noise is acceptable in many cases. In fact, the reconstruction of
such display holograms looks very good. Nevertheless, such an example
is deceiving because the repeated convolutions and correlations of
equation 4.10 become more detrimental for more complicated objects,
especially if the object has low contrast.32 The harmonics combine to
produce intermodulation terms within the bandpass of the desired
information, causing an increase in background noise. When used for
matched filtering, the decision to use phase modulation is a balance
between hologram efficiency and signal-to-noise ratio.
An interesting case occurs when a binary amplitude hologram is
converted to a phase modulation hologram. The bleaching process maps
an amplitude of zero and one to a phase shift of plus and minus pi.
This equates to an amplitude of plus and minus one. For this binary
mapping, the transfer function is 2x-1, which is a linear process. In
that sense, the binary hologram is inherently linear. The binary
hologram represents the continuous-tone amplitude hologram by opening
more or fewer binary "windows". Through the use of many "windows,"
the amplitude can be accurately represented by the appropriate
combination of binary values. The subsequent bleaching of the binary
hologram is a linear process and thus no additional harmonics are
contributed. This provides a means by which high efficiency holograms
may be produced without sacrificing signal-to-noise ratio due to non-
linearity. A sufficient number of points is necessary in the binary
hologram in order to minimize the non-linearity of the binary CGH
mapping. When a computer and writing device are available to produce
such binary holograms, subsequent bleaching or phase modulation
greatly improves the efficiency without any adverse effect on signal-