A coherent imaging system images a frame or an object onto a changing diffuser and projects the resulting pattern which generally contains speckles. Using a spatial light modulator (SLM) as the changing diffuser, the speckles in the pattern are suppressed without the need for any other mechanisms. With $M$ random phasor arrays being displayed in the SLM during the integration time of a detector, a suppression factor (Cf) of speckles, 1/√M, is achievable in the projected pattern, which is the sum of the intensity of M uncorrelated patterns. This paper shows both theoretically and in simulations that the Cf of the sum pattern was considerably reduced when two elementary patterns with fully developed speckles were negatively correlated. With the correlation coefficients of the elementary patterns found at [-0.3, -0.25], the Cf of the sum of 10 negatively-correlated speckle patterns was 48% lower than the Cf of the sum of 10\,uncorrelated speckle patterns. The negatively correlated patterns can be implemented using spatial light modulators or diffractive optical elements, and are used to suppress speckle noise in digital holography, laser projection display, and holographic display projections with relatively high efficiency.
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