Study On Measurement Method Of Optical Freeform Surfaces Based On Fringe Deflectometry

Optical freeform surfaces can be employed to realize new optical function that cannot be realized by traditional optical components,which has great research values and wide application prospect.The functionality and optical performance of the freeform surfaces largely depends on their form accuracy.Therefore,the main objective of form measurement,form accuracy evaluation and form error compensation is to improve the form accuracy of the freeform surfaces.Moreover,A remounting process is necessary for compensating workpieces after off-machine measurement.Therefore,the positioning of freeform surfaces with high precision is an important step of surface measurement and form error compensation.However,due to its complexity and non-rotational symmetry,there are no effective methods to measure the form accuracy and calculate the position of the freeform surfaces.Therefore,the lack of effective measuring method and location method of freeform surfaces limits its improvement of form accuracy and application range.In addition,for optical freeform surface lenses,the users often pay more attention to their optical properties.However,the lack of effective measurement and evaluation methods of optical freeform surface lenses has limited the further development and applications.On the basis of the analysis above,the measurement and positioning method of optical freeform surfaces is studied based on the fringe deflectometry in reflection and transmission.The studies in this thesis can be summarized as follows:1)To compensate for the phase error caused by the Gamma effect of the liquid crystal display(LCD)and CCD camera in fringe deflectometry system,a nonlinear gray scale polynomial response model of the camera and display was established.By mathematical deviation,the phase error distribution law was deduced,and a four-times four-step phase error compensation method was proposed to compensate for phase error caused by the Gamma effect.By theoretical deduction and simulation analysis,it was proved that the four-times four-step phase error compensation method can reduce the phase error by 98.8%,and the phase precision can meet the requirement of phase accuracy of fringe deflection method.2)Using the high sensitivity of the fringe to the surface change in reflected fringe deflectometry,a mathematical model of the distorted fringe captured by the camera and the orientation of the surface under test was established.Based on this model,a high positioning method of optical freeform surface based on fringe deflection was then proposed.This positioning method could solve the surface shape error evaluation,remounting process,and optical alignment of optical freeform surface effectively.It was proved by experimental results that the proposed positioning method has an angular standard deviation of less than 0.005° and a displacement standard deviation of less than 5.0 ?m.3)Using the positioning method based on fringe deflection to calculate the position of the surface under test,a virtual reference phase calculation model was established.And then a fringe deflectometry measurement model was proposed based on the virtual reference phase calculation model.This fringe deflectometry measurement model could measure the surface shape deviation and surface shape simultaneously,which could avoid the matching problem in the shape error evaluation process.Moreover,this measurement model was much simpler and more flexible,which could be easy to realize miniaturization.It was proved by experimental results that the proposed measurement model had a resolution of about 10 nm,and the measurement error was less than 100 nm.4)Because the measurement result of transmitted fringe deflectometry is the wavefront of the lens,a wavefront aberration measurement method based on transmitted fringe deflectometry was proposed.The system measurement error when measuring wavefront aberration is analyzed,including the aberration of the reference wavefront caused by shape distribution and the tilt and decentration of the phase object.Based on this,the system error model was established and the system error compensation method was also presented.It was proved by experimental results that the measurement error of the proposed wavefront aberration measurement method was less than 100 nm.5)According to the measurement needs of the progressive additional lens(PALs),a novel method on simultaneously evaluating the lens power and user power of a PAL was proposed based on an equivalent model of the PALs and refractive-power calculation method.Using the transmitted fringe deflectometry to measure the wavefront of the PAL,the lens power and user power of the PAL could then be obtained using the equivalent model of the PALs and refractive-power calculation method.The proposed method is based on a full-field measurement technique and need not an accuracy adjustment of lens in the measuring process.It therefore shows a good flexibility and generality.It was proved by experimental results that the measurement error of the proposed wavefront aberration measurement method was less than 0.03 D.