Design and analysis of modified version of double aperture speckle interferometer consisting of holographic optical element: Application to measurement of in plane displacement component

Abstract

Duffy's double aperture speckle interferometer consists of two apertures placed symmetrically over an imaging lens and is used to measure in plane displacement component parallel to the line joining the two apertures using speckle photography. Diffraction limited imaging performance almost free from all monochromatic aberration over the two apertures is desirable for accurate measurement. In present work twin apertures are placed over a compact holographic lens (hololens) system. Lens system consists of two properly recorded and played back holographic lenses cemented together with proper alignment. Recording and play back geometry of holographic lenses has been designed for ease of alignment similar that of an on-axis imaging performance obtained by a conventional lens. Experimental results on measurement of in plane displacement along a line joining the two apertures using the designed interferometer is presented and compared with the actual displacement given to a diffuser between the two exposures. Further, results on measurement of in-plane displacement by analyzing speckle correlation fringes contained in zero order and ±1st order are presented to show that measurement made by analyzing fringes contained in ±1st order give better result than that of results obtained by analyzing speckle correlation fringes contained in zero order. In plane displacement measurement carried out by measuring fringe width of young's fringes contained in ±1st order provides an experimental technique to avoid cumbersome mathematical calculation for correction in the measured value of fringe spacing as suggested by several researchers.