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%.

An effective method of speckle suppression using one 2D diffractive optical element (DOE) moving with constant velocity based on the periodic Barker code sequence is developed. We prove that this method has the same optical parameters as the method based on two 1D Barker code DOEs stretched and moving in orthogonal directions. We also show that DOE movement in a special direction allows the full numerical aperture of the objective lens to be used for speckle averaging by angle diversity. It is found that the 2D DOE based on a Barker code of length of 13 allows the speckle contrast to be decreased below the sensitivity of the human eye with optical losses of less than 10%.

A method for speckle suppression based on Barker code and M-sequence code diffractive optical elements (DOEs) is analyzed. An analytical formula for the dependence of speckle contrast on the wavelength of the laser illumination is derived. It is shown that speckle contrast has a wide maximum around the optimal wavelength that makes it possible to obtain large speckle suppression by using only one DOE for red, green, and blue laser illumination. Optical schemes for implementing this method are analyzed. It is shown that the method can use a simple liquid-crystal panel for phase rotation instead of a moving DOE; however, this approach requires a high frequency of liquid-crystal switching. A simple optical scheme is proposed using a 1D Barker code DOE and a simple 1D liquid-crystal panel, which does not require a high frequency of liquid-crystal switching or high-accuracy DOE movement.

This paper reports the findings from an experimental evaluation of speckle suppression efficiency using a method based on a moving 2D Barker code diffractive optical element (DOE). The optical setup and the optical scheme parameters of the method are presented. A speckle contrast of ~4.4-5.3% and speckle suppression coefficient (coefficient of speckle contrast reduction) of k>8 was obtained in experiments. However, the experimentally obtained speckle suppression coefficient was approximately 1.5 times smaller than the theoretical prediction. It is speculated that the discrepancy between the theoretical and the experimental data is due to an inexact match between the optical setup and the optimal optical parameters of the method. Analysis of the experimental data revealed that once the optical scheme is optimized, it will be possible to obtain a speckle suppression that is closer to the theoretical prediction.