Speckle noise reduction

Holography related topics.
Joe Farina
Posts: 804
Joined: Wed Jan 07, 2015 2:10 pm

Speckle noise reduction

Post by Joe Farina »

Thanks Jeffrey and Dave for your comments.

I'm running some ideas around, regarding speckle reduction, and the comments on this thread have been very helpful.

Maybe it will help if I phrase something differently. Let's forget about apertures for the moment, and say we have the following scenario. A split-beam reflection hologram with two object beams. Each object beam will of course produce a different speckle pattern. It seems to follow that overall speckle will be slightly reduced in this hologram, because some of the "dark" speckle resulting from the first object beam will get "filled in" by the "bright" speckle of the second object beam. Bob had also mentioned earlier that multiple object beams will reduce speckle.

Now, let's use this same example, except that instead of allowing both object beams to strike the object, we block off one of them, for half of the exposure time. Then, we reverse it, and block off the other object beam, for the remaining half of the exposure. So the net result should be very similar to the above, since the only difference was that, in this case we used sequential exposures, instead of simultaneous.

At this point, let's reconsider a moving aperture in a single object beam. Any change to the size or shape of the beam passing through the aperture (and then through the diffuser) will cause a different speckle pattern on the object. Of course, if the moving aperture does not illuminate a completely new spot on the diffuser, then some portions of the speckle pattern will remain the same on the object. But the object will also be overlaid with another speckle pattern from the "new" areas of the diffuser which have now been illuminated.

So, I don't see any major difference between the "sequential" exposure with two object beams, and a moving aperture with one object beam. The only difference I see is that, with two completely different speckle patterns (two object beams), a more effective speckle reduction would seem likely. However, in that case, there would only be a single variation to the speckle pattern (from the second object beam). With a moving aperture, even though there will be many overlapping speckle patterns, many new patterns could be created during the exposure, which might compensate for the overlapping portions.

The aperture would not necessarily need to increase/decrease in size (although some change in size would be acceptable, I think) but could simply move to a new spot in the expanded beam.
Ed Wesly
Posts: 513
Joined: Wed Jan 07, 2015 2:16 pm

Speckle noise reduction

Post by Ed Wesly »

Here are some simple, non-holographic tests to try out your idea.

#1: Put the sliding contraption in a leg of your favorite interferometer (Michelson, Mach-Zehnder, Fabry-Perot, etc.) and see if there are fringe shifts when your sliding device is used.

#2: Photograph the speckle pattern with a camera and compare the two views after moving the diffuser and observe the difference.

#3: Photograph the speckle patterns with the experiment described with the iris.

I hate to be pessimistic, but if speckle is moving during exposure, the interference pattern is moving during exposure, and no hologram!
"We're the flowers in the dustbin" Sex Pistols
Joe Farina
Posts: 804
Joined: Wed Jan 07, 2015 2:10 pm

Speckle noise reduction

Post by Joe Farina »

Thank you Ed, all three of those are very good ideas, and don't require the shooting of a hologram.

Even if the speckle can't be moved during exposure, I think it would be well worthwhile to move it between multiple exposures. This would be one benefit of sequential RGB exposures like they did in Lake Forest (I always wondered why HB used cumbersome sequential exposures rather than simultaneous, but the moving diffuser makes sequential more interesting now). The table couldn't be disturbed in the slightest way of course. I could also try getting a fringe-locker online.
Joe Farina
Posts: 804
Joined: Wed Jan 07, 2015 2:10 pm

Speckle noise reduction

Post by Joe Farina »

Yesterday I was reading Bjelkhagen's new book, and there was some mention of the reduction of speckle noise in multi-color holographic recordings. The abstract to one of the references is given below.

I am again wondering about a related question, which met with skepticism on this thread, that a diffuser moved in the object beam (in a split-beam reflection hologram) might have the same averaging effect. Assuming of course the diffuser did not touch the table. Although I would prefer to simply try it, my layout is still under construction.

Some have said that this would mess up the hologram, but I have doubts. Say we have a ground-glass diffuser that moves enough to produce a moving speckle pattern on the object. This is not the same thing as "path length" change in the usual sense, affecting one set of fringes. The way I see it, it would be more like a multiple-exposed hologram. In a hologram with multiple exposures, I don't know of any adverse effects if the layout is completely stable. Say for example we made a hologram with an arbitrary number of exposures, say for example 10, with a few seconds of interruption between them (a shutter is closed). As long as there is no movement of any kind between exposures, shouldn't the result be about the same as a continuous exposure? The way I see it, this is comparable to a moving diffuser which does not touch the table.

***

Speckle phase averaging in high-resolution color holography

Jacques Harthong, John Sadi, Marc Torzynski, and Dalibor Vukicevic »View Author Affiliations

JOSA A, Vol. 14, Issue 2, pp. 405-410 (1997)

Abstract

Interest in wavelength multiplexing in holography derives naturally from the need for realistic color rendition as well as from resolution requirements. Imaging in coherent illumination is compromised by speckle. Speckle is prejudicial to quality, sharpness, contrast—in a word, to the fidelity of reproduction or holographic reconstruction. In incoherent light these patterns are canceled by spatial phase averaging. Incoherent light can indeed be regarded as a superposition of a very large number of coherent components whose phase factors are distributed at random. It is demonstrated that the averaging effect, ultimately caused by the law of large numbers, is achieved by the superposition of only three components, thus allowing simultaneously a true color rendition and an improvement in spatial resolution. The spatial statistical behavior of the amplitude of the sum of three intrinsically coherent waves, when they are incoherently superposed in an imaging system, is investigated. A random variable representing the amplitude of this sum is introduced. Then the cumulative probability function and the probability density function of the resulting amplitude are calculated. The white-light (infinite-wave illumination) case and the purely coherent (one-wave) case are analyzed. The results are interpreted with a heuristic vector model.

© 1997 Optical Society of America
Ed Wesly
Posts: 513
Joined: Wed Jan 07, 2015 2:16 pm

Speckle noise reduction

Post by Ed Wesly »

If you can make it to my Annual Open House in honor of Hans passing through town on his way home to Wales from Photonics West on Sunday, February 9th, anytime after 1:00PM, you can ask him those questions yourself! Or anyone else in the Chicago area who wishes to join in the fun!

Other out of town holographic luminaries who frequent this forum who will be here include Jeff Weil, John Klayer, and Rob Taylor, Konrad from Poland, plus the usual contingent of locals.

Dalibor was one of Hans's collaborators on quite a few experiments, so Hans might have even seen these holograms. And we might even be shooting some RGB holograms chez moi, on new Polygrama Pan and Ultimate U04!

Hope to see any and all of you here!
"We're the flowers in the dustbin" Sex Pistols
Dinesh

Speckle noise reduction

Post by Dinesh »

Joe Farina wrote: The way I see it, it would be more like a multiple-exposed hologram. In a hologram with multiple exposures, I don't know of any adverse effects if the layout is completely stable. Say for example we made a hologram with an arbitrary number of exposures, say for example 10, with a few seconds of interruption between them (a shutter is closed). As long as there is no movement of any kind between exposures, shouldn't the result be about the same as a continuous exposure? The way I see it, this is comparable to a moving diffuser which does not touch the table.
Maybe, but you'd be lucky and you may have to choose your diffusion screen carefully. With modern lasers you may not have a problem.

Consider that speckle is a function of the surface on which the light is falling, and not in any interruption in the path of the light. Thus, the phase relationship between all the lght that hits a particular point on the surface would give rise interference effects if the rms were in the order of lambda. Typically, a reasonable rms of a few microns would give rise to such effects, since a micron is roughly 2 lambda. However, if the phase relationships were "scrambled" by a diffuser - effectively a stochastic effect - then, provided the change of the phase wrt to the path was fast enough (d(phi)/dt > response time of eye, which is roughly a few microseconds ), the speckle would not be noticed. However, the hologram is recording a phase relationship. So, the very alteration of the phase relationship to suppress the speckle is also contributing to the variation in phase stability at the recording position. Having said this, if the variation in phase were small enough, you may get away with a decent recording anyway, since, in a display hologram, you do not have a single frequency and so you are recording "overtones" above and below the fundamental. The overtones may be smaller than the 'overtones' caused by the random phase variation of a diffuser. This could be analogous to the small variations along the response of an amplifier in the linear region, in addition to the actual bandwidth of the signal being amplified.

By the way, turning a shutter on and off will probably cause phase variations, albeit small ones. This usually gives rise to a very low frequency overlap which shows up as an optical beat frequency. Consider two harmonic oscillators, signal generators if you will, tuned to the same frequency. Keep one on all the time, but turn the other one on and off. I suspect the small but random variations in the state of the two generators will cause a beat frequency.
Dinesh

Speckle noise reduction

Post by Dinesh »

By the way, Joe, if you're interested, a new journal was created and I was asked to evaluate it with what I think was a pre-publication issue. I never responded to the request, since speckle is not a particular interest of mine. So, I have no idea if the journal is still being published. However, if you're interested, I can send you a copy of the journal, or an article in it. I'm showing the front cover and the contents page.
Speckle070.jpg
Speckle071.jpg
Joe Farina
Posts: 804
Joined: Wed Jan 07, 2015 2:10 pm

Speckle noise reduction

Post by Joe Farina »

Thanks Dinesh, I will keep those points in mind. This is just one of those things which needs a simple test, and I'm a bit frustrated at the moment because the layout is getting a substantial re-build. At least I have the framework around the table established (not touching it) and this will have attachment points for a "floating" diffusion screen.

That's an interesting journal, thanks for posting it. So far, I've tried to do a little research concerning speckle, but the subject has so many facets, and none of these seem relevant to what I'm doing. At the moment, I'm only interested in speckle reduction for split-beam reflection display holograms. It seems to me that this area hasn't been explored adequately, at least judging from the published literature. The only times I've really seen it discussed were in Bjelkhagen's two books, and the references he gave (which I haven't seen for the most part), plus some comments provided by Bob in connection with Simian.

Published accounts of color holography seem exclusively concerned with single-beam, pure Denisyuk holograms (Gentet, Bjelkhagen, etc.) and of course, if split-beam geometries are excluded, then there would be no real incentive to explore speckle-reduction techniques. I don't think anything can be done about pure single-beam reflection color holograms, except maybe to hit them with as many wavelengths as possible.
Dinesh

Speckle noise reduction

Post by Dinesh »

Joe Farina wrote:Published accounts of color holography seem exclusively concerned with single-beam, pure Denisyuk holograms (Gentet, Bjelkhagen, etc.) and of course, if split-beam geometries are excluded, then there would be no real incentive to explore speckle-reduction techniques. I don't think anything can be done about pure single-beam reflection color holograms,
It's true that there are no examples of split beam, white light reflection colour holograms (there ought to be an acronym for all that! WLIPRCH?). The teapot I showed earlier was an H1 in full colour, and we did do an image planed reflection H2 copy. To the best of my knowledge, it's the first and only example of an image planed reflection colour. The number of optics on the table for the split beam geometry in three colours is itself pretty daunting, to say nothing about carefully controlling aberrations, since you're effectively superimposing three non-coherent images by reconstruction by three coherent sources from the H1 and then one incoherent white source for the H2. Due to various factors like z coord mismatch, the smallest aberrations show up as a colour mixing fiasco! But, I gotta say that speckle doesn't really show up on reconstruction, since the reconstruction is by incoherent light. Now, if you're also reconstructing the H2 with three coherent sources, then it's an issue.

By the way, when I say that the teapot is the first image plane full colour H2, I'm talking traditional holography. I understand the people who use printers for digital holography (Zebra, Geola and Rabbitholes) do make image planed full colour. Personally, I'm the Last of the Luddites, so I like using traditional methods wherever possible!
Joe Farina
Posts: 804
Joined: Wed Jan 07, 2015 2:10 pm

Speckle noise reduction

Post by Joe Farina »

Dinesh wrote:To the best of my knowledge, it's the first and only example of an image planed reflection colour.
As far as I know also.

If someone has already gone to the trouble of 2 or 3 color Denisyuk, then it shouldn't be that much effort to split the beam somewhere, and use the split beam for side lighting. I'm working on this.

By the way, I wonder if it's possible to use a color reflection (not transmission) master, then make color copies. Maybe it would avoid crosstalk problems in the master? (But then again, my knowledge of copy configurations is extremely limited.)
Post Reply