衍射光栅效率自动测试仪光学系统设计与测量误差修正方法研究
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摘要
本文对衍射光栅效率自动测试仪的光学系统进行设计和仿真，并对仪器的测量误差修正方法进行了深入研究。平面衍射光栅效率自动测试仪的主要研究工作如下：第一，在仪器光学系统设计和仿真方面，提出了双光栅单色仪系统的设计方法，在保证出射光通量没有损失的前提下，确定了双光栅单色仪系统的光源、光路结构、探测器参数，并且给出了系统的像面点列图和实际光线追迹结果。第二，在仪器的波长校准算法研究方面，提出以符合光栅方程的正弦曲线作为仪器出射波长的校准方程，基于最小二乘法原理给出校准方程的拟合残差的表达式，由于校准方程的非线性，应用二维Nelder-Mead单纯形法求解拟合残差的待定系数，建立了波长与光栅转角的精确表达式，并通过实验验证了该算法的准确性，完成了对前置单色仪的波长校准。第三，在仪器系统误差修正方法研究方面，通过对测量过程中影响测量结果的光栅出射光谱增宽和衍射光束截面变化等主要因素进行分析，给出了两者关于入射波长和光栅刻线密度的关系式，在大量实验数据的基础上，运用多元线性回归分析的数学方法，建立了回归修正模型，并将此修正模型编入测量程序，可以在测量结束的同时自动修正测量结果；经过修正后的测量偏差均在±2%以内，其测量精度比未修正前提高了一个数量级。
基于平面衍射光栅效率自动测试仪的研究基础上，对凹面衍射光栅效率自动测试仪展开了一系列相似的研究工作。第四，分别对Ⅲ型凹面光栅和Ⅳ型凹面光栅各自组成的光学系统进行设计和仿真，确定了适合多种类型被测凹面光栅的光路结构、探测器参数。第五，提出了Ⅲ型凹面光栅衍射效率的测试方法并进行验证；采用与平面衍射光栅效率自动测试仪相同的误差修正方法和步骤，实现了凹面光栅衍射效率的准确测量。
最后，分别对平面衍射光栅效率自动测试仪和凹面衍射光栅效率自动测试仪的测量性能进行分析，从测量数据中得知，两台仪器的测量准确性为±2%；测量稳定性为0.29%；测量重复性在2%以内；测量速度为15块光栅/小时；其测量结果均达到预期要求。
This paper was mainly focused on the design and simulation of optical system ofthe automatic test instrument for the grating diffraction efficiency, and the method ofmeasurement error correction was also investigated. The main research on theautomatic test instrument for the plane grating diffraction efficiency are as follows:firstly, the design method of the double monochromator of the plane grating wasproposed, on the basis of lossless luminous flux, the light source, detector and thestructure of the optical path was selected, and the spot diagram of the image surfaceand the results of real ray trace were given. Secondly, the sinusoid that accords withthe grating equation was proposed to be served as the function of the wavelengthcalibration of the instrument. Based on the principle of the least square method, theformula of the fitting residual error of the wavelength calibration was given. Usingthe Nelder-Mead simplex method, the undetermined coefficient of the fitting residualerror was solved, which founded the precise formula between the wavelength and thegrating turning angle. The accuracy of the method was verified through theexperiment, based on which the research of wavelength was calibrated. Thirdly,through analyzing the main factors, the spectral broadening of exit beam and section-changed of diffraction beam that influence the testing results duringmeasurement, the relationship between them and wavelength and groove density wasgiven. Based on a large number of experiment data, the correction model wasestablished using the multiple linear regression analysis. Additionally, the correctionmodel was compiled as the testing programming, which can correct the testingresults automatically when the test was finished. The results deviation after modifiedwas less than±2%, which enhanced the measurement precision for one order ofmagnitude.
On the basis of the research on the automatic test instrument for the planegrating diffraction efficiency, a series of similar work was developed according to theautomatic test instrument for the concave grating diffraction efficiency. fourthly, theoptical system of the type III and the type Ⅳ concave gratingwas designed andsimulated respectively, the detector parameters and the structure of the optical paththat suitable for multi-type concave grating were selected. Fifthly, the testing methodof the diffraction efficiency of the type III concave grating was proposed and verified.Using the same measurement error correction method with the automatic testinstrument for the plane grating diffraction efficiency, the precise testing of theconcave grating diffraction efficiency was achieved.
Finally, the measurement performance of the automatic test instrument for theplane and concave grating diffraction efficiency respectively was analyzed. Thetesting data showed that, the testing accuracy of the two instruments, the testingstability and the testing speed were±2%,0.29%and15pieces/hour respectively. Andthe testing repeatability were less than2%. The above performance index satisfies theexpected requirement.
基于平面衍射光栅效率自动测试仪的研究基础上，对凹面衍射光栅效率自动测试仪展开了一系列相似的研究工作。第四，分别对Ⅲ型凹面光栅和Ⅳ型凹面光栅各自组成的光学系统进行设计和仿真，确定了适合多种类型被测凹面光栅的光路结构、探测器参数。第五，提出了Ⅲ型凹面光栅衍射效率的测试方法并进行验证；采用与平面衍射光栅效率自动测试仪相同的误差修正方法和步骤，实现了凹面光栅衍射效率的准确测量。
最后，分别对平面衍射光栅效率自动测试仪和凹面衍射光栅效率自动测试仪的测量性能进行分析，从测量数据中得知，两台仪器的测量准确性为±2%；测量稳定性为0.29%；测量重复性在2%以内；测量速度为15块光栅/小时；其测量结果均达到预期要求。
This paper was mainly focused on the design and simulation of optical system ofthe automatic test instrument for the grating diffraction efficiency, and the method ofmeasurement error correction was also investigated. The main research on theautomatic test instrument for the plane grating diffraction efficiency are as follows:firstly, the design method of the double monochromator of the plane grating wasproposed, on the basis of lossless luminous flux, the light source, detector and thestructure of the optical path was selected, and the spot diagram of the image surfaceand the results of real ray trace were given. Secondly, the sinusoid that accords withthe grating equation was proposed to be served as the function of the wavelengthcalibration of the instrument. Based on the principle of the least square method, theformula of the fitting residual error of the wavelength calibration was given. Usingthe Nelder-Mead simplex method, the undetermined coefficient of the fitting residualerror was solved, which founded the precise formula between the wavelength and thegrating turning angle. The accuracy of the method was verified through theexperiment, based on which the research of wavelength was calibrated. Thirdly,through analyzing the main factors, the spectral broadening of exit beam and section-changed of diffraction beam that influence the testing results duringmeasurement, the relationship between them and wavelength and groove density wasgiven. Based on a large number of experiment data, the correction model wasestablished using the multiple linear regression analysis. Additionally, the correctionmodel was compiled as the testing programming, which can correct the testingresults automatically when the test was finished. The results deviation after modifiedwas less than±2%, which enhanced the measurement precision for one order ofmagnitude.
On the basis of the research on the automatic test instrument for the planegrating diffraction efficiency, a series of similar work was developed according to theautomatic test instrument for the concave grating diffraction efficiency. fourthly, theoptical system of the type III and the type Ⅳ concave gratingwas designed andsimulated respectively, the detector parameters and the structure of the optical paththat suitable for multi-type concave grating were selected. Fifthly, the testing methodof the diffraction efficiency of the type III concave grating was proposed and verified.Using the same measurement error correction method with the automatic testinstrument for the plane grating diffraction efficiency, the precise testing of theconcave grating diffraction efficiency was achieved.
Finally, the measurement performance of the automatic test instrument for theplane and concave grating diffraction efficiency respectively was analyzed. Thetesting data showed that, the testing accuracy of the two instruments, the testingstability and the testing speed were±2%,0.29%and15pieces/hour respectively. Andthe testing repeatability were less than2%. The above performance index satisfies theexpected requirement.
引文
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