WO2024036885A1 - 一种光学延迟系统延迟时间非线性校准方法 - Google Patents

一种光学延迟系统延迟时间非线性校准方法 Download PDF

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WO2024036885A1
WO2024036885A1 PCT/CN2023/073108 CN2023073108W WO2024036885A1 WO 2024036885 A1 WO2024036885 A1 WO 2024036885A1 CN 2023073108 W CN2023073108 W CN 2023073108W WO 2024036885 A1 WO2024036885 A1 WO 2024036885A1
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rotating
prism
delay time
rotation angle
rotating prism
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PCT/CN2023/073108
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English (en)
French (fr)
Inventor
薛竣文
李丽娟
祝莉莉
任姣姣
张丹丹
顾健
梁嵬
张霁旸
陈奇
牟达
孔诗媛
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长春理工大学
长春理工大学中山研究院
成都神龙爵光电科技有限公司
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Priority to EP23735954.2A priority Critical patent/EP4350536A1/en
Publication of WO2024036885A1 publication Critical patent/WO2024036885A1/zh

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Classifications

    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
    • G01B9/00—Measuring instruments characterised by the use of optical techniques
    • G01B9/02—Interferometers
    • G01B9/02055—Reduction or prevention of errors; Testing; Calibration
    • G01B9/0207—Error reduction by correction of the measurement signal based on independently determined error sources, e.g. using a reference interferometer
    • G01B9/02072—Error reduction by correction of the measurement signal based on independently determined error sources, e.g. using a reference interferometer by calibration or testing of interferometer
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01J—MEASUREMENT OF INTENSITY, VELOCITY, SPECTRAL CONTENT, POLARISATION, PHASE OR PULSE CHARACTERISTICS OF INFRARED, VISIBLE OR ULTRAVIOLET LIGHT; COLORIMETRY; RADIATION PYROMETRY
    • G01J9/00—Measuring optical phase difference; Determining degree of coherence; Measuring optical wavelength
    • G01J9/02—Measuring optical phase difference; Determining degree of coherence; Measuring optical wavelength by interferometric methods
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/18—Complex mathematical operations for evaluating statistical data, e.g. average values, frequency distributions, probability functions, regression analysis
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
    • G01B2290/00—Aspects of interferometers not specifically covered by any group under G01B9/02
    • G01B2290/70—Using polarization in the interferometer
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01J—MEASUREMENT OF INTENSITY, VELOCITY, SPECTRAL CONTENT, POLARISATION, PHASE OR PULSE CHARACTERISTICS OF INFRARED, VISIBLE OR ULTRAVIOLET LIGHT; COLORIMETRY; RADIATION PYROMETRY
    • G01J9/00—Measuring optical phase difference; Determining degree of coherence; Measuring optical wavelength
    • G01J9/02—Measuring optical phase difference; Determining degree of coherence; Measuring optical wavelength by interferometric methods
    • G01J2009/0261—Measuring optical phase difference; Determining degree of coherence; Measuring optical wavelength by interferometric methods polarised
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01J—MEASUREMENT OF INTENSITY, VELOCITY, SPECTRAL CONTENT, POLARISATION, PHASE OR PULSE CHARACTERISTICS OF INFRARED, VISIBLE OR ULTRAVIOLET LIGHT; COLORIMETRY; RADIATION PYROMETRY
    • G01J9/00—Measuring optical phase difference; Determining degree of coherence; Measuring optical wavelength
    • G01J9/02—Measuring optical phase difference; Determining degree of coherence; Measuring optical wavelength by interferometric methods
    • G01J2009/028—Types
    • G01J2009/0284—Michelson

Definitions

  • the invention relates to a delay time nonlinear calibration method for an optical delay system, and is particularly suitable for processing and installing delay lines in optical detection systems such as terahertz time domain spectroscopy, optical coherence tomography, ultrafast time resolution spectroscopy and pump-detection.
  • optical detection systems such as terahertz time domain spectroscopy, optical coherence tomography, ultrafast time resolution spectroscopy and pump-detection.
  • Nonlinear fast rotating optical delay system with high precision requirements.
  • the optical delay system is used in terahertz time domain spectroscopy, optical coherence tomography, ultrafast time resolution spectroscopy and pump-detection technologies. It has a wide range of applications and is also a key subsystem that affects the accuracy of collected signals, signal-to-noise ratio and spectrum resolution.
  • the fast optical delay system is driven by a motor to rotate multiple mirrors, non-planar total reflection mirrors or rotating cubes and other reflective structures to produce periodic changes in optical path length.
  • Typical fast optical delay systems include involute rotating optical delay systems, spiral surface rotation Optical delay system, polyhedral rotating optical delay system, etc.
  • the fast optical delay system can realize fast scanning of the optical detection system, and the maximum scanning frequency can exceed 1kHz.
  • the linearity of the delay time of the fast optical delay system is poor.
  • the nonlinear degree of the delay time of the optical delay system directly affects the accuracy and consistency of the sampling signal of the optical detection system.
  • the nonlinear delay time causes nonlinear changes in the optical path of the detection light pulse, which in turn causes the sampling signal to also appear nonlinear.
  • the greater the nonlinearity of the system sampling signal the more serious the distortion of the collected signal, and the greater the difficulty of subsequent data processing.
  • the present invention provides a delay time nonlinear calibration method for an optical delay system, which reduces the impact of delay time nonlinearity on signal acquisition caused by low actual processing and installation accuracy of a fast optical delay system, and can Suitable for calibration of different types of fast optical delay systems.
  • a nonlinear calibration method for delay time of an optical delay system including the following steps:
  • the polarized Michelson interferometry system includes a light source system, a spectroscopic system, a reference arm system, a measurement arm system, and an interference system.
  • the measurement arm system includes a rotating optical delay system, rotating optical
  • the delay system includes a rotating prism and a rotating displacement stage.
  • the rotating prism is coaxially fixed on the rotating displacement stage and is driven by the rotating displacement stage to rotate horizontally around the central axis; the laser beam L1 emitted from the light source system reaches the spectroscopic system and is polarized
  • the beam splitter prism splits the reference arm beam L2 and The measuring arm beam L3; the reference arm beam L2 enters the reference arm system and is reflected and then returns to the polarizing beam splitting prism; the measuring arm beam L3 enters the measuring arm system and reaches the rotating prism in the rotating optical delay system, and is reflected by the facets of the rotating prism , and finally returns to the polarizing beam splitter on its original path after another reflection;
  • the reference arm beam L2 returned by the reference arm system and the measuring arm beam L3 returned by the measuring arm system merge into the interference beam L4 after catadioptric reflection by the polarizing beam splitting prism, and the interference Beam L4 enters the interference system and obtains interference fringes on the CCD camera of the interference system;
  • Step 2 The rotary displacement stage drives the rotating prism to rotate at a rotation interval ⁇ , and collects the corresponding interference fringe image in the CCD camera during the angle change of a single facet of the rotating prism;
  • Step 3 Process the interference fringe image collected in Step 2 to obtain the actual delay time of the rotation angle of a single facet of the rotating prism in the rotating optical delay system;
  • Step 4 Use the least squares method to fit the relationship between the rotation angle ⁇ i of the rotating prism in the rotating optical delay system and the actual delay time t i : Repeat steps two to three several times to rotate a single facet of the rotating prism. The average delay time of the angle ⁇ i obtained under this repeated measurement is regarded as the actual delay t i of the facet, and the least squares method is used to calculate the rotation angle ⁇ i of the single facet of the rotating prism and the actual delay time t i Fit the relationship; repeat the above steps for all the facets in the rotating prism, and obtain the least squares fitting relationship between the rotation angle and the actual delay time of each facet of the rotating prism;
  • Step 5 Based on the least squares fitting relationship in step 4, establish the sensitivity relationship between the rotating prism delay time and the rotational displacement stage angle in the rotating optical delay system, and realize the nonlinear calibration of the delay time of the rotating optical delay system and the rotating optical delay. System encoder selection.
  • the light source system of the polarized Michelson interferometry system includes a helium-neon laser, a lens, and a polarizer arranged in sequence along the optical axis direction;
  • the reference arm system includes a quarter wave plate and a plane arranged along the optical axis direction.
  • the measurement arm system includes a 1/4 wave plate set along the optical axis and a rotating optical delay system.
  • the rotating optical delay system includes a lens, a fixed plane reflector, a rotating prism, a rotating displacement stage, and a fixed plane reflector.
  • the interference system includes an analyzer and a CCD camera arranged along the optical axis;
  • the laser beam L1 emitted by the helium-neon laser passes through the lens and the polarizer. After linear beam expansion, it is converted into polarized light; after the polarized light reaches the spectroscopic system, it is divided into the reference arm beam L2 and the measurement arm beam L3 by the polarizing beam splitter prism; the reference arm beam L2 enters the reference arm system and passes through the 1/4 wave plate and the plane reflector in turn.
  • the measuring arm beam L3 enters the measuring arm system, passes through the 1/4 wave plate and reaches the rotating prism in the rotating optical delay system, and is reflected by the facet of the rotating prism to the lens, and finally by Fix the reflector and return it to the polarizing beam splitting prism of the spectroscopic system; adjust the angle and position of the plane reflector in the reference arm system so that the reference arm beam L2 returned by the reference arm system and the measuring arm beam L3 returned by the measuring arm system are in the polarized beam splitter. After refraction by the prism, it merges into an interference beam L4.
  • the interference beam L4 enters the interference system, passes through the analyzer and finally reaches the CCD camera, and obtains interference fringes on the CCD camera.
  • the helium-neon laser uses a helium-neon laser 1 with a wavelength of 632.8 nm.
  • the second step specifically includes:
  • the rotary displacement stage continues to drive the rotating prism to rotate at the rotation angle interval ⁇ until the rotating prism rotates through the working angle of its single prism; the CCD camera records: when the rotary displacement stage rotates at the rotation angle interval ⁇ , the rotating prism The interference fringe image of a single prism rotated i times at the working angle, where i is the number of rotations of the rotational displacement stage at the rotation angle interval ⁇ .
  • the third step specifically includes:
  • the gray value p j is greater than the threshold p l and is recorded as 1, and the gray value p j is less than the threshold p l and is recorded as 0, then the rotating prism rotates.
  • the stripe change amount ⁇ during the rotation angle interval ⁇ is recorded as:
  • the fourth step specifically includes:
  • step 4.1) Use the average delay time obtained in step 4.1) as the actual delay time t i of the rotation angle ⁇ i of the single facet of the rotating prism, and use the least squares method to calculate the sum of the rotation angles of the single facet in the rotating prism.
  • t i is the actual delay time obtained by testing a single facet of the rotating prism
  • ⁇ i is the rotation angle of a single facet of the rotating prism
  • n is the number of data to be fitted
  • i is the number of rotations of the rotational displacement stage at the rotation angle interval ⁇ ;
  • a is the sensitivity of the fitting delay time to the rotation angle of the rotating prism
  • the rotation angle interval ⁇ is 0.1°.
  • the fifth step specifically includes:
  • the actual delay time and rotational displacement of each facet of the rotating prism in the rotating optical delay system are obtained after fitting.
  • the corresponding relationship between the stage rotation angle is used to calibrate the nonlinearity of the rotating optical delay system;
  • the minimum resolution ⁇ min of the encoder of the rotating optical delay system is:
  • ⁇ max is the maximum sensitivity obtained based on least squares fitting on each facet of the rotating prism.
  • the invention can calibrate the nonlinearity introduced by the low processing and assembly accuracy of the fast optical delay system in the optical detection system, and can effectively reduce the optical detection system's requirements for high processing and assembly accuracy of the fast rotating optical delay system, and promote the rapid rotation of optical delay systems. Provides the basis for a wide range of applications of delay systems.
  • the invention has a good nonlinear calibration effect for a system with high precision requirements for a fast rotating optical delay system, can greatly reduce the processing cost of the rotating optical delay system, and has wide practicability.
  • Figure 1 is a flow chart of a nonlinear calibration method for delay time of an optical delay system according to an embodiment of the present invention
  • Figure 2 is a schematic diagram of the optical path of the polarized Michelson interferometry system according to the embodiment of the present invention
  • Figure 3 is a side view of the optical path of the rotating optical delay system according to the embodiment of the present invention.
  • Figure 4 is a schematic diagram of the grayscale calculation area of the interference fringe image collected according to the embodiment of the present invention.
  • Figure 5 is a schematic diagram of the grayscale threshold area of the interference fringe image collected according to the embodiment of the present invention.
  • this embodiment is a nonlinear calibration method for the delay time of an optical delay system, which includes the following steps:
  • Step 1 Set up a polarized Michelson interferometry system:
  • the polarized Michelson interferometry system includes five parts: a light source system, a spectroscopic system, a reference arm system, a measurement arm system, and an interference system; the measurement arm system includes a rotating optical delay system 14.
  • the optical delay system 14 includes a rotating prism 10 and a rotating displacement stage 11.
  • the rotating prism 10 is coaxially fixed on the rotating displacement stage 11 and is driven by the rotating displacement stage 11 to rotate horizontally around the central axis; the laser beam emitted by the light source system After L1 reaches the spectroscopic system, it is divided into the reference arm beam L2 and the measurement arm beam L3 by the polarizing beam splitting prism 4; the reference arm beam L2 enters the reference arm system and is reflected back to the polarizing beam splitting prism 4; The measuring arm beam L3 enters the measuring arm system, reaches the rotating prism 10 in the rotating optical delay system 14, is reflected by the edge of the rotating prism 10, and finally returns to the polarizing beam splitter prism 4 after another reflection; the reference arm The reference arm beam L2 returned by the system and the measuring arm beam L3 returned by the measuring arm system merge into an interference beam L4 after refraction by the polarizing beam splitter 4. The interference beam L4 enters the interference system and is obtained on the CCD camera 13 of the interference system. interference fringes.
  • the light source system includes a helium-neon laser 1, a lens 2, and a polarizer 3 arranged sequentially along the optical axis direction;
  • the light splitting system includes a polarizing beam splitter prism 4;
  • the reference arm system includes a 1/4 wave plate 5 arranged along the optical axis direction and Plane reflector 6;
  • the measuring arm system includes a quarter wave plate 7 and a rotating optical delay system 14 arranged along the optical axis;
  • the interference system includes an analyzer 12 and a CCD camera 13 arranged along the optical axis;
  • the rotating optical delay system 14 includes a lens 8, a fixed plane mirror 9, a rotating prism 10, and a rotating displacement stage 11; the rotating prism 10 is coaxially fixed on the rotating displacement stage 11, and the rotating prism 10 is mounted on the rotating displacement stage 11. It is driven to rotate around the central axis in the horizontal plane; the lens 8 and the fixed plane reflector 9 are arranged in sequence along the reflected light path of the rotating prism 10.
  • the polarized Michelson interferometry system requires high power stability of the interference light source, and the helium-neon laser with a wavelength of 632.8nm is preferred1.
  • the laser beam L1 emitted by the helium-neon laser 1 is expanded by the lens 2 and the polarizer 3 and then converted into polarized light; after the polarized light reaches the spectroscopic system, it is divided into the reference arm beam L2 by the polarizing beam splitter prism 4 and the measuring arm beam L3; the reference arm beam L2 enters the reference arm system, passes through the 1/4 wave plate 5 and the plane reflector 6, and then returns to the polarizing beam splitting prism 4 of the spectroscopic system; the measuring arm beam L3 enters the measuring arm system, and passes through 1 /4 wave plate 7 then reaches the rotating prism 10 in the rotating optical delay system 14, is reflected by the prism surface of the rotating prism 10 to the lens 8, and finally returns to the polarizing beam splitting prism 4 of the light splitting system via the fixed reflector 9.
  • the interference beam L4 enters the interference system, passes through the analyzer 12 and finally reaches the CCD camera 13, and obtains interference fringes on the CCD camera 13.
  • Step 2 Use 0.1° as the rotation interval of the rotating displacement stage 11 to drive the rotating prism 10 to rotate, and collect the corresponding interference fringe images in the CCD camera 13 during the angle change of a single facet of the rotating prism 10:
  • the rotary displacement stage 11 continues to drive the rotating prism 10 to rotate at 0.1° rotation angle intervals until the rotating prism 10 rotates through the working angle of a single prism; the CCD camera 13 records: the rotational displacement stage 11 rotates at 0.1° intervals.
  • the interference fringe image of the rotating prism 10 rotated i times at a single prism working angle, where i is the number of times the rotary displacement stage rotates at intervals of 0.1°;
  • Step 3 Obtain the actual delay time of the single facet rotation angle of the rotating prism 10 in the rotating optical delay system 14:
  • Step 4 Use the least squares method to fit the relationship between the rotation angle ⁇ i of the rotating prism 10 in the rotating optical delay system 14 and the actual delay time t i : Repeat steps two to three to separate the single facets of the rotating prism 10 The average delay time of the rotation angle ⁇ i obtained under three repeated measurements is used as the actual delay t i of the facet, and the least squares method is used to calculate the rotation angle ⁇ i of a single facet of the rotating prism 10 and the actual delay time t i The above steps are repeated for all facets in the rotating prism 10 to obtain the least square fitting relationship between the rotation angle of each facet of the rotating prism 10 and the actual delay time.
  • t i is the actual delay time obtained by testing a single facet of the rotating prism 10;
  • ⁇ i is the rotation angle of a single facet of the rotating prism 10
  • n is the number of data to be fitted
  • i is the number of times the rotational displacement stage rotates at intervals of 0.1°;
  • a is the sensitivity of the fitting delay time to the rotation angle of the rotating prism
  • Step 5 Based on the least squares fitting relationship of Step 4, establish the sensitivity relationship between the rotation prism delay time of the rotating optical delay system 14 and the angle of the rotating displacement stage 11 to achieve nonlinear calibration and rotation of the delay time of the rotating optical delay system 14 Selection of encoders for optical delay systems.
  • ⁇ max is the maximum sensitivity obtained based on least squares fitting in each facet of the rotating prism 10 .

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Abstract

一种光学延迟系统（14）延迟时间（t i）非线性校准方法，首先搭建偏振式迈克尔逊干涉测量系统，其旋转光学延迟系统（14）包括旋转棱体（10）、旋转位移台（11），旋转棱体（10）由旋转位移台（11）驱动其绕中轴水平转动；旋转位移台（11）以旋转间隔（β）驱动旋转棱体（10）旋转，并在旋转棱体（10）单个棱面的角度变化过程中采集CCD相机（13）中对应的干涉条纹图像；基于干涉条纹图像获得旋转光学延迟系统（14）中旋转棱体（10）单个棱面旋转角度（γ i）的实际延迟时间（t i）；利用最小二乘法拟合旋转棱体（10）的旋转角度（γ i）与实际延迟时间（t i）的关系；基于最小二乘法拟合关系，建立旋转光学延迟系统（14）中旋转棱体(10)拟合延迟时间（t i'）与旋转棱体（10）旋转角度（γ i）的灵敏度（a k）关系，实现对旋转光学延迟系统（14）延迟时间（t i）非线性的校准和旋转光学延迟系统（14）编码器的选型。

Description

一种光学延迟系统延迟时间非线性校准方法
本发明要求于2022年08月17日提交中国专利局、申请号为202210986603.8、申请名称为“一种光学延迟系统延迟时间非线性校准方法”的中国专利申请的优先权，其全部内容通过引用结合在本申请中。
技术领域
本发明涉及光学延迟系统延迟时间非线性校准方法，尤其适用于太赫兹时域光谱、光学相干层析成像、超快时间分辨率光谱和泵浦-探测等光学探测系统中对延迟线加工及安装精度要求高的非线性快速旋转光学延迟系统。
背景技术
光学延迟系统作为一种能够改变光学探测系统中参考光及探测光相对延迟时间的系统，在太赫兹时域光谱、光学相干层析成像、超快时间分辨率光谱和泵浦-探测等技术中有着广泛的应用，同时也是影响采集信号准确性、信噪比以及频谱分辨率的关键子系统。
快速光学延迟系统由电机驱动多个反射镜、非平面全反射镜或旋转立方体等反射结构旋转产生周期性变化光程，典型的快速光学延迟系统有渐开线型旋转光学延迟系统、螺旋面旋转光学延迟系统、多面棱体旋转光学延迟系统等。快速光学延迟系统能够实现光学探测系统的快速扫描，最高扫描频率可超过1kHz，但受表面形状的限制，快速光学延迟系统延迟时间的线性度差。光学延迟系统延迟时间的非线性程度直接影响光学探测系统采样信号的准确性和一致性，非线性的延迟时间引起探测光脉冲光程产生非线性变化，进而导致采样信号也呈现非线性。系统采样信号的非线性越大，采集得到的信号失真情况越严重，后续数据处理的难度越大。为实现光学探测系统的高精度测量，急需对快速光学延迟系统系统设 计、实际加工及安装精度低带来的延迟时间非线性进行校准。
目前光学探测系统的信号误差研究，多集中于后期数据处理阶段采用算法校正采集信号的延迟时间误差。但对于快速光学延迟系统，反射体实际加工过程中存在反射体平行度误差、反射体反射面的平整度误差和反射体的位置度误差，以及安装过程中存在横向偏心误差和纵向偏心误差，这些误差将导致采样信号产生更复杂的失真，因此需要对加工及安装后的旋转光学延迟系统实际延迟时间非线性进行校准。文献[DOI:10.1364/OE.25.007547]搭建了与太赫兹时域光谱系统同轴光路的马赫-曾德干涉仪，可直接获得线性延迟线下太赫兹波形的光学延迟时间。但由于该干涉仪与太赫兹时域光谱系统光路使用同一分光棱镜，这不仅要求太赫兹时域光谱系统必须为空间光路且与干涉仪波长相近，更增加了干涉仪光路结构的复杂程度，使得光路调节难度大幅度增加。因此需要一种更为灵活简单，便于调节的干涉仪系统对旋转延迟线的延迟时间进行标定。
因此，亟需一种光学延迟系统延迟时间非线性校准方法，降低旋转光学延迟系统实际加工和安装精度低对系统非线性影响。
发明内容
为了解决现有技术存在的上述问题，本发明提供一种光学延迟系统延迟时间非线性校准方法，降低快速光学延迟系统由于实际加工及安装精度低造成的延迟时间非线性对信号采集的影响，可适用于不同种类快速光学延迟系统的校准。
本发明是通过以下技术方案实现的：
一种光学延迟系统延迟时间非线性校准方法，包括以下步骤：
步骤一、搭建偏振式迈克尔逊干涉测量系统：偏振式迈克尔逊干涉测量系统包括光源系统、分光系统、参考臂系统、测量臂系统、干涉系统，所述测量臂系统包括旋转光学延迟系统，旋转光学延迟系统包括旋转棱体、旋转位移台，旋转棱体同轴固定在旋转位移台上且由旋转位移台驱动其绕中轴水平转动；所述光源系统出射的激光光束L1到达分光系统后由偏振分光棱镜分成参考臂光束L2和 测量臂光束L3；参考臂光束L2进入参考臂系统反射后回到偏振分光棱镜；测量臂光束L3进入测量臂系统，到达旋转光学延迟系统中的旋转棱体，由旋转棱体的棱面进行反射，最后再经一次反射后原路返回到偏振分光棱镜；参考臂系统返回的参考臂光束L2和测量臂系统返回的测量臂光束L3在偏振分光棱镜的折反射后进行汇合为干涉光束L4，干涉光束L4进入到干涉系统，在干涉系统的CCD相机上获得干涉条纹；
步骤二、旋转位移台以旋转间隔β驱动旋转棱体旋转，并在旋转棱体单个棱面的角度变化过程中采集CCD相机中对应的干涉条纹图像；
步骤三、对所述步骤二采集的干涉条纹图像进行处理，获得所述旋转光学延迟系统中旋转棱体单个棱面旋转角度的实际延迟时间；
步骤四、利用最小二乘法拟合所述旋转光学延迟系统中旋转棱体的旋转角度γi与实际延迟时间ti的关系：重复步骤二至步骤三若干次，将旋转棱体单个棱面旋转角度γi在让按此次重复测量下获得的延迟时间平均值作为该棱面实际延迟ti，并利用最小二乘法对旋转棱体单个棱面的旋转角度γi和实际延迟时间ti的关系进行拟合；对旋转棱体中的所有棱面重复上述步骤，获得旋转棱体每个棱面的旋转角度和实际延迟时间的最小二乘法拟合关系；
步骤五、基于步骤四的最小二乘法拟合关系，建立旋转光学延迟系统中旋转棱体延迟时间与旋转位移台角度的灵敏度关系，实现对旋转光学延迟系统延迟时间非线性的校准和旋转光学延迟系统编码器的选型。
优选的，所述偏振式迈克尔逊干涉测量系统的光源系统包括沿光轴方向依次设置的氦氖激光器、透镜、起偏器；参考臂系统包括沿光轴方向设置的1/4波片和平面反射镜；测量臂系统包括沿光轴方向设置的1/4波片和旋转光学延迟系统，旋转光学延迟系统包含透镜、固定平面反射镜、旋转棱体、旋转位移台，透及固定平面反射镜沿旋转棱体反射光路依次设置；干涉系统包括沿光轴方向设置的检偏器和CCD相机；由氦氖激光器出射的激光光束L1，经透镜和起偏器对激光进 行扩束后转成偏振光；偏振光到达分光系统后由偏振分光棱镜分成参考臂光束L2和测量臂光束L3；参考臂光束L2进入参考臂系统，依次经1/4波片和平面反射镜后回到分光系统的偏振分光棱镜；测量臂光束L3进入测量臂系统，经1/4波片后到达旋转光学延迟系统中的旋转棱体，由旋转棱体的棱面反射到透镜，最后由固定反射镜原路返回到分光系统的偏振分光棱镜；调节参考臂系统中平面反射镜的角度和位置，使得参考臂系统返回的参考臂光束L2和测量臂系统返回的测量臂光束L3在偏振分光棱镜的折反射后进行汇合为干涉光束L4，干涉光束L4进入到干涉系统，经由检偏器最后到达CCD相机，并在CCD相机上获得干涉条纹。
优选的，所述氦氖激光器使用波长632.8nm的氦氖激光器1。
进一步地，所述步骤二具体包括：
2.1)调节参考臂系统、测量臂系统、干涉系统光轴方向以及CCD相机位置，直至干涉条纹位于CCD相机中心区域；
2.2)以旋转角度间隔β微调旋转位移台，驱动旋转棱体旋转；通过CCD相机持续采集旋转棱体角度变化过程中，对应干涉条纹的变化图像；
2.3)旋转位移台持续以旋转角度间隔β驱动旋转棱体旋转，直至旋转棱体转过其单个棱面的工作角度；CCD相机记录下：旋转位移台以旋转角度间隔β转动时，旋转棱体单个棱面工作角度下旋转i次的干涉条纹图像，其中i为旋转位移台以旋转角度间隔β旋转的次数。
进一步地，所述步骤三具体包括：
3.1)设CCD相机获得的每帧干涉条纹图像中，中心圆环位置干涉级次为m，临近中心圆环的干涉条纹级次为m-1；选择m-1级次条纹作为观察对象，计算干涉条纹图像上以该m-1级次条纹宽度大小d为边长的正方形区域的平均灰度值p，记录旋转棱体转动所述旋转角度间隔β过程中，每帧干涉条纹图像在该正方形面积区域对应的灰度值pj，整个旋转角度间隔β角度旋转过程中采集到的干涉条纹图 像总帧数为N，j代表其中第j帧图片；
3.2)利用浮动阈值的方法，选择干涉条纹图像的条纹变化过程中亮条纹和暗条纹面积等于正方形区域面积1/2时的平均灰度值pl记为阈值；
3.3)将在旋转角度间隔β旋转采集到的第j帧图像中灰度值pj大于阈值pl的记为1，灰度值pj小于阈值pl的记为0，则旋转棱体转过旋转角度间隔β过程中的条纹变化量Δ记为：
3.4)重复上述步骤3.1)至步骤3.3)，将旋转光学延迟系统14单个棱面角度在旋转角度间隔β角度变化下，干涉图像中固定区域的灰度值转换成条纹变化量；
3.5)实际延迟时间ti＝条纹变化量Δ×波长λ；最终将旋转棱体每个旋转角度间隔β角度旋转下的条纹变化量Δ转换为延迟时间ti，进而获得旋转棱体的旋转角度γi与实际延迟时间ti的对应关系；其中，i为旋转位移台以旋转角度间隔β旋转的次数，γi为旋转棱体单个棱面的旋转角度。
进一步地，所述步骤四具体包括：
4.1)将步骤二至步骤三重复若干次，求取旋转棱体单个棱面旋转角度在按照旋转角度间隔β旋转时，对应实际延迟时间的平均值；
4.2)将步骤4.1)求取的延迟时间平均值作为旋转棱体单个棱面旋转角度γi的实际延迟时间ti，并利用最小二乘法对旋转棱体中所述单个棱面的旋转角度和实际延迟时间的关系进行拟合，最小二乘法拟合得到的关系模型为：
ti′＝aγi′+b             (2)
其中，ti为旋转棱体单个棱面测试得到的实际延迟时间；
ti′为拟合延迟时间；
γi为旋转棱体单个棱面旋转角度为；
n为待拟合的数据个数；
i为旋转位移台以旋转角度间隔β旋转的次数；
a为拟合延迟时间对旋转棱体旋转角度的灵敏度；
4.3)重复步骤4.1)至步骤4.2)，直至利用最小二乘法完成对旋转棱体中所有棱面的旋转角度γi和实际延迟时间ti关系的拟合，得到所有棱面的拟合延迟时间对旋转角度的灵敏度ak，其中k为旋转棱体的第k个棱面。
优选的，所述旋转角度间隔β取0.1°。
进一步地，所述步骤五具体包括：
基于步骤四获得的旋转棱体每个棱面的旋转角度和实际延迟时间的最小二乘法拟合关系，得到拟合之后旋转光学延迟系统中旋转棱体的各个棱面的实际延迟时间与旋转位移台旋转角度的对应关系，用以校准旋转光学延迟系统的非线性；
为满足光学探测系统最小采样间隔Δtmin要求，旋转光学延迟系统编码器的最小分辨率Δθmin为：
其中，αmax为旋转棱体各个棱面中基于最小二乘法拟合得到的最大灵敏度。
本发明具有以下优点：
本发明可以对光学探测系统中快速光学延迟系统加工及装配精度较低引入的非线性进行校准，可有效降低光学探测系统对快速旋转光学延迟系统高加工及装配精度的要求，为推动快速旋转光学延迟系统的广泛应用提供基础。
本发明对快速旋转光学延迟系统的精度要求高的系统，非线性校准效果好，可大幅度降低旋转光学延迟系统的加工成本，具有广泛的实用性。
附图说明
为了更清楚地说明本申请实施例的技术方案，下面将对实施例中所需要使用的附图作简单地介绍，显而易见地，下面描述中的附图仅仅是本申请的一些实施例，对于本领域普通技术人员来讲，在不付出创造性劳动的前提下，还可以根据这些附图获得其它的附图。
图1为本发明实施例所述光学延迟系统延迟时间非线性校准方法流程图；
图2为本发明实施例所述偏振式迈克尔逊干涉测量系统光路示意图；
图3为本发明实施例所述旋转光学延迟系统光路侧视图；
图4为本发明实施例采集到的干涉条纹图像灰度计算区域示意图；
图5为本发明实施例采集到的干涉条纹图像灰度阈值区域示意图。
具体实施方式
下面通过具体实施例对本发明作进一步详述，以下实施例只是描述性的，不是限定性的，不能以此限定本发明的保护范围。
如图1所示，本实施例为一种光学延迟系统延迟时间非线性校准方法，包括以下步骤：
步骤一、搭建偏振式迈克尔逊干涉测量系统：
如图2、图3所示，偏振式迈克尔逊干涉测量系统包括光源系统、分光系统、参考臂系统、测量臂系统、干涉系统5个部分；所述测量臂系统包括旋转光学延迟系统14，旋转光学延迟系统14包括旋转棱体10、旋转位移台11，旋转棱体10同轴固定在旋转位移台11上且由旋转位移台11驱动其绕中轴水平转动；所述光源系统出射的激光光束L1到达分光系统后由偏振分光棱镜4分成参考臂光束L2和测量臂光束L3；参考臂光束L2进入参考臂系统反射后回到偏振分光棱镜4； 测量臂光束L3进入测量臂系统，到达旋转光学延迟系统14中的旋转棱体10，由旋转棱体10的棱面进行反射，最后再经一次反射后原路返回到偏振分光棱镜4；参考臂系统返回的参考臂光束L2和测量臂系统返回的测量臂光束L3在偏振分光棱镜4的折反射后进行汇合为干涉光束L4，干涉光束L4进入到干涉系统，在干涉系统的CCD相机13上获得干涉条纹。
其中，光源系统包括沿光轴方向依次设置的氦氖激光器1、透镜2、起偏器3；分光系统包括偏振分光棱镜4；参考臂系统包括沿光轴方向设置的1/4波片5和平面反射镜6；测量臂系统包括沿光轴方向设置的1/4波片7和旋转光学延迟系统14；干涉系统包括沿光轴方向设置的检偏器12和CCD相机13；
所述旋转光学延迟系统14包含透镜8、固定平面反射镜9、旋转棱体10、旋转位移台11；旋转棱体10同轴固定在旋转位移台11上，旋转棱体10在旋转位移台11驱动下在水平面内绕中轴转动；透镜8及固定平面反射镜9沿旋转棱体10反射光路依次设置。
偏振式迈克尔逊干涉测量系统为保证干涉条纹的稳定性，需要干涉光源功率稳定性高，优先使用波长632.8nm的氦氖激光器1。
光源系统中，由氦氖激光器1出射的激光光束L1，经透镜2和起偏器3对激光进行扩束后转成偏振光；偏振光到达分光系统后由偏振分光棱镜4分成参考臂光束L2和测量臂光束L3；参考臂光束L2进入参考臂系统，依次经1/4波片5和平面反射镜6后回到分光系统的偏振分光棱镜4；测量臂光束L3进入测量臂系统，经1/4波片7后到达旋转光学延迟系统14中的旋转棱体10，由旋转棱体10的棱面反射到透镜8，最后由固定反射镜9原路返回到分光系统的偏振分光棱镜4；调节参考臂系统中平面反射镜6的角度和位置，使得参考臂系统返回的参考臂光束L2和测量臂系统返回的测量臂光束L3在偏振分光棱镜4的折反射后进行汇合为干涉光束L4，干涉光束L4进入到干涉系统，经由检偏器12最后到达CCD相机13，并在CCD相机13上获得干涉条纹。
步骤二、以0.1°为旋转位移台11旋转间隔，驱动旋转棱体10旋转，并在旋转棱体10单个棱面的角度变化过程中采集CCD相机13中对应的干涉条纹图像：
2.1)调节1/4波片5、1/4波片7和检偏器12光轴方向以及CCD相机13位置，直至干涉条纹位于CCD相机13中心区域，且中心各条级次干涉条纹清晰稳定、条纹间距较大、对比度高；
2.2)以0.1°为旋转角度间隔，稳定缓慢地微调旋转位移台11，驱动旋转棱体10旋转；通过CCD相机13持续采集旋转棱体10角度变化过程中，对应干涉条纹的变化图像；
2.3)旋转位移台11持续以0.1°为旋转角度间隔驱动旋转棱体10旋转，直至旋转棱体10转过单个棱面的工作角度；CCD相机13记录下：旋转位移台11以0.1°为旋转角度间隔转动时，旋转棱体10单个棱面工作角度下旋转i次的干涉条纹图像，其中i为旋转位移台以0.1°为间隔旋转的次数；
步骤三、获得所述旋转光学延迟系统14中旋转棱体10单个棱面旋转角度的实际延迟时间：
3.1)设CCD相机13获得的每帧干涉条纹图像中，中心圆环位置干涉级次为m，临近中心圆环的干涉条纹级次为m-1；选择m-1级次条纹作为观察对象，计算干涉条纹图像上以该m-1级次条纹宽度大小d为边长的正方形区域的平均灰度值p，记录旋转棱体10转动0.1°过程中每帧干涉条纹图像在该正方形面积区域对应的灰度值pj，整个0.1°角度旋转光程中采集到的干涉条纹图像总帧数为N，j代表其中第j帧图片；
3.2)利用浮动阈值的方法，选择干涉条纹图像的条纹变化过程中亮条纹和暗条纹面积等于正方形区域面积1/2时的平均灰度值pl记为阈值；
3.3)将在0.1°旋转角度间隔旋转采集到的第j帧图像中灰度值pj大于阈值pl的记为1，灰度值pj小于阈值pl的记为0，则旋转棱体10旋转0.1°过程中的条纹变化量Δ可记为：
3.4)重复上述步骤3.1)至步骤3.3)，将旋转光学延迟系统14单个棱面角度在0.1°角度变化下，干涉图像中固定区域的灰度值转换成条纹变化量；
3.5)实际延迟时间ti＝条纹变化量Δ×波长λ；最终将旋转棱体10每0.1°角度旋转下的条纹变化量Δ转换为延迟时间ti，进而获得旋转棱体10的旋转角度γi与实际延迟时间ti的对应关系；其中，i为旋转位移台以0.1°为间隔旋转的次数，γi为旋转棱体10单个棱面的旋转角度。
步骤四、利用最小二乘法拟合所述旋转光学延迟系统14中旋转棱体10的旋转角度γi与实际延迟时间ti的关系：重复步骤二至步骤三，将旋转棱体10单个棱面旋转角度γi在3次重复测量下获得的延迟时间平均值作为该棱面实际延迟ti，并利用最小二乘法对旋转棱体10单个棱面的旋转角度γi和实际延迟时间ti的关系进行拟合；对旋转棱体10中的所有棱面重复上述步骤，获得旋转棱体10每个棱面的旋转角度和实际延迟时间的最小二乘法拟合关系。
4.1)将步骤二至步骤三重复3次，求取旋转棱体10单个棱面旋转角度旋转0.1°时，对应实际延迟时间的平均值；
4.2)将步骤4.1)求取的延迟时间平均值作为旋转棱体10单个棱面旋转角度γi的实际延迟时间ti，并利用最小二乘法对旋转棱体10中所述单个棱面的旋转角度和实际延迟时间的关系进行拟合，最小二乘法拟合得到的关系模型为：
ti′＝aγi′+b             (2)
其中，ti为旋转棱体10单个棱面测试得到的实际延迟时间；
ti′为拟合延迟时间；
γi为旋转棱体10单个棱面旋转角度为；
n为待拟合的数据个数；
i为旋转位移台以0.1°为间隔旋转的次数；
a为拟合延迟时间对旋转棱体旋转角度的灵敏度；
4.3)重复步骤4.1)至步骤4.2)，直至利用最小二乘法完成对旋转棱体10中所有棱面(本实施例为24个棱面)的旋转角度γi和实际延迟时间ti关系的拟合，得到24个棱面的拟合延迟时间对旋转角度的灵敏度ak，其中k为旋转棱体10的第k个棱面。
步骤五、基于步骤四的最小二乘法拟合关系，建立旋转光学延迟系统14旋转棱体延迟时间与旋转位移台11角度的灵敏度关系，实现对旋转光学延迟系统14延迟时间非线性的校准和旋转光学延迟系统编码器的选型。
5.1)由于不同工作面存在加工和装配的误差，因此，旋转棱体各棱面的实际延迟时间与旋转角度的对应关系各不相同，因此每个棱面延迟时间的非线性也不相同；
5.2)基于旋转棱体10单个棱面旋转角度和实际延迟时间的最小二乘法拟合公式(2)，可得到拟合之后旋转光学延迟系统14中，旋转棱体10的24个棱面的实际延迟时间与旋转位移台11旋转角度的对应关系，用以校准旋转光学延迟系统14的非线性。
5.3)基于旋转光学延迟系统14中旋转棱体10每个棱面旋转角度和实际延迟时间的灵敏度关系模型，可知在实际工作中延迟时间对旋转角度的灵敏度a并不完全相同，因此旋转光学延迟系统14在同样采样间隔下，旋转棱体10每个棱面产生相同的延迟时间，所需转过的角度也不相同，为满足光学探测系统最小采样间隔Δtmin要求，旋转光学延迟系统编码器的最小分辨率Δθmin为：
其中，αmax为旋转棱体10各个棱面中基于最小二乘法拟合得到的最大灵敏度。

Claims (8)

  1. 一种光学延迟系统延迟时间非线性校准方法，其特征在于，包括以下步骤：
    步骤一、搭建偏振式迈克尔逊干涉测量系统：偏振式迈克尔逊干涉测量系统包括光源系统、分光系统、参考臂系统、测量臂系统、干涉系统，所述测量臂系统包括旋转光学延迟系统，旋转光学延迟系统包括旋转棱体、旋转位移台，旋转棱体同轴固定在旋转位移台上且由旋转位移台驱动其绕中轴水平转动；所述光源系统出射的激光光束L1到达分光系统后由偏振分光棱镜分成参考臂光束L2和测量臂光束L3；参考臂光束L2进入参考臂系统反射后回到偏振分光棱镜；测量臂光束L3进入测量臂系统，到达旋转光学延迟系统中的旋转棱体，由旋转棱体的棱面进行反射，最后再经一次反射后原路返回到偏振分光棱镜；参考臂系统返回的参考臂光束L2和测量臂系统返回的测量臂光束L3在偏振分光棱镜的折反射后进行汇合为干涉光束L4，干涉光束L4进入到干涉系统，在干涉系统的CCD相机上获得干涉条纹；
    步骤二、旋转位移台以旋转间隔β驱动旋转棱体旋转，并在旋转棱体单个棱面的角度变化过程中采集CCD相机中对应的干涉条纹图像；
    步骤三、对所述步骤二采集的干涉条纹图像进行处理，获得所述旋转光学延迟系统中旋转棱体单个棱面旋转角度的实际延迟时间；
    步骤四、利用最小二乘法拟合所述旋转光学延迟系统中旋转棱体的旋转角度γi与实际延迟时间ti的关系：重复步骤二至步骤三若干次，将旋转棱体单个棱面旋转角度γi在让按此次重复测量下获得的延迟时间平均值作为该棱面实际延迟ti，并利用最小二乘法对旋转棱体单个棱面的旋转角度γi和实际延迟时间ti的关系进行拟合；对旋转棱体中的所有棱面重复上述步 骤，获得旋转棱体每个棱面的旋转角度和实际延迟时间的最小二乘法拟合关系；
    步骤五、基于步骤四的最小二乘法拟合关系，建立旋转光学延迟系统中旋转棱体延迟时间与旋转位移台角度的灵敏度关系，实现对旋转光学延迟系统延迟时间非线性的校准和旋转光学延迟系统编码器的选型。
  2. 如权利要求1所述的一种光学延迟系统延迟时间非线性校准方法，其特征在于，所述偏振式迈克尔逊干涉测量系统的光源系统包括沿光轴方向依次设置的氦氖激光器、透镜、起偏器；参考臂系统包括沿光轴方向设置的1/4波片和平面反射镜；测量臂系统包括沿光轴方向设置的1/4波片和旋转光学延迟系统，旋转光学延迟系统包含透镜、固定平面反射镜、旋转棱体、旋转位移台，透8及固定平面反射镜沿旋转棱体反射光路依次设置；干涉系统包括沿光轴方向设置的检偏器和CCD相机；由氦氖激光器出射的激光光束L1，经透镜和起偏器对激光进行扩束后转成偏振光；偏振光到达分光系统后由偏振分光棱镜分成参考臂光束L2和测量臂光束L3；参考臂光束L2进入参考臂系统，依次经1/4波片和平面反射镜后回到分光系统的偏振分光棱镜；测量臂光束L3进入测量臂系统，经1/4波片后到达旋转光学延迟系统中的旋转棱体，由旋转棱体的棱面反射到透镜，最后由固定反射镜原路返回到分光系统的偏振分光棱镜；调节参考臂系统中平面反射镜的角度和位置，使得参考臂系统返回的参考臂光束L2和测量臂系统返回的测量臂光束L3在偏振分光棱镜的折反射后进行汇合为干涉光束L4，干涉光束L4进入到干涉系统，经由检偏器最后到达CCD相机，并在CCD相机上获得干涉条纹。
  3. 如权利要求2所述的一种光学延迟系统延迟时间非线性校准方法，其特征在于，所述氦氖激光器使用波长632.8nm的氦氖激光器1。
  4. 如权利要求1所述的一种光学延迟系统延迟时间非线性校准方法，其特征在于，所述步骤二具体包括：
    2.1)调节参考臂系统、测量臂系统、干涉系统光轴方向以及CCD相机位置，直至干涉条纹位于CCD相机中心区域；
    2.2)以旋转角度间隔β微调旋转位移台，驱动旋转棱体旋转；通过CCD相机持续采集旋转棱体角度变化过程中，对应干涉条纹的变化图像；
    2.3)旋转位移台持续以旋转角度间隔β驱动旋转棱体旋转，直至旋转棱体转过其单个棱面的工作角度；CCD相机记录下：旋转位移台以旋转角度间隔β转动时，旋转棱体单个棱面工作角度下旋转i次的干涉条纹图像，其中i为旋转位移台以旋转角度间隔β旋转的次数。
  5. 如权利要求1所述的一种光学延迟系统延迟时间非线性校准方法，其特征在于，所述步骤三具体包括：
    3.1)设CCD相机获得的每帧干涉条纹图像中，中心圆环位置干涉级次为m，临近中心圆环的干涉条纹级次为m-1；选择m-1级次条纹作为观察对象，计算干涉条纹图像上以该m-1级次条纹宽度大小d为边长的正方形区域的平均灰度值p，记录旋转棱体转动所述旋转角度间隔β过程中，每帧干涉条纹图像在该正方形面积区域对应的灰度值pj，整个旋转角度间隔β角度旋转过程中采集到的干涉条纹图像总帧数为N，j代表其中第j帧图片；
    3.2)利用浮动阈值的方法，选择干涉条纹图像的条纹变化过程中亮条纹和暗条纹面积等于正方形区域面积1/2时的平均灰度值pl记为阈值；
    3.3)将在旋转角度间隔β旋转采集到的第j帧图像中灰度值pj大于阈值pl的记为1，灰度值pj小于阈值pl的记为0，则旋转棱体转过旋转角度间隔β过程中的条纹变化量Δ记为：
    3.4)重复上述步骤3.1)至步骤3.3)，将旋转光学延迟系统14单个棱面角度在旋转角度间隔β角度变化下，干涉图像中固定区域的灰度值转 换成条纹变化量；
    3.5)实际延迟时间ti＝条纹变化量Δ×波长λ；最终将旋转棱体每个旋转角度间隔β角度旋转下的条纹变化量Δ转换为延迟时间ti，进而获得旋转棱体的旋转角度γi与实际延迟时间ti的对应关系；其中，i为旋转位移台以旋转角度间隔β旋转的次数，γi为旋转棱体单个棱面的旋转角度。
  6. 如权利要求1所述的一种光学延迟系统延迟时间非线性校准方法，其特征在于，所述步骤四具体包括：
    4.1)将步骤二至步骤三重复若干次，求取旋转棱体单个棱面旋转角度在按照旋转角度间隔β旋转时，对应实际延迟时间的平均值；
    4.2)将步骤4.1)求取的延迟时间平均值作为旋转棱体单个棱面旋转角度γi的实际延迟时间ti，并利用最小二乘法对旋转棱体中所述单个棱面的旋转角度和实际延迟时间的关系进行拟合，最小二乘法拟合得到的关系模型为：
    ti'＝aγi'+b    (2)

    其中，ti为旋转棱体单个棱面测试得到的实际延迟时间；
    ti'为拟合延迟时间；
    γi为旋转棱体单个棱面旋转角度为；
    n为待拟合的数据个数；
    i为旋转位移台以旋转角度间隔β旋转的次数；
    a为拟合延迟时间对旋转棱体旋转角度的灵敏度；
    4.3)重复步骤4.1)至步骤4.2)，直至利用最小二乘法完成对旋转棱体中所有棱面的旋转角度γi和实际延迟时间ti关系的拟合，得到所有棱面的拟合延迟时间对旋转角度的灵敏度ak，其中k为旋转棱体的第k个棱面。
  7. 如权利要求1、4、5、6中任意一项所述的一种光学延迟系统延迟时间非线性校准方法，其特征在于，所述旋转角度间隔β取0.1°。
  8. 如权利要求1所述的一种光学延迟系统延迟时间非线性校准方法，其特征在于，所述步骤五具体包括：
    基于步骤四获得的旋转棱体每个棱面的旋转角度和实际延迟时间的最小二乘法拟合关系，得到拟合之后旋转光学延迟系统中旋转棱体的各个棱面的实际延迟时间与旋转位移台旋转角度的对应关系，用以校准旋转光学延迟系统的非线性；
    为满足光学探测系统最小采样间隔Δtmin要求，旋转光学延迟系统编码器的最小分辨率Δθmin为：
    其中，αmax为旋转棱体各个棱面中基于最小二乘法拟合得到的最大灵敏度。
PCT/CN2023/073108 2022-08-17 2023-01-19 一种光学延迟系统延迟时间非线性校准方法 WO2024036885A1 (zh)

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