Talk:Diffraction

From Wikipedia, the free encyclopedia

	Physics Portal This article is within the scope of WikiProject Physics, which collaborates on articles related to physics.
???	This article has not yet received a rating on the assessment scale. [FAQ]
High	This article is on a subject of high importance within physics.
Help with this template Please rate this article, and then leave comments here to explain the ratings and/or to identify the strengths and weaknesses of the article.

Contents 1 Added derivation 2 Two issues 3 Picture 4 Style issues 5 question 6 Diffraction limit of telescopes 7 This page is confusing 8 Proposed picture 9 Mathematical description 10 Question about equation 11 Extra Discriptions of diffraction conditions 12 Which sinc? 13 I Don't Think the Definition Is Complete 14 How does diffraction happen? 15 math section 16 [edit] Quantitative analysis of N-slit diffraction: slit as variable 17 major improvement 18 what is a diffraction pattern? 19 On the blueness of the sky and the domain of diffraction 20 moved math

[edit] Added derivation

I added a derivation of single-slit diffraction. I will add the N-slit derivation later, after some order is imposed on this page. Perhaps a TOC? - SNH

[edit] Two issues

Hold on one minute. I'll be the first to admit I know very little more about diffraction above what you learn in a standard Phys with Calc course, but I've got two issues with this page.

First off, the picture of water waves impinging on double slits is not really an example of diffraction. It's an example of entirely different wave phenomena called interference. Diffraction is what happens when the wave hits the slit. After that, diffraction is over and what you see is the interference between two point wave sources. Interference, not diffraction. Or am I going crazy?

Secondly, I have a few issues with the single slit diffraction intensity derivation. The derivation explicitly says that unprimed coordinates "x" label slit points, and that primed coordinates "x'" label the target points. This is backwards from standard notation (ie- Jackson, Griffiths, Panofsky and Phillips, etc). Usually, primed coordinates label the source point (ie- the slit here) and unprimed coordinates label field points (ie- the target here). But never mind that. A good physicist is flexible (but I still think we should follow standard notation for pedagogical reasons).

But never mind that. With this convention, we want to integrate dslit, meaning, we want to integrate over dx dy, and the resulting function should be a function of x'. From the stated convention, the resulting function which should describe intensity on the screen should be a function of x'.

However, the derivation then integrates over x' and y'. The function that describes intensity at the target is a function of x. This is completely backwards from the stated convention that x' labels the target and x labels the slit.

The derivation is a mess. I'm not going to change it just in case somebody slipped LSD into my morning coffee, and I'm totally way off base on this. In case I'm not way off base, I recommend changing:

"We will assume that the slit is infinitely thin in the z direction, so dslit = dxdy. Take the center of the slit to be at x and the wave hits its target at x'."

To:

"We will assume that the slit is infinitely thin in the z' direction, so dslit = dx'dy'. Take the center of the slit to be at x' and the wave hits its target at x." --Sliver

I agree with many of your points, Silver but have a few points of contention. First, diffraction is correctly defined on the page and is the same phenomenon in water waves as in EM waves and particle waves. Interference is caused by differring peaks and troughs in the diffracted wave, due to differing path lengths to a given screen from different slits. In other words, diffraction and interference are related phenomena. Referring to interference on a page about diffraction conforms to common usage (see Nobel prize lectures in 1914, 1915, 1937 and 1994 in physics, 1936, 1962, 1964 in Chemistry). However, a good argument can be made that the two pages should be better cross-referenced.

I appreciate the note on my mixing up prime and un-primed frame. However, I was consistent. To get a function in terms of unprimed x, we need to integrate over primed x. If x-prime is the source with width a, then integrating over the slit will go from -a/2 to a/2 and yield a function in terms of unprimed x. I've made your suggested change at the outset of the derivation.

Could you be more specific about which part of the derivation is a mess? Any suggestions on how we can improve it?

--SNH

Re the water waves, in my opinion SNH is correct and Sliver is incorrect. The example with the water waves is diffraction, and is exactly analogous to double-slit diffraction of light waves (except that light has two modes of polarization). Both cases are also examples of interference. Interference is the reason diffraction occurs. Diffraction is one type of interference. You can take my opinion with a grain of salt, since I wrote the water wave stuff in the first place. --Bcrowell 22:50, 28 Feb 2005 (UTC)

Hecht's "Optics" says that there is no real distinction between interference and diffraction, but the term "interference" is customary when talking about only a few waves and "diffraction" when talking about a large number of waves. As far as I've seen, the double slit example is universally described as "diffraction", although it would also be accurate to call it "interference". Also we're not talking about point sources; the slits have finite width. Pfalstad 23:37, 28 Feb 2005 (UTC)

Agreed. It's a fallacy to put too much weight into the fact that we divide physical phenomena into conceptual boxes like "diffraction" or "interference". There's just wave propagation, and there is really no separating "diffraction" from "interference" in reality. Birge 22:37, 28 March 2006 (UTC)

Re the x, x', dx', etc., if the center of the slit is at x', then x' is a constant, not a variable, and there can't be any dx'. We really have three different values of x: the x at the center of the slit, the x where the final intensity pattern occurs, and the x at which we're integrating the wave. It seems simplest to me to define x=0 to be at the center of the slit, in which case we can cut it down to two variables. I'm going to go ahead and change it to be that way. --Bcrowell 23:45, 28 Feb 2005 (UTC)

I've gone through the derivation and tried to fix things that seemed broken. I'm not sure to what extent my changes will address what SNH didn't like, but maybe we're converging. --Bcrowell 00:41, 1 Mar 2005 (UTC)

Re: Primed and Unprimed

I think that there may be some confusion on the primed and unprimed variables and what they represent. The surface into which the slits are cut is a plane defined by (x', y', z') where z'=0 because the slit is infinitely thin. These define a coordinate system rather than precise points. In this manner, the waves originate at (0,0,0) rather than (x',y',0). In fact, I have made an assumption (not stated...my fault) than x=0 when integrating from -a/2 to a/2 over the slit. When the wave hits a second plane defined by (x, y, z)--where z is unimportant because we are measuring point density -- the consequence of assuming the originating slit is of infinite height (integrating from y=-&inf; to y=&inf;) is that the diffraction pattern (on the unprime plane) also has infinite height.

So perhaps the lead-in paragraph should read:

Let the slit lie in the unprimed x-y plane with infinite height in the y direction and width a in the x direction. Consider an infinite number of particles passing through this slit. Let the screen on which the diffraction pattern is projected by a distance z' away from the origin and the diffraction pattern be represented by the plane (x', y').

--S.N. Hillbrand 14:00, 1 Mar 2005 (UTC)

[edit] Picture

Bcrowell, the picture that's used to display "two slit diffraction" is misleading and used incorrectly. Pfalstad is correct when he says that it's customary to call interference of a few waves (typically two) "interference" and interference by an infinite or nearly infinite number of waves "diffraction". Interference is very simple, both conceptually and mathematically. Diffraction, the effect of many interferences, is very difficult. The two slit plicture we use is a great demonstration of interference. It's a misleading (at best) demonstration of diffraction. These are my references to back up that claim:

• Richard Feynman: Feynman Lectures (Addison Wesley), vol I pg 37-3. He has the same diagram as an example of "interference".
• Susan Lea, John Burke: Physics, the Nature of Things (Brooks Cole), pg 567. Again, interference, not diffraction.
• Lerner, Trig: Encyclopedia Of Physics, 2nd Ed (VCH), pg 634. Interference, not diffraction.
• Halliday, Resnick: Fundamentals Of Physics, 7th ed (Wiley), pg 964-965. Picture in Interference chap, not Diffraction chap.

The list goes on and on. I've heard of "Young's two slit interference experiment". I've never heard of "Young's two slit diffraction experiment". If you don't like my references, go here: http://images.google.com/ and do an image search on "interference". Then do an image search on "diffraction". Compare the two groups of pictures.

There are SO many great pictures of diffraction out there. Pictures that nobody in their right mind would look at and say "Huh?" to. Why use this one which, at worst is wrong but at best is confusing? Suggestion:

Remove the image of the two-slit water wave interference. It belongs on the interference page, not the diffraction page. Replace that picture with a good, solid picture of diffraction, like:

  * A GREAT instructional picture:  http://www.gcsescience.com/pwav37.htm
  * This is a canonical picture of diffraction: http://micro.magnet.fsu.edu/primer/lightandcolor/images/diffractionfigure2.jpg
  * Nice demonstration of diffraction by EM waves and matter waves:  http://hackensackhigh.org/~rkc2/diffraction.jpg

The gcsescience picture is excellent; it's unmistakable diffraction. I'll do the legwork to get permission to use the picture if other people like it. I could even draw my own version of the pictures if we can't secure permission. I'm pretty hand with The Gimp, and Flash.

As for the derivation, it's perfect now. The prime/unprime question was completely resolved and it follows Jackson's convention, which is always a good thing. Thanks!  :)

LEo- THIS HAS GOT TO BE ONE OF THE MOST TRIVIAl AND POINTLESS ARGUMENTS EVER!!! diffraction is just when waves "spread out" for god's sake! interference is a broad phenomenon that can encompass diffraction and yes, it is related when the diffraction PRODUCES interference patterns. What in the world is the point of this? you all obviously know what it is about, this is so stupid!

--Sliver

Hmm... I think that Pfalstad has hit the nail on the head that diffraction and interference are often used interchangably. Sliver, please reference your copy of Feynman's Lectures, Chapter 30-1 (Diffraction). To quote:

This chapter is a direct continuation of the previous one, although the name has been changed from Interference to Diffraction. No one has ever been able to define the difference between interference and diffraction satisfactorily. It is just a question of usage, and there is no specific, important physical difference between them.

So, in this spirit, perhaps a link to the interference page would be appropriate along with a note explaining the confusing usage.

--S.N. Hillbrand 17:38, 2 Mar 2005 (UTC)

My dictionary says, "diffraction: modification of the behavior of light or of other waves resulting from limitation of their lateral extent, as by an obstacle or aperture," and "interference: the phenomenon of two or more waves of the same frequency combining to form a wave in which the disturbance at any point is the algebraic or vector sum of the disturbances due to the interfering waves at that point." This means that all diffraction is interference, but not all interference is diffraction. The water wave example is an example of diffraction, and therefore of interference as well. If I have two speakers broadcasting sine waves in phase with each other, then that's an example of interference, but not diffraction (because there's no obstacle or aperture). If you do a google search on "double slit," the first screenful of results includes both "double-slit interference" and "double-slit diffraction." Double-slit diffraction happens to be the simplest example of diffraction, so that's why it's appropriate to lead off the article with it. A real 2-d diffraction photo with no legal problems would be great to see later in the article, once the reader has been prepared to understand the basics of the phenomenon; a fake one would, IMO, not add anything to the article (and would also be difficult to do right). --Bcrowell 21:58, 2 Mar 2005 (UTC)

I think it would be great to have at least one 2-d diffraction image in the particle. The razor blade image would be perfect. The GCSE physics images get the message across, but they lower image isn't very accurate; there would be a lot of diffraction in that case. The aperture isn't nearly wide enough compared to the wavelength to make it look that neat and tidy. Pfalstad

I just finished writing an n-slit derivation for the page. I never liked the phasor method derivation, so I've stayed clear of that. Hopefully this way is a clear explanation and follows naturally from the single-slit case. 00:55, 6 Mar 2005 (UTC)

Hi Hillbrand -- Why did you delete all my new introductory material? If you're going to delete such a big chunk, it would make sense to say what you're doing in the edit summary, and discuss your reasons on the talk page. --Bcrowell 03:03, 6 Mar 2005 (UTC)

Mmm...I just noticed two other edits of mine that you reverted without explanation: the deletion of the Newton's rings stuff (which is not diffraction, as noted in my original edit summary), and the uniting of the two separate discussions of diffraction of particles. Again, please don't do huge reverts like that without explanation, please give accurate edit summaries, and please discuss things here. --Bcrowell 03:31, 6 Mar 2005 (UTC)

Bcrowell- my sincere apologies. I did not mean to revert any of your work. I must have posted an older version, although I could have sworn I grabbed the most receent version before posting the new material. But page histories do not lie, I suppose. I'll be more careful in the future. S.N. Hillbrand 04:55, 6 Mar 2005 (UTC)

Oh, I see -- no problem. Thanks for explaining. :-) --Bcrowell 15:43, 6 Mar 2005 (UTC)

[edit] Style issues

According to the Wikipedia:Manual of Style, the section headins must not have many capitals. So, things like

==See Also==

should be

== See also==

This article needs to be edited to confirm to the style. Thank you. Oleg Alexandrov 04:52, 9 Apr 2005 (UTC)

Go ahead. No need to ask first.--Bcrowell 15:31, 9 Apr 2005 (UTC)

I hope I can get to it today. Oleg Alexandrov 17:11, 9 Apr 2005 (UTC)

 ? Just curious, was that a joke? I mean, itd be far easier to just correct it? Ha, why would it be difficult to "get to it"? Fresheneesz 05:58, 20 March 2006 (UTC)

[edit] question

why does the patter on the screen seem to scintillate when i did the single slit diffraction?

• If you used a laser, you're probably seeing the effects of its speckle pattern. One way to reduce this is to focus the laser through a pinhole first. -- Bob Mellish 15:27, 3 October 2005 (UTC)

[edit] Diffraction limit of telescopes

Is it possible to compensate for diffraction if one knows the detailed shape of the telescope?

Unfortunately not. Light diffraction is an artifact of the wave nature of photons. It happens when the waves pass through an aperture. You can precisely know the shape of the aperture or even idealize it (2-d, infitely long, etc) and still have a limited resolution.S.N. Hillbrand 20:10, 2 January 2006 (UTC)

[edit] This page is confusing

• "When the dimensions of the diffracting object are reduced, the angular spacing of the diffraction pattern is increased in inverse proportion."

Increased in inverse proportion? Theres got to be a better way to say that, but I don't know how because I can't understand that sentence.

I made an attempt to rewrite this in a clearer way, let me know if this works out. Abiermans 21:23, 2 April 2006 (UTC)

Yes its more clear, thanks. By "wider" did you mean the maxima and minima of the interference pattern are spread at farther intervals? Fresheneesz 20:31, 3 April 2006 (UTC)

• "Diffraction is one particular type of wave interference"

Would it be correct to say that diffraction is interference from a solid object, and not from another wave? This page mixes the concepts of diffraction and constructive/destructive interference so much, that its difficult to sort it out.

• "a dimension, a, of the diffracting object."

Not only is the variable "a" of "a dimention" confusing, (easily fixable), but the "dimension" of the "diffracting object" is also a very confusing description. I'm pretty sure that difraction will occur, say, on the corner of table, how do you measure the "dimension" of that object? In the case of two slits, the "dimension" is the distance between the slits, or maybe its not? I'm not quite sure.

• "Quantitative analysis"

I don't have time to read that whole thing, but neither its title, nor the intro under that heading quite describe what the purpose of those sections are. I *think* they look like mathematical justifications for some sort of equation. If thats the case, they're long as all hell and I propose that they go on their own page, perhaps called "mathematical justfication for (whatever-they're-proving)" or something.

Anyway, I don't know enough to correct these ambiguities, but I can sure complain about it until someone else does : ) Fresheneesz 06:36, 20 March 2006 (UTC)

Also, I disagree with the use of prime notation at all. On other pages, I've changed them to subscripts, and noted that prime notation is commonly used. Although prime notation is commonly used, I think it is terribly confusing and hard to read - especially when using derivatives. Fresheneesz 06:41, 20 March 2006 (UTC)

[edit] Proposed picture

I drew this picture:

But i'm fairly certain it isn't accurate or complete. The θ is supposed to be the θ used in the equation for near-field diffraction. I'd love it if someone overwrote my picture with a better one, so that we could put a good picture on the page to explain the matehmatical equations. Fresheneesz 03:52, 21 March 2006 (UTC)

[edit] Mathematical description

I added explanations of variables to the mathematical description, but it isn't clear and i'm not sure if some of its right. The angle in that formula is the angles pointing to areas of destructive interference right? However, it goes on to say that at m=0 it gives a maximum (constructive interference). So... what gives? Fresheneesz 03:52, 21 March 2006 (UTC)

I believe this section actually gives the equation for the maxima. It is a very simple situation involving a couple right angle triangles, I don't see how it could be minima. 220.253.4.174 07:37, 19 October 2006 (UTC)

I have consulted a physics lecturer, and changed the formula to what we both thought was correct. Sebrofb 12:54, 20 October 2006 (UTC)

[edit] Question about equation

Now, in Fraunhoffer diffraction, is small, so . The same approximation holds for . Thus, taking , this results in:

In this equation, where does the a/2 on the bottom line come from? Is the integration wrong? 129.67.111.130 11:57, 21 April 2006 (UTC)

The 2 in the denominator of the denominator matches the 2 in the numerator of the denominator, to put it into the right form. But I can't see where the a comes from. Looks wrong to me. The difference of exponentials in the numberator is proportional to slit width a for small a, which would make a sensible wave function magnitude for small slits; dividing by a makes the magnitude constant as slit width goes to zero, which is non-physical, so that supports the idea that the a doesn't belong there. After that, I have a hard time following the rest of the derivation, so I hesitate to try to fix it. Dicklyon 04:13, 24 May 2006 (UTC)

I think I see it now. He needed the a down there to get to the sinc. But he should have put a compensating a on top to make it physical, too. Here's what I recommend as a fix:

It can be noted through Euler's formula and its derivatives that and .

where the sinc function is given by .

Now, substituting in , the intensity I of the diffracted waves at an angle θ is given by:

Now tell me if that's not better...and tell me what the c/8pi represents, too... Dicklyon 04:34, 24 May 2006 (UTC)

I agree. That now clears up the matter. Thanks!

[edit] Extra Discriptions of diffraction conditions

How about adding in Von Laue and Billouin Diffraction, for a more complete description????

also could then link with reciprocal lattice stuff......

Go for it. Dicklyon 03:54, 24 May 2006 (UTC)

[edit] Which sinc?

The article was recently edited to replace the "mathematical sinc" (sin(x)/x) with the "engineering sinc" or "normalized sinc" (sin(pi x)/(pi x)). Why? My quick look at other documents on diffraction suggests that the mathematical sinc is most commonly used in this field. Votes? Dicklyon 17:09, 8 June 2006 (UTC)

See Talk:Sinc_function#i_believe_i_have_found_all_the_places_with_.22sinc.22_in_equations.... Bad idea. See Hecht, for example, which uses the mathematical definition. I will revert this one. Pfalstad 22:32, 8 June 2006 (UTC)

[edit] I Don't Think the Definition Is Complete

1:

The current definition for diffraction refers to a gap and an obstruction as separate entities. Is it not true to say that a gap is just 2 obstructions placed close together. Would it not be more accurate to say that diffraction is exacerbated by two objects being closer together and creating a small gap or aperture?

For example: "Diffraction is the bending, spreading and interference of waves when they pass by an obstruction and is exacerbated" (<-I think a better verb could be used here) "by passing between 2 obstacles that form a gap/aperture."

Intead of the current version: "Diffraction is the bending, spreading and interference of waves when they pass by an obstruction or through a gap."

the current one is better and more general. It doesn't take two obstructions to form a hole or gap, and diffraction isn't "exacerbated" or "worse" in one situation than in another. There's no such comparative dimension. Dicklyon 18:50, 1 August 2006 (UTC)

2:

I don't think "interference" should be included in the definition either, as diffraction and interference are accepted as distinct phenomena for ease of understanding (even if they boil down to the same equations or whatever).

where are they so accepted? Diffraction depends totally on interference. Dicklyon 18:50, 1 August 2006 (UTC)

For example, in a 2-D propagating wave on the surface of water say, the wave reaches an object and the part of the wave closest to the object, is slowed down by friction and/or electrostatic attraction to the object (correct me if I'm wrong) and is pulled "towards" the object. So the "inside" of the wave slows down while the "outside" stays at the same speed... but the molecules in the wave are bound to each other by hydrogen-bonding (or dipole-dipole bonding), so the outside of the wave is "pulled" around the corner too. That to me is how diffraction happens in a mechanical system.

You're wrong. Diffraction has nothing to do with being slowed down by friction with the object. It's just interference among paths not blocked by the object. Dicklyon 18:50, 1 August 2006 (UTC)

Interference is where the waves simply sum linearly and either add to, or subtract from each other's amplituded...

and so is diffraction. Dicklyon 18:50, 1 August 2006 (UTC)

Why is interference needed to define diffraction?

because that's how linear wave phenomena are computed? Maybe we need to add something to make it more clear that diffraction if just a linear wave effect, based on distributed interference. Or is that just renaming it? Dicklyon 18:50, 1 August 2006 (UTC)

--Biledemon 13:29, 1 August 2006 (UTC)

I agree with everything Dicklyon has said here. Perhaps we do need a better definition of diffraction, but I think it will have to be a phenomenological definition. As with many things in physics, the different labels and categories we apply to things often have nothing to do with distinctions in the underlying physics, but more in how they manifest from our perspective. Interference is a very general phenomenon, and diffraction of light is a manifestation of it. In practice, diffraction is usually used to refer to the (nonintuitive) way light beam spatial profiles broaden and change shape during propagation. I think it is a mistake to complicate things by mentioning apertures or objects in the initial definition, because that is too restrictive. For example, people will often talk about the diffraction of a laser beam leaving a cavity. An aperture or slit is just one way the initial condition of a light beam can be set. Birge 18:05, 7 August 2006 (UTC)

[edit] How does diffraction happen?

This article seems to focus more on diffraction patterns than the actual diffraction itself? The 'Explanation' section gives a series of descriptions, not explanations. Perhaps someone could post stuff on how diffraction actually occurs, in terms of wave interaction with the barrier/obstruction/aperture. Maybe more focus on single slit diffraction would be nice. Just my thoughts. —The preceding unsigned comment was added by 58.28.149.206 (talk • contribs).

The waves don't interact with the barriers; they just go through the apertures. Diffraction is the pattern that results. There's not much more to it. Or, if you wish, describe the aperture as a set of sources, distributed uniformly across the aperture, all radiating in all directions. Their interference pattern is the diffraction. It's in the Explanation section. Simple sources, or uniform arrays of simple sources. If it's not clear, it's probably my fault, because it's pretty much as I wrote it. Specific suggestions for improvements are welcome. Dicklyon 07:28, 19 November 2006 (UTC)

[edit] math section

This is written more like a teaching textbook than a reference. It's inappropriate in tone and should be rewritten. Night Gyr (talk/Oy) 21:34, 17 December 2006 (UTC)

I agree. Is there any chance that we can make an article such as mathematics of diffraction, and then it's not so textbook-esque? J O R D A N ^[talk ] 14:54, 24 January 2007 (UTC)

I agree, too. Way too much math. I think some of the integrals to show the result might be useful, but the long detailed derivations are essentially pointless. Reference a textbook instead. I nobody objects here, I might undertake a cleanup. Dicklyon 05:37, 25 January 2007 (UTC)

[edit] [edit] Quantitative analysis of N-slit diffraction: slit as variable

Quantitative analysis of -slit diffraction begins with the integral. I dislike the notation.

The variable of integration (slit) appears as the lower limit of integraiton.

As for the integrand, it does not seem to depend on this variable...

Perhaps, the variable should be something like , and the slit should be some Boolean-valued function of this variable.

dima 09:33, 1 February 2007 (UTC)

The slit is not a variable, not a lower limit of integration. It is a symbolic way of saying what to integrate over (the slit). Maybe it's not perfectly rigorous, but it's perhaps more general than picking a particular parameterization that limits the form of the slit. Maybe instead of dslit it should say slit(y)dy, where slit(y) is a function that says where the slits are open. Dicklyon 15:17, 1 February 2007 (UTC)

"The slit is not a variable, not a lower limit of integration." ... ? J O R D A N ^[talk ] 14:44, 2 February 2007 (UTC)

[edit] major improvement

This article is a good start, but it could benefit from a major improvement. It is listed as "high" importance, so lets try to make this article into something that is deserving of at least "GA" status. Here are are some things that would merit improvement:

• the definition in the lead should be more general, i.e. no aperture is required for diffraction, not even a sharp edge, any object, as long as it is not completely transparent, will diffract a wave.
• The math section is too focussed on the math and not enough on the physics, i.e. what the math means and why this approach is valid. (some errors there too)
• make a clear distinction between Fresnel, Fraunhofer, Bragg diffraction and whatever else there is.
• lets have more on why diffraction is important and where we can see it on a daily basis, like resolution of a camera. Holograms.
• Applications to science, like grating interferometers.
• naturally, references to all this stuff.

I would be willing to do this stuff over the next week or so, so please comment on what else you would like to see. what other examples of diffraction can we see, is there an example of diffraction of waves in the ocean? What is the first instance of diffraction observed, does anyone know a good history book about this stuff? --V. 00:49, 22 February 2007 (UTC)

Good, I look forward to your improvements. Maybe I'll jump in and help. As to the history, I think what it says is about right. The book Lenses and Waves: Christiaan Huygens and the Mathematical Science of Optics in the Seventeenth Century that I read recently has more detail on it, but if I recall correctly basically supported what our article says. I'll find it and take another look, since the relevant pages aren't previewed on GBS. Dicklyon 03:43, 22 February 2007 (UTC)

On second thought, maybe it was some other book. This one has only a line about Grimaldi, and little on diffraction: "1660s... The investigations of Grimaldi, Boyle, Hooke, Newton, Bartholinus, brought to light a collection of new properties shaking the foundations of optics." Dicklyon 05:20, 23 February 2007 (UTC)

[edit] what is a diffraction pattern?

currently the 'explanation' section refers to the semicircular wave produced by a very narrow aperture as a diffraction pattern. Later however, the intensity pattern on a screen is also referred to as a diffraction pattern. These are however two entirely different cases, the first being a picture at one instant in time and the second one being time independent.

I would say the diffraction pattern is the pattern visible in the time averaged intensity of a wave. In that case, the diffraction pattern of a very small aperture would be the 1/r^2 dependence of the intensity and not the semicircular wave. --V. 23:03, 24 February 2007 (UTC)

In looking for sources on this, the first one I looked at contradicts your interpretation: this book page. I'll look for more. Dicklyon 23:14, 24 February 2007 (UTC)

Wow, thanks for the quick response and the effort to look up a reference. I, however, dont think that the book makse that point you're saying it makes. The book you referenced states 'the diffraction pattern produced on a screen consists of a central image with a large number of radiating spectra surrounding it'. It refers to the intensity pattern we can see on a screen as the diffraction pattern.

But before that it refers to the different portions of diffraction pattern that need to make it through the lens to make the final image; transmit less of the diffraction pattern and you get a fuzzier image; that was Abbe's breakthrough theory of diffraction-limited image formation in a microscope.

At the same time, the far more subtle point that the book is trying to make is that the only way to completely reconstruct a radiating object we must know the amplitude and phase of the waves it produces on a closed surface bounding the object (see Hecht, Optics, chap 10.4 ). That is what it means by 'transmitting' the 'entire' diffraction pattern. So here it refers to the complete amplitude and phase information on a surface as the diffraction pattern. And still not the pattern in amplitude at an instant in time viewed over some space (i.e. like a photograph of the amplitude in of water waves).

You don't have to know it, you just have to transmit it through and let the final image form by interference. It's talking about the pattern as it propagates, not the final pattern which it calls the image.

'know' as in 'that is the information required', sure we dont have to write it down, but that information does need to reach the 'image' in order for the image to be an exact representation of the object.

I am just concerned that people will get confused if we refer to different things with the same words. When I look at the picture of water waves coming through a small aperture, I see rings. It would be tempting to conclude that the diffraction pattern here consists of a set of concentric semicircles. At the same time I might look at an Airy pattern and similarly conclude that the diffraction pattern consists of a set of concentric circles. Now by comparing the two I conclude that they must be similar situations. And sure enough, the explanations of both phenomena refer to diffraction from small apertures. I continue browsing the wikipedia convinced that I now understand diffraction. --V. 00:37, 25 February 2007 (UTC)

I understand the concern, and I'm not sure what the right solution is. The reality is that the term diffraction pattern is used to mean different kinds of patterns, in different domains. Dicklyon 03:48, 25 February 2007 (UTC)

yes, in practice people refer to different patterns resulting from diffraction with the term diffraction pattern. So perhaps we should just avoid using a sentence like 'this is called a diffraction pattern'. Alternatively we could come up with a clear definition, and at least be consistent.

I do believe that in the large majority of the situations I have seen, the diffraction pattern refers to a pattern still visible after one has averaged over time. After all, isnt that the true beauty of diffraction? Even in the ocean there are times of relative quiet between waves, but diffracted waves that interfere can create regions where there simply are no waves, ever. Certainly with diffraction of light we always speak of the time average as we can simply not observe the actual oscillations in time. --V. 07:53, 25 February 2007 (UTC)

Certainly NOT always, as the example I found illustrates. I also constructed that nice picture of propagating waves after a single slit, and called it a diffraction pattern; what would you suggest we call it instead? Dicklyon 08:51, 25 February 2007 (UTC)

That is a very nice image, I do like it very much. This is what you would see when say a water wave is incident on a single opening. For light however, you would never be able to observe this image, without doing something very unusual. The reference that you gave doesnt speak of time dependence at all and the phenomenon it speaks about is only concerned with the amplitude and the relative phase of different parts of the wave, not any explicit time dependence. Thats the beauty of it, if you specify the amplitudes and relative phase, you have all the information you need to make the image it speaks of.

anyway, to answer your question, the image you made, I would call a picture of a wave. Of course the pattern of low and high intensity caused by diffraction is visible. But if this were actually a physical system, if I were to take a picture again a little time later, the picture would look different. The intensity pattern however would be the same. A fact that is not evident from the picture. --V. 10:32, 25 February 2007 (UTC)

Speaking of time dependence, having an animation would be really cool! :) --V. 10:32, 25 February 2007 (UTC)

I might work on that. Making the frames isn't hard, in matlab, from the code I did already. How do you assemble an animated gif from them? Dicklyon 17:22, 25 February 2007 (UTC)

[edit] On the blueness of the sky and the domain of diffraction

When some one asks why the sky is blue, the answer usually involves terms like Raleigh scattering. But is Raleigh scattering a form of diffraction? After all the blue sky is a result of light scattering from molecules with a polarizability (and no other kind of small particles). The induced oscillating dipoles radiate light themselves and the power radiation is wavelength dependent (the same way it is for all oscillating dipoles). I am not sure how this fits in with all the other phenomena we associate with diffraction.

I am not sure what to include in the domain of diffraction and what not to include. Personally, when thinking about diffraction, I take the mechanism of scattering, absorption and phase shifts as a given and limit myself to what happens to the wave after that. --V. 00:15, 26 February 2007 (UTC)

OK, you're probably right; it might be best omitted. But then what atmospheric phenomena ARE diffraction? Dicklyon 00:22, 26 February 2007 (UTC)

[edit] moved math

It was agreed above that there was too much math on the page, so I just decided to make the bold move and moved all of the math to a new page Diffraction formalism. I think that to someone with a specialized interest, all these derivations are useful, however, they made it very discouraging to a person with a passing interest to actually read the article. Hence the move. I would say a minimum of math would be sufficient for this page since it is possible to understand (and calculate!) most of the common effects of diffraction without the need for integrals or complex numbers (remember, most of us are not mathmagicians ;) ). I would be happy with the amount of math that is on the page now (after move). And to link to the other page for details. But I am open to ideas, if there should be more math and if so, how much. --V. 09:46, 3 March 2007 (UTC)