Abstract

We present a new method for recording digital Fourier holograms under incoherent illumination. A single exposure recorded by a digital camera is sufficient to record a real-valued hologram that encodes the complete three-dimensional properties of an object.

© 2012 Optical Society of America

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References

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2012 (1)

2011 (3)

2010 (1)

2009 (1)

2007 (1)

1997 (1)

1974 (1)

1965 (1)

G. W. Stroke and R. C. Restrick, Appl. Phys. Lett. 7, 229 (1965).
[CrossRef]

Breckinridge, J. B.

Brooker, G.

Bryanston-Cross, P.

Claus, D.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw Hill, 1996), Chap. 9, pp. 295–392.

Iliescu, D.

Katz, B.

Kelner, R.

Poon, T.-C.

Restrick, R. C.

G. W. Stroke and R. C. Restrick, Appl. Phys. Lett. 7, 229 (1965).
[CrossRef]

Rosen, J.

Siegel, N.

Stroke, G. W.

G. W. Stroke and R. C. Restrick, Appl. Phys. Lett. 7, 229 (1965).
[CrossRef]

Wang, V.

Yamaguchi, I.

Zhang, T.

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Figures (4)

Fig. 1.
Fig. 1.

Schematic of a FISCH recorder: RC, resolution chart; BPF, bandpass filter; BS, beam splitter; SLM, spatial light modulator; M, mirror; CCD, charge-coupled device; P1 and P2, polarizers.

Fig. 2.
Fig. 2.

Schematic of the reconstruction apparatus.

Fig. 3.
Fig. 3.

(a), (b), and (c) are digitally reconstructed images for zs=30cm from a single exposure, two and three exposures holograms, respectively; (d) is the optically reconstructed equivalent of (b). (e) is a two exposures hologram (shown partially to reveal details, recorded with zs=25cm) and (f) is its digitally reconstructed image at the best plane of focus. (g) and (h) are optical reconstructions of (e) at the best plane of focus of one of the images and its twin, respectively.

Fig. 4.
Fig. 4.

Simplified schematic of a FISCH recorder.

Equations (10)

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C1(x,y;r⃗s,zs)=T(x,y;r⃗s,zs)·Q(1f0)*Q(1d0+2f1),
C2(x,y;r⃗s,zs)=T(x,y;r⃗s,zs)·Q(1f0)*Q(1d0)·Q(1f1)*Q(12f1)·Q(1f1),
Dk(x,y;r⃗s,zs)=Ck(x,y;r⃗s,zs)*Q(1f2)·Q(1f2)*Q(12f2)·Q(1f2)*Q(1d2),
I(x,y;r⃗s,zs)=Is(|b1|2+|b2|2)+[b1b2*Is·L(2r⃗sfezs·f3f324f12)·Q(4f1f324f12)+c.c.],
H(x,y)=I(x,y;r⃗s,zs)dxsdysdzs.
I(x,y;r⃗s,f0)=Is(|b1|2+|b2)|2)+[b1b2*Is·L(2r⃗sf0)+c.c.].
s(x,y,zr)=(v[1λfr]F1{H(x,y)})*Q(1/zr),
zr=±4f1fr2/(f324f12).
h(r⃗)=v[1λfr]F1{I(x,y;r⃗s,f0)P(R0)},
hF(r⃗)Jinc(2πR0λfr(xMTxs)2+(yMTys)2),

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