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A new method for producing point holograms

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Abstract

A new method is proposed for producing point holograms by utilising highly correlated, extended sources rather than point-like sources in the recording process. The theory of this method is presented. Its feasibility is demonstrated experimentally. A multiple imaging experiment is described which utilises this kind of hologram. Advantages and limitations of holograms of extended sources are discussed.

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Abbreviations

R :

complex amplitude of the reference wavefront in the hologram plane

S :

complex amplitude of the signal wavefront in the hologram plane

D :

complex amplitude of the reconstructing wavefront in the hologram plane

T :

complex amplitude of the reconstructed wavefront in the hologram plane

r :

complex amplitude of the wavefront illuminating the reference transparency

s :

complex amplitude of the wavefront illuminating the reference transparency

d :

complex amplitude of the wavefront illuminating the reference transparency

t :

complex amplitude of the wavefront illuminating the reference transparency

p :

amplitude transmittance of the reference transparency

σ :

amplitude transmittance of the signal transparency

δ(δ-function):

amplitude transmittance of the reconstructing transparency

τ:

amplitude transmittance of the reconstructed transparency

P r ,P s :

propagation functions at distancesz r ,z s , respectively (equation 3)

x, y :

co-ordinates in the source plane

σ, η :

co-ordinates in the hologram plane

z r ,z s :

distances of the reference, signal source from the hologram plane

X r ,y r :

co-ordinates of the reconstructing source (δ-function)

a, h :

shift co-ordinates in the autocorrelation integral (equation 12)

f r,f s :

Fourier transform operator at distances zr,z s (equation 7a) wavelength

k=2π/λ :

wavenumber

*:

conjugate complex

(*):

convolution

References

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Author information

Authors and Affiliations

  1. Philips Forschungslaboratorium GmbH, Laboratorium Hamburg, Germany

    G. Groh

Authors
  1. G. Groh
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Groh, G. A new method for producing point holograms. Opto-electronics 2, 73–80 (1970). https://doi.org/10.1007/BF01419155

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  • DOI: https://doi.org/10.1007/BF01419155

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