Spatiotemporal phase-shifting method for interferograms of apertures with arbitrary shape

Phase-shifting interferometry is a highly sensitive non-contact optical measurement method that has been widely used in the field of precision measurement. The spatiotemporal phase-shifting method (ST-PSM) is a phase-shifting algorithm known for its high accuracy, which can avoid periodic errors that are typical of traditional phase-shifting algorithms. This makes it suitable for use in the presence of uneven background light intensity, modulation fluctuations and phase-shifting errors, as well as for measuring distorted interferometric fringe images. However, the interpolation fitting step of this method requires the interferogram to be in a rectangular region, which makes it difficult to measure the complete surface shape of optical elements with non-rectangular apertures. To address this limitation, a novel approach that combined the interferogram spreading technology with the ST-PSM method was proposed. This involved spreading the interferogram into a rectangle, which enabled the ST-PSM method to extract the phase and obtain the complete surface shape information. Numerical simulations and experimental results show that for interferograms with the same shape, the peak-valley values and root mean square values of the wave surface measured by the ST-PSM method with spreading are more accurate than those obtained by using the ST-PSM method without spreading. Taking the circle as an example, the peak-valley value decreases from 0.123 6 λ to 0.044 6 λ after extension, and the root mean square value decreases from 0.011 7 λ to 0.010 9 λ (where λ is 633 nm). The above results demonstrate that the proposed method can be used for accurate measurement of non-rectangular optical elements.