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We describe significant improvements to a well-established method of obtaining optical sectioning in a conventional wide-field microscope. This method relies on the projection of a single-frequency grid pattern onto an object followed by mathematical manipulation of three images taken with the grid in different phases. Here, we present the use of Bayesian Spectral Analysis to determine accurate estimates of the phase of the grid pattern, permitting rapid and precise calibration of grid location. In common with previous algorithms, multiple images are combined to produce both an optical section and a wide-field image. We describe innovations such as the use of non-uniform phase or least-squares solutions involving more than three images, in conjunction with direct phase estimates obtained using Bayesian Spectral Analysis, to yield images substantially free of artefacts. Auxiliary results, such as a method for determining the tilt of the grid, are also presented. [ABSTRACT FROM AUTHOR]