Research On Diffraction Properties Of Random Sampling And Random Scattering Fields As Well As Their Applications In Wavefront Measurement And Control

Scattering is one of the common phenomenons in physics.For example,light passing through a random scattering medium is affected by the random scattering.Wavefront information(including amplitude and phase)will be scrambled by the random scattering events,which often brings some difficulties to imaging.Hence,the random scattering has always been considered as a limiting condition for imaging.In addition,the object to be measured is often hidden inside the scattering media or wrapped by scattering media,how to overcome the scattering effects to realize focusing and imaging through the scattering media is a research hotspot in modern optics.Although the amplitude and phase information of the object wavefront is hidden in the random scattering fields,the random scattering enhances the random process and the intensity variation of the output scattering fields.The diversities of the recorded intensities can be obtained by designing a random sampling mask to modulate the wavefront.At the same time,the enhanced intensity variation may be help for improving the phase retrieval efficiency and accuracy in the field of the coherent diffraction imaging and the quantitative microscopy.Combining with the constraints on the sampling plane and the captured intensities with enhanced variations on the recording plane,wavefront measurement(or wavefront sensing)can be realized directly.Moreover,there are abundant amplitude,phase and polarization information in these random scattering fields that provides the favorable conditions for studying the phase singularities and polarization singularities.Such as for a more general nondiffracting beam,named the random nondiffracting beam,has drawn a lot of attentions because of its characteristic random vortex distributions.The random nondiffracting beam can be considered to be a good random array of optical vortices(or phase singularities),which are very suited for being used as writing beams to optically induce longitudinally elongated two-dimensional random photonic structures and to research Anderson localization.Recently,a method to overcome the random scattering effect based on the measurement of the transmission matrix(TM)of the random scattering media has been presented.The scattering process of light propagation in the random scattering media is linear and deterministic.It is recognized that the changes of complex amplitudes and polarization states of the incident light fields and the output light fields through the scattering media can be used to characterize the transmission properties of the scattering media.TM is a complex coefficient matrix that characterizes the deterministic relationships between the input and output light fields.Further,the vector transmission matrix(VTM)can characterize the changes of the complex amplitudes and polarization states of the input fields and the output fields through the random scattering media.Wavefront control,focusing and scanning imaging through the scattering media can be also realized based on the measured TM or VTM,and the scattering effects will not be the restrictive conditions for imaging.This dissertation mainly focuses on the random-sampling-based lensless wavefront measurement techniques,the diffraction characteristics of random nondiffracting beams,the characterization and the measurement of the VTM of the random scattering media and realizing arbitrary vector beams focusing through the random scattering media.The research contents of the main chapters are listed as follows:1.Basic concepts and problems about the optical information transmission,recording,acquisition,imaging and scattering are outlined.This chapter summarizes the research background,latest progress and applications of phase retrieval with random wavefront modulation,random nondiffracting beams and wavefront control through the random scattering media.2.Transmission theory and numerical calculation of light propagating through the homogeneous medium and inhomogeneous medium are studied.This chapter mainly focuses on the multiple phase screens method which can be adopted to simulate the laser propagating through the inhomogeneous medium especially for the turbulent atmosphere.And the numerical simulation of Laguerre-Gauss(LG)vortex beam propagating through the turbulent atmosphere based on the multiple phase screens method has been demonstrated by using Matlab.The LG vortex beam will be broadened when propgating through the turbulence atmosphere.In addition,all the amplitude profile and phase profile of this LG vortex beam will encounter perturbation.3.The methods for numerically calculating the phase singularities and polarization singularities in the random scattering fields are reviewed.Firstly,we describe the definition of the phase singularities,where the phase singularities can be characterized by a path integral along a closed loop.Secondly,the phase singularities distributions around the singularities of the diffraction fields of the Laguerre-Gaussian vortex beams and the Gaussian vortex beams have been investigated.The diffraction field of a high-charge vortex will always appear as an assembly of a series of phase singularities(or unity-charge vortices)in singularities.At the same time,the algebraic sum of all the phase singularities keeps a constant and is equal to the topological charge of the vortex beam.Then the relation of the phase singularities density in a speckle field and the diffraction distance is analyzed.It can be found that the phase singularities density can be determined by the scattering area,wavelength and the diffraction distance.Next,we introduce the polarization characteristics of the light which can be represented by Jones vector and Stokes vector.And typical polarization singularities C points(S1=S2=0)and L line(S3=0)have been calculated based on the Stokes parameters.The C points density of the polarization speckle field has been quantitively evaluated,which is about twice as much as the phase singularities density of each polarization component of the polarization speckle field.4.A wavefront measurement method based on a spatial light modulator(SLM)and an incremental binary random sampling(IBRS)algorithm is presented.In this method,the recording setup is just composed by a transmittance SLM and an image sensor.The tested wavefront incident to the SLM plane can be quantitatively retrieved from the diffraction intensities of the wavefront passed through the SLM displaying an incremental binary random sampling pattern.Because only two modulation states(opaque and transparent)of the SLM are used,the method does not need to know the concrete modulation function of the SLM in advance.In addition,by introducing the concept of the incremental random sampling into wavefront(or wavefront measurement),the adaptability of phase retrieval based on the diffraction intensities is significantly improved.Some experimental results are given for demonstrating the feasibility of our method.5.The evolutionary and statistical properties of the optical vortices that exist in random nondiffracting beams(RNDBs)are analyzed.It is found that the phase singularities(PSs)in the RNDBs originate from the zero rings of Bessel beams with the same ring-shaped spatial spectrum structure(but with zero phase fluctuations)as those of the RNDBs provided.It is also found that the average PSs density or vortex density is determined by the average duration of the zero rings of the corresponding Bessel function.According to this model,we successfully derived an analytical formula for quantitatively predicting the PSs density of the RNDBs.This formula could be helpful for understanding and designing RNDBs in their applications.6.The characterization and the fast measurement of complex vector transmission matrix (VTM)of the random scattering media are studied.Firstly,the different characterization methods of the VTM and the principle of vector spatial light modulator(VSLM)are quantitatively described.A system for fast measuring the complex VTM of the scattering media based on a VSLM and a two-channel angular-multiplexing holographic polarization recording geometry is set up.The VSLM,which serves as a vital unit of our VTM measuring system,is composed of a SLM and a small-angle birefringent beam splitter closing to the back of the SLM.At the same time,the singularity of the measured VTM is investigated.And the average phase singularities densities of the four components of the VTM corresponding to each input point are about half of the C point densities in polarization speckle fields generated from the two orthogonal polarization components of the same input point.7.Two methods for realizing arbitrary vector beams focusing through the scattering media are proposed.One is the numerical filtering-based vector point spread function engineering.The vector point spread function concepts is generalized to the vector wavefront control through the random scattering media.In this method,a conjugate transpose operation need to be firstly performed on the measured complex VTM,then a numerical filtering operation need to be carried out on the virtual Fourier plane of each output mode of the transposed VTM to calculate a desired VTM.Arbitrary vector beams can be generated on the output plane by designing the required input vector field extracted from the desired VTM directly.The other one is the discrete convolution-based vector point spread function engineering.In this method,arbitrary vector beams focusing can be generated by calculating the corresponding input vector fields,where the required input fields can be obtained by combining a well-defined discrete vector point spread function and the conjugate transpose of the measured complex VTM without complicate Fourier transforms.Meanwhile,the redundancy for calculating the required input vector fields has been reduced.Further,the second method can be applied to fast focus the big size or arbitrary shape output vector field through the scattering media.However,the numerical filtering-based vector point spread function engineering method can guarantee the fine structures of the focused vector beams.