Reduction of Speckle in Coherent Imaging by Spatial Frequency Sampling

One method which has been suggested for reducing speckle in the holographically reconstructed image of a diffusing object is the use of a moving aperture in the pupil plane of the imaging lens (this is equivalent to sampling the spatial frequency spectrum of the object). An expression is derived for the average power spectrum of the speckle in the image of a coherently illuminated diffusing object when a number of exposures are superimposed with a shift of the sampling aperture located in the spatial frequency plane between successive exposures, and experimental results are presented which confirm that an appreciable reduction in speckle can be obtained even when the shift of the sampling aperture between two exposures is less than its dimensions. This analysis is then extended to the case of a rectangular sampling aperture which is moving continuously for the duration of the exposure. The results show that, for a given range of movement, an exposure with a continuously moving aperture should be more effective in suppressing speckle than a series of exposures with the aperture moved in steps by its own width between exposures.