Volume moire tomography based on projection extraction by spatial phase shifting of double crossed gratings

摘要

To realize volume moire tomography (VMT) for the real three-dimensional (3D) diagnosis of combustion fields, according to 3D filtered back projection (FBP) reconstruction algorithm, the radial derivatives of the projected phase should be measured firstly. In this paper, a simple spatial phase-shifting moire deflectometry with double cross gratings is presented to measure the radial first-order derivative of the projected phase. Based on scalar diffraction theory, the explicit analytical intensity distributions of moire patterns on different diffracted orders are derived, and the spatial shifting characteristics are analyzed. The results indicate that the first-order derivatives of the projected phase in two mutually perpendicular directions are involved in moire patterns, which can be combined to compute the radial first-order derivative. And multiple spatial phase-shifted moire patterns can be simultaneously obtained; the phase-shifted values are determined by the parameters of the system. A four-step phase-shifting algorithm is proposed for phase extraction, and its accuracy is proved by numerical simulations. Finally, the moir, deflectometry is used to measure the radial first-order derivative of projected phase of a propane flame with plane incident wave, and the 3D temperature distribution is reconstructed. (C) 2017 Elsevier B.V. All rights reserved.