Measurement of arbitrary apertures by near-field diffraction digital holography and phase-visibility-modulating interferometry

The lack of generality and accuracy of experimental methods for measuring apertures is a notable problem that has to be addressed. Most of the current approaches measure circular apertures directly using geometric tools. This paper presents a method for calculating the arbitrary shape of apertures with high resolution and accuracy using digital holography and near-field diffraction theory. It applies a back-propagation Fresnel diffraction algorithm to a diffracted optical field of an arbitrary aperture. The complex amplitude of the diffracted field is measured with high resolution and accuracy using the recent automated Phase-Visibility-Modulating Interferometry (PVMI) method. The automated PVMI is implemented in a triple-aperture common-path interferometer (TACPI) and applied for the first time to digital holography. To the best of our knowledge, it has never been used to measure arbitrary apertures with high accuracy and resolution. The TACPI is based on a $4f$ optical system using a 2D grating in the Fourier plane to recombine three optical beams at the output plane that were present in the input plane. On–off modulation (OOM) is applied to the three beams entering the TACPI to implement the PVMI method. The automation of OOM allows high accuracy and resolution in the so-called automated PVMI. The present approach is explained and demonstrated experimentally for some symmetric and non-symmetric apertures. The measurement uncertainty is 0.01 mm for arbitrary apertures within the diameters $(1.5,8)\mathrm{mm}$.