The exponential expression in 4.5 can be expanded with a series
expression.
H(u,v)= 1 + jF(u,v) (1/2)F2(u,v) j(1/6)F3(u,v) +...
S [jF(u,v)]n (4.9)
n!
When reconstructed, this hologram can be expressed as a series of
convolutions.
h(x,y) = (x,y) + jf(x,y) (1/2)f(x,y)f(x,y) -
-j(1/6)f(x,y)@f(x,y)f(x,y) + ...
= jn f(n)(x,y) (4.10)
n!
where f(n)(x,y) = f(x,y)@f(x,y) .. f(x,y) n convolutions
and f(O)(x,y) = S(x,y)
f(1)(x,y) = f(x,y)
f(2)(x,y) = f(x,y)f(x,y)
and so on.
Thus, the phase modulation technique is very non-linear and the
resultant reconstruction is rich with harmonics. The reconstruction
from such a hologram is noisy due to the harmonic content. The higher
order correlations are broader, thus contributing less flux into the
reconstruction. Phase modulation in the form of bleached and
dichromated gelatin holograms have become the rule in display
holography due to the bright images. This fact indicates that the