Kelly, D.P. and Hennelly, B.M. and McElhinney, C. and Naughton, T.J.
A Practical Guide to Digital Holography and Generalized
Proceedings of SPIE, 7072.
The theorems of Nyquist, Shannon and Whittaker have long held true for sampling optical signals. They showed
that a signal (with finite bandwidth) should be sampled at a rate at least as fast as twice the maximum spatial
frequency of the signal. They proceeded to show how the continuous signal could be reconstructed perfectly
from its well sampled counterpart by convolving a Sinc function with the sampled signal. Recent years have
seen the emergence of a new generalized sampling theorem of which Nyquist Shannon is a special case. This
new theorem suggests that it is possible to sample and reconstruct certain signals at rates much slower than
those predicted by Nyquist-Shannon. One application in which this new theorem is of considerable interest is
Fresnel Holography. A number of papers have recently suggested that the sampling rate for the digital recording
of Fresnel holograms can be relaxed considerably. This may allow the positioning of the object closer to the
camera allowing for a greater numerical aperture and thus an improved range of 3D perspective. In this paper
we: (i) Review generalized sampling for Fresnel propagated signals, (ii) Investigate the effect of the twin image,
always present in recording, on the generalized sampling theorem and (iii) Discuss the effect of finite pixel size
for the first time.
||Digital holography; phase shifting interferometry; generalized sampling; Nyquist-Shannon; Fresnel; Fourier Transform;
||Science & Engineering > Computer Science
Dr. Thomas Naughton
||18 Jan 2011 11:52
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||Proceedings of SPIE
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