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-