Abstract

A volume hologram has two degenerate Bragg-phase-matching dimensions and provides the capability of volume holographic imaging. We demonstrate two volume holographic imaging architectures and investigate their imaging resolution, aberration, and sensitivity. The first architecture uses the hologram directly as an objective imaging element where strong aberration is observed and confirmed by simulation. The second architecture uses an imaging lens and a transmission geometry hologram to achieve linear two-dimensional optical sectioning and imaging of a four-dimensional (spatial plus spectral dimensions) object hyperspace. Multiplexed holograms can achieve simultaneously three-dimensional imaging of an object without a scanning mechanism.

© 2004 Optical Society of America

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2002

2001

2000

C. Moser, I. Maravic, B. Schupp, A. Adibi, D. Psaltis, “Diffraction efficiency of localized holograms in doubly doped LiNbO3 crystals,” Opt. Lett. 25, 1243–1245 (2000).
[CrossRef]

A. Stadelmaier, J. H. Massig, “Compensation of lens aberrations in digital holography,” Opt. Lett. 25, 1630–1632 (2000).
[CrossRef]

G. W. Burr, H. Coufal, J. A. Hoffnagle, C. M. Jefferson, M. Jurich, B. Marcus, R. M. Macfarlane, “Optical data storage enters a new dimension,” Phys. World 13, 37–42 (July2000).

J. Michaells, C. Hettich, J. Mlynek, V. Sandoghdar, “Optical microscopy using a single-molecule light source,” Nature (London) 405, 325–327 (2000).
[CrossRef]

N. V. Joshi, H. Medina, “Multiple beam interference confocal microscopy: tool for morphological investigation of a living spermatozoon,” Microsc. Microanal. 6, 471–477 (2000).
[PubMed]

X. H. Zhang, J. J. Xu, Q. Sun, S. Liu, G. Q. Zhang, H. J. Qiao, F. F. Li, G. Y. Zhang, “Dual-wavelength nonvolatile holographic storage,” Opt. Commun. 180, 211–215 (2000).
[CrossRef]

C. Moser, B. Schupp, D. Psaltis, “Localized holographic recording in doubly doped lithium niobate,” Opt. Lett. 25, 162–164 (2000).
[CrossRef]

B. Javidi, E. Tajahuerce, “Three-dimensional object recognition by use of digital holography,” Opt. Lett. 25, 610–612 (2000).
[CrossRef]

1999

A. Diaspro, S. Annunziata, M. Raimondo, P. Ramoino, M. Robello, “A single-pinhole confocal laser scanning microscope for 3-d imaging of biostructures,” IEEE Eng. Med. Biol. Mag. 18, 106–110 (1999).
[CrossRef] [PubMed]

G. Barbastathis, D. J. Brady, “Multidimensional tomographic imaging using volume holography,” Proc. IEEE 87, 2098–2120 (1999).
[CrossRef]

E. Chuang, W. H. Liu, J.-J. P. Drolet, D. Psaltis, “Holographic random access memory,” Proc. IEEE 87, 1931–1940 (1999).
[CrossRef]

M. Levene, G. J. Steckman, D. Psaltis, “Method for controlling the shift invariance of optical correlators,” Appl. Opt. 38, 394–398 (1999).
[CrossRef]

G. Barbastathis, M. Balberg, D. J. Brady, “Confocal microscopy with a volume holographic filter,” Opt. Lett. 24, 811–813 (1999).
[CrossRef]

W. H. Liu, D. Psaltis, “Pixel size limit in holographic memories,” Opt. Lett. 24, 1340–1342 (1999).
[CrossRef]

1998

T. Zhang, I. Yamaguchi, “Three-dimensional microscopy with phase-shifting digital holography,” Opt. Lett. 23, 1221–1223 (1998).
[CrossRef]

D. Psaltis, G. W. Burr, “Holographic data storage,” Computer 31(2), 52 (1998).
[CrossRef]

K. Buse, A. Adibi, D. Psaltis, “Nonvolatile holographic storage in doubly doped lithium niobate crystals,” Nature (London) 393, 665–668 (1998).
[CrossRef]

1997

A. Pu, R. Denkewalter, D. Psaltis, “Real-time vehicle navigation using a holographic memory,” Opt. Eng. 36, 2737–2746 (1997).
[CrossRef]

M. R. Taghizadeh, P. Blair, B. Layet, I. M. Barton, A. J. Waddie, N. Ross, “Design and fabrication of diffractive optical elements,” Microelectron. Eng.219–242 (1997).
[CrossRef]

J.-J. P. Drolet, E. Chuang, G. Barbastathis, D. Psaltis, “Compact, integrated dynamic holographic memory with refreshed holograms,” Opt. Lett. 22, 552–554 (1997).
[CrossRef] [PubMed]

E. Chuang, D. Psaltis, “Storage of 1000 holograms with use of a dual-wavelength method,” Appl. Opt. 36, 8445–8454 (1997).
[CrossRef]

1996

1995

1994

1993

H.-Y. S. Li, Y. Qiao, D. Psaltis, “Optical network for real-time face recognition,” Appl. Opt. 32, 5026–5035 (1993).
[CrossRef] [PubMed]

J. Rosen, M. Segev, A. Yariv, “Wavelength-multiplexed computer-generated volume holography,” Opt. Lett. 18, 744–746 (1993).
[CrossRef] [PubMed]

S. Yin, H. Zhou, F. Zhao, M. Wen, Z. Zhang, F. T. S. Yu, “Wavelength-multiplexed holographic storage in a sensitive photorefractive crystal using a visible-light tunable diode laser,” Opt. Commun. 101, 317–321 (1993).
[CrossRef]

D. Psaltis, Y. Qiao, “Adaptive multilayer optical networks,” Prog. Opt. 31, 227–261 (1993).
[CrossRef]

E. Betzig, R. J. Chichester, “Single molecules observed by near-field scanning optical microscopy,” Science (London) 262, 1422–1425 (1993).

1992

1991

1990

D. Psaltis, D. Brady, X. G. Xu, S. Lin, “Holography in artificial neural networks,” Nature (London) 343, 325–330 (1990).
[CrossRef]

1989

H. Lee, X.-G. Gu, D. Psaltis, “Volume holographic interconnections with maximal capacity and minimal cross talk,” J. Appl. Phys. 65, 2191–2194 (1989).
[CrossRef]

1982

1969

D. Gabor, “Associative holographic memories,” IBM J. Res. Dev. 13, 156–159 (1969).
[CrossRef]

1966

1963

Adibi, A.

C. Moser, I. Maravic, B. Schupp, A. Adibi, D. Psaltis, “Diffraction efficiency of localized holograms in doubly doped LiNbO3 crystals,” Opt. Lett. 25, 1243–1245 (2000).
[CrossRef]

K. Buse, A. Adibi, D. Psaltis, “Nonvolatile holographic storage in doubly doped lithium niobate crystals,” Nature (London) 393, 665–668 (1998).
[CrossRef]

A. Adibi, “Persistent holographic storage in photorefractive crystals,” Ph.D. dissertation (California Institute of Technology, Pasadena, Calif., 2000).

Annunziata, S.

A. Diaspro, S. Annunziata, M. Raimondo, P. Ramoino, M. Robello, “A single-pinhole confocal laser scanning microscope for 3-d imaging of biostructures,” IEEE Eng. Med. Biol. Mag. 18, 106–110 (1999).
[CrossRef] [PubMed]

Balberg, M.

Barbastathis, G.

Barton, I. M.

M. R. Taghizadeh, P. Blair, B. Layet, I. M. Barton, A. J. Waddie, N. Ross, “Design and fabrication of diffractive optical elements,” Microelectron. Eng.219–242 (1997).
[CrossRef]

Betzig, E.

E. Betzig, R. J. Chichester, “Single molecules observed by near-field scanning optical microscopy,” Science (London) 262, 1422–1425 (1993).

Blair, P.

M. R. Taghizadeh, P. Blair, B. Layet, I. M. Barton, A. J. Waddie, N. Ross, “Design and fabrication of diffractive optical elements,” Microelectron. Eng.219–242 (1997).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Cambridge University, Cambridge, England, 1980).

Brady, D.

D. Brady, D. Psaltis, “Control of volume holograms,” J. Opt. Soc. Am. A 9, 1167–1182 (1992).
[CrossRef]

D. Psaltis, D. Brady, X. G. Xu, S. Lin, “Holography in artificial neural networks,” Nature (London) 343, 325–330 (1990).
[CrossRef]

Brady, D. J.

Burr, G. W.

G. W. Burr, H. Coufal, J. A. Hoffnagle, C. M. Jefferson, M. Jurich, B. Marcus, R. M. Macfarlane, “Optical data storage enters a new dimension,” Phys. World 13, 37–42 (July2000).

D. Psaltis, G. W. Burr, “Holographic data storage,” Computer 31(2), 52 (1998).
[CrossRef]

Buse, K.

K. Buse, A. Adibi, D. Psaltis, “Nonvolatile holographic storage in doubly doped lithium niobate crystals,” Nature (London) 393, 665–668 (1998).
[CrossRef]

Chichester, R. J.

E. Betzig, R. J. Chichester, “Single molecules observed by near-field scanning optical microscopy,” Science (London) 262, 1422–1425 (1993).

Chuang, E.

Coufal, H.

G. W. Burr, H. Coufal, J. A. Hoffnagle, C. M. Jefferson, M. Jurich, B. Marcus, R. M. Macfarlane, “Optical data storage enters a new dimension,” Phys. World 13, 37–42 (July2000).

Crossland, W. A.

Curtis, K.

Denkewalter, R.

A. Pu, R. Denkewalter, D. Psaltis, “Real-time vehicle navigation using a holographic memory,” Opt. Eng. 36, 2737–2746 (1997).
[CrossRef]

DeVre, R.

Diaspro, A.

A. Diaspro, S. Annunziata, M. Raimondo, P. Ramoino, M. Robello, “A single-pinhole confocal laser scanning microscope for 3-d imaging of biostructures,” IEEE Eng. Med. Biol. Mag. 18, 106–110 (1999).
[CrossRef] [PubMed]

Drolet, J.-J. P.

Gabor, D.

D. Gabor, “Associative holographic memories,” IBM J. Res. Dev. 13, 156–159 (1969).
[CrossRef]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996).

Gu, X.-G.

H. Lee, X.-G. Gu, D. Psaltis, “Volume holographic interconnections with maximal capacity and minimal cross talk,” J. Appl. Phys. 65, 2191–2194 (1989).
[CrossRef]

Gurkan, K.

Heanue, J. F.

Herman, B.

B. Herman, J. J. Lemasters, Optical Microscopy (Academic, San Diego, Calif., 1993).

Hesselink, L.

Hettich, C.

J. Michaells, C. Hettich, J. Mlynek, V. Sandoghdar, “Optical microscopy using a single-molecule light source,” Nature (London) 405, 325–327 (2000).
[CrossRef]

Hoffnagle, J. A.

G. W. Burr, H. Coufal, J. A. Hoffnagle, C. M. Jefferson, M. Jurich, B. Marcus, R. M. Macfarlane, “Optical data storage enters a new dimension,” Phys. World 13, 37–42 (July2000).

Isenberg, G.

G. Isenberg, Modern Optics, Electronics, and High Precision Techniques in Cell Biology (Springer-Verlag, New York, 1998).
[CrossRef]

Javidi, B.

Jefferson, C. M.

G. W. Burr, H. Coufal, J. A. Hoffnagle, C. M. Jefferson, M. Jurich, B. Marcus, R. M. Macfarlane, “Optical data storage enters a new dimension,” Phys. World 13, 37–42 (July2000).

Joshi, N. V.

N. V. Joshi, H. Medina, “Multiple beam interference confocal microscopy: tool for morphological investigation of a living spermatozoon,” Microsc. Microanal. 6, 471–477 (2000).
[PubMed]

Jurich, M.

G. W. Burr, H. Coufal, J. A. Hoffnagle, C. M. Jefferson, M. Jurich, B. Marcus, R. M. Macfarlane, “Optical data storage enters a new dimension,” Phys. World 13, 37–42 (July2000).

Kozma, A.

Külich, H.

Layet, B.

M. R. Taghizadeh, P. Blair, B. Layet, I. M. Barton, A. J. Waddie, N. Ross, “Design and fabrication of diffractive optical elements,” Microelectron. Eng.219–242 (1997).
[CrossRef]

Lee, H.

H. Lee, X.-G. Gu, D. Psaltis, “Volume holographic interconnections with maximal capacity and minimal cross talk,” J. Appl. Phys. 65, 2191–2194 (1989).
[CrossRef]

Leith, E. N.

Lemasters, J. J.

B. Herman, J. J. Lemasters, Optical Microscopy (Academic, San Diego, Calif., 1993).

Levene, M.

Leyva, V.

Li, F. F.

X. H. Zhang, J. J. Xu, Q. Sun, S. Liu, G. Q. Zhang, H. J. Qiao, F. F. Li, G. Y. Zhang, “Dual-wavelength nonvolatile holographic storage,” Opt. Commun. 180, 211–215 (2000).
[CrossRef]

Li, H.-Y. S.

Lin, S.

D. Psaltis, D. Brady, X. G. Xu, S. Lin, “Holography in artificial neural networks,” Nature (London) 343, 325–330 (1990).
[CrossRef]

Liu, S.

X. H. Zhang, J. J. Xu, Q. Sun, S. Liu, G. Q. Zhang, H. J. Qiao, F. F. Li, G. Y. Zhang, “Dual-wavelength nonvolatile holographic storage,” Opt. Commun. 180, 211–215 (2000).
[CrossRef]

Liu, W. H.

W. H. Liu, D. Psaltis, G. Barbastathis, “Real-time spectral imaging in three spatial dimensions,” Opt. Lett. 27, 854–856 (2002).
[CrossRef]

W. H. Liu, D. Psaltis, “Pixel size limit in holographic memories,” Opt. Lett. 24, 1340–1342 (1999).
[CrossRef]

E. Chuang, W. H. Liu, J.-J. P. Drolet, D. Psaltis, “Holographic random access memory,” Proc. IEEE 87, 1931–1940 (1999).
[CrossRef]

W. H. Liu, “Holographic resolution and its application in memory and imaging,” Ph.D. dissertation (California Institute of Technology, Pasadena, Calif., 2001).

Lugt, A. V.

Macfarlane, R. M.

G. W. Burr, H. Coufal, J. A. Hoffnagle, C. M. Jefferson, M. Jurich, B. Marcus, R. M. Macfarlane, “Optical data storage enters a new dimension,” Phys. World 13, 37–42 (July2000).

Manolis, I. G.

Maravic, I.

Marcus, B.

G. W. Burr, H. Coufal, J. A. Hoffnagle, C. M. Jefferson, M. Jurich, B. Marcus, R. M. Macfarlane, “Optical data storage enters a new dimension,” Phys. World 13, 37–42 (July2000).

Marks, J.

Massey, N.

Massig, J. H.

Matsumoto, B.

B. Matsumoto, Methods in Cell Biology (Academic, San Diego, Calif., 1993).

Mayers, A. W.

F. T. S. Yu, S. Wu, A. W. Mayers, S. Rajan, “Wavelength multiplexed reflection matched spatial filters using LiNbO3,” Opt. Commun. 81, 343–347 (1991).
[CrossRef]

Mears, R. J.

Mears, R. T.

Medina, H.

N. V. Joshi, H. Medina, “Multiple beam interference confocal microscopy: tool for morphological investigation of a living spermatozoon,” Microsc. Microanal. 6, 471–477 (2000).
[PubMed]

Michaells, J.

J. Michaells, C. Hettich, J. Mlynek, V. Sandoghdar, “Optical microscopy using a single-molecule light source,” Nature (London) 405, 325–327 (2000).
[CrossRef]

Mlynek, J.

J. Michaells, C. Hettich, J. Mlynek, V. Sandoghdar, “Optical microscopy using a single-molecule light source,” Nature (London) 405, 325–327 (2000).
[CrossRef]

Mok, F.

D. Psaltis, F. Mok, “Holographic memories,” Sci. Am. 273, 70–76 (November1995).

Molecular Probes, I.

I. Molecular Probes, in Handbook of Fluorescent Probes and Research Chemicals, 7th ed., R. P. Haugland, ed. ( http:www.probes.com , 2001).

Moser, C.

Psaltis, D.

D. Psaltis, “Coherent optical information systems,” Science 298 (5597), 1359–1363 (2002).
[CrossRef]

W. H. Liu, D. Psaltis, G. Barbastathis, “Real-time spectral imaging in three spatial dimensions,” Opt. Lett. 27, 854–856 (2002).
[CrossRef]

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Opt. Commun.

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Figures (34)

Fig. 1
Fig. 1

Planar imaging by an optical lens.

Fig. 2
Fig. 2

Confocal microscope architecture.

Fig. 3
Fig. 3

Recording of a volume holographic spatial filter with a point source and its corresponding coherent plane-wave reference beam in 90-deg geometry. Another point source at a different wavelength is used as a probe.

Fig. 4
Fig. 4

Numerically calculated degenerate surface (space and color) of the architecture in Fig. 3. The shape in the figure represents the shape of the 2-D slice that the sensor extracts from the 4-D object and projects onto a contiguous area of the detector. Each point on the grid represents one object texel and its corresponding pixel on the detector.30

Fig. 5
Fig. 5

Multiple-volume holograms optically sectioning different hyperplanes from a 4-D object hyperspace and projecting them onto different 2-D image sensors.

Fig. 6
Fig. 6

Three-dimensional integral of the small cubic volume of the holographic grating. The small cubic volume ΔV = Δx × Δy × Δz is centered at r i . The full integral over the volume V is ∭V d3 r = ∑ i ΔV i d3 δr .

Fig. 7
Fig. 7

Numerical simulation and theoretical calculation of the shift selectivity of 90-deg geometry. The simulation parameters are assumed: NA = 0.5, n = 2.2: ○, numerical simulation; solid curve, theoretical integral of the selectivity curve in Eq. (30); dashed curve, approximation as a sinc function in Eq. (31).

Fig. 8
Fig. 8

Function of Fresnel integrals, where the first minimum is at s = 1.91.

Fig. 9
Fig. 9

Numerical simulation and theoretical calculation of depth selectivity of 90-deg geometry. Simulation parameters: NA = 0.5, n = 2.2: ○, numerical simulation; solid curve, theoretical phase integral of the selectivity curve in Eq. (34); dotted curve, approximation as a Fresnel function in Eq. (35).

Fig. 10
Fig. 10

Experimental measurements of (a) shift selectivity and (b) depth selectivity: ○, experimental measurements; solid curve, their theoretical phase-integral approximation.

Fig. 11
Fig. 11

Numerical simulation and theoretical calculation of the wavelength selectivity of 90-deg geometry. Simulation parameters: NA = 0.5, n = 2.2: ○, numerical simulation; solid curve, theoretical phase integral of the selectivity curve in Eq. (42); dotted curve, approximation as a sinc function in Eq. (40).

Fig. 12
Fig. 12

Numerical simulation of the image pattern as the probe beam is shifted away from the Bragg-phase-matching condition along the selective directions. Simulation parameters: NA = 0.5, n = 2.2. (a) The probe beam is shifted along the direction by (3λ)/n for each step, causing weaker and distorted image patterns. (b) The probe beam is shifted along the depth direction by (10λ)/n for each step. The intensity of the image decay is slower than shifting, and the intensity deviates dramatically along the ŷ direction. (c) The simulated image pattern as the wavelength of the probing beam shifts from the original recording wavelength by (Δλ)/λ = 4 × 10-5 for each pattern.

Fig. 13
Fig. 13

Numerical simulation of a series of point sources aligned in the direction and the image pattern and background. Simulation parameters: NA = 0.5, n = 2.2. (a) Depth-selectivity curves and the location of objective point sources; (b) image intensity pattern for the central Bragg-matched object point source; (c) background pattern from the mismatched object points along the direction.

Fig. 14
Fig. 14

Numerical simulation of a point source shifting along the degenerate ŷ direction. Simulation parameters: NA = 0.5, n = 2.2. (a) Image patterns as a point source shifts along the ŷ direction by (20λ)/n between each step. (b) Image plane responses for a set of point sources linearly aligned on the ŷ direction. The large aberration leads to a decaying butterfly intensity-distributed patterns.

Fig. 15
Fig. 15

Experimental holographic diffraction image patterns in 90-deg geometry with a spherical wave as the signal: (a) image patterns as the signal point source shifts along the direction, 2 μm for each step; (b) image patterns as the signal point source shifts along the degenerate ŷ direction, 10 μm for each step; (c) image patterns as the signal point source shifts along the depth direction, 6 μm for each step. Owing to the selectivity in the , directions, the images in (a) and (c) are enhanced for visibility. The arrows point to the Bragg-phase-matching position with the signal at the recording position.

Fig. 16
Fig. 16

Transmission geometry hologram recording with point source (x r , y r , z r , λ r ) and probing with another point source (x p , y p , z p , λ p ).

Fig. 17
Fig. 17

Angle selectivity of a general transmission geometry hologram by two plane waves R, S and readout with a tilted reference R′. The hologram is assumed to have an infinite transverse dimension alonĝ 1 and a thickness D along 2. The incident angles for the reference and signal inside the material are θ Rn , θ Sn .

Fig. 18
Fig. 18

Simulated angular selectivity of a general transmission geometry hologram in Fig. 16. Simulation condition: f c = f i = 104λ, D = 1400λ, NA = 0.5, n = 2.2, θ R = θ S = π/4: ○, simulation results of the intensity integral over the 2-D image pattern on the image plane; solid curve, theoretical sinc2 function in Eq. (49).

Fig. 19
Fig. 19

Simulated intensity distribution patterns on the image plane of a general transmission geometry hologram in Fig. 16. The simulation conditions are the same as in Fig. 18. Top to bottom, the probing point source at the recording wavelength moves from the recording position to the p direction by 2λ/step. The image pattern intensity and the location change are as in Eqs. (49) and (47), respectively.

Fig. 20
Fig. 20

Simulated diffraction intensity on the image plane of the general transmission geometry hologram in Fig. 16 as the probing point source shifts along the depth p direction. The simulation conditions are the same as in Fig. 18: ○, numerical simulation; solid curve, approximate integral as in Eq. (51).

Fig. 21
Fig. 21

Simulated diffraction intensity on the image plane of a general transmission geometry hologram in Fig. 16 as the probing point source shifts along the depth p direction by 20λ for each step, at the recording wavelength. The simulation conditions are the same as in Fig. 18.

Fig. 22
Fig. 22

Experimental measurements and theoretical intensity selective calculation of the shift selectivity of DuPont polymer 100 μm thick in the transmission geometry in Fig. 16. The collimating objective lens is ×10, NA = 0.25; the DuPont polymer is assumed to be n = 1.5; and the wavelength is 488 nm. (a) Shift selectivity in the p direction, where Eq. (47) gives Δx p = 104 μm at the first null. (b) Depth selectivity in the p direction; Eq. (53) gives Δz p1/2 = 400 μm at the half-magnitude.

Fig. 23
Fig. 23

Simulated diffraction intensity on the image plane of a general transmission geometry hologram in Fig. 16 as the wavelength of the probing point source changes at the original recording location. The simulation conditions are the same as in Fig. 18.

Fig. 24
Fig. 24

Simulated intensity distribution patterns on the image plane of the general transmission geometry hologram in Fig. 16 as the probing point source changes wavelength from the recording wavelength by Δλ/λ = -4 × 10-4 for each step. The simulation conditions are the same as in Fig. 18.

Fig. 25
Fig. 25

Experimental measurement of the intensity distribution pattern on the image plane of a general transmission geometry hologram in Fig. 16 for a chromatic point source located at the original recording position. The full width of the first null of the intensity profile determines the spatial-image resolution along d ′ on the image plane.

Fig. 26
Fig. 26

Simulated diffraction intensity on the image plane of a general transmission geometry hologram in Fig. 16 as the probing point source shifts along the depth p at different wavelengths: (a) original wavelength (Δλ)/λ = 0; (b) (Δλ)/λ = -5 × 10-4; (c) (Δλ)/λ = -10-3; (d) (Δλ)/λ = 5 × 10-4; (e) (Δλ)/λ = 10-3. The simulation conditions are the same as in Fig. 18.

Fig. 27
Fig. 27

Simulated diffraction intensity on the image plane of a general transmission geometry hologram in Fig. 16 as the probing point source shifts along the y p direction at the original wavelength. The simulation conditions are the same as in Fig. 18.

Fig. 28
Fig. 28

Simulated diffraction image patterns on the Fourier plane of a general transmission geometry hologram in Fig. 16 as the probing point source shifts along the ŷ p direction by 50λ for each step at the original wavelength. The simulation conditions are the same as in Fig. 18.

Fig. 29
Fig. 29

Wave-vector k sphere for a holographic grating K recorded by R 1, S 1 at wavelength k 0. The hologram can be Bragg phase matched by a pair of beams R 2, S 2 rotated around the K direction at the same wavelength. At a different wavelength k 1, there is another pair of beams R 3, S 3 with a corresponding tilting angle that can be Bragg phase matched while rotated around the K direction.

Fig. 30
Fig. 30

Experimental demonstration of Bragg phase matching by wavelength-shift coupling in a transmission geometry in Fig. 16. The experimental parameters are as follows: LiNbO3 crystal thickness, 5 mm; collimating objective lens, ×10, NA = 0.25; and recording wavelength, 488 nm. (a) Image pattern while the probing pinhole is illuminated by 488 nm. (b) Image pattern as the white-light-illuminated pinhole shifts in the p direction. The image point shifts correspondingly in the d ′ direction with a different wavelength component determined by Eqs. (68) and (69).

Fig. 31
Fig. 31

Experimental demonstration of 2-D imaging by Bragg phase matching in the spatial and the wavelength-shift coupling dimension of a single transmission geometry hologram in Fig. 16. The experimental parameters are the same as in Fig. 30. (a) Image pattern of a 2-D mask across the original recording point-source location and illuminated by 488 nm. A vertical-line image is formed from spatial degeneracy along the ŷ p direction. (b) Image pattern as the white light illuminates the 2-D mask. At a different d ′ position, a different wavelength component Bragg phase matches and forms the 2-D color-coded image, determined by Eqs. (68) and (69).

Fig. 32
Fig. 32

Depth-selectivity measurement and comparison with the theoretical prediction in a PQ polymer 2 mm thick. The experimental setup is as in Fig. 16: collimating objective lens, ×40; NA = 0.65; wavelength, 488 nm. (a) Single strong hologram with a diffraction efficiency of >15%. The depth selectivity is consistent with the theoretical calculation by Eq. (51). (b) Three holograms multiplexed with a different recording depth z r 50 μm apart.

Fig. 33
Fig. 33

Images of fluorescent microspheres (15 μm in diameter) excited by 488 nm and emitting at a peak fluorescent wavelength of 515 nm, by holographic and normal microscope imaging systems with the same collimating and imaging lenses.

Fig. 34
Fig. 34

Images of fluorescent microspheres (15 μm in diameter) in a liquid sample, excited by 488 nm and emitting at a peak fluorescent wavelength of 515 nm: (a) with a single hologram with the depth-sectioning ability as in Fig. 32(a); (b) with three multiplexed holograms for imaging three optical sections of different depth.

Equations (69)

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Iu, v=2u2U12u, v+U22u, vI0,
u=2πλaf2z,
v=2πλafr,
I0=πa2|A|2λf22,
Unu, v=s=0-1suvn+2sJn+2sv,
I0, v=2J1vv2I0,
δr=0.610 λNA,
NA=af.
Iu, 0=sinu/4u/42I0,
δz=2λNA2
δz0.5λNA2.
Esr; rr, λr=expiks · r-rr,
ksr; rr, λr=2πλrr-rr|r-rr|,
Erefr, λr=expikref · r,
krefλr=2πλr-1-u222xˆ+uzˆ.
Δr=|Erefr+Esr|2
Es*rErefr,
Epr; rp, λp=expikp · r-rp,
kpr; rp, λp=2πλpr-rp|r-rp|,
Edr=V EprΔrexpi2π |r-r|λpd3r.
EFx-f, y, z=- Edx; y, z×exp-i2π yy+zzλpfdydz,
=V d3rEpr, λpEs*r; rr, λr×Erefr, λr×Ed*r; r, λp,
Edr; r, λp=expikdr, λp·r,
kdr, λp=2πλp-1-y22f2-z22f2xˆ+yfŷ+zfzˆ.
EFx-f, y, z=V d3rexpikp·r-rp-iks·r-rrexpikref-kd·r.
ϕ=kpr; rp, λp·r-rp-ksr; rr, λr·r-rr+kref-kd·r,
=0.
EFx-f, y, z=iexpiϕiriΔVi×d3δr expiΔKi·δr,
=iexpiϕiriΔV×sincΔKixΔX2πsincΔKiyΔY2π×sincΔKizΔZ2π,
Ed-NA/nNA/ndα expi 2πnΔxλα1+α21/2.
|Ed|sinc2NAΔxλr,
Δx=λr2NA.
ϕri,Δz=2πλnΔzz0x2+z021/2,
Ed-NA/nNA/ndα expi 2πΔzλn11+α21/2.
|Ed|C2s+S2s1/2s,
s=NA2Δznλ01/2,
Cs=0scosπt22dt,
Ss=0ssinπt22dt.
Δz=1.82 nλ0NA2.
|Ed|sinc2NAz0Δλλ02,
Δλλ0=λ02NAz0,
|Ed|21z2-z1z1z2dzsinc2NAzΔλλ022.
ΔθRn=θRn-θRn  1,
ΔθSn=θSn-θSn,
=-cos θRncos θSn ΔθRn,
ΔK=kntan θSn+tan θRncos θRnΔθRn.
Δxpfccos θS=-Δzdficos θR,
η=sinc2ΔKD2π,
=sinc2ΔxpfcΔα,
Δα=λD1cos θStan θSn+tan θRn,
ηΔzp1α0αsinc2tΔαdt,
α=LΔzp2fc2.
Δzp1/2=1.80 fc2L Δα,
Δzdfi=-n Δλλsin θRn+sin θSncos θR,
ηΔλλ=sinc2ΔλλΔβ,
Δβ=λnDcos θRn1-cosθSn+θRn,
ΔzdΔλλ=ΔβΔzdΔxpfc=Δα=sin θRn+sin θSntan θRn+tan θSncos θRn1-cosθSn+θRn,
η=sinc2yp2fc21Δαy,
Δrd=-fifc Δypŷ-Δyp22fc2 fizˆd,
Δαy=2n2-141/2λD,
Δλp=0,
Δrp=Δxp+Δyp,
Δrd=Δzd+Δyd,
Δxpfc=-Δzdfi  1,
=-sin θ+cos θ2-n2-sin θ2t21/2sin θ+cos θ2-n2-sin θ2t21/2,
Δypfc=-Δydfi,
=-21/2n2-sin θ21/2tsin θ+cos θ2-n2-sin θ2t21/2
Δxpfc=-Δλpλ,
=Δzdfi,

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