half-magnitude extensions of resolution and field of view in digital holography by scanning and...

Half-magnitude extensions of resolution and field ofview in digital holography by scanning and

magnification

Ferenc Gyímesi,1,* Zoltán Füzessy,1 Venczel Borbély,1 Béla Ráczkevi,1,5

György Molnár,1 Aladár Czitrovszky,2 Attila Tibor Nagy,2 Győző Molnárka,3

Abdelhakim Lotfi,3 Attila Nagy,3 István Harmati,3 and Dezső Szigethy4

1Budapest University of Technology and Economics, Department of Physics, Budafoki út 8, 1111 Budapest, Hungary2HAS Research Institute for Solid State Physics and Optics, Konkoly-Thege Miklós út 29-33, 1121 Budapest, Hungary

3Széchenyi István University, Jedlik Ányos Institute of IEME, Egyetem tér 1, 9026 Győr, Hungary4Technoorg Linda Ltd. Co., Rózsa út 24, 1077 Budapest, Hungary

5Currently with HAS Institute for Particle and Nuclear Physics, Konkoly-Thege Miklós út 29-33, 1121 Budapest, Hungary

*Corresponding author: [email protected]

Received 12 August 2009; accepted 29 September 2009;posted 8 October 2009 (Doc. ID 115593); published 28 October 2009

Digital holography replaces the permanent recording material of analog holography with an electroniclight sensitive matrix detector, but besides the many unique advantages, this brings serious limitationswith it as well. The limited resolution of matrix detectors restricts the field of view, and their limited sizerestricts the resolution in the reconstructed holographic image. Scanning the larger aerial hologram (theinterference light field of the object and reference waves in the hologram plane) with the small matrixdetector or using magnification for the coarse matrix detector at the readout of the fine-structured aerialhologram, these are straightforward solutions but have been exploited only partially until now. We havesystematically applied both of these approaches and have driven them to their present extremes, overhalf a magnitude in extensions. © 2009 Optical Society of America

OCIS codes: 090.0090, 090.1995.

1. Introduction

Analog holography uses a relatively permanent re-cording material for recording the interferencefringes of an aerial hologram (the interference lightfield of the object and reference waves in the holo-gram plane) and subsequently for providing a realmaterialized hologram grating for the reference lightwave to diffract on it at reconstruction. Therefore,from our present point of view, it could quite right-fully be called “material holography,” too. Digital ho-lography, on the other hand, replaces this permanent

recording material with an electronic light sensitivematrix detector that relatively instantly converts theinterference fringes of the aerial hologram into digi-tal information for a computer. No materializedgrating is produced; instead the reconstruction isperformed purely numerically. Digital holographyhas the great advantage of the really unique flexibil-ity of the numerical reconstruction, but it suffersfrom the basic physical shortcomings of the convert-ing electronic matrix detector.

A charge-coupled device (CCD) or a complemen-tary metal-oxide semiconductor (CMOS) camera hasa very limited resolution in comparison with thephotographic recording materials of material holo-graphy, and the matrix detector of the camera has

0003-6935/09/316026-09$15.00/0© 2009 Optical Society of America

6026 APPLIED OPTICS / Vol. 48, No. 31 / 1 November 2009

a size much smaller than the possible size of thesephotographic plates. The limited resolution restrictsthe field of view of the reconstruction, while the lim-ited size restricts the resolution in the reconstructedholographic image. Since the invention of digital ho-lography, many attempts have been made to over-come these two basic limitations.As for the limited size of the matrix detector, scan-

ning the larger aerial hologram somehow with thesmall matrix detector is the most straightforward ap-proach. Although there are other important methodsto build up some type of a synthetic aperture, thismostly means the relative motion of the camera andthe object with respect to each other [1–6]. The syn-thetic aperture can be in the real hologram plane di-rectly [3–6] or somewhere before it, in the Fourierplane of an intermediate optical system [1], or in avirtual calculation-transformed hologram plane [2].In most cases [2,5,6] the camera is the only movingelement. In [1] some part of the optical setup movestogether with the camera, and in [2] separate fixedcameras are used. Besides, there is an opposite pos-sibility of moving the object instead of the camera [3].Both on-axis [5,6] and off-axis [1–4] optical arrange-ments are practiced. A phase shifting procedure isapplied in an on-axis arrangement [5] or in a movingreference case [1]. The stitching of the holograms isgenerally performed by correlation calculation ontheir overlapping side areas.The present paper reports results in probably the

simplest version possible of the synthetic apertureapproach, which does not seem to have been directlyexploited until now. An optics-free small bottom linecamera is moved directly in the aerial hologramplane in a conventional off-axis arrangement, up to8 times its original size. The increase achieved thisway in the resolution is by a factor 6.As for the limited size of the detector pixels, the

application of some magnification is again anothermost straightforward approach for the readout of thefine-structured aerial hologram. Nevertheless, ac-cording to the best knowledge of the authors of thispaper, no attempts have been made at all in this di-rection until now.Here the present paper we would like to report re-

sults with a microscope objective mounted camera fo-cused on the aerial hologram plane, with scanningperformed with it as before. At 10× magnification,the increase in the field of view is a factor of 7 withoutloss in image resolution, and at 4× magnification, itbecomes a factor of 4 with a simultaneous increase inimage resolution, too, by a factor of 3.

2. Theoretical Background

A. Digital Holographic Resolution and Field of View

The numerical calculation of the digital holographicreconstruction is usually performed with discreteFourier transformation, as it is treated in detail in[7]. The discrete Fourier transformation itself im-poses already certain mathematical limits on the cal-

culated image field: on image pixel size and on imagefield size. These mathematical limits, most fortu-nately, happen to be equal or quite close to the phy-sical limits, which result from diffraction theory andfrom the Shannon sampling theorem applied on theinterference fringes of the aerial hologram.

According to the notations of Fig. 1(a), if x and y arethe coordinates in the hologram plane,Δx andΔy arethe pixel sizes of the matrix detector, and Lx and Lyare the sizes of the matrix detector itself, then in thecalculated image plane, with a distance d apart fromthe hologram, the pixel sizes become mathematically

Δ ~x ¼ λdLx

; Δ~y ¼ λdLy

: ð1Þ

These values are just equal to the half sizes of thecentral spot of the diffraction pattern of a converginglight beam entering through an aperture of sizes Lxand Ly from a distance d, which is just the opticallimit of resolution, and which is the average specklesize as well.

Nevertheless, in spite of this fortunate coincidence,it proves to be worth densifying the calculationpoints further to have a more detailed display ofthe calculated image, which still remains the samediffraction limited one. This can be achieved withinthe discrete Fourier transformation by the zero pad-ding technique; that is, the detected hologram areahas to be extended by zero values to larger sizes. Ac-cording to the authors experience, a factor of 4 is anadequate and practical choice for this zero paddingextension, that is, with

LðDFTÞx ¼ 4Lx; LðDFTÞ

y ¼ 4Ly; ð2Þ

the practically decreased image pixel sizes become

Δ~xðDFTÞ ¼ λdLðDFTÞx

¼ λd4Lx

; Δ~yðDFTÞ ¼ λdLðDFTÞy

¼ λd4Ly

:

ð3Þ

These densified values will be used for the image pix-el sizes everywhere in the calculation of the experi-mental results to follow.

On the other hand, the pixel numbers remain thesame during the discrete Fourier transformation,and thus the calculated image field sizes, too, becomemathematically limited to the sizes

~LðDFTÞ~x ¼ λd

Δx; ~LðDFTÞ

~y ¼ λdΔy

; ð4Þ

on which the previous zero padding has no influenceat all, but the DFT superscript has been kept for uni-formity. These values are just equal to double themaximum distances in the object plane from wheretwo point sources can produce an interferometricfringe system that is just detectable by the matrix

1 November 2009 / Vol. 48, No. 31 / APPLIED OPTICS 6027

detector pixels, according to the Shannon samplingtheorem. It seems reasonable that the hologram-fringe sampling limit values should be regarded asthe physical limits of the field of view for the matrixdetector. Nevertheless, according to the authors’ ex-perience, the larger calculation limits of Eq. (4) canbe reached as well, although at the price of some re-solution inhomogenity in the reconstructed images.Because of this resolution inhomogenity within the

wider limits, only the hologram-fringe sampling lim-its have been considered adequate for image recon-struction. Furthermore, to completely eliminate theslightest possible disturbing effects of the correlationspot in the origin of the image field (although DCterm compensation has been applied in the recon-struction calculation), the authors have avoided thisorigin area completely. This reduced the investigatedimage field further, to one half of the hologram-fringesampling limit values, that is, to

~LðDFT;homÞ~x ¼ λd

4Δx; ~LðDFT;homÞ

~y ¼ λd4Δy

; ð5Þ

and with a shift in its position from the origin in thepositive x direction, equal to ~LðDFT;homÞ

~x , as can be seenin Fig. 1(a) with an object filling completely the in-vestigated homogeneous image field.

B. Extension of Resolution by Scanning

According to Eq. (3), the image resolution in digitalholography is inversely proportional to the size ofthe matrix detector. The matrix detector size canbe increased virtually by scanning. As can be seenin Fig. 1(b), the optics-free camera canmove stepwisein x and y directions (e.g., on a meandering path) tocover a larger hologram, and at each step the actualhologram parts can be recorded. Afterwards thesehologram parts only have to be stitched into a largerhologram, although with interferometric precision.

This can be achieved in two ways. The motion ofthe camera can be followed with interferometric pre-cision with appropriate precision stages, althoughonly within a more or less limited range. Afterwardsthe hologram parts can be matched according to therecorded interferometrically correct position data ofthe stages.

The second solution does not require stages withinterferometric precision for the camera motion, andtherefore it is more economical, first of all. The cam-era is moved with an accuracy of about one tenth ofthe matrix detector size only, and the hologram partsare recorded with overlapping border areas. The in-terferometric precision of their relative positions is tobe achieved by correlation calculations within theseoverlapping border areas at different positions and

Fig. 1. Digital holographic reconstruction showing resolution and field of view (a) reconstructing directly with the original aperture of theoptics-free digital camera, (b) reconstructing by scanning with the original aperture of the optics-free digital camera, and (c) reconstructingwith the demagnified aperture of the microscope objective mounted on a digital camera, by scanning up to the original aperture size (andhigher).


by looking for the maximum of the correlation valuesand for the positions belonging to it.The authors of the present paper have chosen the

latter approach as well, but not only because of itsalready well known cheaper feasibility. It has turnedout that the correlation based hologram stitching isalso excellent for the compensation of the unwantedmotions of the hologram fringes too, during a long re-cording procedure. The shifts or vibrations of holo-gram fringes are usually present in the long run,even in a well air-conditioned laboratory room andon a vibration isolated table. As for the large scan-nings, a scanning of 25 × 25 steps, for instance, cantake more than half an hour, as well, where hologrammotion is already practically unavoidable.As can be seen on the right side of Fig. 2, a 2 × 2

stitching of hologram parts by looking for a correla-tion maximum in the overlapping areas can producethe same result as a whole, unstitched, one piece ho-logram (the gray column in the middle). The left sideproves that a 2 × 2 hologram is much inferior ifstitched according to precisely controlled motion.The object is a simulated 1951 USAF resolution

test chart in a diffuse reflection version (with groupþ4 and þ5). The last resolvable elements are de-tected by the authors’ own “fringe-integrator”(FRIINT) program to make the evaluation more ob-jective than simple human observation. FRIINT is acombined fringe enhancing and fringe identifyingprogram that carries out fringe enhancing with in-

tensity integration along the fringes while lookingfor the fringe direction and spacing by systematicsearch. The enhanced fringes are painted on the ori-ginal ones to prove even visually that they could bereally identified by the program.

The holograms themselves are simulated ones toprovide exactly the same situations all along the si-mulated scannings for both stitching versions. Thesubsequent hologram parts always suffered a phaseshift of π in the reference wave at each exposure. Thisis most clearly visible in the white circle in thestitched hologram of the controlled motion version.There the fringes are shifted by exactly half of thefringe spacing; the fringes are broken. Naturally,the positionally accurate stitching of the hologramcannot compensate for fringe motion. On the otherhand, the fringes in the white circle in the stitchedhologram of the correlation maximum version arestraight, precisely as in the one-piece hologram cir-cle. It is interesting to note that in the correlationmaximum version the speckles themselves get bro-ken because of the compensation of fringe motion,but this does not affect reconstruction superiority.

C. Extension of Field of View by Magnification and ItsSubsequent Combination with Scanning

According to Eq. (5), in digital holography the fieldof view is inversely proportional to the size of thedetector pixels. The detector pixel size can be de-creased virtually by using a microscope objective to

Fig. 2. Stitching the hologram parts in different ways.


demagnify the matrix detector. This is the same as tosay that the hologram can be magnified by the micro-scope objective onto the matrix detector, but the pre-vious description is more convenient to describe theconsequences. However, the demagnified pixel sizesmean a demagnified matrix detector, as well, whichautomatically decreases the resolution.As can be seen in Fig. 1(c), the microscope objective

mounted camera has to scan in the x and y directionsto cover the area of the original, not the demagnified,matrix detector, to get back the resolution of theimages reconstructed with the original matrix detec-tor. Thus if a resolution decrease is not the price forthe increase of the field of view, then scanning has togo together with demagnification of the pixels. Natu-rally, scanning can be continued even further.Nevertheless, stitching of hologram parts can be-

come problematic in the case of demagnification ofthe matrix detector. Demagnification can introducedistortions at the demagnified matrix detector, andbecause the border areas of the hologram parts aredetected just by opposite edges of the demagnifiedmatrix detector, their different distortions can influ-ence the correlation maximum significantly. The so-lution is the proper limitation of the field of view ofthe microscope objective around its better center re-gion. Unfortunately, the specifications of the micro-scope objectives do not contain information abouttheir distortion properties on that scale. The proper

limitation can be found only by trials, and it mayprove to be quite strong at larger magnifications.

3. Experimental Details and Results

A. Scanning the Aerial Hologram for Better Resolution

Figure 3(a) shows the joint arrangement for record-ing digital holography and for recording materialholography, to compare their achievements. The ar-rangement is a conventional off-axis arrangementwith the reference wave objective LR close to the ob-ject. The laser light is split into object and referencewaves by beam splitter BS, and the mirrors MO andMR direct them toward the object O and toward theaerial hologram plane AHP through microscope ob-jectives (and spatial filters) LO and LR. Two differentrecording devices can be put in the aerial hologramplane AHP: the optics-free camera COf and thephotographic hologram plate HP1 (the third device,the microscope objective mounted camera CMo, is forlater use in the magnification case). The COf camerais used by scanning or first without it, while the ho-logram plate is conventionally motionless.

As for the reconstructions, digital holographynaturally does not require any optical arrangement.However, material holography does, and in two dif-ferent arrangements: Fig. 3(b) shows reconstructionof the real image, and Fig. 3(c) shows reconstructionof the virtual image. In both cases the photographichologram plate HP1 is in its original place after its

Fig. 3. Recording and reconstruction/observation arrangements: (a) recording with two versions of digital cameras, and with a holo-graphic plate, (b) reconstructing and observing a real image from a holographic plate, (c) reconstructing and observing a virtual imagefrom a holographic plate, and (d) observing a real object directly by the lens system.


development. In both cases the same lens systemL1−L2 is used to make a 1∶1 image although in op-posite directions and about different elements. Thelens system L1−L2 has some distance between theirfoci, and the interim images fall symmetrically be-tween them. At the real image, it makes a 1∶1 imageof the point source at lens LRc onto the point source atlens LR to produce a reversed reference beam, andthe reconstructed real image OR of the object is ob-served by the optics-free camera CR. At the virtualimage, it makes a 1∶1 image OV of the reconstructedvirtual image of the object O to be observed by theoptics-free camera CV. For comparison with the di-rect imaging by lenses, as seen in Fig. 3(d), the lenssystem L1−L2 makes a 1∶1 real image OL of the ori-ginal object O, too, to be observed by the optics-freecamera CL [quite similar to Fig. 3(c)]. The object Oremains illuminated in this latter case, while inthe previous two cases object illumination is blocked.This way, in all the four cases, exactly the same con-dition could be provided to make the comparisonscorrect.The small bottom line camera was simulated by

cutting out a 512 × 512 pixel portion from a largercamera of pixel size 7:4 μm×7:4 μm. The camera mo-tion was controlled only with 0:1mm accuracy inboth x and y directions. A meandering path was cho-sen for scanning. The translation stages and the ex-

posures were driven by a PC computer. The distancebetween object and hologram plane was chosen to be1m, and the object was maximized to 16mm×16mm,according to Eq. (5) in the case of a laser wavelengthof 488nm.

Special variants of the 1951 USAF resolution testcharts were used to detect the maximum resolutionachieved. These charts were fabricated especially forthis research; they were made in different sizes andwith proper repetitions of the groups required at theactual measurements. The charts had to fill the com-plete image field investigated to show resolutioneverywhere within it. The charts were made on aglass substrate and with a diffuse white surfaceput behind to make them diffusely reflective, as mostholographic objects are. Unfortunately, the number-ing of the groups and elements did not become prop-erly large, and their visibility was in most cases verypoor. Therefore the experimental results presentedalways contain group numbers separately besidesthe photos, and final resolution numbers as wellare given below them.

Figure 4 on the outmost right shows the result ofscanning in digital holography: an extension in thereconstructed resolution by a factor of 6. The originalaperture of 512 × 512 pixels (3:8mm×3:8mm)started with a resolution of 2:24 line pairs=mm,while the 10 × 10 synthetic aperture of 4096 × 4096

Fig. 4. Results of scanning the aerial hologram, and the comparison of the achievement of digital holography with material holographyand with direct imaging by a lens.


pixels (30:3mm×30:3mm) could reach a resolutionof 12:7 line pairs=mm.For comparison with the case of ideal conditions,

simulated digital holography was used to find theidealized limits of digital holography (Fig. 4, secondcolumn from the right). Simulated digital holographyworked slightly better at the original aperture, but itaccomplished significantly better at the size of the10 × 10 synthetic aperture, 17:95 line pairs=mm. Itdid not take into account hologram stitching; it al-ways worked with an unstitched one-piece hologram.Thus the difference in the achievements should bebecause of the not completely proper stitching ofthe holograms. This could be expected because theaccuracy of hologram stitching with correlation isabout one (or sometimes two pixels), according to si-mulation experiments. In a 10 × 10 synthetic aper-ture the accumulated error can grow considerably.For comparison with the case of material hologra-

phy, photographic plate holograms were investigatedwithin the same conditions (Fig. 4, third column fromthe right). They started together with digital holo-graphy, but they lagged behind (both at real and vir-tual images) at the size of the 10 × 10 synthetic

aperture, 6:35 line pairs=mm. This may come as asurprise after having identified the problem of inac-curacies in stitching. However, in spite of holographybeing “lensless photography,” it does require finally alens or lenses to have the reconstructed holographicimages recorded photographically or even electroni-cally (and digitally). The 10 × 10 synthetic aperturealready has a size of 30:3mm×30:3mm, and this istoo large already even for extreme photo objectives.In the lens system L1−L2, special large size telephotoobjectives were used that were originally designedfor taking picture with sizes of 6 cm×6 cm (Sonnar2:8=180). They were positioned with their rear partstoward each other to reach the best quality possible.Even so, the aberration of the lens system grew sig-nificant at that large aperture size. Nevertheless, inthe case of smaller aperture sizes, the aberrationproved to be negligible. The holographic recordingsdid not lag behind and even became better thanscanned digital holography.

Finally, for comparison with the “holography-less”direct imaging, the lens system L1−L2 was used tomake images directly from the illuminated object(Fig. 4, fourth column from the right). Resolution

Fig. 5. Result of magnifying the aerial hologram by a factor of 4 and the results of the combination of this magnification with scanning.


starts the same as digital holography, it is a little bitbetter than material holography, and it lags behindat the size of the 10 × 10 synthetic aperture, almostthe same as material holography, again. This verifiesthat the aberrations of the lens system are the deter-minant factor at large apertures and that at theselarge apertures, scanned digital holography canproduce the best resolution, in spite of its stitchinginaccuracies.

B. Magnifying the Aerial Hologram for Larger Field ofView and Its Combination with Scanning

Figure 5 shows the results of magnifying the aerialhologram by a factor of 4, where the magnificationresults in an extension in the reconstructed field ofview similarly by a factor of 4. The 4× microscope ob-jective reduces the pixel size to 1:85 μm×1:85 μm and

increases the observable object size from 16 × 16 to64mm×64mm. At the same time, naturally, the re-solution in the reconstructed images decreases to1=4 of the resolution achieved by the original matrixdetector, to 0:5 line pair=mm.

The original resolution of 2:24 line pairs=mm,within this extended field of view, can be reachedonly by a 5 × 5 synthetic aperture of 2048 × 2048 pix-els, which has a size of 3:8mm×3:8mm, just equal tothe size of the original matrix detector.

Both the field of view and the resolution can beincreased if a larger synthetic aperture is produced:a 20 × 20 synthetic aperture of 8912 × 8912 pixels(15:2mm×15:2mm) could reach a resolution of7:13 line pairs=mm. This means a combined exten-sion in field of view and resolution by a factor of3–4 for both aspects. Besides, the pure resolution

Fig. 6. Result of magnifying the aerial hologram by a factor of 10 and the results of the combination of this magnification with scanning.


increase with respect to the decreased resolution of0:5 line pair=mm is more than a factor of 14 inthis case.Figure 6 shows the results of magnifying the aerial

hologram by an even greater factor, by a factor of 10;an extension in the reconstructed field of view is ex-pected similarly by a factor of 10, but only a factor of7 could be reached.The 10×microscope objective reduces the pixel size

to 0:74 μm×0:74 μm and increases the observableobject size from 16mm×16mm theoretically to160mm×160mm, but practically only to 120mm×120mm if homogeneity in the resolution is requiredin the whole field of view. With the magnification,as a natural consequence, the resolution in the re-constructed images decreases to 1=10 of the resolu-tion achieved by the original matrix detector, to0:25 line pair=mm.The original resolution of 2:24 line pairs=mmwith-

in this extended field of view can be reached by a 12 ×12 synthetic aperture of 5120 × 5120 pixels, whichhas a size, again, equal to the size of the original ma-trix detector (3:8mm×3:8mm).Both the field of view and the resolution could be

increased if a larger synthetic aperture were pro-duced, but this time the resolution increase becamevery limited. Only 50% could be reached, evenwith an extremely large 25 × 25 synthetic aper-ture of 10240 × 10240 pixels (7:6mm×7:6mm),3:17 line pairs=mm. Most certainly the accumulatedlarge stitching errors can be held responsible for this.If decrease and even inhomogenities in resolution

are acceptable for achieving an extremely largefield of view, a 12 × 12 synthetic aperture of 5120 ×5120 pixels (3:8mm×3:8mm) can have a resolution1:12 line pairs=mm (half of the resolution pro-duced by the original matrix detector), even on330mm×330mm. This means an extension of afactor of 20 in the field of view, and even with1:12 line pairs=mm, it is a quite good joint achieve-ment from 1m.It is worth mentioning that neither the 4× nor the

10× microscope objectives had any distortion pro-blem at the 512 × 512 pixel matrix detector size,which would have disturbed the correlation calcula-tions. However, the 10× microscope objective alreadydid have this problem very significantly above the1024 × 1024 pixel matrix detector size.

4. Summary

Digital holography seems not to have fully exploited,or at all, the two most straightforward possibilities ofovercoming the basic physical shortcomings of elec-tronic matrix cameras. The limited matrix detectorsize can be extended upward by producing a syn-

thetic aperture with camera scanning, directly in theaerial hologram plane and in a conventional off-axisarrangement, too. On the other hand, the limited pix-el size can be extended downward by a demagnifyingmicroscope objective before the matrix detector,although this approach has to be combined immedi-ately with some synthetic aperture extension, too, iforiginal resolution is to be retained.

With a 10 × 10 synthetic aperture of 4096 × 4096pixels, 1:27 line pairs=mm resolution could bereached from 1 m distance with a basic 512 × 512pixel camera, which is an extension of resolutionby a factor of 6. This resolution is better than whatan extremely large photo objective can produce fromthe same distance.

On the other hand, a 4× microscope objective mag-nification could provide an extension of the field ofview by a factor of 4, and a concurrent resolutionincrease by a factor of 3 with the help of a 20 × 20synthetic aperture of 8192 × 8192 pixels. A 10× mi-croscope objective could provide an extension ofthe field of view even by a factor of 7 (up to an objectsize of 120mm from 1m), retaining the original reso-lution (2:24 line pairs=mm).

Hologram stitching based on correlation calcula-tions proved to be not only economically beneficialbut even uniquely noise resistant, too, at the longscannings.

The work was performed within the scope of theHungarian Economic Competitiveness OperativeProgram (GVOP) under grant 3.1.1.-2004-05-0403/3.0 and was also supported by the EU StructuralFund. The authors would like to thank JózsefSchmelzer for his contributions in the FRIINTprogram.

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periment in the visible with on-axis digital heterodyne holog-raphy,” Opt. Lett. 26, 1550–1552 (2001).

2. J. Massig, “Digital off-axis holography with synthetic aper-ture,” Opt. Lett. 27, 2179–2181 (2002).

3. R. Binet, J. Colineau, and J.-C. Lehureau, “Short-range syn-thetic aperture imaging at 633nm by digital holography,”Appl. Opt. 41, 4775–4782 (2002).

4. T. Kreis, M. Adams, and W. Jüptner, “Aperture synthesis indigital holography,” Proc. SPIE 4777, 69–76 (2002).

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half-magnitude extensions of resolution and field of view in digital holography by scanning and...

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