Digital phase-stepping holographic interferometry in measuring 2-D density fields

This paper presents a holographic interferometer technique for measuring transparent (2-D or quasi 2-D) density fields. To be able to study the realization of such a field at a certain moment of time, the field is frozen on a holographic plate. During the reconstruction of the density field from the hologram the length of the path traversed by the reconstruction beam is diminished in equal steps by applying a computer controlled voltage to a piezo-electric crystal that translates a mirror. Four phase-stepped interferograms resulting from this pathlength variation are digitized and serve as input to an algorithm for computing the phase surface. The method is illustrated by measuring the basically 2-D density field existing around a heated horizontal cylinder in free convection.List of symbols wavelength - x, y cartesian coordinate system - phase - phase step - K Gladstone-Dale constant - L width of 2-D density field - density - ₀ density at reference conditions - I₀, I₁, I₂, I₃ recorded interferograms - I_mod modulation intensity - I_bias bias intensity - N numerator determining tan { (x, y)} - D denominator determining tan { (x, y)} - dimensionless temperature - T temperature - T_c temperature of cylinder - T temperature of environment - p pressure - R gas constant