In this paper,by using the tools of second order smooth module,we discusses the conformal mapping from a unit circle onto a simply connected domain enclosed by a smooth Jordan curve L ,and further improves the Kellog...In this paper,by using the tools of second order smooth module,we discusses the conformal mapping from a unit circle onto a simply connected domain enclosed by a smooth Jordan curve L ,and further improves the Kellogg theorem.展开更多
We propose a new algorithm for wavefront sensing based on binary intensity modulation. The algorithm is based on the fact that a wavefront can be expended with a series of orthogonal and binary functions, the Walsh se...We propose a new algorithm for wavefront sensing based on binary intensity modulation. The algorithm is based on the fact that a wavefront can be expended with a series of orthogonal and binary functions, the Walsh series. We use a spatial light modulator（SLM） to produce different binary-intensity-modulation patterns which are the simple linear transformation of the Walsh series. The optical fields under different binary-intensity-modulation patterns are detected with a photodiode.The relationships between the incident wavefront modulated with the patterns and their optical fields are built to determinate the coefficients of the Walsh series. More detailed and strict relationship equations are established with the algorithm by adding new modulation patterns according to the properties of the Walsh functions. An exact value can be acquired by solving the equations. Finally, with the help of phase unwrapping and smoothing, the wavefront can be reconstructed. The advantage of the algorithm is providing an analytical solution for the coefficients of the Walsh series to reconstruct the wavefront. The simulation experiments are presented and the effectiveness of the algorithm is demonstrated.展开更多
文摘In this paper,by using the tools of second order smooth module,we discusses the conformal mapping from a unit circle onto a simply connected domain enclosed by a smooth Jordan curve L ,and further improves the Kellogg theorem.
基金Project supported by the National Innovation Fund of Chinese Academy of Sciences(Grant No.CXJJ-16M208)the Preeminent Youth Fund of Sichuan Province,China(Grant No.2012JQ0012)the Outstanding Youth Science Fund of Chinese Academy of Sciences
文摘We propose a new algorithm for wavefront sensing based on binary intensity modulation. The algorithm is based on the fact that a wavefront can be expended with a series of orthogonal and binary functions, the Walsh series. We use a spatial light modulator（SLM） to produce different binary-intensity-modulation patterns which are the simple linear transformation of the Walsh series. The optical fields under different binary-intensity-modulation patterns are detected with a photodiode.The relationships between the incident wavefront modulated with the patterns and their optical fields are built to determinate the coefficients of the Walsh series. More detailed and strict relationship equations are established with the algorithm by adding new modulation patterns according to the properties of the Walsh functions. An exact value can be acquired by solving the equations. Finally, with the help of phase unwrapping and smoothing, the wavefront can be reconstructed. The advantage of the algorithm is providing an analytical solution for the coefficients of the Walsh series to reconstruct the wavefront. The simulation experiments are presented and the effectiveness of the algorithm is demonstrated.
