Spatial Phase Modulation of Wavefronts in Spatial Filtering and Holography

Spatial phase modulation of wavefronts as used in holography and in spatial filtering is treated, and means of preventing or reducing noise and distortion are discussed. The phase index of modulation must be less than 0.2 rad to prevent intermodulation noise if a square-law detector is used. Phase holograms satisfy this requirement and, with care, so do spatial filters. In spatial filtering, however, an intolerable amount of distortion is introduced because the upper range of intensity levels of the fringe subcarrier exceeds the dynamic range of the recorder-modulator (photographic plates in this study). The impulse responses of spatial phase modulation filters show the effects of this distortion. Filters using spatial amplitude modulation have the same distortion but it is reduced because of the increasing opacity of the film in the overexposed regions. Simple blocking of the regions producing distortions effectively reduces the noise in the impulse response of the filter.