# Are quantum effects significant in lens design?

Stan Rogers' answer on photography.SE seems to be claiming that QED is not just sufficient but also necessary to explain the the effect of the lens's shape. This is wrong. Ray optics suffices at ordinary magnifications, and even at high magnifications, classical wave optics suffices.

Let's say you use a rectangular lens rather than a cylindrical one. First off, the shape of the lens won't matter at all unless you have the aperture all the way open; on any slower setting, the approximately circular shape of the diaphram will be the determining factor. Assuming that you do have the aperture all the way open, the main effect, which is purely a geometrical optics (ray optics) effect will be as follows. You will have a certain depth of field. If object point A is at the correct distance to produce a pointlike image, then this point is still a point regardless of the rectangular shape of the lens. However, if object point B is at some other distance, we get a blur as the image of that point. The blur occurs because there is a bundle of light rays, and the bundle has some finite size where it intersects the film or chip. Since the lens is rectangular, this bundle is pyramidal, and the blur will be a rectangular blur rather than the usual circular one. For example, say you're photographing someone's face with a starry sky in the background. You focus on the face. The stars will appear as little fuzzy rectangles.

At very high magnifications (maybe with a very long lens that's effectively a small telescope), it's possible that you would also see diffraction patterns. In the example of the face with the starry background, suppose that we change the focus to infinity, putting the face out of focus. Wave optics would now predict that (in the absence of aberrations), the diffraction pattern for a star would be a central (order 0) fringe surrounded by a ring (first-order fringe) if you used a circular aperture, but a rectangular aperture would give a different pattern (more like a rectangular grid of fringes). In practice, I don't think a camera would ever be diffraction-limited with the aperture all the way open. Diffraction decreases as the aperture gets wider, while ray-optical aberrations increase, so aberration would dominate diffraction under these conditions.

Quantum effects are totally irrelevant here.

Stan Rogers says:

It's difficult to explain without launching into a complete explanation of quantum electrodynamics, but all of the light that reaches the sensor "goes through" all of the lens, at least in a sense, even if we're just talking about a single photon. A photon doesn't take just one path (unless you make the mistake of trying to figure out which path it took), it takes all possible paths. Weird, but true.

This is an OK description of why QED suffices for a description of the phenomenon, but it's completely misleading in its implication that QED is necessary. The word "photon" can be replaced with the word "ray" wherever it occurs in this quote, and the description remains valid.

Your intuition is correct, you don't need quantum electrodynamics to explain/model/engineer camera lenses. When considering the propagation of light, the results of geometric optics can be interpreted in terms of path integrals, as Feynman does in his QED: The Strange Theory of Light and Matter, but this is not necessary for lens design. Geometric optics itself suffices in most cases, but there are some design tasks which require an incorporation of the wave nature of light (or the application of empirical rules). (Thanks @Matt J for this info)

Well Phillip, I guess you ARE the original questioner on this site, and your real question seems to be is QED or any form of quantum mechanics needed in "modern" lens design. So let me try again.

First some history. Significant lens design goes back certainly to the start of the 20th century; but the foundations go back much earlier.

Computation was an expensive chore, so "tracing geometrical rays" was time consuming. Certainly, wave based diffraction theory was prohibitively expensive for "design" as distinct from research.

So much work was done on purely mathematical theoretical calculation of ray paths and aberration theory. The Seidel aberration theory, was a great leap forward,

Now the actual math used is ordinary Algebra, and ordinary Trigonometry. Euclidean Geometry of course.

Since ray tracing was time consuming; aberration theory was very important, so fewer rays needed to be traced.

Between WW-I and WW-II lens design was such that one could design an achromatic cemented doublet objective lens for a telescope or binocular, completely to manufacturing specs, by ray tracing just three special rays in two different colors. That allowed correction for primary chromatic aberration, primary spherical aberration, and primary coma.

Eventually, this theory was condensed into a classic text book, that no optics designer should be without. That is "Applied Optics and Optical Design." By A. E. Conrady. It is available in two paperback Penguin book for a few dollars. The first volume material dates from his lecture notes from 1926. It is an intensely equation filled text but as I said, simple algebra trig, and geometry, and he developed a formalism that many designers adopted even using it today (I do)

Now of course we have high speed computers in our pockets, and ray tracing is cheap.

Geometrical optics is a mathematical simplification that basically assumes that the wavelength is zero so diffraction wave effects don't occur. So it breaks down when real practical wavelengths are used. But the difference between the geometrical and the diffraction based calculations, doesn't affect many real cases, so the basic design is still done with geometrical ray optics, and the diffraction optics is used to polish things up, once a reasonable solution is reached. And the mathematical aberration theory is till often used to establish a likely successful architecture.

The Seidel Aberrations; spherical aberration, coma, astigmatism, Petzval curvature, distortion, and then chromatic aberration, are all related, and you can specifically control each of them (given enough variables), but often, in modern design, the software can optimize spot sizes, or modulation transfer functions, paying no attention to the Seidel theory. The successful result (if you get one) doesn't care whether you used aberration theory to achieve it, or whether you simply told the computer to find the best result.

BUT ! there are some serious "you can't get there from here" restrictions. Little nuisances like the second law of thermodynamics, and failure to heed those will keep you from finding your answer, because you are asking for something that physics doesn't permit.

But I can't ever prove that you don't need QED to design any lens. But as Einstein told us, you only have to identify A SINGLE CASE that does require QED, to prove me wrong.

Lens design is a very heierarchical discipline; so simple lens formulae, Seidel theory, geometrical ray tracing, and full diffraction theory, are used interactively.

It is well known at the university entry level, that geometrical optics predicts a different spot size from the true diffraction result, and moreover, the best spot image is in a different location. But that is just icing the cake.

But get the Conrady books if you really are interested; I keep it at my elbow at all times. Of course , Born and Wolfe is a well known text, and Warren J. Smith's "Modern Optical Design" is a must have text book. I'll let you know if I ever have to use QED