Abstract

It is known that the cumbersome ${2}\pi$ correction is needed in the traditional module-${2}\pi$ method (i.e., the phase wrapping method) due to the ${2}\pi$ deviation of the phase modulation depth of spatial light modulators (SLMs). To avoid the cumbersome ${2}\pi$ correction in the module-${2}\pi$ method, this paper proposes a module-${\rm n}\pi$ method, and it can directly utilize any full-field phase modulation depth. First, for a Gaussian phase with a phase depth of 30 rad, wrapped by the module-${3.6}\pi$, it is reconstructed with the root-mean-square (RMS) values of its phase response are ${0.1006}\lambda$ (for the Twyman–Green interferometer) and ${0.1101}\lambda$ (for the Shack–Hartmann wavefront sensor method), respectively, which proves that the monitoring accuracy is relatively consistent. Subsequently, some comparative experiments based on the traditional module-${2}\pi$ are performed. The experimental results show that the RMS values of its phase response are ${0.8886}\lambda$ (for a modulation depth of 11.3 rad) and ${0.2261}\lambda$ (for a modulation depth of 6.28 rad), respectively. All the results have proved that the SLM with a phase modulation depth exceeding ${2}\pi$ (e.g., 11.3 rad) has more prominent advantages. More specifically, increasing the SLM’s phase modulation depth can effectively reduce the fringe orders of the wrapped patterns generated by the module-${\rm n}\pi$ method. With the further reduction of the fringe orders, the influence of the fly-back zone error on the wavefront phase modulation is reduced, that is, the modulation accuracy is improved (the RMS values are reduced from ${0.2261}\lambda$ to ${0.1006}\lambda$). Different from the traditional module-${2}\pi$ method, there is no need to consider the problems of the SLMs’ over modulation or the insufficient modulation in the module-${\rm n}\pi$ method. Furthermore, it avoids the cumbersome ${2}\pi$ correction process, which will make the use of the SLM more convenient.

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