基于视线标定立体偏折术的离轴非球面面形检测

Stereo Deflectometry for Measuring Off-Axis Aspherical Surface Based on Vision Ray Model

为实现离轴非球面光学元件面形的准确高效测量,提出一种基于立体偏折术并结合点云匹配数据处理的方法,该方法可用于离轴非球面光学元件结构参数的拟合与面形测量。首先,根据立体偏折术原理获得离轴非球面的点云数据,然后,利用点云数据与离轴非球面理论模型的几何关系,通过非线性最小二乘算法对姿态误差和非球面结构参数进行优化,最后,利用上述的几何关系、姿态误差和优化后的结构参数完成点云数据和理论模型的匹配,进而获得离轴非球面元件面形。为了验证所提方法的可行性,对顶点曲率c=1/678.91 mm^(-1)、离轴量b=100 mm、圆锥系数k=-1、口径为142 mm且有附加面形误差的离轴非球面元件进行了数值模拟,并实验测量了一块离轴非球面光学元件,对其结构参数进行优化后,得到了与干涉仪较为接近的面形测量结果。仿真和实验结果表明了所提方法用于离轴非球面光学元件面形测量时的可行性。

Objective In recent years,the demand for improved optical systems has resulted in the utilization of spherical elements,which can correct aberrations and enhance imaging quality.However,the common practice of incorporating additional optical elements for aberration correction increases the volume and weight of optical instruments,thus contradicting the trend toward lightweightness and miniaturization.By contrast,aspherical optical elements with varying curvatures can effectively correct aberrations,improve imaging quality,and satisfy the requirements of lightweightness for optical systems.Consequently,they have broader applications in healthcare,aerospace,astronomy,and high-power lasers.The non-coincidence of the geometric and optical axes in off-axis aspherical elements provides additional degrees of freedom for aberration correction in optical system designs.Whereas this addresses issues such as center obstruction,which can degrade the imaging quality,it increases the difficulty in measuring the surface of the elements.Commonly used methods for measuring the surfaces of off-axis aspherical elements include interferometry and profilometry.Interferometry utilizes changes in the optical-path difference to generate interference fringes,thereby enabling high-precision surface measurements.However,interferometric precision is affected by the environment and typically requires additional compensatory devices for off-axis aspherical-element measurements.Profilometry,which uses a mechanical probe in contact with the surface of an element and a detector to sense changes in the height of the contact point,achieves point-by-point measurements of an element s profile.However,its motion mechanism renders high-precision measurement challenging and contact between the probe and the tested element s surface can cause surface damage.Conventional phase-measuring deflectometry has been widely applied as a nondestructive and efficient technique for measuring the shape of optical-element surfaces.However,obtaining highly accurate coordinates of the reflection points is challenging because of the ambiguity between the slope and height.The off-axis aspherical element introduces an additional off-axis parameter in the standard aspherical configuration.As a countermeasure,the measurement region is modified,which renders it difficult to determine the central position.Therefore,accurate and efficient methods for the surface measurement of off-axis aspheric elements are scarce.Methods To accurately and efficiently measure an off-axis aspheric surface,this study proposes a method based on stereo deflectometry combined with point-cloud-matching data processing.This approach was utilized to accommodate the structural parameters and measure the surfaces of off-axis aspheric mirrors.First,the point-cloud data of an off-axis aspherical mirror were obtained based on the principles of stereo deflectometry.Subsequently,the geometric relationship between the point-cloud data and the theoretical model of the off-axis aspheric mirror was utilized.A nonlinear least-squares algorithm was employed to optimize the pose errors and aspherical structural parameters.Finally,utilizing the geometric relationships,pose errors,and optimized structural parameters,the point-cloud data were matched with the theoretical model,which yielded the surface of the off-axis aspherical mirror.To validate the feasibility of the proposed method,numerical simulations were conducted on an off-axis aspheric mirror with vertex curvature c=1/678.91 mm^(-1),off-axis distance b=100 mm,and conic constant k=-1 within a measurement range of 142 mm,including the surface error.In the experiments,measurements were performed on the off-axis aspherical mirror,and its structural parameters were optimized,which yielded surface measurement results similar to those achieved via interferometry.This method is viable for the surface measurement of off-axis aspherical mirrors.Results and Discussions This study introduces a point-cloud-matching method based on stereo deflectometry.The proposed approach is validated via numerical simulations and experiments on targeted elements.In the numerical simulations,the parameters are consistent with the actual measurements,and surface errors are introduced[Fig.6(a)].The simulation results are presented in Figs.6(b) and (c).The surface yielded by the proposed method is consistent with the actual surface.Based on a comparison of the Zernike coefficients (Fig.7),the simulation results closely approximated the defocus,astigmatism,coma,and spherical aberration terms set in the preset parameters.During the experiments,the surface of an off-axis aspherical mirror with a diameter of 142 mm was measured.The experimental results (Fig.10) indicate that the proposed method achieves an element surface RMS value of approximately 31 nm,whereas the interferometer achieves an RMS value of approximately 15.9 nm.The optimized structural parameters are obtained (Table 1),which can serve as reference for the measurement of actual mirror structural parameters.The results show that the proposed method exhibits good accuracy for off-axis aspherical surface measurements.Conclusions This study introduces a point-cloud data-matching method for stereo deflectometry based on a vision ray model,which facilitates the fitting of structural parameters and surface measurements for off-axis aspherical mirrors.First,the principles of stereo deflectometry point-cloud reconstruction within the vision ray model are described.Subsequently,the point-cloud-matching method and specific data-processing procedures are explained in detail.The reconstructed results are matched with the theoretical model via point-cloud matching,thus enabling an accurate measurement of the surface of the off-axis aspherical mirror.Moreover,the proposed method is validated via numerical simulations,where the surface error of an off-axis aspherical mirror is incorporated.In the experiment,a measurement system is implemented to confirm the effectiveness of the proposed method for off-axis aspherical surface measurements.The reconstructed surface is consistent with the interferometer results.