does a laser beam "clean itself" in air?

[Din]

Oh, I see what you mean. You're implying that if the diffraction pattern of a dust mote is stationary on the plate, it should be possible to make a hologram of that pattern, as if you're making a hologram of a porcelain cat. Then, you reconstruct the hologram to see a floating dust mote in mid-air. Then, no, you can't. Well, you can, but you won't get a dust mote floating in air.

When you make a hologram of a porcelain cat, you're recording the reflection wavefront of the cat, not it's diffraction pattern. In other words, you're recording the phase difference between any point on the cat with reference to the reference beam. Or, in still other words (well, symbols) Given a position on the cat at some distance d from a given position on the plate, the phase difference (kd - k.r ) is being translated to a density or absorption value. Generally, because the cat is billions of wavelengths in size, it contains billions of atoms and so while any given ray originates from a single atom (or crystal), the net effect of billions of rays creates an overall wavefield. As a result, the spatial frequencies are relatively large; on the order of about 1000 l/mm

In the case of the dust mote, only 2 lambda or so in size, the diffraction pattern is similar to the diffraction pattern from an aperture of about 2 lambda in diameter (by Babinet's Principle). So, the diffraction pattern that hits the plate is a jinc function (that is, the ratio of a Bessel function to it's argument) of relatively low spatial frequency. If you hit the plate with a reference beam, you'll be recording a very, very low spatial frequancy. All you'll get is a (weak) diffraction grating at low angles. Those people who always say that "holography is diffraction" have no clue what it actually is. "Holography", at least display holography, is a three fold process comprising of reflection/transmission - interference and diffraction. Actually, diffraction and interference is the same phenomenon, so it's a two-fold process. Without the reflection/transmission aspect, you're not "reconstructing a wavefront".

In the case of a dust mote, the diffraction pattern is a jinc function of low frequency (higher than the zero order, which is why we pinhole). However, as the dust mote moves, while the amplitude remains fixed, but the phase changes. Thus, since the phase is what you're trying to record, you may not get a "hologram", but the amplitude profile still has a pretty low spatial frequency. Basically, it's "noise".

[BobH]

But in the paper you referenced, didn't Thompson rear illuminate small particles like that, making Gabor type holograms of them floating in space? If that's not the paper, it's an earlier one. I've seen diffraction patterns on large screens in plateholders, made by particles floating through a beam.

To go back to the point though, I'll still say that the particles floating in the air inside a beam do not contribute to any objective speckle in the beam. Sorry to get us off on a thought experiment here. You did qualify what you said about particles in a beam by saying "So long as the particulates are moving relatively slowly, ... ". My point is that they will never be moving slowly enough for what you suggest to be of any consequence. Not in a typical lab, making HOEs or porcelain cats.

[Martin]

To come back to Joe's initial question about self cleaning a laser beam in air. What about using a thick volume Bragg grating for spatial filtering? Would that be along those lines?

http://proceedings.spiedigitallibrary.o ... id=1342671 mentions a SPIE paper (Spatial filtering for high power laser beam by volume Bragg grating):

Nowadays, the most widespread used space filters are pinhole filters, consisted of a lens with a pinhole in the focal plane, requiring for matching spatially a focused laser beam to a small hole. Experimentally, the initial alignment of spatial filters is difficult, if the pinhole position changes, a laser can damage the pinhole when the power is increased or even permanent damage due to heating. In contrast, non-spatial filtering, a holographic filter element, which made of volume Bragg grating, is inserted in the laser beam path to selectively diffract light propagating at a particular angle, without a lens or a pinhole. A volume Bragg grating is operated directly on the laser beam propagation angle without focus, made use of the grating's angular selectivity, which alignment is easier than pinhole filter, and endures a high-power laser. In this thesis, a volume Bragg grating was fabricated in a 40μm-thick photopolymer, with period of 911.3nm, preparing for a low-pass non-spatial filtering. It achieves an angular selectivity of 35mrad; diffraction efficiency about 95%. Nevertheless, the results of the experiment can be verified with the theory, but not suitable for high-power application. In that case, the photopolymer's grating should be replaced with a photo-thermo-refractive glass.

[Joe Farina]

Thanks Martin, that is interesting.

The "self cleaning" (in air) phenomenon isn't often mentioned. It may be quite useful, though. There seem to be 2 different "causes" of the cleaning 1) something due to the dust motes in the air, and 2) something due to variations in density of the air in the path of the laser beam (suggested by Rallison, who I believe was a laser engineer among other things).

There also seem to be 2 different "types" of cleaning, 1) the reduction (in number and/or intensity) of visible specks, swirls, patterns, etc. in a spread beam, caused by dust or imperfections on the surface of optics, such as when the beam goes through a dirty lens or spatial filter, and 2) the "evening-out" of the Gaussian power distribution in a spread beam.

Rallison did not mention dust motes specifically, only "rarefactions in the air, vibrations, laser cavity wandering, etc. No spatial filtering is advised."

(I don't know why he advised against spatial filtering, that's the only way to get a very clean reference beam, as far as I know.)

Rather than actually have the beam traverse a long distance to produce the cleaning effect, maybe the same effect could "artificially" be produced in a shorter distance (?)

[BobH]

Rallison didn't mention dust motes because they have nothing to do with cleaning a beam by increasing path length. All the things he does mention affect beam pointing, and all have the same effect as vibrating a mirror that directs the beam.

[Joe Farina]

Well, it is certain that the beam encounters innumerable dust motes as it travels through the air to expose a hologram. And Rallison did make the comment that "rarefactions" were responsible for some kind of "cleaning" effect (without being specific however). By rarefactions I assume some kind of change in density to the air in the beam path. That dust motes cause scattering is of course true, but wouldn't at least a little light be transmitted through the dust particles, and continue down the length of the beam? If that were so, the light would be going through a less dense medium (air) to a more dense medium (dust). In that case, the dust would qualify as a type of "rarefaction."

[Din]

That dust motes cause scattering is of course true, but wouldn't at least a little light be transmitted through the dust particles, and continue down the length of the beam? If that were so, the light would be going through a less dense medium (air) to a more dense medium (dust). In that case, the dust would qualify as a type of "rarefaction."

It depends on the material of the dust mote. However, bear in mind that the diffraction pattern of a dust mote is in the forward direction. In other words, along ( and surrounding) the k vector.Remember also that a dust mote, typically about <~ 5 lambda is not going to significantly refract simply because there are too few oscillators in a volume of a few lambda cubed. Refraction occurs because a very large number of atomic oscillators are driven into oscillations as a result of an income wave. The oscillators radiate in all directions. However, due to the fact that an oscillator driven by a high amplitude wave is pi out of phase with the driving force (the incoming wave), the backward wave is destroyed by interference. Hence only the forward component survives. As an aside, the forward component is phase shifted with respect to the incoming wave, causing an apparent loss in velocity of the wave; this is the origin of the refractive index. Anyway, this is the basic mechanism of refraction, but it does need a fairly large number of oscillators. If only a few oscillators exist, then there may not be enough oscillators to destroy the backwards propagation. In this case, scattering and diffraction are the major cause of light interacting with the particle.

Variation of density in air may cause scattering, but the passage of the laser beam itself will mitigate this. Basically the energy in the beam will cause passage of air, causing a more uniform distribution.

Martin, I'm a little puzzled over the use of a Bragg grating to pinhole. The point of a pinhole is to filter away the higher order Fourier components on the beam, caused by dust and other imperfections in the beam. The pinhole effectively only passes the zero order, within the first Airy radius. I don't see how angular selectivity will accomplish this. If the author is suggesting that the variation in angle of the first Airy radius has a slightly different k vector, and so will be Bragg selected out, I doubt that any volume hologram will actually do this. The first Airy radius is in the order of 10 microns and, typically, the focal length of a microscope objective is about a mm or so. This gives a beam divergence of ~0.15 degree. While it's possible to insert these values into the xi parameter in Kogelnik and calculate the angular variation of a Bragg grating, I'd have to believe that the Bragg selectivity has to be bloody good!

To go back to the point though, I'll still say that the particles floating in the air inside a beam do not contribute to any objective speckle in the beam. Sorry to get us off on a thought experiment here. You did qualify what you said about particles in a beam by saying "So long as the particulates are moving relatively slowly, ... ". My point is that they will never be moving slowly enough for what you suggest to be of any consequence. Not in a typical lab, making HOEs or porcelain cats.

Well, Bob, there's no way to actually determine this except for experimental evidence backed by theoretical models. As you know, I don't accept anything because some "expert" says so, be it Rallison, yourself or me. However, I can well appreciate Einstein's comment, "I have been punished for my disregard for experts by becoming one myself" I, unfortuantely, think I'm in the same position!

[Joe Farina]

I asked Don Gillespie some questions and got a couple comments:

Hi Don,

I hope things are going well.

We were having a discussion on the Holoforum, and it seems I need professional help 

If you have a moment, could you please look at this:

http://holographyforum.org/forum/viewto ... f=5&t=1051

The question has arisen: Does a laser beam “clean itself” (for holographic purposes) after it travels a longer distance through air?

I have noticed that if an expanding lens is placed 2 feet after the laser, the spread beam has a lot of specks, swirls, patterns, etc., caused by the dirty/imperfect lens, while the same lens after 25 feet of air travel from the laser to the lens shows less visible specks, swirls, etc. in the spread beam. There was some discussion about this on the thread noted above. Other than the different amounts of air travel, the only other thing which seems to change is that the beam diameter increases from about 1mm to 5mm.

You are correct. For all intents of this discussion there will be no discernable change in the beam or the gaussian.

It was also suggested that the normal Gaussian power distribution of a beam is changed as it travels a greater distance through the air. In other words, the power distribution becomes “more even” and less Gaussian as it travels through air.

;Nonesense! Who came up with this one? If nothing has been introduced into the beam, why should the beam change at any distance (from gaussian)? The only change in the beam will be a scaling factor..........the beam is expanding.....

Does any of this make sense?

Thanks

Don,

Joe

[Din]

Ah! Another "expert".
Actually, it cannot become "less Gaussian". This Don Gillespie is correct, a Gaussian profile is a Gaussian profile and remains so unless an optic with power is placed in the beam,. What i said was that across any given surface, the beam becomes more uniform, simply because the surface will only be illuminated by the portion of the beam it interrupts. See beneath (I hate to simply say, "So-and-so is right, or wrong" and simply leave it at that, or say, believe me because I'm an "author" or "expert" or "professor" or some such. There has to be some justification, some theory, some experimental results.

laserbeam030.jpg (47.45 KiB) Viewed 4037 times

[BobH]

The illumination will become "less gaussian" at the recording plane if the beam is being steered around by "rarefactions in the air" (like temperature gradients or air flow, not refraction through dust particles), or the other things mentioned above that can redirect the beam slightly over time. The beam itself remains gaussian, like Don says.