Abstract

Optical data manipulation technologies increasingly employ densely aperiodic optical 3D phase elements. Refinement of such technologies will require the capability to quantitatively characterize the volumetric dielectric modulation of an optical sample to a high level of precision and spatial resolution. We present a scanning transmission microscopy system that uses a position-sensitive detector to impart sensitivity to both the phase and absorption components. We describe the layout of the instrument and then derive its phase and absorption transfer functions. Simulations and experiments are presented to validate the analysis. For phase detection, the instrument possesses depth-sectioning properties similar to those of a confocal microscope without the use of a pinhole, enabling full 3D object reconstruction.

© 2006 Optical Society of America

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  1. K. Curtis, W. L. Wilson, and L. Dhar, "High density holographic storage," presented at the International Symposium on Optical Memory, Jeju Island, South Korea, 11-15 October 2004; www.isom.jp.
  2. R. R. McLeod, A. J. Daiber, M. E. McDonald, T. L. Robertson, T. Slagle, S. L. Sochava, and L. Hesselink, "Microholographic multilayer optical disk data storage," Appl. Opt. 44, 3197-3207 (2005).
    [CrossRef] [PubMed]
  3. R. R. McLeod, A. C. Sullivan, M. W. Grabowski, and T. F. Scott, "Hybrid integrated optics in volume holographic photopolymer," in Organic Holographic Materials and Applications II, K. Meerholz, ed., Proc SPIE 5521, 55-62 (2004).
  4. R. R. McLeod, A. C. Sullivan, and M. W. Grabowski, "Direct-write waveguides in volume photopolymers," presented at Integrated Photonics Research, San Francisco, Calif., 30 June-2 July 2004 (Optical Society of America, 2004).
  5. M. Will, S. Nolte, B. N. Chichkov, and A. Tunnermann, "Optical properties of waveguides fabricated in fused silica by femtosecond laser pulses," Appl. Opt. 41, 4360-4364 (2002).
    [CrossRef] [PubMed]
  6. M. Minsky, "Microscopy apparatus," U.S. Patent 3,013,467 (19 December 1961).
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    [CrossRef] [PubMed]
  11. M. R. Ayres, "Methods for measuring optical characteristics by differential diffractive scanning," U.S. patent application 10/800,111 (27 January 2005).
  12. J. T. Wallmark, "A new semiconductor photocell using lateral photoeffect," Proc. IRE 45, 474-483 (1957).
    [CrossRef]
  13. H. Kogelnik, "Coupled wave theory for thick hologram gratings," Bell Syst. Tech. J. 48, 2909-2947 (1969).
  14. C. J. R. Sheppard and M. Gu, "Three-dimensional transfer functions for high-aperture systems," J. Opt. Soc. Am. A 11, 593-598 (1994).
    [CrossRef]
  15. C. J. R. Sheppard and A. Choudhury, "Image formation in the scanning microscope," Opt. Acta 24, 1051-1073 (1977).
    [CrossRef]
  16. J. W. O'Byrne, P. W. Fekete, M. R. Arnison, H. Zhao, M. Serrano, D. Philp, W. Sudiarta, and C. J. Cogswell, "Adaptive optics in confocal microscopy," in Proceedings of the Second International Workshop on Adaptive Optics for Industry and Medicine, G. D. Love, ed. (World Scientific, 1999), pp. 85-90.
  17. C. J. Sheppard and T. Wilson, "Depth of field in the scanning microscope," Opt. Lett. 3, 115-117 (1978).
    [CrossRef] [PubMed]
  18. M. Born and E. Wolf, Principles of Optics, 6th ed. (Cambridge U. Press, 1980), p. 437.

2005 (2)

R. R. McLeod, A. J. Daiber, M. E. McDonald, T. L. Robertson, T. Slagle, S. L. Sochava, and L. Hesselink, "Microholographic multilayer optical disk data storage," Appl. Opt. 44, 3197-3207 (2005).
[CrossRef] [PubMed]

M. R. Ayres, "Methods for measuring optical characteristics by differential diffractive scanning," U.S. patent application 10/800,111 (27 January 2005).

2004 (1)

R. R. McLeod, A. C. Sullivan, M. W. Grabowski, and T. F. Scott, "Hybrid integrated optics in volume holographic photopolymer," in Organic Holographic Materials and Applications II, K. Meerholz, ed., Proc SPIE 5521, 55-62 (2004).

2002 (1)

1996 (1)

1994 (1)

1989 (1)

1985 (1)

1978 (1)

1977 (1)

C. J. R. Sheppard and A. Choudhury, "Image formation in the scanning microscope," Opt. Acta 24, 1051-1073 (1977).
[CrossRef]

1969 (1)

H. Kogelnik, "Coupled wave theory for thick hologram gratings," Bell Syst. Tech. J. 48, 2909-2947 (1969).

1967 (1)

B. R. Frieden, "Optical transfer of the three-dimensional object," J. Opt. Soc. Am. 57, 55-57 (1967).
[CrossRef]

1961 (1)

M. Minsky, "Microscopy apparatus," U.S. Patent 3,013,467 (19 December 1961).

1957 (1)

J. T. Wallmark, "A new semiconductor photocell using lateral photoeffect," Proc. IRE 45, 474-483 (1957).
[CrossRef]

Arnison, M. R.

J. W. O'Byrne, P. W. Fekete, M. R. Arnison, H. Zhao, M. Serrano, D. Philp, W. Sudiarta, and C. J. Cogswell, "Adaptive optics in confocal microscopy," in Proceedings of the Second International Workshop on Adaptive Optics for Industry and Medicine, G. D. Love, ed. (World Scientific, 1999), pp. 85-90.

Ayres, M. R.

M. R. Ayres, "Methods for measuring optical characteristics by differential diffractive scanning," U.S. patent application 10/800,111 (27 January 2005).

Born, M.

M. Born and E. Wolf, Principles of Optics, 6th ed. (Cambridge U. Press, 1980), p. 437.

Chichkov, B. N.

Choudhury, A.

C. J. R. Sheppard and A. Choudhury, "Image formation in the scanning microscope," Opt. Acta 24, 1051-1073 (1977).
[CrossRef]

Cogswell, C. J.

J. W. O'Byrne, P. W. Fekete, M. R. Arnison, H. Zhao, M. Serrano, D. Philp, W. Sudiarta, and C. J. Cogswell, "Adaptive optics in confocal microscopy," in Proceedings of the Second International Workshop on Adaptive Optics for Industry and Medicine, G. D. Love, ed. (World Scientific, 1999), pp. 85-90.

Curtis, K.

K. Curtis, W. L. Wilson, and L. Dhar, "High density holographic storage," presented at the International Symposium on Optical Memory, Jeju Island, South Korea, 11-15 October 2004; www.isom.jp.

Daiber, A. J.

Dhar, L.

K. Curtis, W. L. Wilson, and L. Dhar, "High density holographic storage," presented at the International Symposium on Optical Memory, Jeju Island, South Korea, 11-15 October 2004; www.isom.jp.

Fekete, P. W.

J. W. O'Byrne, P. W. Fekete, M. R. Arnison, H. Zhao, M. Serrano, D. Philp, W. Sudiarta, and C. J. Cogswell, "Adaptive optics in confocal microscopy," in Proceedings of the Second International Workshop on Adaptive Optics for Industry and Medicine, G. D. Love, ed. (World Scientific, 1999), pp. 85-90.

Frieden, B. R.

B. R. Frieden, "Optical transfer of the three-dimensional object," J. Opt. Soc. Am. 57, 55-57 (1967).
[CrossRef]

Grabowski, M. W.

R. R. McLeod, A. C. Sullivan, M. W. Grabowski, and T. F. Scott, "Hybrid integrated optics in volume holographic photopolymer," in Organic Holographic Materials and Applications II, K. Meerholz, ed., Proc SPIE 5521, 55-62 (2004).

R. R. McLeod, A. C. Sullivan, and M. W. Grabowski, "Direct-write waveguides in volume photopolymers," presented at Integrated Photonics Research, San Francisco, Calif., 30 June-2 July 2004 (Optical Society of America, 2004).

Gu, M.

Hesselink, L.

Juskaitis, R.

Kawata, S.

Kawata, Y.

Kogelnik, H.

H. Kogelnik, "Coupled wave theory for thick hologram gratings," Bell Syst. Tech. J. 48, 2909-2947 (1969).

Mao, X. Q.

McDonald, M. E.

McLeod, R. R.

R. R. McLeod, A. J. Daiber, M. E. McDonald, T. L. Robertson, T. Slagle, S. L. Sochava, and L. Hesselink, "Microholographic multilayer optical disk data storage," Appl. Opt. 44, 3197-3207 (2005).
[CrossRef] [PubMed]

R. R. McLeod, A. C. Sullivan, M. W. Grabowski, and T. F. Scott, "Hybrid integrated optics in volume holographic photopolymer," in Organic Holographic Materials and Applications II, K. Meerholz, ed., Proc SPIE 5521, 55-62 (2004).

R. R. McLeod, A. C. Sullivan, and M. W. Grabowski, "Direct-write waveguides in volume photopolymers," presented at Integrated Photonics Research, San Francisco, Calif., 30 June-2 July 2004 (Optical Society of America, 2004).

Minsky, M.

M. Minsky, "Microscopy apparatus," U.S. Patent 3,013,467 (19 December 1961).

Nolte, S.

O'Byrne, J. W.

J. W. O'Byrne, P. W. Fekete, M. R. Arnison, H. Zhao, M. Serrano, D. Philp, W. Sudiarta, and C. J. Cogswell, "Adaptive optics in confocal microscopy," in Proceedings of the Second International Workshop on Adaptive Optics for Industry and Medicine, G. D. Love, ed. (World Scientific, 1999), pp. 85-90.

Philp, D.

J. W. O'Byrne, P. W. Fekete, M. R. Arnison, H. Zhao, M. Serrano, D. Philp, W. Sudiarta, and C. J. Cogswell, "Adaptive optics in confocal microscopy," in Proceedings of the Second International Workshop on Adaptive Optics for Industry and Medicine, G. D. Love, ed. (World Scientific, 1999), pp. 85-90.

Robertson, T. L.

Scott, T. F.

R. R. McLeod, A. C. Sullivan, M. W. Grabowski, and T. F. Scott, "Hybrid integrated optics in volume holographic photopolymer," in Organic Holographic Materials and Applications II, K. Meerholz, ed., Proc SPIE 5521, 55-62 (2004).

Serrano, M.

J. W. O'Byrne, P. W. Fekete, M. R. Arnison, H. Zhao, M. Serrano, D. Philp, W. Sudiarta, and C. J. Cogswell, "Adaptive optics in confocal microscopy," in Proceedings of the Second International Workshop on Adaptive Optics for Industry and Medicine, G. D. Love, ed. (World Scientific, 1999), pp. 85-90.

Sheppard, C. J.

Sheppard, C. J. R.

Slagle, T.

Sochava, S. L.

Streibl, N.

Sudiarta, W.

J. W. O'Byrne, P. W. Fekete, M. R. Arnison, H. Zhao, M. Serrano, D. Philp, W. Sudiarta, and C. J. Cogswell, "Adaptive optics in confocal microscopy," in Proceedings of the Second International Workshop on Adaptive Optics for Industry and Medicine, G. D. Love, ed. (World Scientific, 1999), pp. 85-90.

Sullivan, A. C.

R. R. McLeod, A. C. Sullivan, M. W. Grabowski, and T. F. Scott, "Hybrid integrated optics in volume holographic photopolymer," in Organic Holographic Materials and Applications II, K. Meerholz, ed., Proc SPIE 5521, 55-62 (2004).

R. R. McLeod, A. C. Sullivan, and M. W. Grabowski, "Direct-write waveguides in volume photopolymers," presented at Integrated Photonics Research, San Francisco, Calif., 30 June-2 July 2004 (Optical Society of America, 2004).

Tanaka, T.

Tunnermann, A.

Wallmark, J. T.

J. T. Wallmark, "A new semiconductor photocell using lateral photoeffect," Proc. IRE 45, 474-483 (1957).
[CrossRef]

Will, M.

Wilson, T.

Wilson, W. L.

K. Curtis, W. L. Wilson, and L. Dhar, "High density holographic storage," presented at the International Symposium on Optical Memory, Jeju Island, South Korea, 11-15 October 2004; www.isom.jp.

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 6th ed. (Cambridge U. Press, 1980), p. 437.

Zhao, H.

J. W. O'Byrne, P. W. Fekete, M. R. Arnison, H. Zhao, M. Serrano, D. Philp, W. Sudiarta, and C. J. Cogswell, "Adaptive optics in confocal microscopy," in Proceedings of the Second International Workshop on Adaptive Optics for Industry and Medicine, G. D. Love, ed. (World Scientific, 1999), pp. 85-90.

Appl. Opt. (3)

Bell Syst. Tech. J. (1)

H. Kogelnik, "Coupled wave theory for thick hologram gratings," Bell Syst. Tech. J. 48, 2909-2947 (1969).

J. Opt. Soc. Am. (1)

B. R. Frieden, "Optical transfer of the three-dimensional object," J. Opt. Soc. Am. 57, 55-57 (1967).
[CrossRef]

J. Opt. Soc. Am. A (3)

Opt. Acta (1)

C. J. R. Sheppard and A. Choudhury, "Image formation in the scanning microscope," Opt. Acta 24, 1051-1073 (1977).
[CrossRef]

Opt. Lett. (1)

Proc. IRE (1)

J. T. Wallmark, "A new semiconductor photocell using lateral photoeffect," Proc. IRE 45, 474-483 (1957).
[CrossRef]

Other (7)

K. Curtis, W. L. Wilson, and L. Dhar, "High density holographic storage," presented at the International Symposium on Optical Memory, Jeju Island, South Korea, 11-15 October 2004; www.isom.jp.

M. Born and E. Wolf, Principles of Optics, 6th ed. (Cambridge U. Press, 1980), p. 437.

J. W. O'Byrne, P. W. Fekete, M. R. Arnison, H. Zhao, M. Serrano, D. Philp, W. Sudiarta, and C. J. Cogswell, "Adaptive optics in confocal microscopy," in Proceedings of the Second International Workshop on Adaptive Optics for Industry and Medicine, G. D. Love, ed. (World Scientific, 1999), pp. 85-90.

M. R. Ayres, "Methods for measuring optical characteristics by differential diffractive scanning," U.S. patent application 10/800,111 (27 January 2005).

M. Minsky, "Microscopy apparatus," U.S. Patent 3,013,467 (19 December 1961).

R. R. McLeod, A. C. Sullivan, M. W. Grabowski, and T. F. Scott, "Hybrid integrated optics in volume holographic photopolymer," in Organic Holographic Materials and Applications II, K. Meerholz, ed., Proc SPIE 5521, 55-62 (2004).

R. R. McLeod, A. C. Sullivan, and M. W. Grabowski, "Direct-write waveguides in volume photopolymers," presented at Integrated Photonics Research, San Francisco, Calif., 30 June-2 July 2004 (Optical Society of America, 2004).

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Figures (9)

Fig. 1
Fig. 1

Schematic of setup constructed for experiments.

Fig. 2
Fig. 2

(a) Coupled plane-wave probe components interact with a Bragg-matched grating within the sample and are detected at points p and d on the detector in the far field. (b) k space representation of the grating and wave vectors.

Fig. 3
Fig. 3

(a) Contour map of a cross section of the imaginary part of the coupled-mode transfer function mapping the imaginary (absorptive) dielectric to the optical power channel. (b) Corresponding impulse response.

Fig. 4
Fig. 4

(a) Contour map of a cross section of the imaginary part of the coupled-mode transfer function mapping the real (phase) dielectric to the x PSD channel. (b) Corresponding impulse response.

Fig. 5
Fig. 5

Optical Depth sectioning as determined by the integrated magnitude of the impulse response within depth (z) planes.

Fig. 6
Fig. 6

Simulated response of the PSD channel to unslanted phase gratings and of the power channel to unslanted absorption gratings compared to their respective predicted transfer functions. Grating frequencies are normalized to 1 / λ = 1 .

Fig. 7
Fig. 7

Depth sectioning properties determined by simulated scanning of a thin phase or absorptive knife edge at various depths.

Fig. 8
Fig. 8

Image of Fourier-plane data hologram stack recorded at oblique angle showing intraobject modulation fringes.

Fig. 9
Fig. 9

Image of a point-written waveguide in photopolymer connecting to the core of a single-mode telecommunications fiber.

Equations (47)

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k d = k p + k ε ,
| k d | = | k p | = 2 π n 0 λ k n ,
E d ( k d ) = j κε ( k ε ) E p ( k d k ε ) ,
ε ( r ) = ε ( k ε ) exp [ j k ε ( r r s ) ] ,
E p ( r ) = E p ( k d ) exp ( j k d r ) ,
E d ( r ) = j κ ε ( k ε ) exp [ j k ε ( r r s ) ] E p ( k d k ε ) × exp [ j ( k d k ε ) r ] ,
I ( r s ) = | E p ( r ) + E d ( r ) | 2 = | E p ( k d ) exp [ j k d r ] + j κ ε ( k ε ) E p ( k d k ε ) × exp [ j ( k d r k ε r s ) ] | 2 = | E p ( k d ) | 2 + | κ ε ( k ε ) E p ( k d k ε ) | 2 + E p ( k d ) ( j ) κε ( k ε ) E p ( k d k ε ) exp ( j k ε r s ) + E p ( k d ) j κε ( k ε ) E p ( k d k ε ) exp ( j k ε r s ) .
I ( r s ) E p ( k d ) ( j ) κε * ( k ε ) E p * ( k d k ε ) × exp ( j k ε r s ) + c . c . ,
P ( r s ) = d k d A ( k d ) I ( r s )
= j κε * ( k ε ) exp ( j k ε r ) d k d A ( k d ) E p ( k d ) × E p * ( k d k ε ) + c . c . ,
A ( k ) { 1 , k  strikes   the   detector 0, otherwise.
F ( k ) G ( k ) = F * ( k ) G ( k ) ,
P ( r s ) = j κ ε * ( k ε ) exp ( - j k ε r s ) E p ( k ε ) [ A ( k ε ) E p ( k ε ) ] + c . c .
M * ( k ) E p ( k ) [ A ( k ) E p ( k ) ] .
P ( k s ) = j κ [ ε ( k ε ) M ( k ε ) δ ( k s k ε ) ε * ( k ε ) M * ( k ε ) × δ ( k s + k ε ) ] .
P ( k s = k ε ) = j κε * ( k ε ) M * ( k ε ) ,
P ( k s = + k ε ) = + j κ ε ( k ε ) M ( k ε ) ,
H S S ( k ) P ( k ) ε ( k ) = j 2 κ M ( k ) ,
ε ( k ) = ε pr ( k ) + j ε pi ( k ) + ε ar ( k ) + j ε ai ( k ) , where
real phase , ε pr ( k ) , is   even ,
imaginary phase,   ε pi ( k ) , is   odd ,
real absorption , ε ar ( k ) , is   odd ,
imaginary   absorption,   ε ai ( k ) , is   even.
P d ( k ) = + j κ ε ( + k ) M ( + k ) ,
P p ( k ) = j κ ε * ( k ) M ( k ) .
P ( k ) = P d ( k ) + P p ( k ) = j κ M ( k ) [ ε ( + k ) ε * ( - k ) ] ,
P ( k ) = j 2 κ M ( k ) ε a ( k ) ,
H CS ( k ) P ( k ) ε a ( k ) = j 2 κ M ( k ) .
I d ( r s ) = E p ( k d ) ( j ) κ ε * ( k ε ) E p * ( k d k ε ) × exp ( j k ε r s ) + c . c . ,
C d x ( r s ) = d k d k d x A ( k d ) I d ( r s ) d k d A ( k d ) I d ( r s ) ,
C d x ( r s ) = j κ ε * ( k ε ) exp ( j k ε r s ) d k d k d x A ( k d ) × E p ( k d ) E p * ( k d k ε ) + c . c .
C d x ( r s ) = j κ ε * ( k ε ) exp ( j k ε r s ) E p ( k ε ) [ k ε x A ( k ε ) E p ( k ε ) ] + c . c .
S x ( k ) E p ( k ) [ k x A ( k ) E p ( k ) ] ,
C d x ( k s ) = j κ S x ( k ε ) [ ε ( k ε ) δ ( k s k ε ) ε * ( k ε ) δ ( k s + k ε ) ] ,
C d x ( k ) = + j 2 κ S x ( k ) ε ( k ) ,
C p x ( k ) = j 2 κ S x ( k ) ε * ( k ) .
C x ( k ) = 1 2 [ C d x ( k ) + C p x ( k ) ] = j κ [ S x ( k ) ε ( k ) S x ( k ) ε * ( - k ) ] .
C x ( k ) = j κ { [ S x ( k ) S x ( k ) ] ε p ( k ) + [ S x ( k ) + S x ( k ) ] j ε a ( k ) } .
ε p ( k ) = C x ( k ) + κ [ S x ( k ) + S x ( k ) ] ε a ( k ) j κ [ S x ( k ) S x ( - k ) ] .
H x PSD ( k ) = C x ( k ) ε p ( k ) = j κ [ S x ( k ) S x ( k ) ] 2 κ D x ( k ) .
D x ( k ) = j k x { E p ( k ) [ A ( k ) E p ( k ) ] } = j k x M ( k ) .
M ( k ) = 4 πk n cos - 1 [ k n | k z | 2 ( k x 2 + k y 2 ) ( 1 1 4 k n 2 ) ( 2 cos α | k z | + 1 ) ] .
H x PSD ( k ) = j 8 κ k x π k n cos - 1 [ k n | k z | 2 ( k x 2 + k y 2 ) ( 1 ( 1 / 4 ) k n 2 ) × ( 2 cos α | k z | + 1 ) ] .
ε ̂ p x ( k ) = C x ( k ) H x PSD ( k ) , ε ̂ p y ( k ) = C y ( k ) H y PSD ( k ) .
ε ̂ p ( k ) = | H x ( k ) | 2 | H x ( k ) | 2 + | H y ( k ) | 2 ε ̂ p x ( k ) + | H y ( k ) | 2 | H x ( k ) | 2 + | H y ( k ) | 2 ε ̂ p y ( k ) .
psf int ( z ) | psf ( r ) | d x d y ,
u = k n z tan 2 α .

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