The theory of speckle noise in a scanning beam is presented. The general formulas for the calculation of speckle contrast, which apply to any scanning display, are obtained. It is shown that the main requirement for successful speckle suppression in a scanning display is a narrow autocorrelation peak and low sidelobe level in the autocorrelation function of the complex amplitude distribution across a scanning light beam. The simple formulas for speckle contrast for a beam with a narrow autocorrelation function peak were obtained. It was shown that application of a diffractive optical element (DOE) with a Barker code phase shape could use only natural display scanning motion for speckle suppression. DOE with a Barker code phase shape has a small size and may be deposited on the light modulator inside the depth of the focus of the reflected beam area, and therefore, it does not need an additional image plane and complicated relay optics.

The mathematical model of a speckle-suppression method based on two Barker code-type diffractive optical elements (DOEs) moving in orthogonal directions is developed. The analytic formulae for speckle suppression efficiency are obtained. The model indicates that the one pair of DOEs can be used for laser beams of different colors. The speckle contrast is not dependent on the distance from the viewer to the screen until the distance decreases below the distance where the spatial resolution of the eye on the screen is less than the length of the image of the DOE structure period on the screen. The analysis of the simulated results demonstrates that the method can decrease the speckle contrast to less than 5%, which is below human eye sensitivity, with an optical efficiency greater than 90%.

Aberration and defocusing effects in the mechanism of speckle suppression in laser projection displays were studied using the Fresnel approximation and the thin lens model. The analysis was performed with the assumption that aberrations change only the phase (and not the amplitude) in the rear principal plane of the display projection system. The analysis showed that aberrations should not have any influence on speckle contrast. It also showed that a screen shift relative to the image plane (defocusing) results only in a rescaling of the scanning beam autocorrelation function, which is equivalent to refocusing the objective lens to a new position of the screen. The optimal beam shape for optimal speckle suppression was also studied. A homogeneous field intensity distribution in the spatial frequency domain was found to provide close to the best speckle suppression.

An optical scheme for speckle suppression using two or three partially coherent beams in a projection system is proposed. Diffractive optical elements (DOE) placed in the intermediate image plane create several beams carrying the image to a screen. Transparent plates of different thicknesses are placed in the Fourier plane of the projective lens and used for beam decorrelation. The coherence matrix algorithm for speckle suppression is used to calculate the speckle contrast ratio. It is shown that for a small decorrelation length and using the same maximum thickness of the transparent plates, two partially coherent beams would provide better suppression than three beams with different diffraction orders. However, for a large decorrelation length, the three beam setup provides better speckle suppression for all three colors examined with a suppression coefficient close to theoretical limits. Verification of speckle suppression using three-beam decorrelation is reported.

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