Abstract

A theory of optical sectioning by image plane holography is developed, emphasizing the use of broad-spectrum holographic methods to enhance the process. It is shown that a broad-spectrum source in a grating interferometer imitates the behavior of a monochromatic broad source.

© 2003 Optical Society of America

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References

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    [CrossRef]

1994 (1)

1986 (1)

1981 (2)

1970 (1)

1968 (2)

1966 (1)

1962 (1)

Bryngdahl, O.

Caulfield, H. J.

DeSilversti, S.

Fujimoto, J. G.

Ingalls, A. G.

Ippen, E. P.

Leith, E. N.

Lohmann, A.

Lukosz, W.

Margollis, R.

Oseroff, A.

Sun, P.-C.

Swanson, G. W.

Upatnieks, J.

Yang, G. G.

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Figures (8)

Fig. 1
Fig. 1

Portion of a broad source holographic process, showing light from a broad source being collimated by a lens of focal length F and then illuminating an object plane P, which is then imaged to an output plane. Ls is the source size, Lc is the size of the coherence cell on the object plane, and Lx is the size of the defocused spot falling on the object plane; z is the distance between in-focus and out-of-focus plane.

Fig. 2
Fig. 2

Conventional confocal system.

Fig. 3
Fig. 3

Finding the coherence function γ12(0) for a spectrally dispersed source.

Fig. 4
Fig. 4

Grating interferometer for producing an image plane hologram with spectral and spatially broad source.

Fig. 5
Fig. 5

Generalized grating interferometer for coherence analysis.

Fig. 6
Fig. 6

Grating interferometer for analysis of γ12(0).

Fig. 7
Fig. 7

Asymmetric grating interferometer.

Fig. 8
Fig. 8

Grating interferometer for analysis of optical sectioning.

Equations (23)

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Lc/Lx=λF2/zLsA.
Lob/Lx=λF2/zA2.
S(ν, ξ)=δ(ν-νo-kξ),
If=1+cos{2πbν/cz[x+(ν-νo)/k]},
rect[(ν-νo)/Δν]cos{2πνb/cz[x+(ν-νo)/k]}dν.
S(λ, ξ)=δ(λ-λo-kξ).
I=rect[(λ-λo)/Δλ]×cos[2πb/kz(1-λo/λ+kx/λ)]dλ,
u1=exp[i2π(fs+fp+f1)x]×exp[-iπλd(fs+fp+f1)2]×exp[-i2π(2 f1+fx)]×exp[-iπλ(d-z)(fs+fp-f1-fx)2],
u2=exp[i2π(fs+fp-f1)x]×exp[-iπλd(fs+fp-f1)2]×exp[i2π(2 f1)x]×exp[-iπλ(d-z)(fs+fp+f1)2],
I=|u1+u2|2=1+cos[2π(2 f1+fx)x+ϕ],
ϕ=πλd(fx2-2 fsfx-2 fpfx+2 f1fx)+πλz(-fx2+4fsf1+4fpf1+2 fsfx+2 fpfx-2 f1fx).
ϕ=πλd(fx2-2 fsfx-2 fpfx+2 f1fx).
ϕ=πλd(fx2+2 f1fx).
I=cos[2π(f1+fx)x-πλd(f12+fx2+2 fsf1+2 fsfx+2 fxf1)+πλd(f12+2 f1fs)],
d(f1+fx)-df1=0,
I=1+cos[2π(f1+fx)x-2πλdf1fx].
λ2/Δλ=OPD.
I=1+cos[2π(f1+fx)x+πλdfx2].
I=1+cos[2π(f1+fx)x-πλd(fx2+2 f1fx)].
I=1+cos[2π(2 f1-fx)x+πλzfx(fx+2 fs-2 f1)].
Hθc=sinc 2zθcfx.
HΔλ=sinc zfx(fx-2 f1)Δλsinc 2zf1fxΔλ,
fx=(dλofso+dΔλfso/2+df1Δλ)-1.

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