Abstract

We propose a new kind of shearing interferometry employing laser illumination, heterodyne detection, and digital shearing. An array of heterodyne measurements are made of an optical field reflected from a distant coherently illuminated object but are perturbed by phase errors. As the object rotates slightly or translates, additional realizations of the optical field, but with the same phase errors, are measured. The product of the optical field with the complex conjugate of a sheared version of the optical field is digitally computed and averaged over the realizations. This is performed for two orthogonal shears, and the phases of the resulting averages approximate phase differences of the phase-error function. The phase-error function is then reconstructed from the phase differences by means of the same reconstruction algorithms as are used in conventional shearing (or Hartmann) wavefront sensors. The phase-error function, thus computed, can be digitally subtracted from the phase of each of the realizations of the measured optical fields and yields corrected measurements from which diffraction-limited, coherent, speckled images of the object can be computed by Fourier (or Fresnel) transformation. The squared magnitudes of these speckled images can be averaged to yield a speckle-free, incoherent image of the object.

© 1990 Optical Society of America