A versatile angular shearing interferometer for measurement of spatial coherence

Abstract

Shearing interferometry provides a very convenient method of measuring the spatial (transverse) coherence of optical beams. A wavefront folding interferometer produces an interferogram with shear varying from zero up to the full beam width, however such an interferometer is not ideal for measurement of sources having very low transverse coherence, and measures the second order degree of coherence in only one spatial dimension. In this paper an angular/rotary shearing interferometer for measurement of spatial coherence is presented. The interferometer (shown schematically in the figure) is analogous to that proposed by Armitage and Lohmann [1] for use in measurement of aberrations in optical elements. The plane mirror of one arm of a Michelson type interferometer is replaced by a pair of 45° mirrors such that the return beam is laterally displaced. A second beamsplitter is inserted to recombine this beam with the reference and form the interferometer output. Such an interferometer represents a very convenient and easily aligned wavefront folding interferometer in its own right. Insertion of an image rotating dove prism as indicated in the figure converts the wavefront folding interferometer into an angular (rotary) shearing interferometer, where the shear varies from zero in the centre of the interferogram to a maximum at the edge. For a dove prism rotation angle θ (where θ = 0 is defined as the reflecting hypotenuse of the prism being vertical) a shear angle of 2θ is produced in the interferogram. The shear produced at distance r from the centre of the interferogram is therefore 2r sinθ. For small θ, very low shears and hence low spatial coherence values can be measured, and for θ =90° the maximum shear corresponds to the full beam diameter. An angular shear also enables coherence measurement of beams with anisotropic (with respect to angular co-ordinate) coherence. Note that polarisation rotation within the dove prism can be compensated using quarter wave ‘polarisation coupling’ [1], however the amount of polarisation rotation/introduced elipsicity produced by the dove prism is in practice very small [2].