Phase-change visualization in two-dimensional phase objects with a semiderivative real filter

A method of visualization of phase changes in two-dimensional pure-phase objects by use of two orthogonal Fourier plane filters that realize the half-order differentiation is presented. Real semiderivative filters used in two dimensions and in sequence yield output-image intensity signals proportional to the first derivatives of the input-object phase that appear on a constant background. This nonlinear filtration of spatial frequencies permits the alleviation of the consequences of square-law detection and makes phase changes visible. Phase changes in gradient-index phosphate glass are calculated experimentally. We discuss the accuracy of the proposed method.