h(x,y):= f(x,y) + A ej27a 12 (3.2)


 = A2 + If(x,y) 2 + A f(x,y)ej2Tay + A f (x,y)e-j2aay.


The function recorded on the film contains a D.C. bias, A2, the base

band magnitude, If(x,y)12, and two terms heterodyned to plus and minus

a. These heterodyned terms contain the complex valued information

describing the input function f(x,y). If the spatial carrier

frequency is sufficiently high, the heterodyned terms are separable

and no aliasing exists. The original input function can be retrieved

with no distortion by re-illuminating the film with the reference beam

and spatially filtering the output to separate the various terms.

 To make the hologram of the Fourier transform of an image, the

same procedure is applied. That is, the Fourier transform of the

image f(x,y) is used as the input to the hologram. Now


h(u,v) = A2 + F(u,v)2 + A F(u,v)eJ2,au + A F*(u,v)e-j27au (3.3)


where F(u,v) = Fourier Transform of f(x,y) = F {f(x,y)} and


A e-j27au = the off-axis reference wave used to provide the spatial

carrier for the hologram.


a = sin e = the filter spatial carrier frequency (9 = off-axis angle)
 X

This filter contains the D.C. bias, A2; the power spectral density,

IF(uv)12; and two terms heterodyned to plus and minus a. These

heterodyned terms contain the complex valued information describing

the Fourier transform of the input f(x,y).

 These optically generated holograms are formed

interferometrically by combining a plane wave with the wavefront to be