Displacement and its derivatives measurement from a single fringe pattern in coherent optical techniques

In this paper, displacement and displacement derivatives measurement methods are proposed for digital holographic and speckle pattern interferometry. A complex-phasor method is proposed to determine high quality wrapped phase maps in digital holographic interferometry. A Teager operator based phase derivative determination method is developed to determine unwrapped slope maps from a reconstructed complex field obtained from complex phasors method. Since this method is not suitable for direct slope measurements from a single fringe pattern, a novel method to determine phase derivatives from fringe density and fringe orientation map is developed. In addition, a novel regularized phase tracker model for phase demodulation from a single fringe pattern is proposed. This model utilizes predetermined phase derivatives values so it requires less computation time. The proposed methods are validated with corresponding experiments and results show that they are accurate and robust against speckle noise. The proposed methods have common advantages that they require only one frame at every deformed state and do not require any phase shifting. Hence the methods are suitable for real time dynamic measurements.