Abstract

Scanning heterodyne holography is an alternative way of capturing three-dimensional information on a scattering or fluorescent object. We analyze the properties of the images obtained by this novel imaging process. We describe the possibility of varying the coherence of the system from a process linear in amplitude to a process linear in intensity by changing the detection mode. We illustrate numerically the properties of the three-dimensional point-spread function of the system and compare it with that of a conventional imaging system with equal numerical aperture. We describe how it is possible, by an appropriate choice of the reconstruction algorithm, to obtain an ideal transfer function equal to unity up to the cutoff frequency, even in the presence of aberrations. Some practical implementation issues are also discussed.

© 2000 Optical Society of America

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References

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1998 (3)

1997 (1)

1995 (2)

W. Wang, A. T. Freiberg, E. Wolf, “Structure of focused fields in systems with large Fresnel numbers,” J. Opt. Soc. Am. A 12, 1947–1953 (1995).
[CrossRef]

T.-C. Poon, K. Doh, B. Schilling, M. Wu, K. Shinoda, Y. Suzuki, “Three-dimensional microscopy by optical scanning holography,” Opt. Eng. 34, 1338–1344 (1995).
[CrossRef]

1994 (2)

1993 (1)

1992 (1)

1989 (1)

D. A. Agard, Y. Hiraoka, P. Shaw, J. W. Sedat, “Fluorescence microscopy in three-dimensions,” Methods Cell Biol. 30, 353–377 (1989).
[CrossRef]

1986 (1)

G. Indebetouw, T.-C. Poon, “Parallel synthesis of bipolar point spread functions in a scanning heterodyne optical system,” Opt. Acta 33, 827–834 (1986).
[CrossRef]

1985 (1)

1984 (3)

G. Indebetouw, “Nonlinear, adaptive image processing with a scanning optical system,” Opt. Eng. 23, 73–78 (1984).
[CrossRef]

D. A. Agard, “Optical sectioning microscopy,” Annu. Rev. Biophys. Bioeng. 13, 191–219 (1984).
[CrossRef]

G. Indebetouw, T.-C. Poon, “Incoherent spatial filtering with a scanning heterodyne system,” Appl. Opt. 23, 4571–4574 (1984).
[CrossRef] [PubMed]

1969 (1)

1962 (1)

1948 (1)

D. Gabor, “A new microscopic principle,” Nature (London) 161, 777–778 (1948).
[CrossRef]

Agard, D. A.

D. A. Agard, Y. Hiraoka, P. Shaw, J. W. Sedat, “Fluorescence microscopy in three-dimensions,” Methods Cell Biol. 30, 353–377 (1989).
[CrossRef]

D. A. Agard, “Optical sectioning microscopy,” Annu. Rev. Biophys. Bioeng. 13, 191–219 (1984).
[CrossRef]

Bertero, M.

M. Bertero, C. de Mol, “Super resolution by data inversion,” in Progress in Optics, E. Wolf, ed. (Elsevier, Amsterdam, 1996), Vol. 36, pp. 129–178.

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1970).

Chen, J.

Cohen, F.

M. Davidson, K. Kaufman, I. Mazor, F. Cohen, “An application of interference microscopy to integrated circuit inspection and metrology,” in Integrated Circuit Metrology, Inspection & Process Control, K. M. Monahan, ed., Proc. SPIE775, 233–247 (1987); G. S. Kino, S. S. C. Chim, “Mirau correlation microscope,” Appl. Opt. 29, 3775–3783 (1990).
[CrossRef] [PubMed]

Conchello, J.-A.

Davidson, M.

M. Davidson, K. Kaufman, I. Mazor, F. Cohen, “An application of interference microscopy to integrated circuit inspection and metrology,” in Integrated Circuit Metrology, Inspection & Process Control, K. M. Monahan, ed., Proc. SPIE775, 233–247 (1987); G. S. Kino, S. S. C. Chim, “Mirau correlation microscope,” Appl. Opt. 29, 3775–3783 (1990).
[CrossRef] [PubMed]

de Mol, C.

M. Bertero, C. de Mol, “Super resolution by data inversion,” in Progress in Optics, E. Wolf, ed. (Elsevier, Amsterdam, 1996), Vol. 36, pp. 129–178.

Doh, K.

T.-C. Poon, K. Doh, B. Schilling, M. Wu, K. Shinoda, Y. Suzuki, “Three-dimensional microscopy by optical scanning holography,” Opt. Eng. 34, 1338–1344 (1995).
[CrossRef]

Freiberg, A. T.

Gabor, D.

D. Gabor, “A new microscopic principle,” Nature (London) 161, 777–778 (1948).
[CrossRef]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1988).

Hiraoka, Y.

D. A. Agard, Y. Hiraoka, P. Shaw, J. W. Sedat, “Fluorescence microscopy in three-dimensions,” Methods Cell Biol. 30, 353–377 (1989).
[CrossRef]

Hussain, F.

Indebetouw, G.

Ishizuka, K.

Joshi, S.

Kaufman, K.

M. Davidson, K. Kaufman, I. Mazor, F. Cohen, “An application of interference microscopy to integrated circuit inspection and metrology,” in Integrated Circuit Metrology, Inspection & Process Control, K. M. Monahan, ed., Proc. SPIE775, 233–247 (1987); G. S. Kino, S. S. C. Chim, “Mirau correlation microscope,” Appl. Opt. 29, 3775–3783 (1990).
[CrossRef] [PubMed]

Kim, T.

Lai, G.

Lieth, E. N.

Mazor, I.

M. Davidson, K. Kaufman, I. Mazor, F. Cohen, “An application of interference microscopy to integrated circuit inspection and metrology,” in Integrated Circuit Metrology, Inspection & Process Control, K. M. Monahan, ed., Proc. SPIE775, 233–247 (1987); G. S. Kino, S. S. C. Chim, “Mirau correlation microscope,” Appl. Opt. 29, 3775–3783 (1990).
[CrossRef] [PubMed]

McNally, J.

Miller, M. I.

Poon, T.-C.

Preza, C.

Schilling, B.

Sedat, J. W.

D. A. Agard, Y. Hiraoka, P. Shaw, J. W. Sedat, “Fluorescence microscopy in three-dimensions,” Methods Cell Biol. 30, 353–377 (1989).
[CrossRef]

Shaw, P.

D. A. Agard, Y. Hiraoka, P. Shaw, J. W. Sedat, “Fluorescence microscopy in three-dimensions,” Methods Cell Biol. 30, 353–377 (1989).
[CrossRef]

Shinoda, K.

B. Schilling, T.-C. Poon, G. Indebetouw, B. Storrie, K. Shinoda, M. Wu, “Three-dimensional holographic fluorescence microscopy,” Opt. Lett. 22, 1506–1508 (1997).
[CrossRef]

T.-C. Poon, K. Doh, B. Schilling, M. Wu, K. Shinoda, Y. Suzuki, “Three-dimensional microscopy by optical scanning holography,” Opt. Eng. 34, 1338–1344 (1995).
[CrossRef]

Stokseth, P. A.

Storrie, B.

Suzuki, Y.

T.-C. Poon, K. Doh, B. Schilling, M. Wu, K. Shinoda, Y. Suzuki, “Three-dimensional microscopy by optical scanning holography,” Opt. Eng. 34, 1338–1344 (1995).
[CrossRef]

Thomas, L. J.

Tonomura, A.

Upatnieks, J.

Wang, W.

Wolf, E.

Wu, M.

B. Schilling, T.-C. Poon, G. Indebetouw, B. Storrie, K. Shinoda, M. Wu, “Three-dimensional holographic fluorescence microscopy,” Opt. Lett. 22, 1506–1508 (1997).
[CrossRef]

T.-C. Poon, K. Doh, B. Schilling, M. Wu, K. Shinoda, Y. Suzuki, “Three-dimensional microscopy by optical scanning holography,” Opt. Eng. 34, 1338–1344 (1995).
[CrossRef]

Yamaguchi, I.

Zhang, T.

Zimin, V.

Annu. Rev. Biophys. Bioeng. (1)

D. A. Agard, “Optical sectioning microscopy,” Annu. Rev. Biophys. Bioeng. 13, 191–219 (1984).
[CrossRef]

Appl. Opt. (2)

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (5)

Methods Cell Biol. (1)

D. A. Agard, Y. Hiraoka, P. Shaw, J. W. Sedat, “Fluorescence microscopy in three-dimensions,” Methods Cell Biol. 30, 353–377 (1989).
[CrossRef]

Nature (London) (1)

D. Gabor, “A new microscopic principle,” Nature (London) 161, 777–778 (1948).
[CrossRef]

Opt. Acta (1)

G. Indebetouw, T.-C. Poon, “Parallel synthesis of bipolar point spread functions in a scanning heterodyne optical system,” Opt. Acta 33, 827–834 (1986).
[CrossRef]

Opt. Eng. (2)

T.-C. Poon, K. Doh, B. Schilling, M. Wu, K. Shinoda, Y. Suzuki, “Three-dimensional microscopy by optical scanning holography,” Opt. Eng. 34, 1338–1344 (1995).
[CrossRef]

G. Indebetouw, “Nonlinear, adaptive image processing with a scanning optical system,” Opt. Eng. 23, 73–78 (1984).
[CrossRef]

Opt. Lett. (4)

Other (6)

T. Wilson, ed., Confocal Microscopy (Academic, London, 1990).

M. Davidson, K. Kaufman, I. Mazor, F. Cohen, “An application of interference microscopy to integrated circuit inspection and metrology,” in Integrated Circuit Metrology, Inspection & Process Control, K. M. Monahan, ed., Proc. SPIE775, 233–247 (1987); G. S. Kino, S. S. C. Chim, “Mirau correlation microscope,” Appl. Opt. 29, 3775–3783 (1990).
[CrossRef] [PubMed]

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1988).

J. C. Dainty, ed., Laser Speckle and Related Phenomena (Springer-Verlag, Berlin, 1984).

M. Bertero, C. de Mol, “Super resolution by data inversion,” in Progress in Optics, E. Wolf, ed. (Elsevier, Amsterdam, 1996), Vol. 36, pp. 129–178.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1970).

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Figures (4)

Fig. 1
Fig. 1

Sketch of a scanning holographic microscope. AO1 and AO2 are acousto-optic modulators. P1 and P2 are point-source outputs of single-mode fibers. The specimen is on a two-dimensional scanning stage.

Fig. 2
Fig. 2

Cross sections of the in-focus point-spread function amplitude. For low numerical apertures, the point-spread function is nearly independent of the Fresnel number and almost identical with the point-spread function of a clear aperture of equal numerical aperture. For high numerical apertures, the point-spread function has a sharper central lobe than the Airy disk but higher sidelobes.

Fig. 3
Fig. 3

Point-spread function (PSF) of a scanning holographic system with numerical aperture 0.5 and Fresnel number 5. The PSF is nearly identical with that of a clear aperture of equal numerical aperture. (a) Axial sections through the PSF amplitude, where ρ is the radial transverse coordinate and z is the axial coordinate (ξ in the text), (b) three-dimensional representation of the in-focus PSF, (c) topographical plot of the PSF amplitude.

Fig. 4
Fig. 4

Same as Fig. 3 but for a system with numerical aperture 0.95 and Fresnel number 5. Compared with the PSF of Fig. 3 and with J1(x)/2x, the PSF has a sharper central lobe and larger sidelobes. The difference is also displayed in (c).

Equations (47)

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U(r, z, t)=-ikA exp(-iωt)0NAexp[ik(1-s2)1/2z]×J0(ksr)(1-s2)-1/2s ds=-ikAE(r, z)exp[i(kz-ωt)],
E(r, z)=0NAexp(-i12ks2z)J0(ksr)(1-s2)-1/2s ds.
Up(r, z, t)=Ep(r, z)exp[i(kz-ωt)],
Ep(r, z)=0NAexp(-i12ks2z)J0(ksr)s ds.
Et(r, z)=exp[iΦ(r, z)]circ[r/a(z)],
Φ(r, z)=kr2/2z.
a(z)=z×NA
F(z)=a2(z)/λz=(NA)2z/λ.
P(r, z, t)=E(r, z)+E0 exp(iΩt).
δz=z-z0.
ρ=r×NA/λ,
ξ=δz×(NA)2/λ.
μ=ν/νmax=s/NA.
E(ρ, ξ; F0)=01exp(-i2π{1-[1-μ2(NA)2]1/2}×(F0+ξ)(NA)-2)×J0(2πμρ)[1-μ2(NA)2]-1/2μ dμ,
Ep(ρ, ξ; F0)=01exp[-iπμ2(F0+ξ)]J0(2πμρ)μ dμ.
Et(ρ, ξ; F0)=exp[iπρ2(F0+ξ)-1]circ(ρ/F0)exp[iπρ2(1-ξ/F0)/F0]circ(ρ/F0).
Eobj(t)=d2ρdξP(ρ, ξ, t)T(ρ-ρs, ξ).
i(ρs)d2ρ|Fρ{Eobj}|2M(ρ)d2ρd2ρd2ρdξ M(ρ)×exp[-i2π(ρ-ρ)·α]P(ρ, ξ)×P*(ρ, ξ)T(ρ-ρs, ξ)T*(ρ-ρs, ξ),
Fρs{Eobj}=Eobj(ρs)exp(-i2πρs·αρ)d2ρs
M(μ)=M(ρ)exp(-i2πμ·ρ)d2ρ
i(ρs)d2ρd2ρdξ M(αρ-αρ)P(ρ, ξ)×P*(ρ, ξ)T(ρ-ρs, ξ)T*(ρ-ρs, ξ).
H(ρs)=C(ρs)+iS(ρs).
H(ρs)=d2ρd2ρdξ M(αρ-αρ)E(ρ, ξ)×T(ρ-ρs,ξ)T*(ρ-ρs,ξ).
Hcoh(ρs)=H0d2ρdξ E(ρ, ξ)T(ρ-ρs, ξ),
Hinc(ρs)=d2ρdξ E(ρ, ξ)I(ρ-ρs, ξ),
R(ρ, ξR)=H(ρs)ER*(ρs-ρ, ξR)d2ρs=d2ρsd2ρd2ρdξ M(αρ-αρ)×ER*(ρs-ρ, ξR)E(ρ, ξ)×T(ρ-ρs, ξ)T*(ρ-ρs, ξ).
Rcoh(ρ, ξR)=d2ρsd2ρdξ ER*(ρs-ρ, ξR)×E(ρ, ξ)T(ρ-ρs, ξ),
Rinc(ρ, ξR)=d2ρsd2ρdξ ER*(ρs-ρ, ξR)×E(ρ, ξ)I(ρ-ρs, ξ).
Rcoh(ρ, ξ)=d2ρdξ PSF(ρ; ξ, ξR)T(ρ-ρ, ξ)
Rinc(ρ, ξ)=d2ρdξ PSF(ρ; ξ, ξR)I(ρ-ρ, ξ)
PSF(ρ; ξ, ξR)=d2ρER*(ρ-12ρ, ξR)E(ρ+12ρ, ξ).
PSFt(ρ, ξ)=1πF02-(F0-ρ/2)+(F0-ρ/2)dx-[F02-(ρ/2+x)2]1/2+[F02-(ρ/2+x)2]1/2dy×exp-i2πF0ρx+iπξF02[(ρ/2+x)2+y2]forρ<2F00 forρ>2F0.
PSFe(ρ, 0; F0)=P(ρ/2F0)J1[2πρ(1-ρ/2F0)]πρ(1-ρ/2F0)forρ<2F00forρ>2F0,
PSFe(0, ξ; F0)=sinc(ξ/2),
Δρ=0.61orΔr=0.61λ/NA.
Δξ=2orΔz=2λ/(NA)2.
TF(μ; ξ)=ER*(μ; 0)E(μ; ξ),
ER(μ; ξ)=2π0ER(ρ, ξ)J0(2πμρ)ρ dρ.
E(μ; ξ)=exp(-i2π{1-[1-μ2(NA)2]1/2}(F0+ξ)×(NA)-2)[1-μ2(NA)2]-1/2circ(μ).
ER(μ; ξ)E(μ; ξ)[1-μ2(NA)2].
TF(μ; ξ)=exp(-i2π{1-[1-μ2(NA)2]1/2}×ξ(NA)-2)circ(μ).
TF(μ; 0)=circ(μ),
Ep(μ; ξ)=ERp(μ; ξ)=exp[-iπμ2(F0+ξ)]circ(μ),
TFp(μ; ξ)=exp(-iπμ2ξ)circ(μ).
PSF=ER*(ρ-12ρ, 0)E(ρ+12ρ, 0)d2ρ,
TF(μ; 0)=ER*(μ; 0)circ(μ).
ERt=Et(ρ+12ξ)-Et(ρ-12ξ)12(d/dξ)Et(ρ, ξ).

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