We demonstrate that it is possible to study the modal structures of a vibrating object with digitally recorded holograms by use of the time-averaging principle. We investigate the numerical reconstruction from a theoretical point of view, and we show that the numerically reconstructed object from a digital hologram is modulated by the zeroth-order Bessel function. Results of experiments in time-averaged digital holography are presented.

© 2003 Optical Society of America

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  1. E. Cuche, F. Bevilacqua, C. Depeursinge, Opt. Lett. 24, 291 (1999).
  2. I. Yamaguchi, T. Matsumura, and J. Kato, Opt. Lett. 27, 1108 (2002).
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    [CrossRef] [PubMed]
  4. R. L. Powell and K. A. Stetson, J. Opt. Soc. Am. A 55, 1593 (1965).

2003 (1)

2002 (1)

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1965 (1)

R. L. Powell and K. A. Stetson, J. Opt. Soc. Am. A 55, 1593 (1965).

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Figures (3)

Fig. 1
Fig. 1

Experimental setup.

Fig. 2
Fig. 2

Image amplitude of the reconstructed object.

Fig. 3
Fig. 3

Offset phase of the loudspeaker (modulo 2π).

Equations (8)

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Ox,y,d0,t=i exp-i2πd0/λλd0×exp-iπλd0x2+y2×-+-+Ax,y,t×exp-iπλd0x2+y2×exp2iπλd0xx+yydxdy.
t1t1+TR*x,yOx,y,d0,tdt=i exp-i2πd0/λλd0×exp-iπλd0x2+y2R*x,y×-+-+F˜x,yexp2iπλd0xx+yydxdy,
ARX,Y,dR=i exp-i2πdR/λλdR×exp-iπλdRX2+Y2×k=0k=K-1 l=0l=L-1t1t1+TR*kΔx,lΔy×OkΔx,lΔy,d0,tdt×exp-iπλdRk2Δx2+l2Δy2×exp2iπλdRkXΔx+lYΔy,
ARx,y,-d0=ar expiπλd0x2+y2×F˜x-λurd0,y-λvrd0*W˜NMx,y,