In phase-shifting digital holographic interferometry for measuring a displacement distribution of an object, holograms and reconstructed images have speckle noise and they provide large error in the calculation of displacement analysis. In order to decrease the effect of speckle noise, we previously proposed a new method using windowed holograms. In this paper, we propose a new averaging method of the obtained phase-difference values. Many phase-difference values at a point obtained by different windows for a hologram are averaged by considering the weight for each phase value. The weight is changed as the m-th power of the absolute amplitude of the complex amplitude of the reconstructed object. As the result, when the number n of the windowed holograms becomes larger, the standard deviation of the error becomes smaller. When the power m is 2, the error becomes the minimum. The standard deviation of the errors in the case of a flat plate with 316 nano-meter out-of-plane displacement is 88 pico-meter when n=1024 and m=2.

Image resolution is one of the most important performance specifications of aerial display techniques. However, there is no standard method for evaluating the aerial image resolution. In this paper, we propose a method for measuring the modulation transfer function (MTF) of an aerial imaging system based on the slanted knife edge method. We hypothesize that aerial images have a different blur function from standard camera images. In order to explore this, we simulate blurred slanted knife edge images by convolving two types of blur functions. Furthermore, the MTF curves of the aerial image formed using different retro-reflectors are compared using the proposed method.

SUMMARYThis paper reports on the relationships between the performance of retro-reflectors and the sharpness of an aerial image formed with aerial imaging by retro-reflection (AIRR). We have measured the retroreflector divergence angle and evaluated aerial image sharpness by use of the contrast-transfer function. It is found that the divergence angle of the retro-reflected light is strongly related to the sharpness of the aerial image formed with AIRR.

Phase-shifting digital holographic interferometry is a new method to measure displacement distribution on the surface of an object. Usually holography has speckle noise, which leads to a large error in the analysis of displacement and strain distributions. We previously proposed windowed phase-shifting digital holographic interferometry (windowed PSDHI). The use of this method leads to accurate displacement analysis, decreasing the effect of speckle patterns. However, noise reduction involves a defect, which renders the spatial resolution low. In this paper, by comparing the conventional noise reduction method using spatial averaging with the windowed PSDHI on spatial resolution, the effectiveness of noise reduction is discussed.