Phase Retrieval Based On Chromatic Dispersion And Transport Of Intensity Equation In Multi-angle Tilted Light

Intensity and phase are usually used to describe the properties of light field.However,the existing image acquisition system can only measure the intensity change of the light field because of the high oscillation frequency of the light field,but the phase which carries most of the information of the object can not be obtained directly.How to calculate and represent unknown phase information with known intensity distribution,which is called phase retrieval.At present,phase retrieval plays an increasingly important role in many fields,such as adaptive optics,optical measurement,material physics,X-ray diffraction imaging,optical microscopy imaging and so on.As a non-interference non-iterative phase retrieval method,the transport of intensity equation describes the quantitative relationship between the phase of light on the vertical plane of optical axis and the variation of axial intensity in a monochromatic light field.Quantitative phase information can be obtained directly by solving a second-order elliptic partial differential equation.This method has the advantages of non-interference,non-iteration and no phase wrapping problem in general interferometry,but it is also limited by the theoretical premise of monochromatic light.On the other hand,it is necessary to obtain the differential value of the axial intensity in solving the transport of intensity equation,but the value can not be obtained directly.Generally,it requires two or more intensity distributions on the vertical plane of the optical axis,and then approximated by numerical difference.Therefore,the accurate acquisition of intensity image is particularly important.The classical image acquisition system mainly includes 4 f system and single lens system.However,there are two problems in the actual image acquisition:First,intensity image acquisition usually needs to move the object to be tested or CCD,which inevitably leads to slow speed,low accuracy and so on.Secondly,the aperture size of the lens used in the system has a certain restrictive effect,which will affect the resolution of the recovery phase.In view of the above problems,the corresponding improvement algorithm is proposed in this paper.The main research work and innovation are as following:(1)A phase retrieval method based on chromatic dispersion and transport of intensity equation is proposed.The purpose of obtaining focusing and defocusing intensity images without moving mechanically is achieved by setting the light with different central wavelengths to pass through the lens system and image at the same position,and the phase information of an object is calculated from the TIE by combining the relationship between the defocus amount and the wavelength.The proposed method broadens the application of the TIE in multi-wavelength light sources,especially for complex phase reconstruction of natural light scenes in the future.(2)A phase retrieval method based on tilted light modulation with multi-angle is proposed.Introducing multiple sets of tilted light at different angles in phase retrieval based on the transport of intensity equation,by the spatial light modulator loaded with tilted factor,and the plane waves with different wave vectors obliquely incident on the object vertically and evenly,so that the lens aperture of finite size can cover a wider frequency space.The sum of complex fields produced by tilted light with different angles enlarges the pass-bands of the original lens aperture.The proposed method improves the imaging ability of the system in high frequency field without changing the physical parameters of the system lens.