Abstract

We utilize synthetic-aperture Fourier holographic microscopy to resolve micrometer-scale microstructure over millimeter-scale fields of view. Multiple holograms are recorded, each registering a different, limited region of the sample object’s Fourier spectrum. They are “stitched together” to generate the synthetic aperture. A low-numerical-aperture (NA) objective lens provides the wide field of view, and the additional advantages of a long working distance, no immersion fluids, and an inexpensive, simple optical system. Following the first theoretical treatment of the technique, we present images of a microchip target derived from an annular synthetic aperture (NA = 0.61) whose area is 15 times that due to a single hologram (NA = 0.13); they exhibit a corresponding qualitative improvement. We demonstrate that a high-quality reconstruction may be obtained from a limited sub-region of Fourier space, if the object’s structural information is concentrated there.

© 2009 Optical Society of America

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2008 (12)

S. A. Alexandrov and D. D. Sampson, "Spatial information transmission beyond a systems diffraction limit using optical spectral encoding of the spatial frequency," J. Opt. A - Pure Appl. Opt. 10, 025304 (2008).
[CrossRef]

L. Martınez-Leon and B. Javidi, "Synthetic aperture single-exposure on-axis digital holography," Opt. Express 16,161-169 (2008), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-16-1-161.
[CrossRef] [PubMed]

J. Di, J. Zhao, H. Jiang, P. Zhang, Q. Fan, and W. Sun, "High resolution digital holographic microscopy with a wide field of view based on a synthetic aperture technique and use of linear CCD scanning," Appl. Opt. 47, 5654-5659 (2008).
[CrossRef] [PubMed]

M. Paturzo, F. Merola, S. Grilli, S. De Nicola, A. Finizio, and P. Ferraro, "Super-resolution in digital holography by a two-dimensional dynamic phase grating," Opt. Express 16,17107-17118 (2008), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-16-21-17107.
[CrossRef] [PubMed]

C. Yuan, H. Zhai, and H. Liu, "Angular multiplexing in pulsed digital holography for aperture synthesis," Opt. Lett. 33, 2356-2358 (2008).
[CrossRef] [PubMed]

V. Mico, Z. Zalevsky, and J. Garcıa, "Common-path phase-shifting digital holographic microscopy: A way to quantitative phase imaging and superresolution," Opt. Commun. 281, 4273-4281 (2008).
[CrossRef]

V. Mico, O. Limon, A. Gur, Z. Zalevsky, and J. Garcıa, "Transverse resolution improvement using rotatinggrating time-multiplexing approach," J. Opt. Soc. Am. A 25, 1115-1129 (2008).
[CrossRef]

Y. Kuznetsova, A. Neumann, and S. R. J. Brueck, "Imaging interferometric microscopy," J. Opt. Soc. Am. A 25, 811-822 (2008).
[CrossRef]

W. Choi, C. Fang-Yen, K. Badizadegan, R. R. Dasari, and M. S. Feld, "Extended depth of focus in tomographic phase microscopy using a propagation algorithm," Opt. Lett. 33, 171-173 (2008).
[CrossRef] [PubMed]

S. S. Kou and C. J. R. Sheppard, "Image formation in holographic tomography," Opt. Lett. 33, 2362-2364 (2008).
[CrossRef] [PubMed]

S. T. Thurman and J. R. Fienup, "Phase-error correction in digital holography," J. Opt. Soc. Am. A 25, 983-994 (2008).
[CrossRef]

B. Simon, M. Debailleul, V. Georges, V. Lauer, and O. Haeberl’e, "Tomographic diffractive microscopy of transparent samples," Eur. Phys. J. Appl. Phys. 44, 29-35 (2008).
[CrossRef]

2007 (4)

2006 (4)

2005 (4)

2004 (1)

2002 (4)

C. Liu, Z. G. Liu, F. Bo, Y. Wang, and J. Q. Zhu, "Super-resolution digital holographic imaging method," Appl. Phys. Lett. 81, 3143-3145 (2002).
[CrossRef]

J. H. Massig, "Digital off-axis holography with a synthetic aperture," Opt. Lett. 27, 2179-2181 (2002).
[CrossRef]

R. Binet, J. Colineau, and J. C. Lehureau, "Short-range synthetic aperture imaging at 633 nm by digital holography," Appl. Opt. 41, 4775-4782 (2002).
[CrossRef] [PubMed]

V. Lauer, "New approach to optical diffraction tomography yielding a vector equation of diffraction tomography and a novel tomographic microscope," J. Microsc. 205, 165-176 (2002).
[CrossRef] [PubMed]

2001 (1)

1995 (1)

T. Turpin, L. Gesell, J. Lapides, and C. Price, "Theory of the synthetic aperture microscope," Proc. SPIE 2566, 230-240 (1995).
[CrossRef]

1967 (1)

J. W. Goodman and R. W. Lawrence, "Digital image formation from electronically detected holograms," Appl. Phys. Lett. 11, 77-79 (1967).
[CrossRef]

1960 (1)

M. Ryle and A. Hewish, "The synthesis of large radio telescopes," Mon. Not. R. Astron. Soc. 120, 220-230 (1960).

1948 (1)

D. Gabor, "A new microscopic principle," Nature (London) 161, 777-778 (1948).
[CrossRef]

Alexandrov, S. A.

S. A. Alexandrov and D. D. Sampson, "Spatial information transmission beyond a systems diffraction limit using optical spectral encoding of the spatial frequency," J. Opt. A - Pure Appl. Opt. 10, 025304 (2008).
[CrossRef]

S. A. Alexandrov, T. R. Hillman, T. Gutzler, and D. D. Sampson, "Synthetic aperture Fourier holographic optical microscopy," Phys. Rev. Lett. 97,168102 (2006).
[CrossRef] [PubMed]

T. R. Hillman, S. A. Alexandrov, T. Gutzler, and D. D. Sampson, "Microscopic particle discrimination using spatially-resolved Fourier-holographic light scattering angular spectroscopy," Opt. Express 14, 11088-11102 (2006), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-14-23-11088.
[CrossRef] [PubMed]

S. A. Alexandrov, T. R. Hillman, and D. D. Sampson, "Spatially resolved Fourier holographic light scattering angular spectroscopy," Opt. Lett. 30, 3305-3307 (2005).
[CrossRef]

Badizadegan, K.

W. Choi, C. Fang-Yen, K. Badizadegan, R. R. Dasari, and M. S. Feld, "Extended depth of focus in tomographic phase microscopy using a propagation algorithm," Opt. Lett. 33, 171-173 (2008).
[CrossRef] [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, 717-719 (2007).
[CrossRef] [PubMed]

Binet, R.

Bingham, P. R.

Bo, F.

C. Liu, Z. G. Liu, F. Bo, Y. Wang, and J. Q. Zhu, "Super-resolution digital holographic imaging method," Appl. Phys. Lett. 81, 3143-3145 (2002).
[CrossRef]

Brueck, S. R. J.

Charriere, F.

Choi, W.

W. Choi, C. Fang-Yen, K. Badizadegan, R. R. Dasari, and M. S. Feld, "Extended depth of focus in tomographic phase microscopy using a propagation algorithm," Opt. Lett. 33, 171-173 (2008).
[CrossRef] [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, 717-719 (2007).
[CrossRef] [PubMed]

Colineau, J.

Collot, L.

Colomb, T.

Cuche, E.

Dasari, R. R.

W. Choi, C. Fang-Yen, K. Badizadegan, R. R. Dasari, and M. S. Feld, "Extended depth of focus in tomographic phase microscopy using a propagation algorithm," Opt. Lett. 33, 171-173 (2008).
[CrossRef] [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, 717-719 (2007).
[CrossRef] [PubMed]

De Nicola, S.

Debailleul, M.

B. Simon, M. Debailleul, V. Georges, V. Lauer, and O. Haeberl’e, "Tomographic diffractive microscopy of transparent samples," Eur. Phys. J. Appl. Phys. 44, 29-35 (2008).
[CrossRef]

Depeursinge, C.

Di, J.

Emery, Y.

Fan, Q.

Fang-Yen, C.

W. Choi, C. Fang-Yen, K. Badizadegan, R. R. Dasari, and M. S. Feld, "Extended depth of focus in tomographic phase microscopy using a propagation algorithm," Opt. Lett. 33, 171-173 (2008).
[CrossRef] [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, 717-719 (2007).
[CrossRef] [PubMed]

Feld, M. S.

W. Choi, C. Fang-Yen, K. Badizadegan, R. R. Dasari, and M. S. Feld, "Extended depth of focus in tomographic phase microscopy using a propagation algorithm," Opt. Lett. 33, 171-173 (2008).
[CrossRef] [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, 717-719 (2007).
[CrossRef] [PubMed]

Ferraro, P.

Fienup, J. R.

Finizio, A.

Gabor, D.

D. Gabor, "A new microscopic principle," Nature (London) 161, 777-778 (1948).
[CrossRef]

Garcia, J.

Garcia-Martinez, P.

Georges, V.

B. Simon, M. Debailleul, V. Georges, V. Lauer, and O. Haeberl’e, "Tomographic diffractive microscopy of transparent samples," Eur. Phys. J. Appl. Phys. 44, 29-35 (2008).
[CrossRef]

Gesell, L.

T. Turpin, L. Gesell, J. Lapides, and C. Price, "Theory of the synthetic aperture microscope," Proc. SPIE 2566, 230-240 (1995).
[CrossRef]

Goodman, J. W.

J. W. Goodman and R. W. Lawrence, "Digital image formation from electronically detected holograms," Appl. Phys. Lett. 11, 77-79 (1967).
[CrossRef]

Grilli, S.

Gross, M.

Gur, A.

Gustafsson, M.

Gutzler, T.

Hewish, A.

M. Ryle and A. Hewish, "The synthesis of large radio telescopes," Mon. Not. R. Astron. Soc. 120, 220-230 (1960).

Hillman, T. R.

Javidi, B.

Jiang, H.

Kim, M. K.

Kou, S. S.

Kuehn, J.

Kuznetsova, Y.

Lapides, J.

T. Turpin, L. Gesell, J. Lapides, and C. Price, "Theory of the synthetic aperture microscope," Proc. SPIE 2566, 230-240 (1995).
[CrossRef]

Lauer, V.

B. Simon, M. Debailleul, V. Georges, V. Lauer, and O. Haeberl’e, "Tomographic diffractive microscopy of transparent samples," Eur. Phys. J. Appl. Phys. 44, 29-35 (2008).
[CrossRef]

V. Lauer, "New approach to optical diffraction tomography yielding a vector equation of diffraction tomography and a novel tomographic microscope," J. Microsc. 205, 165-176 (2002).
[CrossRef] [PubMed]

Lawrence, R. W.

J. W. Goodman and R. W. Lawrence, "Digital image formation from electronically detected holograms," Appl. Phys. Lett. 11, 77-79 (1967).
[CrossRef]

Le Clerc, F.

Lehureau, J. C.

Limon, O.

Liu, C.

C. Liu, Z. G. Liu, F. Bo, Y. Wang, and J. Q. Zhu, "Super-resolution digital holographic imaging method," Appl. Phys. Lett. 81, 3143-3145 (2002).
[CrossRef]

Liu, H.

Liu, Z. G.

C. Liu, Z. G. Liu, F. Bo, Y. Wang, and J. Q. Zhu, "Super-resolution digital holographic imaging method," Appl. Phys. Lett. 81, 3143-3145 (2002).
[CrossRef]

Lo, C.-M.

Lue, N.

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

Magistretti, P. J.

Mann, C. J.

Marian, A.

Marquet, P.

Martinez-Leon, L.

Massig, J. H.

Merola, F.

Mico, V.

Montfort, F.

Neumann, A.

Oh, S.

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

Paturzo, M.

Price, C.

T. Turpin, L. Gesell, J. Lapides, and C. Price, "Theory of the synthetic aperture microscope," Proc. SPIE 2566, 230-240 (1995).
[CrossRef]

Price, J. R.

Rappaz, B.

Ryle, M.

M. Ryle and A. Hewish, "The synthesis of large radio telescopes," Mon. Not. R. Astron. Soc. 120, 220-230 (1960).

Sampson, D. D.

S. A. Alexandrov and D. D. Sampson, "Spatial information transmission beyond a systems diffraction limit using optical spectral encoding of the spatial frequency," J. Opt. A - Pure Appl. Opt. 10, 025304 (2008).
[CrossRef]

T. R. Hillman, S. A. Alexandrov, T. Gutzler, and D. D. Sampson, "Microscopic particle discrimination using spatially-resolved Fourier-holographic light scattering angular spectroscopy," Opt. Express 14, 11088-11102 (2006), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-14-23-11088.
[CrossRef] [PubMed]

S. A. Alexandrov, T. R. Hillman, T. Gutzler, and D. D. Sampson, "Synthetic aperture Fourier holographic optical microscopy," Phys. Rev. Lett. 97,168102 (2006).
[CrossRef] [PubMed]

S. A. Alexandrov, T. R. Hillman, and D. D. Sampson, "Spatially resolved Fourier holographic light scattering angular spectroscopy," Opt. Lett. 30, 3305-3307 (2005).
[CrossRef]

Sebesta, M.

Sheppard, C. J. R.

Simon, B.

B. Simon, M. Debailleul, V. Georges, V. Lauer, and O. Haeberl’e, "Tomographic diffractive microscopy of transparent samples," Eur. Phys. J. Appl. Phys. 44, 29-35 (2008).
[CrossRef]

Sun, W.

Thomas, C. E.

Thurman, S. T.

Turpin, T.

T. Turpin, L. Gesell, J. Lapides, and C. Price, "Theory of the synthetic aperture microscope," Proc. SPIE 2566, 230-240 (1995).
[CrossRef]

Wang, Y.

C. Liu, Z. G. Liu, F. Bo, Y. Wang, and J. Q. Zhu, "Super-resolution digital holographic imaging method," Appl. Phys. Lett. 81, 3143-3145 (2002).
[CrossRef]

Yu, L.

Yuan, C.

Zalevsky, Z.

Zhai, H.

Zhang, P.

Zhao, J.

Zhu, J. Q.

C. Liu, Z. G. Liu, F. Bo, Y. Wang, and J. Q. Zhu, "Super-resolution digital holographic imaging method," Appl. Phys. Lett. 81, 3143-3145 (2002).
[CrossRef]

Appl. Opt. (3)

Appl. Phys. Lett. (2)

C. Liu, Z. G. Liu, F. Bo, Y. Wang, and J. Q. Zhu, "Super-resolution digital holographic imaging method," Appl. Phys. Lett. 81, 3143-3145 (2002).
[CrossRef]

J. W. Goodman and R. W. Lawrence, "Digital image formation from electronically detected holograms," Appl. Phys. Lett. 11, 77-79 (1967).
[CrossRef]

Eur. Phys. J. Appl. Phys. (1)

B. Simon, M. Debailleul, V. Georges, V. Lauer, and O. Haeberl’e, "Tomographic diffractive microscopy of transparent samples," Eur. Phys. J. Appl. Phys. 44, 29-35 (2008).
[CrossRef]

J. Microsc. (1)

V. Lauer, "New approach to optical diffraction tomography yielding a vector equation of diffraction tomography and a novel tomographic microscope," J. Microsc. 205, 165-176 (2002).
[CrossRef] [PubMed]

J. Opt. A - Pure Appl. Opt. (1)

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Supplementary Material (2)

» Media 1: MOV (6264 KB)     
» Media 2: MOV (8382 KB)     

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Figures (9)

Fig. 1.
Fig. 1.

(a) Depiction of the four spatial domains of the sample wave path from the input to the output plane. The illumination-wave (IW) and reference-wave (RW) polar angles, θi and θr , respectively, are shown; (b),(c) Definition of the coordinate-system and Fourier/inverse-Fourier transform conventions adopted in the paper. The illumination and reference-wave azimuthal angles, ϕi and ϕr , respectively, are displayed.

Fig. 2.
Fig. 2.

(a) Depiction of the illumination wave, and scattered or diffracted waves in the plane of incidence. An off-axis detection solid angle is also shown; (b) Regions depicting the accessible spatial frequencies for different coherent imaging systems. Inner region (purple boundary): Circular range covered by a single 0.75-NA lens (for a conventional coherent imaging system); Region 2 (red solid boundary): Accessible region to coordinates (γξη ); Region 3 (red dotted boundary): Range of spatial frequencies accessible to the synthetic aperture, if the rectangular detector is located on-axis; Outer region (green solid boundary): Range of accessible spatial frequencies when the on-axis restriction is removed; (c) Upper-right quadrant: The rectangular range of spatial frequencies accessible to a single holographic recording. The dependence of this region on the illumination-wave parameters is demonstrated in the other three quadrants.

Fig. 3.
Fig. 3.

Effect of defocusing in object and reconstruction planes. Both quantities g and d, as displayed, are positive.

Fig. 4.
Fig. 4.

(a) Depiction of multiple Ewald hemispheres (as black semicircles) associated with incident wavevectors that lie within the depicted (νξ, νz )-plane. A full Ewald-sphere circle is depicted in magenta, along with its corresponding incident wavevector; the circle passes through the origin. Sphere caps corresponding to a narrow, on-axis detection solid angle are depicted in red. Two are highlighted (in blue and green), corresponding to different polar illumination angles θi . Their projections onto (νξ, νη ) -space overlap, yet they are separated in 3D-space by the distance ∆νz ; (b) The effect of increasing the wavelength λ on the accessible spatial frequencies in 2D- and 3D-space, if θi , ϕi are held fixed. (c) If λ, θi are held constant, but ϕi is varied over 2π, an annular synthetic aperture can be generated in 2D-space, with negligible 3D decorrelation effect.

Fig. 5.
Fig. 5.

Schematic of optical system, showing reference-arm and sample-arm paths. Multiple optical-ray trajectories are shown in the latter path. B1,2: beam-splitters; M1,2,3: mirrors; L1,2,3: lenses; P: pinhole; RFS: rectangular field stop; CCD: recording array.

Fig. 6.
Fig. 6.

Brightfield reflection microscope image of the sample target. A selected region of the image is magnified.

Fig. 7.
Fig. 7.

(Media 1) showing the object reconstructions due to the individual recorded holograms. The accessible region of the Fourier spectrum is depicted with a dark-red boundary in the left-hand panel. The faded-red boundary surrounds the equivalent region for the next hologram in the sequence; the phase difference between the two is presented in the inset. A linear grayscale was used for the spectrum and reconstruction, with its “saturation value” (“Max.”, in arbitrary units), invariant over all frames. The blue labels on the color bar refer to the “Phase difference” inset.

Fig. 8.
Fig. 8.

Object reconstruction as the synthetic aperture is built up cumulatively from 45 holograms at 8° intervals. The region marked with a red square is magnified. The regions marked blue and green feature in Fig. 9. (Media 2)

Fig. 9.
Fig. 9.

Magnified reconstructions due to different hologram subsets, with the top and bottom rows labelled green and blue corresponding to the similarly colored regions of Fig. 8 (middle panel). The left-most panels show 15 holograms, which are combined to generate the second of the three reconstructions presented (green or blue). (The reconstruction is derived from the “Displayed synthetic aperture.”) The first reconstruction (orange) is due to a single hologram, indicated in the left-most panel with an orange border, and the final reconstruction is due to the full set of 90 holograms. The magnified regions in the top row are 25 μm × 25 μm; those in the bottom row are 15 μm × 15 μm. The units for the spatial frequency-domain panel are μm-1, and the color bar from the previous figures is applicable.

Equations (19)

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:V1(ξ,η)𝓥1(νξ,νη),1:U4(x,y)4(νx,νy).
𝓥1(νξ,νη)[V1(ξ,η)] U(ξ,η)exp[j2π(ξνξ+ηνη)]dξdη.
U4(x,y)=jM𝓥1(xM,−yM),
V1(ξ,η)=r(ξ,η) Ai ( ξ , η ) .
νξγξL/(2M) , |νηνηH/(2M).
(νξ,νη)(γξ,γη)<1/λ.
νs=sinθisin θd / λ .
𝓚Δz(νξ,νη)[kΔz(ξ,η)] =exp(j2πΔz/λ) exp [jπλΔz(νξ2+νη2)] .
Urec(x,y)=jM{𝓚d(νx,νy)1[𝓥obj(xM,yM)𝓚g(xM,yM)]},
dMD4λD1;gMD1λD4.
𝓚̂d(νx,νy)=exp(js=26n=0sDn,snνxnνysn),𝓚^g(νξ,νη)=exp(js=26n=0sGn,snνξnνηsn),
Û4(x,y)={[𝓚d(νx,νy)]11[Urec(x,y)]}.
𝓥^obj(xM,yM)=[𝓚̂g(xM,yM)]1{[𝓚̂d(νx,νy)]11[jMUrec(x,y)]},
ΓFS(ξ,η,z,ξ,η,z)FS(ξ,η,z)FS*(ξ,η,z)¯=δ(ξξ,ηη,zz)fT(ξ,η)fA(z).
ΓℱS(νξ,νη,νz;Δνz)S(νξ,νη,νz+Δνz/2)S*(νξ,νη,νzΔνz/2)¯.
μℱS(Δνz)ΓℱS(νx,νy,νz;Δνz)ΓℱS(νx,νy,νz;0)=A(Δνz)A(0),
Δvz=Δ(cosθi)λ sinθiΔθiλ.
fA(z)=C0 exp (z22σh2) ,
μℱs(Δvz)=μℱs(Δvz)=exp[2π2σh2(Δvz)2].

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