An Image Deblurring Method Using Diffraction Gratings

This paper has two major aims; to show a method for making image deblurring masks from simple Ronchi ruling diffraction gratings, and second, to show a simple means for introducing noise-reducing redundancy into an optical processing system when the processing is a one-dimensional operation, as in the case of deconvolution of a one-dimensionally blurred image. Yu has described a method for introducing such redundancy by the use of point source white light [ 11. He used diffraction gratings to disperse a white light source into spectral components that travel @fferent paths in the optical system. The signal S(X) is processed and the additional dimension, y, is used for wavelength dispersion. He showed that a spatial filter of the form Hcf,, y) can be constructed for one dimensional processing, where, as a function of fX, the filter is just the required structure, and as a function of y, the filter retains the same form but changes in scale to accommodate the wavelength variation, since each y = constant section of the filter receives a different wavelength. A similar system was described by Goedgebuer and Gazeu [2] in which prisms are used for dispersion and subsequent undispersion of the light. In either case, the filter must vary by a scaling factor along the y direction. The method we describe for introduction of redundancy employs an old procedure, the use of an incoherent line source, along with some refinements. Holographic complex spatial filters are typically made by recording, with a coherent beam, the Fourier transform of an object distribution. The object is of course then the impulse response of the spatial filter. This procedure assumes that one has available at the beginning, as a transparency, the impulse response, This is normally the case with matched filters, but is generally not the case otherwise. Alternatively, one may use computer methods to produce the filter, but the method is more cumbersome. For image deblurring, the impulse response is typically not available as a photographic transparency; thus, one must resort to other means to produce a deblurring filter. It has been previously shown that a deblurring function can be generated from simple Ronchi rulings by means of spatial filtering [3]. We show here that appropriate deblurring functions (either impulse response or transfer functions) can be generated in other ways from Ronchi rulings.