and thanks for the beer & optics offer. Unfortunately I only make it
there occasionally for unpleasant things like family medical issues. I
miss living in a house full of grad students at school. It was just
such an environment- if someone didn't know the answer, there was
enough knowledge or interest to pursue it somewhat or lead to other
resources. That's the first thing I noticed about leaving school for
employment. Most people were only interested in the beer and not the
topics :O)

Thank you

Murray
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Helpful person
Posted: Thu Mar 13, 2008 2:08 am
Joined: 22 Jun 2004 Posts: 677
On Mar 13, 3:34 am, murrayatuptowngall...@yahoo.com wrote:
Quote:
OK, sorry.

It was a long-winded question. I was kind of looking for an answer
like:

A) I oversimplified a complex subject.
B) Yeah, I nailed it.
C) I misunderstood and made too many assumptions.

It's not for a class, by the way. I couldn't sleep the other day and
that's what I was thinking about. I figured the best kind of Dr. to
talk to about that problem would be here. Born & Wolfe was one of the
books I was reading a year or so ago. I got the big picture but not al
lthe details.

Really all I wanted to know (maybe I can make it fit category A B or
C), were the following, which might better be asked in a photo forum
but for all the old wive's tales, urban legends & krap that gets
passed around there. :O)

1) Am I correct in insisting that pinhole photography works for all
practical purposes solely BECAUSE of diffraction?

2) If Q1 is true, is diffraction fundamental to image formation with a
lens or is it reduced to merely an undesirable side effect to be
controlled like aberrations (I believe diffraction is not an
aberration).

I hope that's more acceptable. If not, I'll keep reading here & there.

Murray


1. Pinhole photography works despite diffraction. If you consider
rays coming from an object point their spread is limited by the
pinhole size. Hence initial thought would lead one to believe that
the smaller the hole, the sharper the image. (Ignore brightness for
now.) However, considering light from a single object point,
diffraction at the pinhole spreads out the light making the image
larger. To optimize the geometry you need to arrange for the
geometric (ray) image size to be similar to the diffracted image
size. (I believe that for best results the pinhole size is equal to
the diffraction size. Others please confirm.)

2. I'm not sure what you mean by "fundamental to image formation".
It could be argued either way. However, diffraction if an important
factor to take into account when designing (and using) well corrected
lenses. It is because of diffractive effects that the lens acts as a
low pass (spatially) filter. Hence it always needs to be considered.

Diffraction will reduce the spatial response of an imaging system, in
some cases limit it (as a filter it results in a high frequency cut
off; see MTF) and in others result in unwanted stray light.

Hope this is helpful!
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Helpful person
Posted: Thu Mar 13, 2008 3:12 am
Joined: 22 Jun 2004 Posts: 677
On Mar 12, 4:19 pm, Philip McCulloch <philip.mccull...@gmail.com>
wrote:
Quote:

If you in Ann Arbor and want to talk optics over a beer I'm around.  I
think there is also an active OSA group here too but I haven't
attended their meetings.

Cheers,
Philip

You should attend them, or at least get on the mailing list. They
have some interesting speakers.
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murrayatuptowngallery
Posted: Thu Mar 13, 2008 3:31 pm
Joined: 09 Jul 2005 Posts: 38 Location: Michigan
Thanks, all.
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Dave Bell
Posted: Sat Mar 15, 2008 9:07 pm
Guest
murrayatuptowngallery@yahoo.com wrote:

Quote:
Lastly, regarding the fact that a simple lens and a pinhole aperture
both invert an image, is either diffraction or the Fourier transform
the common factor causing the inversion. (I'm not entirely comfortable
with this question, as the phenomenon existed before the 'name'
Fourier transform became available...and thus may only be a model or
explanation for the phenomenon.

I was surprised that none of the responses in the newsgroup addresses
this question, the simplest of them all.

Neither diffraction nor Fourier tr4ansformation causes the inversion. It
is a simple matter of geometry, and best visualized if you consider a
pinhole camera. A ray of light, say from the top of a tall tree, passes
through the pinhole aperture or lens, and strikes the film plane near
the bottom. A ray from the base of the tree passes through the same
opening, and strikes the film at the top. The image is inverted, no?

Dave
murrayatuptowngallery
Posted: Mon Mar 17, 2008 2:42 pm
Joined: 09 Jul 2005 Posts: 38 Location: Michigan
Yeah, I'm starting to think whether I'm being narrow minded in
thinking diffraction is responsible for imaging. Geometry, ray
bending,etc alone seemed too simple :O(

Yet diffraction seems to be responsible for more than just limiting
resolution. Maybe it's just wishful thinking on my part!
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Phil Hobbs
Posted: Mon Mar 17, 2008 9:50 pm
Guest
murrayatuptowngallery@yahoo.com wrote:
Quote:
Yeah, I'm starting to think whether I'm being narrow minded in
thinking diffraction is responsible for imaging. Geometry, ray
bending,etc alone seemed too simple :O(

Yet diffraction seems to be responsible for more than just limiting
resolution. Maybe it's just wishful thinking on my part!

Wave propagation (and cleverly designed lenses and mirrors that modify it) is
what is responsible for imaging.
Diffraction is really just a name we give to those phenomena in which wave
propagation is noticeably different from the predictions of the ray model.

For most purposes, ray optics is better than good enough, and it's very
simple and (reasonably) intuitive. Ray optics doesn't take into account the
limitations of imaging caused by the finite wavelength of light or by
polarization, and when that matters, we fix it up afterwards using
diffraction theory and other hand methods.

Cheers,

Phil Hobbs
Brian
Posted: Mon Mar 17, 2008 11:22 pm
Guest
On Mar 18, 7:21 am, Salmon Egg <Salmon...@sbcglobal.net> wrote:
Quote:
In article <47DF2DDF.3090...@electrooptical.net>,
 Phil Hobbs <pcdhSpamMeSensel...@electrooptical.net> wrote:
snip
For paraxial rays, you can calculate most diffraction effects using
GEOMETRICAL OPTICS! This is the method made popular by Kogelnik and Li
using ABCD matrices. This technique was developed to analyze laser
resonators. The method is presented in many books about lasers. AE
Siegman's (who post here) book Lasers is one of them. This technique is
insufficient to describe marginally stable resonators.

snip
Of course it isn't only in optical resonators that this is true. What

most optical designers like me find extraordinary is that for an
optical system which is "useful" (in other words, not too badly
aberrated), the aberrations and hence the diffraction performance, can
be estimated through ray tracing. In other words, starting with the
assumption that light only travels in straight lines, you can come up
with a very good approximation to the distribution of intensity in the
diffraction pattern in the image plane, which is based on the fact
that it doesn't! And because it is the image plane that you are most
interested in most of the time, the fact that these approximations
fall apart in the intervening spaces is irrelevant. What is
particularly stunning about this is that it made the design of
excellent lenses possible long before we had today's computing power.
The earliest calculations of diffraction patterns were carried out
when rays were traced using 7-figure tables.

Brian
Ancient and Modern Optics
Salmon Egg
Posted: Tue Mar 18, 2008 2:21 am
Guest
In article <47DF2DDF.3090901@electrooptical.net>,
Phil Hobbs <pcdhSpamMeSenseless@electrooptical.net> wrote:

Quote:
murrayatuptowngallery@yahoo.com wrote:
Yeah, I'm starting to think whether I'm being narrow minded in
thinking diffraction is responsible for imaging. Geometry, ray
bending,etc alone seemed too simple :O(

Yet diffraction seems to be responsible for more than just limiting
resolution. Maybe it's just wishful thinking on my part!

Wave propagation (and cleverly designed lenses and mirrors that modify it) is
what is responsible for imaging.
Diffraction is really just a name we give to those phenomena in which wave
propagation is noticeably different from the predictions of the ray model.

For most purposes, ray optics is better than good enough, and it's very
simple and (reasonably) intuitive. Ray optics doesn't take into account the
limitations of imaging caused by the finite wavelength of light or by
polarization, and when that matters, we fix it up afterwards using
diffraction theory and other hand methods.

Cheers,

Phil Hobbs

Diffraction theory (of imaging) is not merely a method of determining
the part of the image that is different from geometrical imaging. The
usual approach is in the form of a diffraction integral that gives the
field in a plane. If it is a geometrical image plane, you will get the
geometrical image PLUS all the artifacts attributed to diffraction. For
a wavelength approaching zero, you merely get the geometric image.

For paraxial rays, you can calculate most diffraction effects using
GEOMETRICAL OPTICS! This is the method made popular by Kogelnik and Li
using ABCD matrices. This technique was developed to analyze laser
resonators. The method is presented in many books about lasers. AE
Siegman's (who post here) book Lasers is one of them. This technique is
insufficient to describe marginally stable resonators.

This is a valuable technique to study because variations of it can be
used to cover many fields other than resonators. Electric circuits and
optical thin-films are just two of them. See Louis Pipes in the Condon
and Odishaw Handbook of Physics.

Bill
Salmon Egg
Posted: Tue Mar 18, 2008 12:18 pm
Guest
In article
<81645c03-81c9-4b93-8680-c2c821f1fdbd@e10g2000prf.googlegroups.com>,
Brian <brian4052003@yahoo.co.uk> wrote:

Quote:
Of course it isn't only in optical resonators that this is true. What
most optical designers like me find extraordinary is that for an
optical system which is "useful" (in other words, not too badly
aberrated), the aberrations and hence the diffraction performance, can
be estimated through ray tracing. In other words, starting with the
assumption that light only travels in straight lines, you can come up
with a very good approximation to the distribution of intensity in the
diffraction pattern in the image plane, which is based on the fact
that it doesn't! And because it is the image plane that you are most
interested in most of the time, the fact that these approximations
fall apart in the intervening spaces is irrelevant. What is
particularly stunning about this is that it made the design of
excellent lenses possible long before we had today's computing power.
The earliest calculations of diffraction patterns were carried out
when rays were traced using 7-figure tables.

Can you be confusing aberration with diffraction? Almost all lens design
is based upon geometric optics. The wave nature of light is unimportant.
The pathlength differences from aberrations are usually much greater
than those involving diffraction. Nevertheless, the diffraction integral
will show the effects of diffraction and aberration.

Bill
Phil Hobbs
Posted: Tue Mar 18, 2008 3:39 pm
Guest
Salmon Egg wrote:

Quote:
Diffraction theory (of imaging) is not merely a method of determining
the part of the image that is different from geometrical imaging. The
usual approach is in the form of a diffraction integral that gives the
field in a plane. If it is a geometrical image plane, you will get the
geometrical image PLUS all the artifacts attributed to diffraction. For
a wavelength approaching zero, you merely get the geometric image.

There are different ways of doing it. Probably the most common is to
trace rays to the exit pupil, compute the phase shift by the ray path
lengths and the amplitude by the obliquity factor times the Jacobian,
and then compute the image with either the Huyghens or Kirchhoff
propagator.

Quote:

For paraxial rays, you can calculate most diffraction effects using
GEOMETRICAL OPTICS! This is the method made popular by Kogelnik and Li
using ABCD matrices. This technique was developed to analyze laser
resonators. The method is presented in many books about lasers. AE
Siegman's (who post here) book Lasers is one of them. This technique is
insufficient to describe marginally stable resonators.

No, you can't. You can, e.g. use ABCD matrices to reduce the paraxial
wave propagation to a double integral, which is a very valuable
simplification. However, you still have to do the integral, and that's
where the wave properties get put in.
Quote:

This is a valuable technique to study because variations of it can be
used to cover many fields other than resonators. Electric circuits and
optical thin-films are just two of them. See Louis Pipes in the Condon
and Odishaw Handbook of Physics.

Whether one thinks of diffraction as a perturbation on a ray theory, or
as a first-principles wave propagation calculation is a semantic issue,
not a physical one. I submit that when you're looking at fringes from a
knife edge, you probably aren't thinking of sine integral functions.

Cheers,

Phil Hobbs
AES
Posted: Tue Mar 18, 2008 3:58 pm
Guest
In article (info lost) someone wrote:

Quote:
Of course it isn't only in optical resonators that this is true. What
most optical designers like me find extraordinary is that for an
optical system which is "useful" (in other words, not too badly
aberrated), the aberrations and hence the diffraction performance, can
be estimated through ray tracing.

Is the explanation perhaps that "useful" systems are essentially always
limited to using low spatial frequencies -- or more accurately, small
spatial frequency spreads if viewed in an appropriately chosen
coordinate system?

(since what large spatial frequency spreads do is to scatter / diffract
/ refract light at *large* angles, i.e. out of the optical system --
which is seldom useful.)

Or at least, this is another way of viewing the situation.
 
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