Research On Phase Retrieval And Phase Unwrapping Based On Transport Of Intensity Equation At Two Wavelengths

The light wave field contains intensity and phase,where the phase carries more information about the object.Although light intensity information can be measured with a CCD camera,but direct measurement of the phase is still a rather challenging task.Therefore,it is necessary to retrieval phase information using simple measurable intensity information,which is called the phase retrieval technique.At present,this technology has been applied in many fields such as optical measurement,optical phase microscopy,X-ray diffraction imaging,adaptive optics and the like.As a typical non-interference deterministic phase retrieval method,phase retrieval based on the transport of intensity equation is used to establish the quantitative relationship between the variation of light intensity and phase during the propagation.It is only necessary to measure the intensity distribution at different distances along the light wave propagation direction.The phase information can be recovered by solving the equation.This method has the advantages of non-interference,non-iterative,and no complicated optical system,but there are still many problems that need further study.The transport of intensity equation is derived under the paraxial approximation of monochromatic light,so the traditional transport of intensity equation method has limitations under the complicated conditions such as multi-wavelength.In addition,since the transport of intensity equation is only a linear approximation of the more general nonlinear equation described by the Fresnel or Kirchhoff integral square,it is suitable for the case where the imaging distance is small.In the long-distance propagation,the method has the problem of low phase retrieval accuracy.In addition,phase wrapping has always been a difficult problem in interferometry,and the phase retrieval technique based on transport of intensity equation can directly obtain absolute phase information from the intensity information,and there is no problem of phase wrapping.Therefore,the phase unwrapping method based on the transport of intensity equation has the characteristics of easy implementation and path independence.However,the phase unwrapping algorithm has low precision and can only be applied to monochrome light field.In response to the above mentioned issues,the paper has carried out corresponding research.The main research work and innovations are as follows:(1)By considering the correlation constraints between phases at two wavelengths and introducing the idea of synthetic wavelength,a phase retrieval algorithm based on transport of intensity equation at two wavelengths is proposed.At the same time,considering the problem that the proposed two-wavelength transport of intensity equation method has low phase recovery accuracy during long-distance propagation,it is combined with the angular spectrum iterative algorithm to extend the application range of the two-wavelength transport of intensity equation method.Experimental results show that the proposed algorithm can effectively recover phase information at two wavelengths and is not limited by distance.(2)Phase unwrapping based on the transport of intensity equation at two wavelengths.The two-wavelength transport of intensity equation method is applied to the phase unwrapping field,and a phase unwrapping algorithm based on the transport of intensity equation at two wavelengths is proposed.The algorithm only needs to generate the corresponding plane auxiliary light field for a given wrapping phase,and propagate it to the immediate plane to obtain the light field information required for phase reconstruction,and then use the proposed algorithm to unwrap the wrapping phase.The experimental results show that the method not only improves the accuracy of the unwrapping phase,but also has good anti-noise performance.