Speckle pattern

A speckle pattern is a granular intensity pattern from coherent wave interference. In stellar imaging, residual wavefront errors produce speckles around the central point spread function.

For a small sinusoidal optical path length error $h_0\cos (2\pi x/\Lambda )$, expand its phase factor to first order. The two exponential harmonics each have field amplitude $i\pi h_0/\lambda$ relative to the unperturbed field, so each speckle has contrast $C=(\pi h_0/\lambda {)}^2$. Its angular displacement is $\lambda /\Lambda$. Here $h_0$ is optical path error, not physical mirror displacement; a reflecting mirror introduces twice its surface displacement in the near-normal limit.