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