Research on optical transfer function measurement based on Hartmann wavefront sensor
-
摘要:
为实现光学传递函数的低成本、实时测量，本文提出基于哈特曼探测器的光学传递函数测量方法。首先，基于哈特曼探测器的测量波面，给出光学传递函数的测量方法。然后，设计传函测量光路，并给出焦深、像差和焦距的测量方法。同时，设计了物镜像差的标定光路，并给出标定方法。最后，搭建实验光路，实现了单透镜的调制传递函数（MTF）、像差、焦距、焦深及色差的测量。结果显示，该方法实现了0~1° 视场透镜的MTF测量；透镜的像散、慧差及球差分别为0.114 λ、0.128 λ和0.02 λ；0°视场下透镜的色差在红、绿、蓝三个波长下分别为0.047 λ、0.055 λ、0.048 λ，1°视场下增长到0.117 λ、0.176 λ和0.154 λ；焦深为0.454 mm，误差2%，焦距为74.6 mm，误差0.8%。结果表明该测量方法能够实现透镜的传函测量，为光学系统传函的低成本、实时测量提供技术途径。
Abstract:This study proposes a Hartmann wavefront sensor-based method for cost-effective, real-time measurement of Optical Transfer Function (OTF). First, an OTF measurement framework is established using wavefront data acquired through the Hartmann wavefront sensor. Subsequently, we design an optical configuration for OTF measurement, incorporating methodologies to determine depth of focus, characterize aberrations, and measure focal length. A dedicated calibration optical path is developed for objective lens aberration quantification, accompanied by systematic calibration procedures. Finally, an experimental setup is implemented to comprehensively assess lens performance, including Modulation Transfer Function (MTF), aberration, focal length, depth of focus, and chromatic aberration. The measurement results show that this method can achieve MTF measurement for the lens within a 0−1° field of view. The measured aberrations include astigmatism (0.114 λ), coma (0.128 λ), and spherical aberration (0.02 λ). At 0° field angle, the chromatic aberration values for red, green, and blue wavelengths are 0.047 λ, 0.055 λ, and 0.048 λ, respectively, increasing to 0.117 λ, 0.176 λ, and 0.154 λ at 1° field angle. The depth of focus is measured at 0.454 mm with a 2% error, while the focal length is determined to be 74.6 mm with a 0.8% error. These results confirm that the proposed measurement method enables accurate MTF characterization of optical lenses, providing a low-cost and real-time technical solution for the evaluation of MTF in optical systems.
-
图 2 传函仪系统光路示意图
Figure 2. Schematic diagram of optical layout of the OTF measurement system
图 3 系统光路的等效光路示意图
Figure 3. Equivalent optical path diagram of the system configuration
图 4 物镜像差标定光路示意图
Figure 4. Schematic of the calibration optical path for objective lens aberration
图 8 0°视场下透镜的MTF。(a) MTF的三维分布；(b) x方向及(c) y方向的MTF分布
Figure 8. MTF of the lens at 0° field of view. (a) 3D MTF; (b) MTF in x direction, and (c) MTF in y direction
图 9 不同视场的MTF测量结果。(a) x方向，(b) y方向
Figure 9. MTF measurement results for different fields of view: (a) in the x direction, and (b) in the y direction
图 10 不同视场的镜头传函质量
Figure 10. MTF performance characterization of the lens under different fields of view
图 11 焦深测量波面。(a) 原始波面, (b) 离焦波面
Figure 11. Defocus-dependent wavefront characterization. (a) Original wavefront and (b) defocus wavefront
图 12 透镜的像差测量结果。(a) 总像差, (b) 像散, (c) 彗差, (d) 球差
Figure 12. Aberration measurement results of the lens. (a) Total aberration, (b) astigmatism, (c) comma, and (d) spherical aberration
图 13 色差测量结果。(a) 红、绿、蓝波长的色差；(b) 红、蓝偏移绿波长的色差
Figure 13. Chromatic aberration measurement results. (a) Chromatic aberration at red, green, and blue wavelengths; (b) Chromatic aberration with red/blue wavelengths shifted relative to the green
表 1 前8项Zernike表达式
Table 1. The first 8 terms of Zernike polynomials
Zernike序号 描述 1 倾斜（X方向） 2 倾斜（Y方向） 3 离焦 4 初级像散（X方向） 5 初级像散（Y方向） 6 初级彗差（X方向） 7 初级彗差（Y方向） 8 初级球差 
下载: 导出CSV
-
[1] GOODMAN, JOSEPH W. Introduction to Fourier optics[M]. Roberts and Company publishers, 2005. [2] WILLIAMS T L. The optical transfer function of imaging systems[M]. Routledge, 2018. [3] 张卓成.基于调制传递函数的消费级镜头在线质量检测与评价[D].西安工业大学,2024.ZHANG Z C. Online quality inspection and evaluation of consumer-grade lenses lased on Modulation Transfer Function[D]. Xi’an Technological University, 2024. (in Chinese). [4] 曹天皓,张继艳,林正煜,等. 紧凑式长波红外变焦光学系统设计[J]. 红外技术,2025,47(5):553-562.CAO T H, ZHANG J Y, LIN Z Y,et al. Design of compact long-wave infrared zoom optical system[J]. Infrared Technology, 2025,47(5):553-562. (in Chinese). [5] 马洪涛, 韩冰, 许洪刚,等. 短波中波红外折反射式共口径光学系统设计[J]. 中国光学(中英文), 2025, 18(2): 359-367.MA H T, HAN B, XU H G, et al. Design of SWIR/MWIR catadioptric common-aperture optical system[J]. Chinese Optics, 2025, 18(2): 359-367. (in Chinese). [6] ROBERTO F S, FRANCISCO J P, LUIS A I. Modulation transfer function formula for different age ranges[J]. Opt. Soc. Am. A 40, 1979-1985 (2023 [7] Pierre M D. L' intégrale de Fourier et ses applications à l'optique[M] . Imprimeries Oberthur, 1946. [8] LINDBERG P. Measurement of contrast transmission characteristics in optical image formation[J]. Optica Acta: International Journal of Optics, 1954, 1(2): 80-89. doi: 10.1080/713818664 [9] 庄松林, 钱振邦. 光学传递函数[M]. 北京: 机械工业出版社, 1981.ZHUANG S L, QIAN B Z. Optical Transfer Function[M]. Beijing: China Machine Press, 1981. (in Chinese). [10] 罗敏. 用自相关函数法计算光学传递函数[J]. 云光技术,1996(4):1-13.LUO M. Calculation of optical transfer function by autocorrelation function method[J]. Yunguang Jishu, 1996(4): 1-13. (in Chinese). [11] MADANIPOUR K, TAVASSOLY M T. Moiré fringes as two-dimensional autocorrelation of transmission function of linear gratings and its application for modulation transfer function measurement[J]. Optics and Lasers in Engineering, 2010, 48(1): 43-47. doi: 10.1016/j.optlaseng.2009.07.008 [12] 陈燕芹. 基于图像处理的调制传递函数测试方法研究[D]. 长春: 长春理工大学, 2016.CHEN Y Q. Research on the modulation transfer function testing method based on image processing[D]. Changchun: Changchun University of Technology, 2016. (in Chinese). [13] BATTULA T, GEORGIEV T, GILLE J, et al. Contrast computation methods for interferometric measurement of sensor modulation transfer function[J]. Journal of Electronic Imaging, 2018, 27(1): 013015. [14] SAIGA R, TAKEUCHI A, UESUGI K, et al. Method for estimating modulation transfer function from sample images[J]. Micron, 2018, 105: 64-69. doi: 10.1016/j.micron.2017.11.009 [15] SCHULZE R K W, DOERING C I. Simple computation of the approximated modulation transfer function (MTF) using spreadsheet-software: method and evaluation in five maxillofacial CBCT-devices[J]. Dentomaxillofacial Radiology, 2019, 48(4): 20180350. doi: 10.1259/dmfr.20180350 [16] SCHENKER M, STAVRIDIS M, SCHULZ M, et al. Effects of misalignments on the modulation transfer function measurement of camera lenses analyzed in optomechanical simulations[J]. Optical Engineering, 2020, 59(3): 034101. [17] 朱沁雨, 陈梅蕊, 陆焕钧, 等. 微透镜阵列衍射效应对夏克一哈特曼波前探测器的影响分析[J]. 中国光学(中英文),2023,16(1):94-102. doi: 10.37188/CO.2022-0176ZHU Q Y, CHEN M R, LU H J, et al. Analysis of influence of diffraction effect of microlens array on Shack-Hartmann wavefront sensor[J]. Chinese Optics, 2023, 16(1): 94-102. (in Chinese). doi: 10.37188/CO.2022-0176 [18] 徐雷, 陆欣怡, 李静妮, 等. 基于哈特曼探测器的光波相位三维显示方法[J]. 液晶与显示,2023,38(12):1681-1688. doi: 10.37188/CJLCD.2023-0300XU L, LU X Y, LI J N, et al. Three-dimensional display method of optical phase based on Hartmann wavefront sensor[J]. Chinese Journal of Liquid Crystals and Displays, 2023, 38(12): 1681-1688. (in Chinese). doi: 10.37188/CJLCD.2023-0300 [19] 马卫红. 基于图像分析的光学传递函数测试技术研究[D]. 西安: 中国科学院西安光学精密机械研究所, 2005.MA W H. Study of MTF measurement technique based on image analysis[D]. Xi’an: Xi’an Institute of Optics and Precision Mechanics, Chinese Academy of Sciences, 2005. (in Chinese). [20] 郑克哲. 光学计量[M]. 北京: 原子能出版社, 2002.ZHENG K ZH. Optical Metrology[M]. Beijing: Atomic Energy Publishing House, 2002. (in Chinese). [21] ROBERT E F. Optical System Design[M]. New York: SPIE, 2000. [22] GUO W J, ZHAO L P, CHEN I M. Simulation of the sensing performance of a Shack-Hartmann wavefront sensor related to the lenslet array[J]. Physics Procedia, 2011, 19: 188-191. doi: 10.1016/j.phpro.2011.06.147 [23] 夏明亮. 高精度人眼像差哈特曼探测器的研制[D]. 长春: 中国科学院研究生院(长春光学精密机械与物理研究所), 2011.XIA M L. The development of high precision Hartmann wavefrot detector for eye aberration[D]. Changchun: Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences, 2011. (in Chinese). -
下载:
计量
- 文章访问数: 117
- HTML全文浏览量: 28
- PDF下载量: 6
- 被引次数: 0
