Bessel Optical Wavefront Detection Based On The Light Intensity Transfer Equation

Bessel beam is widely applicated in laser processing?particle manipulating?microscopic imaging and other fields as non-diffraction beam.Axicon is a simple and effective element to generate Bessel beam.However,The application of Bessel beam will be limited because the intensity distribution and non-diffraction characteristic of the beam can be influenced by the machining and misalignment errors of axicon.So the wavefront dectection and compensation for Bessel beam is necessary.Transport of intensity equation(TIE),which is a phase retrieval method,can retrive phase using only two axial intensity images with fast speed and high accuracy.The new idea is proposed that the TIE can be used to retrieve the phase of Bessel beam,then the phase compensation for Bessel beam can be done.Also,the relationship between aberration and effective non-diffraction distance has been established,and the theory is proved correct through experiment.The main search work and contribution are as follows:Based on Kirchhoff's diffraction theory and Virtuallab software,the influence of incident illumination's phase?the axicon's misalignment and machining error on Bessel beam's intensity distribution in different propagation distance have been studied.The advantages of TIE in data processing speed and phase retrieval accuracy compared with Gerchberg-Saxton(GS)algorithm have been shown through simulation,and the influence of two intensity images's axial distance and noise on TIE's phase retrieval accuracy have been analyzed.The theoretical research and simulation of noise reduction for TIE using Savitzky-Golay differential filter has been done.The phase of Bessel beam generated in experiment is retrived by TIE and the result fits well with the phase measured by SID4 wavefront detector.The phase of Bessel beam has been given when axicon exists misalignment and machining error,and the relationship between aberration and effective non-diffraction distance is summarized.The effective non-diffraction distance of the Bessel beam has been measured(zeff=160mm)and found to be consistent with the theoretical analysis(zeff?200mm).