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Simple multiplexing technique for double-exposure hologram interferometry
Vol.tme 9, number 2
OPTICS COMMUNICATIONS
October 1973
SIMPLE MULTIPLEXING TECHNIQUE FOR DOUBLE-EXPOSURE HOLOGRAM INTERFEROMETRY P. H A R I H A R A N * and Z.S. HEGEDUS CSIRO Division o f Physics, National Standards Laboratory, Sydney, Aus,~.ralia 2008 Received 25 July 1973 A simple technique based on spatial division ot the hologram plate is described which permits recording a sequence of holograms of an object under different conditions and then reconstructing the images, two at a time, so that the interferenc~ patterns between any two images can be studied.
1. Introduction "lqle technicue of double.exposure, hologram interferometry has been found extremely useful, because of its simplicity, when a permanent record of the relative displacement of a surface after a certain change in conditions i.s required. However, the application of the method is limited by the fact that the difference between only two positions of the object surfaces can be evaluated. Where the object has to be studied over a range of conditions, it is usually necessary to use realtmw, hologram interferometry, which requires a rather r-,~re elaborate set-up. Even with real-time, holographic measurements, a problem which arises if the total range of movement is relatively large is that a new hologram has to be made whenever the number of interference fringes on the surface of the object becomes too large for conver,,ient evaluation. For such investigations, it would be extremely useful to have a technique by which one could record a sequence of holograms of the object on a sin~e photographic plate and then reconstruct selectively two images at a time, so that the interference pattern between them could be studied. Unfortunately, ~t ts not possible to apply the usual multiplexing technlques based on stgatial division of tile hologram [ 1, 2] t,, do th~s, since it has been shown that interference can take place betv, een two reconstructed images of a dtffusely scattering object only if both the recordings have On lea,,'e from the lndmn Institute of Sctcnce, Bangalore 560 012. India. 152
been made on the same area of the recording rnedium [31. As is well known, an arbitrary defomlation of a sur. face can give rise to hologram interference fringes localized at any distance from the surface, in front of it, or behind it [4]. When the reconstructed image is photographed, it is essential, under these conditions, to slop down the aperture of the camera lens considerably, so that the depth of field is adequate to permit both the surface of the object and the interference fringes to be in good focus simultaneously. There i~, natttrally, all increase m tile grain size of lhe speckle pattern and some l~ss of resolutmn, but these are usually not objectionable within limits. This implies that only a very small area of the hologram is used to reconstruct the final image. The present letter shows how this fact can be utilized in a very simple technique for recording a series of holographic interferograms of an object surface as it undergoes progressive deformation or displacement.
2. Experimental The only change to be made m a conventmnal systen", for hologram interferometrv is to provide tile holder for the hologram plate with a simple registration fixture so that a series of masks can be introduced just in front of the photographic emulsion layer. If the object is to be studied under n different loads, n masks are required, and, if interferograms are required for all possible com-
Volume 9, number 2
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OPTICS COMMUNICATIONS
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Fig. I. Layout of the masks used for multiplexing double-exposure holograms (n = 5 ). Each mask has (n - ! ) apertures, 2.5 mm in diameter, with a separation of 1 mm between adjacent apertures. binations of !oads, these can be of the form shown in fig. 1, each mask having (n -- 1) apertures. (In the present case n = 5, and the apertures were 2.5 mm in diameter with ! mm wide interspaces.) The first exposure, with the initial load, is made wifla the first mask, the second, after applying the required additional load, with the second mask, and so on. The apertures in the masks are arranged to overlap in a systematic fashion so that the series of n exposures results, in this case. in ~n{n- I } double-exposure holograms, corresponding to all possible combinations of loads, arranged in a triangular array as shown in fig. 2. With an object 50 cm from the ht,logram plate, the resolution limit of the individual holograms and the average speckle size are both approximately O. 15 ram, and the corresponding, theoretical depth of focus IS +_3 c!11. The number ol holograms can, of course, be reduced lol many appltcatmns. Typically, tl" only the total de. flection for each load and the mclemental dellecttons for successive changes in the load are to be evaluated, (2n - 3} double.exposure holograms are adequate. De.
®@@@ ®®@ @ Iqg. 2. Array ol n l n I ~/2 double-exposure hologram,;, torrespondmg to all possible combinations of loads, obtained wtth n exp.,sures made ,,ruth the n masks shown m ltg. 1
October 1973
pendivg on the requirements, the number of apertures in the masks as well as their layout can easily be modified to give a suitable, compact array. For photographing the interference fringes, the processed hologram plate is replaced in the plate holder and illuminated once again with the reference beam. The interference pattern corresponding to the displacement of the object surface between any two stages of loading can then be read out selectively by introducing the pair of masks with which exposures were made at these two stages once again in front of the hologram plate. Toler-. antes on registration of the plate and the masks are not at all stringent, since the requirement is just to ensure that only the corresponding elementary hologram produces a reconstructed image. Where the geometry of the system permits, it is quite easy to record the real image of the interference pattern on a film located in its plane. Alternatively, where this is net possible, the virtual image can be photographed with a camera. The only precautions necessary are to see that the camera lens is placed quite close behind the hologram, and that its aperture is large enough to accept the entire fan of rays from the reconstructed image. Under these conditions, the field of view is not restricted by the relatively small aperture of the hologram. A minor problem is the fact that the direction of ob,,ervation of the object varies slightly from one elementary hologram to another, since they are lo~,ated at different points on the plate. Since the palh d~fference measured b~ the interferogram ,wolves a cont~lbu tlon equal to the projection of the displacement of an object point onto the direction of viewing [5], this could, in principle, rest,lt in errors in the estimates of the corresponding displacements. It is obvious that, where ne:essary, a correction can be applied for this change in angle in calculating the actual displacements of the surfact'. l lowever, when the distance of the object from the l~ologram plate is large compared to the width of the ar~y ~,l elementary holograms, as is usually the case, th • error due to this factor is negligible.
3. Results Fig. 3. shows a typical series of mterferogra,ns obtained with this technique for five different loads (q, 1.2, 2.4, 3.6, and 4.8 g} applied to a test oblect cons~s, mg of a vertical metal cantilever ((1.5 cm long, located 153
Volume 9, n u m b e r 2
1.2
OPTICS COMMUNICATIONS
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;i 4,5 [ ~e. 3. Serle~ of d~,ublc-expo,,ure, holographic mt~.rferograms ,~blamed t,~r tlve dllfcrenl load~ ~,lth a vertical metal c,mtdevcr flength ol the cantde~er = 6.5 cm, distance from the hologram plate = 5(1 cm) 1-he figures under each photograph identify the corresponding tw't~ exr~osures The total deflection from the ireful posltl~m for each ~f the loads can be obtained from the top row ~f Interferogram,,, v, hilc the incremental deflecuons between ,~t:~ ~w,~ load,~ t a n be obtained from the lower rows.
154
Fig. 4. Series of double-exposure, hoh~graphlc Intcrlcrograms obtained with a vertical, plastic strip (phcn~l-I~rmaldch.~dc laminate) clamped at the b o t t o m . The figures under each photograph identify the individual two exp~,surcs invt~lvetl in each ht~logram. The first exposure was m a d e with no load, the second 5 mm alter applying a load t~f 0.3 g, and the ~ubscqucnl three exposures with the same load, but after additional intervals of 15 ram. The lower three pictures clearly show that the initial, relatwely large deflection of the strip ms folh~wed by a slow change The strip deles not reach a steady deflection even alter 35 ram.
Volume 9, number 2
OPTICS COMMUNICATIONS
at a distance of 50 cm from the hologram plate) which was clamped at the bottom end. From this series it is possible to evaluate the total deflection for each of the additional loads, as well as the incremental deflections between any two loads. As can be seen, the incremental deflections for equal increases in the load are very nearly the same. Another series of interferograms obtained with a similar test object made with a strip of plastic (pLenolformaldehyde laminate) is shown in fig. 4. in this case, the first exposure was made with no load, while the second was made 5 min after applying a load of 0.3 g, and ~he subsequent three exposures were made with the same load, but at further intervals of ! 5 min. The interferograms of the incremental deflections clearly show that the initial, relatively large deflection of the strip immediately after the load is applied is followed by a slow change in the deflection under constant load. The strip continues to move even after 35 rain.
4. Conclusions This technique requires very iltllc ill tl)e way of addltitinal equit~ment, but gives double-exp()sllre, hol(~-
October 1973
gram interferometry much greater flexibility. It could be a usel;al tool in ma y investigations, such as, for example, studies of non-linear deflections and plastic fl~)w
[6]. Acknowledgements The authors wish to thank Dr. W.H. Steel for helpful discussions.
References l l] tt.J. ('aulfield, Appl. Opt. 9 11970} 1218. 121 J.-('h. Vidnot, .I l)uvernoy, G. 'l'rlbillon and J.l,. I'ribill()n, Prt)c. Tcchmcai Program, l..lectro-Optics 1972 Intern. Conf. (Ind. and So. Conf. Manag., Inc., Chicago, 1972) p. 99. 131 R. Diindlikcr, E. Marom and F.M..Moltier, Opl. ('ommun. 6 (Iq72) 368. 141 K.A. ttames and B.P. ltildebrand, Appl. Opt. 5 (19661 595. 15] E.B. Alcksandrov and A.M. Bonch-llruevich, Soy. Phys. le~.h. Phys. 12 (1967) 258. 161 I K. l,eadbelter and T. Allan, in 'lhc Engineering U,,es ot lloiogral~hY, ed,,. E R. Robcrt,~on anti J.M !tarot3 (('ambridge t)mverstty Press, 1971)) p. 185.
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OPTICS COMMUNICATIONS
October 1973
SIMPLE MULTIPLEXING TECHNIQUE FOR DOUBLE-EXPOSURE HOLOGRAM INTERFEROMETRY P. H A R I H A R A N * and Z.S. HEGEDUS CSIRO Division o f Physics, National Standards Laboratory, Sydney, Aus,~.ralia 2008 Received 25 July 1973 A simple technique based on spatial division ot the hologram plate is described which permits recording a sequence of holograms of an object under different conditions and then reconstructing the images, two at a time, so that the interferenc~ patterns between any two images can be studied.
1. Introduction "lqle technicue of double.exposure, hologram interferometry has been found extremely useful, because of its simplicity, when a permanent record of the relative displacement of a surface after a certain change in conditions i.s required. However, the application of the method is limited by the fact that the difference between only two positions of the object surfaces can be evaluated. Where the object has to be studied over a range of conditions, it is usually necessary to use realtmw, hologram interferometry, which requires a rather r-,~re elaborate set-up. Even with real-time, holographic measurements, a problem which arises if the total range of movement is relatively large is that a new hologram has to be made whenever the number of interference fringes on the surface of the object becomes too large for conver,,ient evaluation. For such investigations, it would be extremely useful to have a technique by which one could record a sequence of holograms of the object on a sin~e photographic plate and then reconstruct selectively two images at a time, so that the interference pattern between them could be studied. Unfortunately, ~t ts not possible to apply the usual multiplexing technlques based on stgatial division of tile hologram [ 1, 2] t,, do th~s, since it has been shown that interference can take place betv, een two reconstructed images of a dtffusely scattering object only if both the recordings have On lea,,'e from the lndmn Institute of Sctcnce, Bangalore 560 012. India. 152
been made on the same area of the recording rnedium [31. As is well known, an arbitrary defomlation of a sur. face can give rise to hologram interference fringes localized at any distance from the surface, in front of it, or behind it [4]. When the reconstructed image is photographed, it is essential, under these conditions, to slop down the aperture of the camera lens considerably, so that the depth of field is adequate to permit both the surface of the object and the interference fringes to be in good focus simultaneously. There i~, natttrally, all increase m tile grain size of lhe speckle pattern and some l~ss of resolutmn, but these are usually not objectionable within limits. This implies that only a very small area of the hologram is used to reconstruct the final image. The present letter shows how this fact can be utilized in a very simple technique for recording a series of holographic interferograms of an object surface as it undergoes progressive deformation or displacement.
2. Experimental The only change to be made m a conventmnal systen", for hologram interferometrv is to provide tile holder for the hologram plate with a simple registration fixture so that a series of masks can be introduced just in front of the photographic emulsion layer. If the object is to be studied under n different loads, n masks are required, and, if interferograms are required for all possible com-
Volume 9, number 2
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•
OPTICS COMMUNICATIONS
' o00
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(1l
(2)
(3)
•
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(~.)
is)
Fig. I. Layout of the masks used for multiplexing double-exposure holograms (n = 5 ). Each mask has (n - ! ) apertures, 2.5 mm in diameter, with a separation of 1 mm between adjacent apertures. binations of !oads, these can be of the form shown in fig. 1, each mask having (n -- 1) apertures. (In the present case n = 5, and the apertures were 2.5 mm in diameter with ! mm wide interspaces.) The first exposure, with the initial load, is made wifla the first mask, the second, after applying the required additional load, with the second mask, and so on. The apertures in the masks are arranged to overlap in a systematic fashion so that the series of n exposures results, in this case. in ~n{n- I } double-exposure holograms, corresponding to all possible combinations of loads, arranged in a triangular array as shown in fig. 2. With an object 50 cm from the ht,logram plate, the resolution limit of the individual holograms and the average speckle size are both approximately O. 15 ram, and the corresponding, theoretical depth of focus IS +_3 c!11. The number ol holograms can, of course, be reduced lol many appltcatmns. Typically, tl" only the total de. flection for each load and the mclemental dellecttons for successive changes in the load are to be evaluated, (2n - 3} double.exposure holograms are adequate. De.
®@@@ ®®@ @ Iqg. 2. Array ol n l n I ~/2 double-exposure hologram,;, torrespondmg to all possible combinations of loads, obtained wtth n exp.,sures made ,,ruth the n masks shown m ltg. 1
October 1973
pendivg on the requirements, the number of apertures in the masks as well as their layout can easily be modified to give a suitable, compact array. For photographing the interference fringes, the processed hologram plate is replaced in the plate holder and illuminated once again with the reference beam. The interference pattern corresponding to the displacement of the object surface between any two stages of loading can then be read out selectively by introducing the pair of masks with which exposures were made at these two stages once again in front of the hologram plate. Toler-. antes on registration of the plate and the masks are not at all stringent, since the requirement is just to ensure that only the corresponding elementary hologram produces a reconstructed image. Where the geometry of the system permits, it is quite easy to record the real image of the interference pattern on a film located in its plane. Alternatively, where this is net possible, the virtual image can be photographed with a camera. The only precautions necessary are to see that the camera lens is placed quite close behind the hologram, and that its aperture is large enough to accept the entire fan of rays from the reconstructed image. Under these conditions, the field of view is not restricted by the relatively small aperture of the hologram. A minor problem is the fact that the direction of ob,,ervation of the object varies slightly from one elementary hologram to another, since they are lo~,ated at different points on the plate. Since the palh d~fference measured b~ the interferogram ,wolves a cont~lbu tlon equal to the projection of the displacement of an object point onto the direction of viewing [5], this could, in principle, rest,lt in errors in the estimates of the corresponding displacements. It is obvious that, where ne:essary, a correction can be applied for this change in angle in calculating the actual displacements of the surfact'. l lowever, when the distance of the object from the l~ologram plate is large compared to the width of the ar~y ~,l elementary holograms, as is usually the case, th • error due to this factor is negligible.
3. Results Fig. 3. shows a typical series of mterferogra,ns obtained with this technique for five different loads (q, 1.2, 2.4, 3.6, and 4.8 g} applied to a test oblect cons~s, mg of a vertical metal cantilever ((1.5 cm long, located 153
Volume 9, n u m b e r 2
1.2
OPTICS COMMUNICATIONS
1,3
1.&
1.5
O c t o b e r 1973
1.2
1.3
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1.5
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2,3
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;i 4,5 [ ~e. 3. Serle~ of d~,ublc-expo,,ure, holographic mt~.rferograms ,~blamed t,~r tlve dllfcrenl load~ ~,lth a vertical metal c,mtdevcr flength ol the cantde~er = 6.5 cm, distance from the hologram plate = 5(1 cm) 1-he figures under each photograph identify the corresponding tw't~ exr~osures The total deflection from the ireful posltl~m for each ~f the loads can be obtained from the top row ~f Interferogram,,, v, hilc the incremental deflecuons between ,~t:~ ~w,~ load,~ t a n be obtained from the lower rows.
154
Fig. 4. Series of double-exposure, hoh~graphlc Intcrlcrograms obtained with a vertical, plastic strip (phcn~l-I~rmaldch.~dc laminate) clamped at the b o t t o m . The figures under each photograph identify the individual two exp~,surcs invt~lvetl in each ht~logram. The first exposure was m a d e with no load, the second 5 mm alter applying a load t~f 0.3 g, and the ~ubscqucnl three exposures with the same load, but after additional intervals of 15 ram. The lower three pictures clearly show that the initial, relatwely large deflection of the strip ms folh~wed by a slow change The strip deles not reach a steady deflection even alter 35 ram.
Volume 9, number 2
OPTICS COMMUNICATIONS
at a distance of 50 cm from the hologram plate) which was clamped at the bottom end. From this series it is possible to evaluate the total deflection for each of the additional loads, as well as the incremental deflections between any two loads. As can be seen, the incremental deflections for equal increases in the load are very nearly the same. Another series of interferograms obtained with a similar test object made with a strip of plastic (pLenolformaldehyde laminate) is shown in fig. 4. in this case, the first exposure was made with no load, while the second was made 5 min after applying a load of 0.3 g, and ~he subsequent three exposures were made with the same load, but at further intervals of ! 5 min. The interferograms of the incremental deflections clearly show that the initial, relatively large deflection of the strip immediately after the load is applied is followed by a slow change in the deflection under constant load. The strip continues to move even after 35 rain.
4. Conclusions This technique requires very iltllc ill tl)e way of addltitinal equit~ment, but gives double-exp()sllre, hol(~-
October 1973
gram interferometry much greater flexibility. It could be a usel;al tool in ma y investigations, such as, for example, studies of non-linear deflections and plastic fl~)w
[6]. Acknowledgements The authors wish to thank Dr. W.H. Steel for helpful discussions.
References l l] tt.J. ('aulfield, Appl. Opt. 9 11970} 1218. 121 J.-('h. Vidnot, .I l)uvernoy, G. 'l'rlbillon and J.l,. I'ribill()n, Prt)c. Tcchmcai Program, l..lectro-Optics 1972 Intern. Conf. (Ind. and So. Conf. Manag., Inc., Chicago, 1972) p. 99. 131 R. Diindlikcr, E. Marom and F.M..Moltier, Opl. ('ommun. 6 (Iq72) 368. 141 K.A. ttames and B.P. ltildebrand, Appl. Opt. 5 (19661 595. 15] E.B. Alcksandrov and A.M. Bonch-llruevich, Soy. Phys. le~.h. Phys. 12 (1967) 258. 161 I K. l,eadbelter and T. Allan, in 'lhc Engineering U,,es ot lloiogral~hY, ed,,. E R. Robcrt,~on anti J.M !tarot3 (('ambridge t)mverstty Press, 1971)) p. 185.
!55