Abstract

Digital and analog holography, along with its many variations, viz., holographic interferometry, holographic microscopy, holographic tomography, multiwavelength digital holography, phase-shifting holography, compressive holography, coherence holography, etc., have become the methods of choice for various metrological applications in three-dimensional (3D) imaging. In this review, we discuss the basic principles of analog and digital holography and the various topics mentioned above, with selected applications to real-world problems. We also discuss other related topics such as dynamic holography, non-Bragg orders, and compressive holographic tomography, nonlinear holography, holographic TV, as well as a nonholographic technique for 3D visualization, viz., transport of intensity imaging. Finally, we expose interested readers to contemporary topics in the area, viz., nonlinear holography and real-time holographic TV.

© 2012 OSA

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2011

G. Nehmetallah and P. P. Banerjee, “Digital holographic interferometry and microscopy for 3-D object visualization,” in Frontiers in OpticsOSA Technical Digest (Optical Society of America, 2011), paper FTuF6.

A. Goy and D. Psaltis, “Digital reverse propagation in focusing Kerr media,” Phys. Rev. A 83(3), 031802 (2011).

J. Barabas, S. Jolly, D. E. Smalley, and V. M. Bove, “Diffraction specific coherent panoramagrams of real scenes,” Proc. SPIE 7957, 795702 (2011).

2010

P. A. Blanche, A. Bablumian, R. Voorakaranam, C. Christenson, W. Lin, T. Gu, D. Flores, P. Wang, W. Y. Hsieh, M. Kathaperumal, B. Rachwal, O. Siddiqui, J. Thomas, R. A. Norwood, M. Yamamoto, and N. Peyghambarian, “Holographic three-dimensional telepresence using large-area photorefractive polymer,” Nature 468(7320), 80–83 (2010).
[PubMed]

G. Nehmetallah and P. P. Banerjee, “SHOT: single-beam holographic tomography,” Proc. SPIE 7851, 785101 (2010).

A. Chirita, “Real-time scaling of micro-objects by multiplexed holographic recording on photo- thermo-plastic structure,” J. Mod. Opt. 57(10), 854–858 (2010).

2009

C. Barsi, W. Wan, and J. W. Fleischer, “Imaging through nonlinear media using digital holography,” Nat. Photonics 3(4), 211–215 (2009).

D. J. Brady, K. Choi, D. L. Marks, R. Horisaki, and S. Lim, “Compressive holography,” Opt. Express 17(18), 13040–13049 (2009).
[PubMed]

2008

P. P. Banerjee, G. Nehmetallah, N. Kukhtarev, and S. C. Praharaj, “Determination of model airplane attitudes using dynamic holographic interferometry,” Appl. Opt. 47(21), 3877–3885 (2008).
[PubMed]

Q. Y. J. Smithwick, D. E. Smalley, V. M. Bove, and J. Barabas, “Progress in holographic video displays based on guided-wave acousto-optic devices,” Proc. SPIE 6912, 69120H (2008).

S. Tay, P. A. Blanche, R. Voorakaranam, A. V. Tunç, W. Lin, S. Rokutanda, T. Gu, D. Flores, P. Wang, G. Li, P. St Hilaire, J. Thomas, R. A. Norwood, M. Yamamoto, and N. Peyghambarian, “An updatable holographic three-dimensional display,” Nature 451(7179), 694–698 (2008).
[PubMed]

2007

J. Kühn, T. Colomb, F. Montfort, F. Charrière, Y. Emery, E. Cuche, P. Marquet, and C. Depeursinge, “Real-time dual-wavelength digital holographic microscopy with a single hologram acquisition,” Opt. Express 15(12), 7231–7242 (2007).
[PubMed]

J. M. Bioucas-Dias and M. A. T. Figueiredo, “A new TwIST: Two-step iterative shrinkage/thresholding algorithms for image restoration,” IEEE Trans. Image Process. 16(12), 2992–3004 (2007).
[PubMed]

W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. R. Dasari, and M. S. Feld, “Tomographic phase microscopy,” Nat. Methods 4(9), 717–719 (2007).
[PubMed]

2006

E. J. Candès, J. K. Romberg, and T. Tao, “Stable signal recovery from incomplete and inaccurate measurements,” Commun. Pure Appl. Math. 59(8), 1207–1223 (2006).

E. J. Candes and T. Tao, “Near-optimal signal recovery from random projections: Universal encoding strategies?,” IEEE Trans. Inf. Theory 52(12), 5406–5425 (2006).

D. L. Donoho, “Compressed sensing,” IEEE Trans. Inf. Theory 52(4), 1289–1306 (2006).

E. Candès, J. Romberg, and T. Tao, “Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inf. Theory 52(2), 489–509 (2006).

F. Charrière, J. Kühn, T. Colomb, F. Montfort, E. Cuche, Y. Emery, K. Weible, P. Marquet, and C. Depeursinge, “Characterization of microlenses by digital holographic microscopy,” Appl. Opt. 45(5), 829–835 (2006).
[PubMed]

2005

2004

M. A. Golub, A. A. Friesem, and L. Eisen, “Bragg properties of efficient surface relief gratings in the resonance domain,” Opt. Commun. 235, 261–267 (2004).

L. Hesselink, S. S. Orlov, and M. C. Bashaw, “Holographic data storage systems,” Proc. IEEE 92(8), 1231–1280 (2004).

O. Ostroverkhova and W. E. Moerner, “Organic photorefractives: Mechanisms, materials, and applications,” Chem. Rev. 104(7), 3267–3314 (2004).

2002

U. Schnars and W. Juptner, “Digital recording and numerical reconstruction of holograms,” Meas. Sci. Technol. 13(9), R85–R101 (2002).

2001

W. Osten, S. Seebacher, T. Baumbach, and W. Jüptner, “Absolute shape control of microcomponents using digital holography and multiwavelength-contouring,” Proc. SPIE 4275, 71–84 (2001).

H. Yoshikawa, S. Iwase, and T. Oneda, “Fast computation of Fresnel holograms employing difference,” Opt. Rev. 8(5), 331–335 (2001).

2000

A. Barty, K. A. Nugent, A. R. Roberts, and D. Paganin, “Quantitative phase tomography,” Opt. Commun. 175(4–6), 329–336 (2000).

1999

1998

1997

1996

U. Schnars, T. Kreis, and W. Juptner, “Digital recording and numerical reconstruction of holograms: reduction of the spatial frequency spectrum,” Opt. Eng. 35(4), 977–982 (1996).

T. Credelle and F. Spong, “Thermoplastic media for holographic recording,” Proc. SPIE 130, 619–633 (1996).

T. Ito, H. Eldeib, K. Yoshida, S. Takahashi, T. Yabe, and T. Kunugi, “Special-purpose computer for holography HORN-2,” Comput. Phys. Commun. 93(1), 13–20 (1996).

B. L. Volodin, B. Kippelen, K. Meerholz, N. V. Kukhtarev, H. J. Caulfield, and N. Peyghambarian, “Non-Bragg orders in dynamic self-diffraction on thick phase gratings in a photorefractive polymer,” Opt. Lett. 21(7), 519–521 (1996).
[PubMed]

1994

1993

M. Lucente, “Interactive computation of holograms using a look-up table,” J. Electron. Imaging 2(1), 28–34 (1993).

1992

K. Sato, K. Higuchi, and H. Katsuma, “Holographic television by liquid-crystal device,” Proc. SPIE 1667, 19–31 (1992).

N. Hashimoto, K. Hoshino, and S. Morokawa, “Improved real-time holography system with LCDs,” Proc. SPIE 1667, 2–7 (1992).

1990

P. St. Hilaire, S. A. Benton, M. Lucente, M. L. Jepsen, J. Kollin, H. Yoshikawa, and J. Underkoffler, “Electronic display system for computational holography,” Proc. SPIE 1212, 174–182 (1990).

1988

R. M. Goldstein, H. A. Zebker, and C. Werner, “Satellite radar interferometry: Two-dimensional phase unwrapping,” Radio Sci. 23(4), 713–720 (1988).

D. Leseberg and C. Frère, “Computer-generated holograms of 3-D objects composed of tilted planar segments,” Appl. Opt. 27(14), 3020–3024 (1988).
[PubMed]

1987

1985

1984

D. Leseberg and O. Bryngdahl, “Computer-generated rainbow holograms,” Appl. Opt. 23(14), 2441–2447 (1984).
[PubMed]

N. Streibl, “Phase imaging by the transport equation of intensity,” Opt. Commun. 49(1), 6–10 (1984).

1983

1982

1978

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetskii, “Holographic storage in electrooptic crystals,” Ferroelectrics 22(1), 949–960 (1978).

A. J. Devaney, “Nonuniqueness in the inverse scattering problem,” J. Math. Phys. 19(7), 1526–1531 (1978).

1972

1970

1969

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Figures (70)

Figure 1
Figure 1

(a) Off-axis setup, (b) on-axis setup. MO-SF, microscope objective-spatial filter; BS, beam splitter; M, mirror; CL, collimating lens; d, distance between object and film or CCD.

Figure 2
Figure 2

(a) Fresnel, (b) Fraunhofer, (c) Fourier hologram, (d) Image, (e) Lensless Fourier hologram. f represents the focal length of the lens, d o , d i are the object and image distance from the lens. BS, beam splitter; CL, converging lens.

Figure 3
Figure 3

AH: (a) optical recording, (b) optical reconstruction. BS, beam splitter.

Figure 4
Figure 4

DH: (a) opto-electronic recording, (b) electronic reconstruction with E R , (c) electronic reconstruction with E R . BS, beam splitter.

Figure 5
Figure 5

Coordinate system for DH reconstruction.

Figure 6
Figure 6

(a) Schematic of the reflection-type Fresnel DH setup, (b) tabletop inline setup. MO-SF, microscope objective spatial filter; BS, beam splitter; M, mirror; CL, collimating lens; d, distance between object and CCD.

Figure 7
Figure 7

(a)–(c) Different objects used, (d)–(f) recorded Fresnel holograms of objects, (g–i) intensity distribution of the reconstructed objects. The resolution for the dime image is Δ ξ = 92 . 5 µ m for a distance of d = 90 cm , λ = 514 nm , N x Δ x = 5 mm , and the size of the dime is found to be 194 pixels or 17.91 mm as expected.

Figure 8
Figure 8

Interference phase modulo 2 π , and its corresponding unwrapped phase: (a) 1D case, and (b) 2D case.

Figure 9
Figure 9

PSDH setup [19].

Figure 10
Figure 10

Numerically reconstructed intensity image of the dice using PSDH. (Adapted from Yamaguchi [19].)

Figure 11
Figure 11

Scheme of the dynamic hologram recording in LN crystal/PTP (object O and reference R waves) with generation of the first non-Bragg orders ( + 3, −3); PC is phase conjugate, R is reference, O is object, and PE is phase enhanced (double the original phase) beam [20].

Figure 12
Figure 12

Imaging and interferometry in Bragg (1, −1) and in non-Bragg (+3, −3) diffraction orders: (a) initial state and (b) object after deformation (rotation around the vertical axis [N. Kukhtarev, Alabama A&M University, personal communication].

Figure 13
Figure 13

3d reconstruction of the object in Fig. 12 by using non-Bragg diffraction orders in PTP.

Figure 14
Figure 14

(a), (b) Recording and (c) reconstruction of a double-exposure holographic interferogram [5].

Figure 15
Figure 15

(a) Recording and (b) reconstruction of a real-time holographic interferogram [5].

Figure 16
Figure 16

Experimental setup for holographic interferometry of a diffuse object (model plane) to determine the attitude deformation (pitch, yaw, and roll). PTP, photothermoplastic.

Figure 17
Figure 17

(a)–(c) Interferograms superposed on image for different amounts of pitch and roll. (d) Interferogram superposed on image for pitch and yaw.

Figure 18
Figure 18

(a) Image of plane with superposed interference fringes corresponding to a roll and pitch (from Fig. 17(a)). (b) Plot of averaged localized intensity around the red dot in (a) along the vertical direction versus the angle by which the picture in (a) is rotated. When the fringes become vertical for a particular rotation angle, maximum intensity should be detected. The amount of rotation imparted should yield information about the original angle of the fringes. (c) Local period of the fringes around the red dot, found after appropriate rotation as described in (b). This information is used to determine the roll and pitch Δ θ = 0 . 518 8 , Δ ψ = 2 . 096 2  [24].

Figure 19
Figure 19

(a) Scheme of the dynamic hologram recording in LN crystal with object O (−1) and reference R ( +1) waves, along with generation of the first non-Bragg orders, viz., phase conjugate PC (3) and phase enhanced PE (−3). (b) Lab setup.

Figure 20
Figure 20

(a) Fringes resulting from readout of stored hologram of original object (CD-ROM) in LN by reference and light from deformed object after heating with a focused laser source. (b) A cropped region of interest of (a) (pixel size of the camera is 5 µm).

Figure 21
Figure 21

(a) is the absolute value of the 2D fast Fourier transform of Fig. 20, (b) and (c) are the filtered versions [see Eq. (34)], and (d) and (e) are the wrapped reconstructed phase diagrams (pixel size of the camera is 5 µm).

Figure 22
Figure 22

(a) 3d deformation of the crater formed due to heating. (b) The red curve is a scan from a profiler, and the blue curve is one slice from the unwrapped phase (pixel size of the camera is 5 µm).

Figure 23
Figure 23

Hilbert transform transfer function.

Figure 24
Figure 24

Digital holographic interferometry of the tilted coin. (a) Intensities of the two reconstructed holograms. (b) Corresponding phases of the reconstructed holograms. (c) The wrapped phase tilt (left), and the unwrapped 3d tilt (right). The xy axis units in all the figures are in pixels (pixel size of the camera is 10 µm and on the image plane is around Δ ξ = 100 µ m ).

Figure 25
Figure 25

(a) Two reconstructed holograms of object in (a) in Fig. 7, (b) corresponding phases, (c) interference phase modulo 2 π , and (d) unwrapped phase, corresponding to deformation immediately after the impact. The xy axis units in all the figures are in pixels (CCD pixel size is 10 µm and on the image plane is Δ ξ = 100 µ m ).

Figure 26
Figure 26

Two-wavelength shape measurement using DH [4].

Figure 27
Figure 27

(a) Reconstructed hologram at λ 1 = 496 . 5 nm , (b) wrapped phase, and (c) unwrapped phase or 3d surface profile. The two wavelengths used are λ 1 = 496 . 5 nm and λ 2 = 488 nm , and the synthetic wavelength is Λ = 28 . 5 µ m .

Figure 28
Figure 28

Schematic of dual-wavelength DH with tilted references. The object is illuminated with two different wavelengths λ 1 , 2 . The scattered light is combined with the tilted reference wave, and the resulting intensity is recorded on a CCD. The reference beams are distinguished by different angular offsets. The inset on the right is the Fourier transform of the image hologram captured on the CCD, showing the Fourier transforms of the two wavelength images (called simply “images” in the inset) and their twins appearing in complementary quadrants. The effect of the tilted references appears as two bright spots in quadrants labeled I and III.

Figure 29
Figure 29

(a) Same as inset in Fig. 28, showing the Fourier transform of the image on CCD resulting from object illumination with two wavelengths using spatial heterodyning. (b) and (c) are cropped and enlarged regions I and II of (a).

Figure 30
Figure 30

Reconstructed objects illuminated by using two wavelengths and spatial heterodyning. Intensity profiles show part of a coin after averaging 32 different speckle realizations for the two wavelengths. The pixel size of the CCD camera is around 10 µm.

Figure 31
Figure 31

(a) Lab setup. (b) Schematic of the reflection-type Fresnel DHM setup [34].

Figure 32
Figure 32

(a) DH of a part of USAF 1950, (b) 3d perspective of the reconstructed height distribution (the pixel size is 10 µm) [34].

Figure 33
Figure 33

(a) Lab setup. (b) Enlargement of the silicon wafer sample with photoresist spherical bumps. (c) Schematic of the holographic microscope for reflection imaging [33,34].

Figure 34
Figure 34

(a) Schematic of the test sample. (b) DH of the silicon wafer. (c) 3d perspective of the reconstructed height distribution. (d) Comparison of the profile of the DHM result and the result from a Veeco profiler [34].

Figure 35
Figure 35

(a) Integrated DHM instrument. (b) Square quartz microlens array [35].

Figure 36
Figure 36

A single cell in a detour-phase hologram technique.

Figure 37
Figure 37

(a) Binary detour-phase hologram; (b) image reconstructed from that hologram [1].

Figure 38
Figure 38

Point source method for CGH [45].

Figure 39
Figure 39

(a) Precomputed holograms; (b) the Cortical Cafe CGH Maker software interface [50].

Figure 40
Figure 40

Experimental setup. An incident plane wave passes through a weakly scattering phase object (index matched to surrounding medium), and images at various focal planes are collected on a CMOS camera. The camera is defocused by being moving along a linear stage by a distance Δ, (resulting in defocus of the imaging plane by Δ effective ), and an image is acquired at each location. The object is rotated between each pair of image captures for tomographic acquisition [57].

Figure 41
Figure 41

(a) Sample images: clockwise from top-left, background, in-focus, over-focused, and under-focused diamond. Background subtraction was applied via pixelwise division by the background image before processing. (b) Phase map generated from TI-based phase retrieval. Areas of higher intensity denote greater phase delay (estimated to linearly correlate with the depth of the object) [57].

Figure 42
Figure 42

Volumetric reconstruction of the phase object. Left, reconstruction from amplitude information alone (without use of the TI equations). Right, reconstruction results from TI-retrieved phase. The reconstruction results were found to agree with actual dimensions of the diamond to within 0.1 mm. Additionally, the number of edges and ridges (red arrow) present in the diamond reconstruction is in agreement with the actual number of edges and ridges on the diamond [57].

Figure 43
Figure 43

(a) Experimental setup of typical SHOT-MT recording scheme. (b) Lab setup showing a typical pulsed frequency-doubled YAG laser, along with four recording high-speed cameras.

Figure 44
Figure 44

Schematic showing the principle of SHOT-MT reconstruction using simulation.

Figure 45
Figure 45

(a) Recorded inline holograms of a 5 mm hemisphere lens, (b) 2D multiple Fresnel reconstructions, and (b) 3D reconstruction using SHOT-MT algorithm.

Figure 46
Figure 46

(a) Recorded inline holograms of two 3 mm spherical lenses, (b) 2D multiple Fresnel reconstructions, and (b) 3D reconstruction using SHOT-MT algorithm.

Figure 47
Figure 47

Schematic of the RTT setup.

Figure 48
Figure 48

(a) Projection matrix, (b) inverse Radon transform matrix, (c) 3D shape.

Figure 49
Figure 49

(a) Recorded inline holograms of water droplet suspended from a syringe along several orientations with M = 10 . The numbers on the horizontal and vertical axes are pixel numbers. (b) the 3D reconstruction (pixel size of the CCD is 10 µm) [59].

Figure 50
Figure 50

Schematic of the different matrices used for CS.

Figure 51
Figure 51

(a) Random samples of the original signal generated by the “A” key on a touch-tone phone. (b) The inverse DCT of the signal [68].

Figure 52
Figure 52

(a) The l 1 solution to A k j c ˆ j = b k and (b) f ˆ , a signal that is nearly identical to the original signal f [68].

Figure 53
Figure 53

(a) The l 2 solution, (b) f ˆ , a signal that bears little resemblance to the original signal [68].

Figure 54
Figure 54

(a) Typical Gabor-type setup using the transmissive geometry of an object surrounded by small objects.

Figure 55
Figure 55

(a) Typical TCH setup, transmissive geometry. (b) A typical hologram is reconstructed at a distance 15 cm and 0°. (c) 3D reconstruction of a collection of small particles by using TCH-MT.

Figure 56
Figure 56

(a) Pen spring 500 µm thick: (b) three representative holograms out of total of 13 angles recorded, 0° to 180° in 15° increments; (c) TwIST reconstruction, 90° and 180° at 33 cm. Tomographic reconstruction using (d) 2 angles, 0°and 90°; (e) 7 angles, 0°–180°, with 30° increments; and (f) 13 angles, 0°–180°, with 15° increments.

Figure 57
Figure 57

(a) Setup. (b) Coherence holography (CH) reconstruction of a dime using the TwIST algorithm in the reflective mode. Feature size in the reconstructed hologram is 28.6 µm for a CCD camera pixel size of 6.7 µm, λ = 633 nm , d = 31 cm , and demagnification M = 0 . 315 .

Figure 58
Figure 58

Optical fields reconstructed from a conventional hologram with a phase-conjugated reference beam [74].

Figure 59
Figure 59

Direct visualization of a coherence image reconstructed from a coherence hologram. The coherence image is directly observable as the contrast and the phase of a fringe pattern [74].

Figure 60
Figure 60

(a) Object. (b) Image reconstructed from phase-only hologram; (c) modulus of spatial coherence function; (d) coherence hologram representing spatially incoherent source distribution; (e) experimentally reconstructed coherence image visualized as a fringe contrast [74].

Figure 61
Figure 61

Typical experimental setup. Laser light (532 nm), polarized along the crystalline c axis, is split into two beams. (a) The object (upper) beam passes through the optical system to generate the input waveform, which is projected onto the crystal. The reference (lower) beam is incremented in phase steps of Δ ϕ = π / 2 ; both beams are imaged onto the CCD camera. (b) A USAF 1951 resolution chart, used as an object, along with the optical system [79].

Figure 62
Figure 62

Numerically reconstructed input fields. (a), (b) Measured input phase. (c), (d) Reconstructed input using linear DH. (e), (f) Reconstructed input using nonlinear DH. Scale bar, 200 µm. Note, for instance, the appearance of enhanced blue regions in (e) as compared with (c). (g) Averaged cross sections of highlighted regions in panels (c) and (e). The nonlinear reconstruction shows a clear enhancement of the field of view of 15% [80].

Figure 63
Figure 63

(a) Stereoscopic 3-D display and mismatch of distance between accommodation and convergence. When an observer fixates on a reconstructed 3-D image, convergence has to move from the display while accommodation should remain constant on the display [96]. (b) In a typical holographic stereogram (left), a hogel (holographic element) emits light in multiple directions with the same wavefront curvature but different intensities. In a diffraction-specific coherent panoramagram (DSCP, right), both intensity and curvature can vary with direction, eliminating accommodation-convergence mismatch and giving smooth motion parallax with fewer views [88].

Figure 64
Figure 64

Kinect camera captures both range and intensity images, which are converted in real time to holograms on the MIT acousto-optic display (right) [88].

Figure 65
Figure 65

Frame from holographic sequence generated from a Kinect camera displayed on the Arizona display (not at full video rate). Courtesy of University of Arizona, College of Optical Sciences [88].

Figure 66
Figure 66

Left, image processing, hologram recording, and display. The 2D perspective views of the object are generated by using a 3D computer model or a video camera moving on tracks around the object. The perspective images are reorganized (hogel data) and uploaded to the SLM. The SLM modulates the object beam, which is focused to the PR polymer and recorded in the Fourier transform geometry. The completed display can be viewed by using a reading beam. The result is realistic 3D imagery with parallax and depth. The holograms can be erased by uniform illumination at the writing wavelength [97]. Right, picture of a 4 × 4 -inch PR polymer thin-film device [97].

Figure 67
Figure 67

Image from the updatable holographic 3D display [97].

Figure 68
Figure 68

Hologram of two model cars recorded on a 12-inch-diameter PR device in HPO geometry [98].

Figure 69
Figure 69

Steps of hologram recording using a PTP device [5,21].

Figure 70
Figure 70

Schematic of the PR effect. θ = 90 ° for pure diffusion case [D. R. Evans and G. Cook, Air Force Research Laboratory, Wright-Patterson Air Force Base, personal communication].

Equations (4)

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φ ( ξ , η ) = arctan ( Im [ Γ ( ξ , η ) ] Re [ Γ ( ξ , η ) ] ) .
φ ( ξ , η ) = arctan ( Im [ Γ ( ξ , η ) ] Re [ Γ ( ξ , η ) ] ) ,
= ( x , y , z ) .
2 = ( 2 x 2 + 2 y 2 )

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