The signal-to-noise ratio in the coherent image of a grating with a rectangular transmission profile is calculated and displayed as a function of the grating frequency relative to the cutoff frequency of the imaging system and as a function of the grating frequency alone. It is shown that the signal-to-noise ratio in the image depends on the object contrast when the average size of the speckle in the image is small compared with the grating constant and that the signal-to-noise ratio approaches asymptotically a constant value independent of the object contrast when the average size of the speckle is large compared with the grating constant. Furthermore, the speckle noise is suppressed when the size of the imaging aperture is increased, thereby enhancing the signal at a given frequency.

© 1989 Optical Society of America

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