Abstract

We derived the point-spread function (PSF) including the recording and reconstruction systems of the modified triangular interferometer; the modified triangular interferometer forms incoherent holograms without bias and the conjugate image. We also derived and analyzed the resolution of the modified triangular interferometer and compared it with that of the conventional one for amplification factor, wavelength, and hologram size.

© 2001 Optical Society of America

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References

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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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1997 (1)

1994 (1)

1992 (2)

1979 (1)

1977 (1)

1969 (1)

1966 (1)

1965 (1)

1948 (1)

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

Aitken, G. J. M.

Cochran, G.

Gabor, D.

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

Jones, P. F.

Kim, E.-S.

Kim, S.-G.

Korpel, A.

Kozma, A.

Lee, B.

Lohmann, A. W.

Massey, N.

Mugnier, L. M.

Pedrotti, F. L.

F. L. Pedrotti, L. S. Pedrotti, Introduction to Optics (Prentice-Hall, New Jersey, 1993).

Pedrotti, L. S.

F. L. Pedrotti, L. S. Pedrotti, Introduction to Optics (Prentice-Hall, New Jersey, 1993).

Poon, T.-C.

Rhodes, W. T.

Sirat, G. Y.

Yu, F. T. S.

F. T. S. Yu, Introduction to Diffraction, Information Processing, and Holography (MIT, Cambridge, Mass., 1973), Chap. 4.

Appl. Opt. (3)

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (2)

Nature (1)

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

Opt. Lett. (2)

Other (2)

F. T. S. Yu, Introduction to Diffraction, Information Processing, and Holography (MIT, Cambridge, Mass., 1973), Chap. 4.

F. L. Pedrotti, L. S. Pedrotti, Introduction to Optics (Prentice-Hall, New Jersey, 1993).

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Figures (9)

Fig. 1
Fig. 1

Modified triangular interferometer.

Fig. 2
Fig. 2

Longitudinal resolution versus magnification factor.

Fig. 3
Fig. 3

Longitudinal resolution versus hologram size.

Fig. 4
Fig. 4

Longitudinal resolution versus wavelength.

Fig. 5
Fig. 5

Lateral resolution versus magnification factor.

Fig. 6
Fig. 6

Lateral resolution versus hologram size.

Fig. 7
Fig. 7

Lateral resolution versus wavelength.

Fig. 8
Fig. 8

Lateral resolution versus linewidth in the MTI.

Fig. 9
Fig. 9

Longitudinal resolution versus linewidth in the MTI.

Tables (1)

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Table 1 Point-Spread Function by Combination of Phase Retardations

Equations (33)

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C=k/22πz0,ϕx, y=k/2z1x-x12+y-y12-x12+y12,x1=x0/α+β,y1=y0/α+β,z1=z0/α2-β2,α-f1/f2,β-f2/f1.
Hx, y=C2 exp±iϕx, y.
Ix, y; z1=C2+C2 cos ϕx, y=C2+12C2 expiϕx, y+12C2 exp-iϕx, y.
Ix, y; z1=C2+C2 cosk2z1xM-x12+yM-y12-x12+y12,
fm=2ΔC-1,
rmh=λz1/2ΔC.
fdm=rd/λz1.
H1x, y=C2 expiϕx, y.
H1x, y=C2 expi k2z1xM2+yM2=C2 expi k2z1rM2.
ρ=12πϕr=rλz1M2.
ρ=Rλz1M2.
rn=2λnz11/2M,  n=0, 1, 2,,
n=λz12 ρ2M2,
x0min1.22λf/d,
f=z1=z0|α2-β2|.
F=R2λf=R2λz0 |α2-β2|=R2λz0f14-f24f12f22,
x0min1.22λz02Rα2-β2.
x0min0.61R/F.
z0min2R2/λF2.
H2x, y=2 cosk2z1x2+y2.
H2x, y=2 cosk2z1x2+y2=expi k2z1x2+y2+exp-i k2z1x2+y2.
Ux, y, z=iλzexp-ikzξ2+η2R2 H2ξ, η×exp-i k2zx-ξ2+y-η2dξdη=iλzexp-ikzξ2+η2R2expi k2z1ξ2+η2+exp-i k2z1ξ2+η2×exp-i k2zx-ξ2+y-η2dξdη.
U0, 0, z=iλzexp-ikzξ2+η2R2expi k2z1ξ2+η2+exp-i k2z1ξ2+η2×exp-i k2zξ2+η2dξdη.
U0, 0, z=iλzexp-ikz0R02πexpi k21z1-1zr02+exp-i k21z1+1zr02r0dr0dθ=1z1-1z-12izexp-ikzexpi k41z1-1zR2sink41z1-1zR2+1z1+1z-12izexp-ikzexp-i k41z1+1zR2sink41z1+1zR2.
I0, 0, z=k2R44z2sinck41z1-1zR22+k2R44z2sinck41z1+1zR22+8z21z1-1z-11z1+1z-1 cosk2z1 R2×sink41z1-1zR2sink41z1+1zR2.
I0, 0, z=k2R44z2sinc2W4+sinc2W14+k2R42z2cosk2z1 R2sincW4sincW14,
Ur, z=iλzexp-ikz-i kr22z0R 2πJ0krr0z×expi k2 Dr02+exp-i k2 Er02r0dr0,
Ir, z=|Ur, z|2.
l=cΔfλ2Δλ,
ΔL=12z1x2+y2=12z1 r2=Fλ2,
Δλ=2λF.
x0min0.61 RF=0.61 RΔλ2λ,
z0min2R2λF2=R2Δλ22λ3.

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