Measurement And Application On Polarimetry Of The Probability Density Of The Polarization Of Light Field

Compared with the theory of the traditional polarization measurement,the theory of the probability density of the polarization of light field can not only be applied to traditional polarization measurement field,but also has a great potential to be applied to the weak light polarization measurement field,quantum entanglement measurement and so on,due to considering the quantum properties of photon.The current theory has established the relationship between the measured probability density of the light field polarization and the point spread function of the pinhole.However,the ideal Jones matrix of the specific phase modulator in measurement system does not appear in the above theoretical formula,and the specific phase modulator in measurement should be perfect and error-free.Because the Jones matrix of phase modulator cannot be measured directly,previous researcher use the ideal Jones matrix during the data process.So,they cannot calibrate the processing error of phase modulator and the error of the measurement system by experiment,which results in the low accuracy of the polarization measurement(the measurement of traditional Stokes parameters of the light and the probability density of polarization of a light field).Therefore,this paper establishes a theory and a model which shows the relationship between the probability density of light polarization and the Mueller matrix of the phase modulator.By measuring the point spread function of a pinhole and the Mueller matrix of phase modulator,the system error calibration and high-accuracy of the measured probability density of the light polarization can be achieved.Furthermore,we apply this theory and model to the measurement of the polarization of the traditional light field.The three research aspects of this paper are as follows.(1)Establishing the theory and model contains the relationship between the probability density of the light polarization and the Mueller matrix of the modulator.It overcomes the problems that the current theory and model hide the Jones matrix of the phase modulator,and the problems that the system error cannot be calibrated,which due to the limitation of measuring Jones matrix of the modulator.Moreover,the theory and model in this paper is suitable for the measurement system using arbitrary phase modulator.(2)The simulation study and the verification of the theory and model.Matlab program was used to simulate the theory and model established in this paper.Firstly,we established the relationship between the Jones matrix and the Mueller matrix of the phase modulator.We used the ideal phase modulator which was used by previous researchers(Triple-stress engineering optics,SEO),to achieve the simulating point spread function of the pinhole and the simulating probability density distribution of the light polarization.The simulation results were aligned with the simulation result of the previous research(ideal and error-free system),which can verify the correctness of our theory and model.Then,by using several different phase modulators to simulate the model,the applicability of the model was achieved:not only the SEO is applicable for the model,but also arbitrary phase modulator which has spatial-distribution Mueller matrix,whose parameters satisfy the certain relationship is applicable for the model.(3)The experiment study on the measurement of the probability density of the light polarization,and the application in polarimetry.we used the phase modulator processed in the same condition as the previous literatures to do comparative experiments.Because of the processing error and the experimental error of the Mueller matrix of phase modulator,first of all we calibrated the Mueller matrix of the phase modulator,and then we achieved the normalized Stokes vector measurement results of the incident light by measuring the point spread function of the experiment system,and we established the method based on the probability density distribution function of the light polarization.By comparing the Stokes vector measurement results before and after the calibration,it indicates that the right measurement results can not be achieved before calibration,but after calibration,the absolute accuracy of the measurement of the normalized Stokes vector parameters s₁,s₂and s₃were 0.0357,0.0445 and 0.0799 respectively.