Optical-field correction with deformable mirrors can be accomplished by correction of both amplitude and phase. As a result of developments over the past 20 years, phase correction with deformable mirrors has become a mature technology. We discuss simply the phase correction when it is concerned with field correction. The basic principle of amplitude correction with deformable mirrors is that if a certain phase distribution is constructed at the deformable mirror, after a vacuum diffraction, a certain amplitude distribution can be obtained. Some algorithms for implementing the principle have been put forward by several researchers [ T. T. Karr, Proc. Soc. Photo-Opt. Instrum. Eng. 1221, 26 ( 1990); Wang Kai-yun et al., Proc. Soc. Photo-Opt. Instrum. Eng. 1628, 244 ( 1992)]. But there are two problems that need to be solved. The first is that the vacuum path is too long. The second is that the precisions of these algorithms are relatively low. We describe a new algorithm, which not only yields a 1–2 order-of-magnitude reduction in the vacuum distance but also improves the amplitude correction precision.
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