Talk:Fourier optics

Cleanup

Tagged June, 2006. This is an important topic in optics and needs to be expanded. The current material is okay for a simple introduction, but needs rewriting in more formal tone. -dmmaus 06:04, 20 June 2006 (UTC)

• Tone seems better, though the language in the intro is a bit hard to understand and might contain grammar errors. The layman will probably be scratching his head afetr reading this. Heaven knows that I was. --Lendorien 19:55, 14 February 2007 (UTC)

Importance rating

I have just rated this article as high. It was hard to choose between high and mid, but I went with high because the whole of optics pretty much depends on it once you get passed some basic geometry. That being said, Fourier optics is taking up a disturbing amount of my time at the moment, so I may have an inflated view of it's importance. --Apyule 11:07, 24 April 2007 (UTC)

I would agree, and I have actually done any for quite a while. We'll see who finds time first, then. --Osquar F 07:17, 4 June 2007 (UTC)

Simple tips in learning Fourier optics

A few key points helped me learn Fourier optics:

• Firstly, clarify the simple distinction that I learned early on when studying Fourier optics which is quite simply that Fourier optics addresses the wave properties of light that geometrical optics can't.
• Then add the Fourier analysis to an aperture / light system to generate a spatial Fresnel integral.
• Go into the far field and the wavefront curvature drops away and the diffraction can then is described by Fraunhofer diffraction.

This helped me to get off on the right foot. There is an excellent online book on the subject worth a browse [here] that may form a decent reference. PD 22:57, 22 June 2007 (UTC)

Regarding these simple tips in learning Fourier optics, I believe it should be better to say that Fourier optics addresses some wave properties of light that geometrical optics can't. This is so because Fourier optics does not addresses properly all the wave properties of light (as for example, polarization). --OdracirBA (talk) 17:47, 2 December 2008 (UTC)

Light wavelenght dependance?

I've seen a demo of this done with a microscope, but it was with monochromatic light. It seems like the idea is that diffraction deflects rays based on the spatial frequency of the image which is what causes the transform. If so, it seems like this would only work with monochromatic light and that white light would lead to a blurry Fourier transform. Is that correct? —Ben FrantzDale 14:13, 28 September 2007 (UTC)

Yes exactly. Usually a monochromatic coherent light source such as a laser is used.Vectis Kitsune (talk) 21:15, 2 November 2009 (UTC)

hard to understand

As someone who works with Fourier optics all the time, I've got to say this latest re-write of the article has made it really hard to understand now for anyone who is not familiar with the field. I realise it is a hard subject to define without getting into the technical details. I would suggest that the opening paragraph is redone so it is similar to that of version 29th June 2007. Then the real detail can left to those who really want to know. Doc phil 10:40, 5 October 2007 (UTC)

Time to Revisit this Article?

I submit that the ratings on this article should be revisited at this time. I'm not convinced that it is any longer confusing or unclear, at least insofar as sections 2-8 are concerned. —Preceding unsigned comment added by 71.177.102.80 (talk) 01:43, 4 April 2008 (UTC)

I think that the titles of the sections need to be shortened and made less book-like. Section 3 has side-notes which make this article sound like a meta-wiki article. JT (talk) 00:10, 16 September 2008 (UTC)

Attempt at introduction

I agree with the confusing tag for the introduction. I think that the current introduction is too involved (and seeing the comments seem to agree with this) and so I've rewritten it. If anyone is still watching this page let me know what you think. JT (talk) 00:10, 16 September 2008 (UTC)

"Attempt" at introduction

The new introduction doesn't make any sense. For example, Fourier Optics is NOT an extension of the Huygens-Fresnel (or, more corrrectly, the Stratton-Chu) Green's function formulation. In fact, the two have NOTHING to do with one another!!! The Stratton-Chu formulation assumes a source distribution, in which each point source gives rise to a Green's fucntion field. Fourier Optics assumes a source-free region, in which the eigenfunction solutions to Maxwell's equations (i.e., the plane-wave functions) propagate. Whoever changed the introduction clearly doesn't understand electromagnetic theory, and will only confuse an unsuspecting reader. —Preceding unsigned comment added by 72.67.192.199 (talk) 04:25, 23 September 2008 (UTC)

Intro is as clear as mud

I'm not a math guy. I fit the type of person that would read an article like this and get a brain hemorage. Look, I understand the article deals with math. That's fine. But the intro is about as clear as mud to someone unversed in this stuff.

Fourier optics is the study of classical optics based on the fact that, in homogeneous source-free regions, the eigenfunction solution to Maxwell's equations is a weighted superposition of uniform plane waves. (Eigenfunction? weighted superposition of uniform plane waves? What the heck are those? Huh?) These uniform plane waves have complex exponential spatial dependence, hence lend themselves to analysis via Fourier transform (FT) techniques. (Complex exponential spacial dependance? What?) More specifically, Fourier Optics refers to optical technologies which result when the plane wave spectrum representation of the electric field (section 2) is combined with the Fourier transforming property of thin lenses (section 3) to yield analog image processing devices (section 4) analogous to 1D signal processing devices. (Plane wave spectrum? Fourier Transforming properties... wait, isn't this article about fourier optics? I don't know what that is! Erm?) Fourier optics forms much of the theory behind analog image processing techniques, as well as finding applications where information needs to be extracted from 2D images, such as in quantum optics. (This part makes sense)

Similar to the conjugate variables, frequency and time, used in the analysis of 1D temporal waveforms, Fourier optics makes use of the spatial frequency domain (kx, ky) as the conjugate of the spatial (x,y) domain. (conjugate... Wait, I thought you conjugated verbs. Huh?) Terms and concepts from 1D signal processing such as, transform theory, spectrum, bandwidth, window functions and sampling are used to describe the nature of optical fields in the FT domain. (You assume I know what 1D signal processing is. What's an FT domain? Wha?)

At the end of that all I now know is that Fourier optics concerns optics. Nothing about why it's important or for that matter, what it is. Look, approach this article's intro from the perspective of someone who doesn't know ANY-thing about optics, much less fourier optics. The intro should be clear enough that the layman, like myself can at least get a gist about what it is and why it's important. --Lendorien (talk) 15:42, 12 November 2008 (UTC)

Clarification

The article, as presently constituted, presents the subject matter from a fairly rigorous theoretical standpoint, based on the foundation of Maxwell's equations. This presentation assumes a familiarity with both Fourier transform methods and some complex variable theory. The presentation assumes that the reader knows about the complex exponential function, defined as: cos(x) + j sin(x), which is fundamental to all Fourier analysis, as well as its conjugate, cos(x) - j sin(x). As a result of the assumptions made in the presentation, it is probably slanted toward an audience having a roughly sophomore to senior level knowledge of math, engineering or physics, depending on the individual.

That being said, it is not the intent to exclude anyone from reading or understanding (or contributing to) the material on this subject. If any potential contributors would like to add one or more sections on the subject, which are more qualitative, descriptive or phenomenological in nature, then of course they would be more than welcome to do so. The more ways of looking at any subject, the better the level of understanding will be of it. —Preceding unsigned comment added by 157.127.124.15 (talk) 19:04, 12 November 2008 (UTC)

At least make the introduction a bit more clear and accessable for the math idiots such as myself. The rest of the article can be deeper as is needed due to the subject matter. --Lendorien (talk) 14:57, 13 November 2008 (UTC)

I think in the present condition (November 2009) it does get too mathematical, too soon. Electromagnetic propagation is dealt with elsewhere on Wikipedia and so can be linked out. Similarly, the Fourier transform is dealt with elsewhere and can be largely linked out. This is after all, an article on Fourier optics, not on Fourier transformation or E.M. propagation. Most of what is written here is not in fact about Fourier optics at all. I accept the mathematical section in the first half might be a theoretical pre-requisite for an analytical understanding of Fourier optics, but the topic of the page, Fourier optics, doesn’t really start to be discussed until about halfway down the article.

The authors of other Wikipedia entries on physics topics don’t feel the need to start the article from analytical principles, but give a description of physical phenomena, possibly followed by a mathematical treatment after for those who want it. Go on, look up a few other serious physics topics of varying complexity and you will probably see a better structure. I just tried, quantum electrodynamics, nuclear magnetic resonance, special relativity, and only the latter had more mathematics on the page than Fourier optics! Vectis Kitsune (talk) 21:11, 2 November 2009 (UTC)

Major Re-Write Needed

This article is not only desperately convoluted, it also misses the most fundamental ideas that form the core of Fourier optics. I do not see any discussion of the 2D Fourier Transform, the notion of a Linear Space- and Time- Invariant optical system, optical transformation from input plane to output plane, the Fresnel Approximation, the transfer function of free space propagation, the impulse response of free space propagation, a simple diagram of an optical system with input and output planes, etc. etc. The article does not even define the notion of an object plane and an image plane, nor does it really discuss imaging at all. It is tempting to delete the entire article and start from scratch, but I am hesitant to do so because that might not go over so well. Does anyone have any suggestions as to how we can re-write this article and create something that is readable, useful, and interesting? First Harmonic (talk) 20:59, 14 February 2009 (UTC)

As a first attempt, I have started a propsed outline for a re-written article (below). Please feel free to help me develop this outline by making additions, deletions, or modifications. I would request that only people who have a username and who are logged in edit this outline. Thanks. First Harmonic (talk) 21:13, 14 February 2009 (UTC)

Work In Progress: Proposed Outline

Please do not edit this outline unless you have a username and you are currently logged in. Thanks.

1. Introduction and Overview
2. Propagation of Light
   1. Wave description of light
   2. The Wave Function
   3. The Wave Equation in a Homogenous Medium
   4. Uniform Plane Waves
   5. Projection of a 3D Wave Function onto a 2D Plane
3. Fourier's Theorem
   1. Decomposition of Arbitrary Wave Functions as Weighted Sums of Sinusoids
   2. The 2D Fourier Transform
      1. Definition
      2. Some simple examples
4. Optical Systems
   1. Input and Output Planes
   2. Spacial Transformation
   3. Linearity
   4. Space Invariance
   5. Plane Waves as Eigenfunctions of LSI Systems
   6. Optical Transfer Function
   7. Point Spread Function, or Spacial Impulse Response
   8. 2D Convolution
5. A simple optical system: propagation of light across a finite distance
   1. System overview
   2. The Optical Transfer Function
   3. The Fresnel Approximation
   4. The Spacial Impulse Response

Major Re-Read Needed

Those who disagree with the form of the article (as presently constituted) may actually find the topics they wish to "have added" right within the article right now. —Preceding unsigned comment added by 157.127.124.14 (talk) 18:06, 26 February 2009 (UTC)

It's not only in need of adding topics that are clearly missing, it also needs to be re-written in plain language so that readers can actually understand what it says, and re-organized so that it flows in a logical progression. First Harmonic (talk) 03:37, 8 March 2009 (UTC)

That's going to be a little difficult. You can say something like, "A Fourier transform is how you take an infinite number or sin/cos waves, add them up and make a square wave." Then you do that with light, but I mean it's going to either have to be really basic or it's just going to be incomprehensible. We can link the crud out of the article, so that people can learn what an eigenvector is, but I don't think a person could really understand what all of this means without knowing a heck of a lot of stuff. Sure, this is important, but it's complicated. Yeah, you can build an engine from a parts manual, bit by bit, but designing an engine? Knowing how thin you can machine the metal, what alloy to use to get strength without throwing cost or weight out the window, understanding how things will expand under heat and cold and... This article isn't about building an engine, it's about designing one -- it's a complicated thing and can't be readily explained to a layman without going into some really deep waters, in my opinion. Any attempt at simplification seems like it would have to be a little... disambiguous, it's going to have to make simplifications that (ultimately) will be wrong. It's like explaining an Interrupt request (IRQ conflict) and saying, "They don't get along well and try to talk over each other." While that explains the concept fairly handily, it's ultimately more complicated than that. Banaticus (talk) 06:23, 6 April 2009 (UTC)

While it might be a little difficult, it is surely possible. See for example the entry for General relativity which manages to discuss many of the important concepts and implications but with very little maths on the page. Wikipedia is after all an encyclopedic project not an archive of 'authoritative texts' on all subjects. For those requiring a deeper understanding, authoritative texts are still accessible through other means, including elsewhere on the world wide web.--Vectis Kitsune (talk) 21:40, 2 November 2009 (UTC)

Derivation Query (section "Fourier transforming property of lenses")

In the discussion under Lens_ft.jpg, in the applications section, the path length of a plane wave propogating from the object plane to the image plane is derived as 2*f. The change in phase from the source to the lens is given as e^jkfcos(theta), and from the lens to the image plane as e^jkf/cos(theta). Is this right? Looking at the picture, I would have expected e^jkf/cos(theta) for the _first_ half of the trip. And a path length of greater than 2*f, which looks more like a lower bound from the picture. Perhaps this needs clarification? 124.169.208.94 (talk) 16:02, 23 June 2009 (UTC)

I agree. I think the left half needs division by cos(θ) rather than multiplication, if the horizontal (axial) object distance is to be one focal length and k is constant, the rays at high θ have a longer optical path. This I guess gives f(1 + θ²/2) in the equation for "plane wave phase" (which I don't find well defined, but I assume the more positive value means the longer optical path). Then the lens gives a phase shift like -f θ²/2 and an additional +f (? at minimum as per Fermat's principle#Derivation, or knowing the lens turns the spherical wave into a paraboloidal wave) for the propagation to the back focal plane. (It is also evident from geometrical optics that the incident plane wave will be focused somewhere in the back focal plane).

Thus the equation f (1 + θ²/2 + 1 - θ²/2) = 2f seems correct but the two equations above it in the article should be switched and perhaps explained more clearly. For instance, I think it should be stated that the "to the lens plane" refers to before the lens has acted by its radial-dependent phase shift.

However, a simple explanation can be given regardles of where the source is: The important thing is to have incident planar waves, to realize that their angle θ is related to spatial frequency (transverse wavenumber) of an object and that if a lens is used all these incident planar waves will be focused to points in the back focal plane, and finally that the location of the point is determined by the angle θ. Now, the amplitude related to each transverse wavenumber appears in a distinct point in the back focal plane, so we have something like a Fourier transform from wavenumber to position. The book Fundamentals of Photonics by B.E.A. Saleh & M.C. Teich (chapter 4.1-4.2 in second edition) explicitly states that the Fourier intensity (amplitude) is given for any object distance, but if the phase factor should disappear so it is a pure Fourier transform the object needs to be in the front focal plane, which is the above discussion about phases.

I should get back to work, so I'm unfortunately not bold enough to actually change the article now. If you agree then go a head, maybe I'll get back some day otherwise. --ErikM (talk) 10:38, 11 May 2011 (UTC)

I agree that the derivation given here is misleading, both for the reasons given above (the geometrical reasoning is wrong) and also for an additional error. The actual derivation needs to incorporate the phase shift incurred by traversing the lens itself to cancel quadratic terms. See, for example, these MIT course slides, particularly starting around slide 6. I unfortunately also don't have time to fix the page right now, but given that there has been a discussion about this for 7 years, I hope someone can fix it soon! --Asdfghqwertyzxcv (talk) 20:59, 10 May 2018 (UTC)

I think the z-component of the k vector, i.e. k_z goes as the cosine of the tilt angle, not as the inverse cosine. This is an infinite plane wave, not a ray.

BTW, I think the last re-write was not a bad one — Preceding unsigned comment added by 134.223.230.155 (talk) 19:12, 9 December 2014 (UTC)

One thing I'm not crazy about in the last rewrite is the use of the general function psi rather than the actual electric field E, which is way more descriptive since you don't have to translate in your head from psi to E. — Preceding unsigned comment added by 134.223.230.155 (talk) 20:03, 9 December 2014 (UTC)

Copyright concerns

Multiple references to "sections", as in a textbook. 71.78.136.211 (talk) 03:16, 27 October 2020 (UTC)