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-