A Fourier transform speckle method to determine the change in angle of illumination

It is analytically shown that the position of the Fourier transform of the speckle pattern produced by a coherently illuminated, diffusely reflecting surface depends upon its angle of illumination. A method is proposed to measure small changes in this angle by doubly exposing the photographic plate with the original and laterally displaced Fourier transforms of the object speckle. The method is well suited for accurate measurements of the wedge angle and tilt of optical surfaces and to determine variations in refractive index or temperature of axially symmetric phase objects.