Electronic holography at infrared and terrahertz

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Electronic holography at infrared and terrahertz
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Electronic holography at terrahertz and infrared frequencies
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We describe a new holography system for recording holograms that is practical from 1 mm through 3 µm wavelengths. These hitherto inaccessible bands of wavelength can now be recorded with excellent sensitivity and resolution using microbolometer arrays that have improved greatly in the past few years. These spectral bands are useful for biomedical imaging as an alternative to x-rays in some situations, for astronomy, for industry and for night vision devices. In holography following Leith and Upatnieks, one records an interference pattern using a coherent source; and thereafter, reconstructs a wavefront which reproduces the phases and amplitudes of the original object waves. For our first experiments we will describe the verification of our assertion that one can truly record interference patterns. We use a simple Mach–Zehnder interferometer with laser illumination at 10.6 µm. It is interesting that one can record the carrier frequency fringe of a hologram using a thermal detector even with a time constant of tens of milliseconds. For reconstructing the object wavefront in holography there are several well-known techniques. First, one needs to choose between an original illumination beam and a reversed beam. Then one can consider scaling the hologram to the visible band. Finally, with the hologram digitally recorded, one can use modern computer-generated visual displays. We will describe our experiments in which we use the efficient, direct sampling of the carrier frequency fringes [9,10]. Using well-known theories for the inverse scattering and the digital computer, one can calculate the field and the intensity back in the object space. Details of the phase unwrapping process will be described. This talk is dedicated to Professors Emmett N. Leith and Stephen A. Benton, eminent scholars and beloved colleagues.
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good good afternoon I'm happy to be here to speak with you I thought session yesterday memorializing lethal Dennis you had you patented and high density was particularly story I'm speaking about Electrooculography had infrared and terahertz here particularly like to acknowledge to various superior post-doctural scholars and my group 1 this could are carry the others 1 the cheese this work gravel couple years worth of effort that we were spending on imaging infrared we were we started working
on these little microbolometers clues to do just imaging at 10 microns in the context of extended depth of field work which is a specialty of 1 of the co-workers 1 Ricci and then we recognize that that that would be fun to make a hologram at 10 . 6 microns and perhaps sometime useful so tribute to have my dear friend and that leads to a new since the days of the the little railroad train copied my 1st slide from his paper uh this outline of the sources as I can tell in the published literature he may have been the 1st to use the language electrooculography good and set up electronic holography newspapers in 9 1990 and 91 to thank and find a little other but he outlined this this this method of of holography the team he said 1st you record a hologram on a 2 D detector then you read out in a digital form in a computer with no physical replay and then you use some digital processing in order to develop the display and in in order and the methods for developing a display the listed to there are a variety and I've added 1st so that there are 2 basic steps but what's going go back that there is a problem you can so the 2 basic steps are you wanna recover the object feel that the detector plane the 2nd step is that you have that field you wanna propagated to reconstruct the object and this image leave called it out that the FFT method which is a baseband filtering thing I'll review it briefly for you there's a phase stepping method where you the output of phase and the reference beam 0 pi over 2 pi and 3 halves and this the method that we added which I believe is a new and it's what we call a direct sampling method by the mathematics of the direct sampling method is covered in a paper by 2 Dakar and myself in optics communication 2002 and I'll talk about that so I'm going to bring briefly review yeah 15 method to put it into context what I call the standard calculation then I'll describe where direct sampling method but after you want to recover the field at the detector you then back to reconstruct the object sometimes that's an inverse Fourier transform or it's an inverse for now propagation at M and so the
1st what I call standard method of getting the image of the whole graph but the whole damn courses a carrier frequency whole grammar have just a little trouble see the error of there is so this is this is a whole fringe pattern and as you all know the intensity in this plane which is the x y plane it's commonly written the intensity in that plane is the reference beam times the reference being conjugate plus it's the picture being picture being conjugate plus it's the picture reference being conjugate + picture conjugate reference and then in the computer you've recorded this pattern the computer you multiply by a conjugate reference being that's this little EVI 2 pi as 0 . 0 0 there disappears barriers and so that this is the is this that is in the computer so we get 1 plus the PP conjugate times this character this computers to essentially just like mine the and then then there's this term which is the of twice reference being conjugate term and then there's the term the conjugate and then you take an after the of this and and and if you just do then is 0 and filtering as represented by the diagram with you take the FFT and then you get this p conjugate term but it it'll be the p conjugate term but In a Fourier transform domain and so then you if I FFT here and then and then you can do this the go back to the object construction and so that's what I call the standard method and describe very nicely in in least were but
this just as a in terms of the direct sampling I want just have in front of us this is the method I call a direct sampling method and this is just some review review slide about kind of fringe patterns that are involved in our experiments what we have and that of the being 10 microns but in the being at 10 microns and thing about the words and so so we haven't been coming in this mock center and a from the this is the reference and we can take With this mirror we can tip that any angle the angles is small and then this is the object being the the object being here is bringing a point to a focused and so in the picture is a very simple thing it's an expanding spherical waves and the reference being if have expanding spherical wave as we all know that the whole of the ground plane what would be recorded hologram plane is this French pattern with a very low frequency stuff on 1 end and high-frequency stuff from the other and at the same time if we were using a converging being we have low frequency stuff understand where the normal from this the converging wave is at the same angle as the reference beam that makes a stationary phase point so those are
2 a whole branch that we started remember now what's the direct sampling the direct sampling as I mentioned we can view was an original thing it's discussed in Optics Communications references mentioned in the text now because of the way that works is here is the being here is the being that the whole course trouble finding the ontology in order period so let let's go let's do this diagram so we have a microbolometer array the microbolometer array we have an expanding spherical wave and the reference wave and then the point that we made is if you're doing carrier frequency points you jump the right of the is there so here is the carrier frequency of a wave of this particular case and if you wanted to directly sample this way you have the function that we have indicated in the top the top right that the intensity function the this the steps in this direction sampling period this system offers you subtract 1 + pp constitute the 2nd thing is you take this whole thing label G of X and Y that's basically the fringe pattern and and you subtract 1 + pp conjugate use simple you simply coarsely sampled the G of X and Y that's what shown on the 2nd part of this figure all of this this shows cost sampling so we simply directly core sample that we show in this paper that as an exact but modest extension of Whittaker-Shannon sampling theory you can you can deduce that p from that sampling but with this formula to g is M over 4 part B 0 that's two-dimensional sampling there should be a 2 period the minus sign 2 pi F. 0 M over f the 0 that's effects that determine that indexes the phase of each 1 of these samples that it has to say in terms 1 for the sampling and the carrier direction right that's case and the other 1 is for the the lateral sampling so from that we immediately as a direct interpolation we we immediately have the of
field in the back plane and we have used this is not this experiment is in the visible we have an interference pattern of a circle wavefront states in the visible we directly can get phase man we get the phase map using that process that I
described and then the separate example we have this again is the visible we have a whole grammar with a resolution mass made a whole of this object which is 4 . 4 millimetres recording and and then we show the direct sampling and interpolation we do the inverse for propagation and that's our recovery that's in optics Letters 2003 so the it's
the new experiment we've done is to apply this to 10 . 6 microns so this is a service that we used we used that 10 what C. W laser and we go through zinc selenium optics we have been expanded we have a marxist and we have the reference beam and I'm expanding spherical wave we use a microbolometer from a commercial camera by thermal ivory nice camera it has 320 by 240 elements and and that's what's label the so we recorded the pattern
and and end at 10 . 6 microns with an angle a small angle . 3 degrees we get this lovely stable French pattern if you go to 1 degree being angle you get this much finer pattern and don't we estimate that we can do a recording and playback and and read about maybe 4 5 lines per millimeter that non another
experiment we've done as we go out out of the the CO 2 ladies unless it's 10 10 what laser and the thing is label layer beam splitters that pass only 10 per cent so they're like neutral densities of 1 and just as a rule of thumb going into the camera which has an aperture 15 mm by 17 we usually have about 1 really wants power the figure that out including the frame rate the sensitivity of the the microbolometer is approximately 50 micronodules per square centimeter which is very close to what the old 649 have film used to be C so it's a very sensitive recording system and then using it now we have to be taken to be expanded and taken the telescope so to converging lens that way back at the point where it comes to a focus between the 2 mayors so the direct beam is an expanding spherical wave of large radius and then the so called picture being hitting the ball on there is a convergent away from the lower level that hits the my commentary good and
that that gives us that this is a recorded fringe pattern which is a 15 15 mm 5 17 mm and so that shows that the French pattern very high-quality pattern from which you can it you know the 48 inches you can then calculate the 10 . 4 the 1 . 4 you 7 using that method of
talked about the next it's and that ends the experiments that we've done the next experiment we're setting up for to increase the view angle we want set up kind of a stereogram sequence were will have 2 of these microblog arrays has faced by about 40 degrees so we can get a much better angular perspective thank you very much seems to be that fact and and what is that that you're using along with well the thing is I think the might I followed the 10 microns holography work and as far as I would say it might be an oversimplification generalization but I think no material has been satisfactory and work for holography 10 microns at such a low level so this material but in order to get infer holograms from terahertz infrared this micro the I believe this this is without question the very best recording system that there is so what if you but it's not an electron hole grand we want to have it isn't in hot and the and the I could do you know paper so I appreciate it the other not the Michael belong to but I need to electroencephalography what is the so yeah OK we finished and