If the arc lamp in standard display projectors is replaced by lasers, the projector can gain several advantages such as improved color gamut, higher contrast and brightness. Coherent by nature, the laser also adds one significant disadvantage to the projector: the presence of speckle, which manifests itself as noise-like intensity fluctuations over the image. In this paper, we present an overview of our work concerning correlated speckle patterns. We give general formulas for the speckle contrast of the sum of N partially correlated speckle patterns. It is shown how the speckle contrast depends on the correlations between the individual speckle patterns, and for the case of a fully developed speckle pattern we present a general expression for the correlations.
As an example, we look at speckle suppression by discrete rotation of a diffraction pattern on a diffuser. We use a sinusoidal phase grating which has the advantage that the zeroth order can be extinguished without loss of power. Hence, no part of the diffraction pattern remains stationary when rotated. Expressions for correlations are found, with different degrees of generality, which enable us to find expressions for the contrast. Furthermore, the influence of the diffraction pattern's complex amplitude distribution on the correlation and speckle contrast is investigated.