WO2022002273A1 - 衍射光学元件的周期优化方法 - Google Patents

衍射光学元件的周期优化方法 Download PDF

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WO2022002273A1
WO2022002273A1 PCT/CN2021/104476 CN2021104476W WO2022002273A1 WO 2022002273 A1 WO2022002273 A1 WO 2022002273A1 CN 2021104476 W CN2021104476 W CN 2021104476W WO 2022002273 A1 WO2022002273 A1 WO 2022002273A1
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period
optical element
diffractive optical
target point
target
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PCT/CN2021/104476
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English (en)
French (fr)
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王牧云
张东亮
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杭州驭光光电科技有限公司
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Priority to US18/004,106 priority Critical patent/US11733536B1/en
Priority to EP21834291.3A priority patent/EP4177666A1/en
Publication of WO2022002273A1 publication Critical patent/WO2022002273A1/zh

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    • G—PHYSICS
    • G02—OPTICS
    • G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
    • G02B27/00—Optical systems or apparatus not provided for by any of the groups G02B1/00 - G02B26/00, G02B30/00
    • G02B27/0012—Optical design, e.g. procedures, algorithms, optimisation routines
    • G—PHYSICS
    • G02—OPTICS
    • G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
    • G02B27/00—Optical systems or apparatus not provided for by any of the groups G02B1/00 - G02B26/00, G02B30/00
    • G02B27/42—Diffraction optics, i.e. systems including a diffractive element being designed for providing a diffractive effect
    • G02B27/4266—Diffraction theory; Mathematical models

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  • the present invention relates to the field of diffractive optics, and more particularly, to a period optimization method for diffractive optical elements.
  • 3D depth perception technology based on structured light has become a hot direction of technology development.
  • the laser speckle projector is one of the key devices of the structured light depth perception technology, and the projected coding pattern will directly affect the complexity of depth decoding calculation, the accuracy and resolution of depth measurement.
  • the laser speckle projector mainly includes a light source and a diffractive optical element in structure.
  • the diffractive optical element can be designed for collimated light or for divergent light.
  • the laser speckle projector also includes a collimating lens for collimating the light emitted by the light source.
  • the light source is preferably a vertical cavity surface emitting laser.
  • the optical cavity is oriented perpendicular to the semiconductor wafer, can emit light from the surface, has a small size, can output a circular spot, and is easy to integrate into a large Area lattice and other advantages.
  • the diffractive optical element is used to modulate the incident light to form a predetermined beam splitting lattice on the target plane, combined with the lattice distribution pattern of the vertical cavity surface emitting laser itself, that is, the lattice distribution of the vertical cavity surface emitting laser
  • the pattern is convolved with the spectroscopic lattice formed by the diffractive optical element, thereby forming a laser speckle pattern covering the target field of view on the target plane, that is, the projected coding pattern.
  • the coding pattern will directly affect the computational complexity of depth decoding, the precision and resolution of depth measurement.
  • each point of the spectroscopic lattice formed by the diffractive optical element on the target plane has precise positioning.
  • the actual The spatial position of the spectroscopic lattice is difficult to perfectly match the positioning position required by the design.
  • the purpose of the present invention is to achieve as perfect matching as possible between the actual spatial position of the spectroscopic lattice and the positioning position required by the design by optimizing the design period of the diffractive optical element.
  • the present invention provides a period optimization method for a diffractive optical element, which is used for lattice structured light projection, comprising the following steps:
  • Spectroscopic lattices can be obtained using diffractive optical elements with different periods. According to the present invention, by comparing the difference between the coordinates of the actual projection point and the coordinates of each target point, it is possible to determine the period used when the difference is the smallest as the optimal period, so that the actually obtained spectroscopic lattice can be positioned with the target spectroscopic lattice. The positions are nearly perfectly matched, thereby optimizing the design cycle of diffractive optical elements.
  • the periodic optimization evaluation parameter is any one of the following, the average distance between each target point A i and its corresponding actual projection point A i ′, or each target point A i and its corresponding The maximum value of the distances between the actual projection points A i ', or the sum of the distances between each target point A i and its corresponding actual projection point A i ', or each target point A i and its corresponding The maximum value of the absolute difference of the abscissa and/or ordinate between the actual projection points A i '.
  • period optimization evaluation parameters are not limited to those listed above, and any suitable period optimization evaluation parameters capable of determining the optimal period according to the method of the present invention are within the protection scope of the present invention.
  • the distance mean is any one of arithmetic mean, geometric mean, harmonic mean, weighted mean, and root mean square mean.
  • the distance mean is an evaluation parameter according to the present invention, and the distance mean may be any suitable mean.
  • the obtained period optimization evaluation parameters are compared to obtain the minimum value of the period optimization evaluation parameters, and the period corresponding to the minimum value is determined as the optimal period.
  • the minimum value of the difference between the actual projection point and the target point can be determined by comparing the minimum value of the period optimization evaluation parameter, so that the period corresponding to the minimum value is determined as the optimal period, and the method is simple and intuitive.
  • the minimum value is obtained using a genetic algorithm.
  • the period d j is adjusted to the period d j+1 by fixing the pixel size and increasing the number of pixels by an increment of the number of pixels.
  • the period d j is adjusted to the period d j+1 by increasing the product of the pixel size and the number of pixels by a product increment.
  • the rounding method is any one of rounding, rounding off decimals, rounding with rounds, rounding on odd numbers, or rounding off even numbers.
  • the rounding method in the method for optimizing the period of the diffractive optical element according to the present invention is not limited to those listed above, and other suitable methods capable of rounding the diffraction order are also within the protection scope of the present invention.
  • the period d j+1 is less than or equal to the size of the diffractive optical element.
  • the selected period of the diffractive optical element cannot be expanded infinitely, which is physically limited by the actual size of the diffractive optical element.
  • the actual spectroscopic lattice projected by the diffractive optical element can match the target spectroscopic lattice as much as possible under a small amount of calculation, thereby improving the design quality and precision of the diffractive optical element.
  • 1 is a flow chart of a method for optimizing the period of a diffractive optical element according to the present invention
  • Figure 2 is a diagram showing a target lattice and its coordinates
  • FIG. 3 is a calculation data table for realizing the target lattice shown in FIG. 2 according to the method for optimizing the period of a diffractive optical element of the present invention
  • FIG. 4 is a graph showing absolute difference values of coordinates derived from the data of FIG. 3 .
  • Diffractive optical elements used for spectroscopic lattice projection are generally designed in the form of periodic close packing.
  • the diffractive optical elements have a microstructure surface, and the microstructure surface includes a plurality of microstructure pattern units arranged adjacently in an array.
  • the microstructure patterns (phases) of the microstructure pattern units are the same, that is, each microstructure pattern unit can perform phase modulation on the incident light, thereby projecting a spectroscopic lattice on the target plane.
  • the size of the microstructure pattern unit is called the period of the diffractive optical element.
  • the machining accuracy of the diffractive optical element determines the pixel size of the diffractive optical element.
  • the period size and pixel size of the diffractive optical element determine the number of pixels of a single microstructure pattern unit.
  • the diffractive optical element used for dot matrix projection can also be designed for a single period of divergent light, and in this case, the size of the diffractive optical element is the period size of the diffractive optical element.
  • the protection scope of the present invention includes both the design mode of periodic close-packing and the design mode of single cycle.
  • the pixel size In the case of a certain processing accuracy, that is, the pixel size is fixed, the larger the period, the more the number of pixels in a single microstructure pattern unit, the greater the design flexibility of the diffractive optical element, and the more flexible the modulation of the incident light. Intricate projection patterns. However, the more pixels there are, the more difficult it is to design the diffractive optical element, and the calculation time of the computer-aided program is longer. Due to the size of the product, the period of the diffractive optical element cannot be infinitely expanded, so it is necessary to optimize the period of the diffractive optical element. .
  • FIG. 1 is a flowchart of a method for optimizing the period of a diffractive optical element according to the present invention.
  • step 101 according to the coordinates (x i , y i ) of each target point A i of the target lattice in the X and Y directions, and the distance a between the diffractive optical element and the target plane, calculate the Diffraction angles ( ⁇ xi , ⁇ yi ) of each target point A i in the X and Y directions, where i is an integer,
  • the design of the diffractive optical element calculates the angular spectral resolution, so in step 101, the coordinates of the target lattice are transferred from the plane to the angular spectral.
  • step 102 the period d j of the diffractive optical element is preliminarily selected, wherein the period is determined by the product of the pixel size and the number of pixels, and the number of pixels is a positive integer.
  • step 104 the diffraction orders (m i , ni ) are rounded to obtain the rounded diffraction orders (m i ', ni ').
  • the diffraction orders are integers, so the calculated diffraction orders (m i , n i ) need to be rounded.
  • step 105 the use of diffraction orders the rounded (m i ', n i' ) to calculate the actual projection point A i 'in the X direction and the Y-coordinate direction (x i', y i ' ).
  • step 105 the point on the angular spectrum is converted to the plane where the target lattice is located, so that the coordinates (x i ', y i ') of the actual projection point A i ' in the X direction and the Y direction can be compared with the target point The coordinates (x i , y i ) of the corresponding target points of the matrix are compared.
  • step 106 the period optimization evaluation parameter is calculated according to the coordinates of each target point A i and the corresponding actual projection point A i '.
  • step 109 it is judged whether the period exceeds the limit of the actual size of the diffractive optical element, if not, the following steps are performed:
  • step 107 the period d j is adjusted to d j+1 , and the above steps 103-106 are repeated to calculate the period optimization evaluation parameter under the adjusted period d j+1.
  • step 108 the optimal period of the diffractive optical element is determined according to the period optimization evaluation parameter.
  • FIG. 2 is a graph showing a 3 ⁇ 3 lattice and its coordinates
  • FIG. 3 is a calculation data table for realizing the 3 ⁇ 3 lattice shown in FIG. 2 according to the method for optimizing the period of a diffractive optical element of the present invention.
  • the distance between the diffractive optical element and the target plane is 700 mm
  • the pixel size is 0.23 ⁇ m
  • the wavelength of the light source is 0.94 ⁇ m.
  • the target point coordinates (x i , y i ) in FIG. 3 are the corresponding coordinates of each target point in the 3 ⁇ 3 lattice in FIG. 2 .
  • the period of the diffractive optical element is initially selected to be 621.23 ⁇ m, and the period of the diffractive optical element is determined by the product of the pixel size and the number of pixels. If the pixel size is 0.23 ⁇ m, the number of pixels is 2701.
  • the calculated diffraction orders (m i , ni ) of the target point are rounded to obtain the rounded diffraction orders (m i ', ni ').
  • odd-digit rounding is used. Since the diffraction order starts from the 0th order, the odd-numbered bits correspond to the even-numbered diffraction orders. In the data table shown in Figure 3, the odd-numbered bits are rounded off, that is, the even-numbered diffraction orders are rounded off to decimals, and the integer bits are rounded off. Round up for odd diffraction orders. Practice has proved that the diffractive optical element designed in this way has better light efficiency, lower non-uniformity of the lattice, and more uniform light spot at each point of the light field.
  • the diffraction angles ( ⁇ xi ', ⁇ yi ') in Fig. 3 are the diffraction angles of the actual projection points calculated according to the rounded diffraction orders (m i ', ni ').
  • diffraction angle ( ⁇ xi ', ⁇ yi' ) the actual coordinates may be further calculated projection point on the target plane (x i ', y i' ).
  • the absolute difference data of the coordinates in Figure 3 is the calculated data.
  • FIG. 4 is a graph showing absolute difference values of coordinates derived from the data of FIG. 3 .
  • the maximum value of the absolute difference of coordinates is selected as the period optimization evaluation parameter of the diffractive optical element.
  • the period optimization evaluation parameter between the target diffraction point and the actual projection point that is, the absolute difference of coordinates
  • the period of the diffractive optical element is further adjusted to d j+1 , and when the period is d j+1 , the above calculation of the absolute difference of coordinates is repeated, and the maximum value of the absolute difference of coordinates under each selected period is selected as the value of the absolute difference of the diffractive optical element.
  • Periodically optimize the evaluation parameters until the period d j+1 is greater than or equal to the actual size of the diffractive optical element or it exceeds a preset threshold range.
  • the above-mentioned preset threshold range can be set according to the experience of those skilled in the art.
  • the lower threshold can correspond to the minimum number of pixels that can satisfy the design flexibility to achieve uniform spectral modulation of incident light
  • the upper threshold can correspond to the pixel number.
  • the amount of the number does not significantly increase the time required for the computer-aided software to calculate the phase distribution of the diffractive optical element, so as to ensure the efficiency when designing the diffractive optical element.
  • the diffractive optical element designed with the optimal period can make the actual spectroscopic lattice projected by the diffractive optical element match the target spectroscopic lattice as much as possible.
  • the cycle optimization evaluation parameter is evaluated by the maximum value of the absolute difference of the coordinates
  • the cycle optimization evaluation parameter can be any of the following: each target point the maximum distance between a i and its corresponding actual projection points a i 'average distance between the, or each target point a i and its corresponding actual projection points a i' in the, or each target point the abscissa of absolute differences and / or longitudinally between a i and its corresponding actual projection points a i 'and the distance between the, or each target point a i and its corresponding actual projection points a i' coordinates the maximum value of the value.
  • the distance average value when used as the periodic optimization evaluation parameter, the distance average value may be any of an arithmetic average value, a geometric average value, a harmonic average value, a weighted average value, and a root mean square average value.
  • the minimum value is calculated by the genetic algorithm, but the present invention is not limited thereto, and other algorithms capable of obtaining the minimum value are also within the protection scope of the present invention.
  • the minimum value here is the minimum of the maximum absolute difference between the calculated coordinate and the target coordinate. The smaller the value is, the closer the calculated coordinate value is to the target value.
  • the period of the diffractive optical element is determined by the product of the pixel size and the number of pixels, and the pixel size is usually determined by the machining accuracy. Therefore, when adjusting the period, the pixel size is usually fixed and the number of pixels is increased by one pixel increment to change the period. Period d j is adjusted to period d j+1 . On the premise that the pixel size satisfies the machining accuracy, the period d j may also be adjusted to the period d j+1 by increasing the product of the pixel size and the number of pixels by a product increment. However, the product of the pixel size and the number of pixels, that is, the period, must meet the product size specifications, neither too large nor too small, and the adjustment range is limited by the actual size of the diffractive optical element.
  • the diffraction orders (m i , ni ) of the target point are rounded by using an odd-digit rounding method, which is a preferred rounding method for this embodiment.
  • odd-digit rounding may be adopted as required, that is, the diffraction orders whose integer bits are odd numbers are rounded off to decimals, and the diffraction orders whose integer bits are even numbers are rounded up.
  • the calculated diffraction orders may also be rounded off, rounded off, or rounded off.
  • the actual spectroscopic lattice projected by the diffractive optical element can match the target spectroscopic lattice as much as possible under a small amount of calculation, thereby improving the design quality and precision of the diffractive optical element.

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Abstract

一种衍射光学元件的周期优化方法，包括：(1)将目标点阵的各个目标点的坐标转换为角谱坐标(101)；(2)选定周期初始值(102)；(3)计算各个目标点的衍射级次(103)；(4)将衍射级次取整(104)；(5)使用取整后的衍射级次计算实际投射点的坐标(105)；(6)计算周期优化评价参数(106)；(7)调整周期值(107)，重复步骤(3)-(6)；(8)比较评价参数，确定衍射光学元件的最优周期（108）。周期优化方法能够在小量的计算下，使得实际点阵尽可能匹配目标点阵，提高衍射光学元件的设计质量和精度。

Description

衍射光学元件的周期优化方法
本申请要求享有于2020年7月3日提交中国专利局、申请号为202010636814.X、发明名称为“衍射光学元件的周期优化方法”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
本发明涉及衍射光学领域，更具体地，涉及衍射光学元件的周期优化方法。
背景技术
随着人脸3D解锁技术在手机上的应用，基于结构光的3D深度感知技术已经成为技术开发的热点方向。其中，激光散斑投射器是结构光深度感知技术的关键设备之一，所投射的编码图案将直接影响深度解码计算的复杂度、深度测量的精度和分辨率。
激光散斑投射器在结构上主要包括光源和衍射光学元件，衍射光学元件可以是针对于准直光设计的，也可以是针对于发散光设计的，当衍射光学元件是针对于准直光设计时，激光散斑投射器还包括准直透镜，用于对光源发射出的光进行准直。其中光源优选使用垂直腔面发射激光器，相比发光二极管LED和激光二极管LD，其光学腔体取向和半导体晶圆垂直，可以从表面发光，具有体积小、能够输出圆形光斑、易集成为大面积点阵等优点。衍射光学元件作为光学调制器件，用于对入射光进行调制，在目标平面上形成预定的分光点阵，结合垂直腔面发射激光器本身的点阵分布图案，即垂直腔面发射激光器的点阵分布图案与衍射光学元件所形成的分光点阵进行卷积，从而在目标平面上形成铺满目标视场的激光散斑图案，即投射的编码图案。该编码图案将直接影响深度解码计算的复杂度、深度测量的精度和分辨率。
为了配合深度提取算法以提高深度测量的精度和分辨率，就要求 衍射光学元件在目标平面上形成的分光点阵的每个点都有精准的定位，然而由于衍射光学元件设计理论的限制，实际的分光点阵的空间位置很难与设计所要求的定位位置完美匹配。
发明内容
本发明的目的是，通过优化衍射光学元件的设计周期，实现实际的分光点阵的空间位置与设计所要求的定位位置尽可能完美匹配。
本发明提出一种衍射光学元件的周期优化方法，用于点阵结构光投射，包括以下步骤：
(1)根据目标点阵的各个目标点A i在X方向和Y方向的坐标(x i，y i)，以及衍射光学元件和目标平面之间的距离a，计算所述目标点阵的各个目标点A i在X方向和Y方向的衍射角(θ xi，θ yi)，其中，i为整数，
Figure PCTCN2021104476-appb-000001
(2)初步选定衍射光学元件的周期d j，其中，所述周期由像素尺寸和像素数的乘积确定，所述像素数为正整数；
(3)计算各个目标点A i在X方向和Y方向的衍射级次(m i，n i)，其中，m i＝sinθ xi/sinΔθ，n i＝sinθ yi/sinΔθ，sinΔθ＝λ/d j，λ为光源波长；
(4)将衍射级次(m i，n i)取整得到取整后的衍射级次(m i’,n i’)；
(5)使用取整后的衍射级次(m i’,n i’)计算出实际投射点A i’在X方向和Y方向的坐标(x i’,y i’)；
(6)根据各个目标点A i和与其相对应的实际投射点A i’的坐标计算周期优化评价参数；
(7)将周期d j调整为d j+1，重复上述步骤(3)-(6)来计算周期d j+1下的周期优化评价参数；
(8)根据所述周期优化评价参数确定所述衍射光学元件的最优周期。
分光点阵可使用具有不同周期的衍射光学元件获得。根据本发明，能够通过比较实际投射点的坐标与各个目标点的坐标的差异，确定差异最小的情况下使用的周期为最优周期，可使得实际获得的分光点阵 与目标分光点阵的定位位置接近完美匹配，由此优化衍射光学元件的设计周期。
优选地，所述周期优化评价参数为以下其中任意一种，各个目标点A i和与其相对应的实际投射点A i’之间的距离平均值，或各个目标点A i和与其相对应的实际投射点A i’之间的距离中的最大值，或各个目标点A i和与其相对应的实际投射点A i’之间的距离之和，或各个目标点A i和与其相对应的实际投射点A i’之间的横坐标和/或纵坐标的绝对差值的最大值。
周期优化评价参数不限于上面所列，能够根据本发明的方法确定最优周期的任何适当的周期优化评价参数都在本发明的保护范围内。
优选地，所述距离平均值为算数平均值、几何平均值、调和平均值、加权平均值、均方根平均值中任一种。
距离平均值是根据本发明的一种评价参数，距离平均值可以是任何适当的平均值。
优选地，比较所获得的周期优化评价参数，得到周期优化评价参数的最小值，确定与所述最小值对应的周期为最优周期。
通常通过比较周期优化评价参数的最小值，即可确定实际投射点与目标点之间的差异的最小值，从而确定于所述最小值对应的周期为最优周期，方法简单直观。
优选地，使用遗传算法来得到所述最小值。
获得最小值的其他算法或方法也在本发明的保护范围内。
优选地，在所述步骤(7)中，通过固定所述像素尺寸，将所述像素数增大一像素数增量，来将周期d j调整为周期d j+1。
优选地，在所述像素尺寸满足加工精度的前提下，通过将所述像素尺寸和像素数的乘积增大一乘积增量，来将周期d j调整为周期d j+1。
优选地，在所述步骤(4)中，所述取整的方法为四舍五入法、舍掉小数、进位取整、奇数取整、或偶数取整中的任意一种。
根据本发明的衍射光学元件周期优化方法中的取整方法不限于上面所列，能够将衍射级数取整的其他适当方法也在本发明的保护范围内。
优选地，所述周期d j+1小于等于衍射光学元件的尺寸。
根据本发明的衍射光学元件周期优化方法中，衍射光学元件所选择的周期不能无限扩大，在物理上受到衍射光学元件的实际尺寸的限制。
根据本发明的衍射光学元件周期优化方法，能够在小量的计算下，使得衍射光学元件所投射的实际分光点阵尽可能的匹配目标分光点阵，提高衍射光学元件的设计质量和精度。
附图说明
通过阅读参照以下附图所作的对非限制性实施例所作的详细描述，本发明的其它特征、目的和优点将会变得更明显：
图1是根据本发明的衍射光学元件周期优化方法的流程图；
图2是显示目标点阵及其坐标的图表；
图3是根据本发明的衍射光学元件周期优化方法实现图2中所示的目标点阵的计算数据表；
图4是根据图3的数据得出的显示坐标绝对差值的图表。
具体实施方式
下面结合附图和实施例对本申请作进一步的详细说明。可以理解的是，此处所描述的具体实施例仅仅用于解释相关发明，而非对该发明的限定。另外还需要说明的是，为了便于描述，附图中仅示出了与发明相关的部分。
用于分光点阵投射的衍射光学元件一般使用周期密排的形式进行设计，衍射光学元件具有微结构面，微结构面上包括多个呈阵列状相邻排布的微结构图案单元，每个微结构图案单元的微结构图案(相位)相同，即每个微结构图案单元都能够对入射光进行相位调制，从而在目标平面上投射出分光点阵。微结构图案单元的大小称为衍射光学元件的周期，加工衍射光学元件时的加工精度决定了衍射光学元件的像素尺寸，衍射光学元件的周期大小和像素尺寸决定了单个微结构图案单元的像素数。衍射光学元件的周期决定了衍射光的角分辨率，sin Δθ＝λ/d，其中Δθ为角分辨率，λ为入射光波长，d为周期。周期d越大，角分辨率Δθ越小，角分辨率Δθ越小，则衍射光学元件能够对投射出的分光点阵的点的位置进行更精细的调制。本领域技术人员容易理解的是，用于分点阵投射的衍射光学元件也可以是针对发散光的单周期设计，此时衍射光学元件的尺寸即为该衍射光学元件的周期大小。本发明的保护范围即包括周期密排的设计方式，也包括单周期的设计方式。
在加工精度一定的情况下，即像素尺寸固定，则周期越大单个微结构图案单元的像素数越多，衍射光学元件的设计灵活度越大，对入射光的调制越为灵活能生成更为复杂精细的投射图案。但是像素数越多，衍射光学元件的设计难度也越高，计算机辅助程序的计算时间也更长，受限于产品外形尺寸，衍射光学元件的周期不能无限扩大，因此需要优选衍射光学元件的周期。
图1是根据本发明的衍射光学元件周期优化方法的流程图。
下面将根据图1中所示，介绍根据本发明的衍射光学元件的周期优化方法的各个步骤。
在步骤101，根据目标点阵的各个目标点A i在X方向和Y方向的坐标(x i，y i)，以及衍射光学元件和目标平面之间的距离a，计算所述目标点阵的各个目标点A i在X方向和Y方向的衍射角(θ xi，θ yi)，其中，i为整数，
Figure PCTCN2021104476-appb-000002
Figure PCTCN2021104476-appb-000003
通常，衍射光学元件的设计计算的是角谱分辨率，因此在步骤101，把目标点阵的坐标从平面转移到了角谱上。
在步骤102，初步选定衍射光学元件的周期d j，其中，所述周期由像素尺寸和像素数的乘积确定，所述像素数为正整数。
在步骤103，根据得到的衍射角(θ xi，θ yi)和初步选定的衍射光学元件的周期d j，计算各个目标点A i在X方向和Y方向的衍射级次(m i，n i)，其中，m i＝sinθ xi/sinΔθ，n i＝sinθ yi/sinΔθ，sinΔθ＝λ/d j，λ为光源波长，Δθ为角分辨率，由该周期d j决定。
在步骤104，将衍射级次(m i，n i)取整得到取整后的衍射级次 (m i’,n i’)。实际上，衍射级次为整数，因此需要将计算得到的衍射级次(m i，n i)取整。
在步骤105，使用取整后的衍射级次(m i’,n i’)计算出实际投射点A i’在X方向和Y方向的坐标(x i’,y i’)。在步骤105，把角谱上的点又换算到了目标点阵所在的平面上，这样才能将实际投射点A i’在X方向和Y方向的坐标(x i’,y i’)跟目标点阵的相对应的目标点的坐标(x i，y i)来比较。
在步骤106，根据各个目标点A i和与其相对应的实际投射点A i’的坐标计算周期优化评价参数。
由于衍射光学元件的周期d j受衍射光学元件的实际尺寸的限制，因此在步骤109，判断周期是否超过衍射光学元件的实际尺寸这一限值，如果没超过，则进行下面的步骤：
在步骤107，将周期d j调整为d j+1，重复上述步骤103-106来计算调整的周期d j+1下的周期优化评价参数。
在步骤108，根据所述周期优化评价参数确定所述衍射光学元件的最优周期。
下面将以3×3的目标点阵为例，具体描述根据本发明的衍射光学元件周期优化方法的实施例。
图2是显示3×3点阵及其坐标的图表；图3是根据本发明的衍射光学元件周期优化方法实现图2中所示的3×3点阵的计算数据表。本实施例中，衍射光学元件距目标平面的距离为700mm，像素尺寸为0.23μm，光源波长为0.94μm。
图3中的目标点坐标(x i，y i)即为图2中的3×3点阵中各个目标点的相应坐标。图3中的目标点衍射角(θ xi，θ yi)由目标点坐标(x i，y i)根据公式
Figure PCTCN2021104476-appb-000004
Figure PCTCN2021104476-appb-000005
计算得到，其中a为衍射光学元件和目标平面之间的距离，在本实施例中为700mm。
本实施例中，初步选定衍射光学元件的周期为621.23μm，衍射光学元件的周期由像素尺寸和像素数的乘积确定，已知像素尺寸为0.23μm，则像素数为2701。
然后，根据图3中计算得到的目标点衍射角(θ xi，θ yi)、初步选定的周期621.23μm以及已知的光源波长0.94μm，由公式m i＝sinθ xi/sinΔθ，n i＝sinθ yi/sinΔθ，sinΔθ＝λ/d j，计算得到图3中的目标点衍射级次(m i，n i)。
接着，将计算得到的目标点衍射级次(m i，n i)进行取整，得到取整后的衍射级次(m i’,n i’)。本实施例中采用了奇数位取整。由于衍射级次从0级开始，因此奇数位对应为偶数衍射级次，在图3中所示的数据表中，奇数位取整即将整数位为偶数的衍射级次舍掉小数，将整数位为奇数的衍射级次进位取整。实践证明，这样设计的衍射光学元件的光效更好，点阵的非均匀性更低，光场各点光斑更均匀，本实施例中，奇数位取整位优选取整方法。
图3中的衍射角度(θ xi’，θ yi’)为根据取整后的衍射级次(m i’,n i’)计算得到的实际投射点的衍射角度，由此根据实际投射点的衍射角度(θ xi’，θ yi’)，可进一步计算得出实际投射点在目标平面上的坐标(x i’,y i’)。
本实施例中，通过计算每一个目的点坐标(x i，y i)和相应的实际投射点坐标(x i’,y i’)分别在x方向和y方向的坐标绝对差值，来评价目标点和实际投射点的位置差异，图3中的坐标绝对差值数据即为计算所得数据。
图4是根据图3的数据得出的显示坐标绝对差值的图表。选取坐标绝对差值中的最大值作为衍射光学元件的周期优化评价参数。
由此，在初步选定的衍射光学元件周期为621.23μm的情况下，计算完成目标衍射点和实际投射点之间的周期优化评价参数，即坐标绝对差值。
进一步将衍射光学元件的周期调整为d j+1，在周期为d j+1情况下，重复上述坐标绝对差值的计算，选取每个选择周期下坐标绝对差值最大值作为衍射光学元件的周期优化评价参数，直到周期d j+1大于或等于衍射光学元件的实际尺寸或者其超出预设的阈值范围。上述预设的阈值范围可以根据本领域技术人员的经验进行设置，例如，阈值下限可以对应于能够满足设计灵活度来实现对入射光的均匀分光调制的最 小像素个数，阈值上限可以对应于像素个数的量不至于显著增加计算机辅助软件计算衍射光学元件相位分布所需的时间，以保证设计衍射光学元件时的效率。
将每个所选周期下得到的坐标绝对差值的最大值进行比较，与坐标绝对差值的最大值中的最小值对应的所选周期即为最优周期。本实施例中，使用遗传算法来得到所述最小值。以该最优周期设计得到的衍射光学元件，能够使得衍射光学元件所投射的实际分光点阵尽可能地匹配目标分光点阵。
应当注意的是，在参照图2-4描述的实施例中，虽然周期优化评价参数以坐标绝对差值最大值进行评价，但实际上，周期优化评价参数可以为以下任意一种：各个目标点A i和与其相对应的实际投射点A i’之间的距离平均值，或各个目标点A i和与其相对应的实际投射点A i’之间的距离中的最大值，或各个目标点A i和与其相对应的实际投射点A i’之间的距离之和，或各个目标点A i和与其相对应的实际投射点A i’之间的横坐标和/或纵坐标的绝对差值的最大值。
而且，在以距离平均值作为周期优化评价参数时，距离平均值可为算数平均值、几何平均值、调和平均值、加权平均值、均方根平均值中任一种。
在参照图2-4描述的实施例中，最小值通过遗传算法计算，但是本发明不限于此，能够获得最小值的其他算法也在本发明的保护范围内。这里的最小值就是计算的坐标跟目标坐标的绝对差值最大值中的最小，这个值越小说明计算的坐标值跟目标值越接近。
衍射光学元件的周期由像素尺寸和像素数的乘积确定，像素尺寸通常由加工精度决定，因此在调整周期时，通常通过固定像素尺寸，将所述像素数增大一像素数增量，来将周期d j调整为周期d j+1。在像素尺寸满足加工精度的前提下，也可以通过将所述像素尺寸和像素数的乘积增大一乘积增量，来将周期d j调整为周期d j+1。但是像素尺寸和像素数的乘积，即周期要满足产品尺寸规格，不能太大也不能太小，调整范围受衍射光学元件的实际尺寸限制。
在参照图2-4描述的实施例中，目标点衍射级次(m i，n i)采用奇 数位取整的方法进行了取整，这是针对本实施例的优选取整方式。在不同的实施例中，可根据需要采用例如偶数位取整，即将整数位为奇数的衍射级次舍掉小数，将整数位为偶数的衍射级次进位取整。也可以采用计算得到的衍射级次全部以四舍五入法、舍掉小数或进位取整。
根据本发明的衍射光学元件周期优化方法，能够在小量的计算下，使得衍射光学元件所投射的实际分光点阵尽可能的匹配目标分光点阵，提高衍射光学元件的设计质量和精度。
以上描述仅为本申请的较佳实施例以及对所运用技术原理的说明。本领域技术人员应当理解，本申请中所涉及的发明范围，并不限于上述技术特征的特定组合而成的技术方案，同时也应涵盖在不脱离所述发明构思的情况下，由上述技术特征或其等同特征进行任意组合而形成的其它技术方案。例如上述特征与本申请中公开的(但不限于)具有类似功能的技术特征进行互相替换而形成的技术方案。

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  1. 一种衍射光学元件的周期优化方法，用于点阵结构光投射，其特征在于，包括以下步骤：
    (1)根据目标点阵的各个目标点A i在X方向和Y方向的坐标(x i，y i)，以及衍射光学元件和目标平面之间的距离a，计算所述目标点阵的各个目标点A i在X方向和Y方向的衍射角(θ xi，θ yi)，其中，i为整数，
    Figure PCTCN2021104476-appb-100001
    (2)初步选定衍射光学元件的周期d j，其中，所述周期由像素尺寸和像素数的乘积确定，所述像素数为正整数；
    (3)计算各个目标点A i在X方向和Y方向的衍射级次(m i，n i)，其中，m i＝sinθ xi/sinΔθ，n i＝sinθ yi/sinΔθ，sinΔθ＝λ/d j，λ为光源波长；
    (4)将衍射级次(m i，n i)取整得到取整后的衍射级次(m i’,n i’)；
    (5)使用取整后的衍射级次(m i’,n i’)计算出实际投射点A i’在X方向和Y方向的坐标(x i’,y i’)；
    (6)根据各个目标点A i和与其相对应的实际投射点A i’的坐标计算周期优化评价参数；
    (7)将周期d j调整为d j+1，重复上述步骤(3)-(6)来计算周期d j+1下的周期优化评价参数；
    (8)根据所述周期优化评价参数确定所述衍射光学元件的最优周期。
  2. 根据权利要求1所述的衍射光学元件的周期优化方法，其中，所述周期优化评价参数为：各个目标点A i和与其相对应的实际投射点A i’之间的距离平均值，或各个目标点A i和与其相对应的实际投射点A i’之间的距离中的最大值，或各个目标点A i和与其相对应的实际投射点A i’之间的距离之和，或各个目标点A i和与其相对应的实际投射点A i’之间的横坐标和/或纵坐标的绝对差值的最大值。
  3. 如权利要求2所述的衍射光学元件的周期优化方法，其中，所述距离平均值为算数平均值、几何平均值、调和平均值、加权平均值 和均方根平均值中任一种。
  4. 如权利要求1-3中任一项所述的衍射光学元件的周期优化方法，其中，比较所获得的所述周期优化评价参数，得到所述周期优化评价参数的最小值，确定与所述最小值对应的周期为最优周期。
  5. 如权利要求4所述的衍射元件的周期优化方法，其中，使用遗传算法来得到所述最小值。
  6. 根据权利要求1所述的衍射光学元件的周期优化方法，其中，在所述步骤(7)中，通过固定所述像素尺寸，将所述像素数增大一像素数增量，来将周期d j调整为周期d j+1。
  7. 根据权利要求1所述的衍射光学元件的周期优化方法，其中，在所述像素尺寸满足加工精度的前提下，通过将所述像素尺寸和像素数的乘积增大一乘积增量，来将周期d j调整为周期d j+1。
  8. 如权利要求1所述的衍射光学元件的周期优化方法，其中，在所述步骤(4)中，所述取整的方法为四舍五入法、舍掉小数、进位取整、奇数位取整和偶数位取整中的任意一种。
  9. 如权利要求8所述的衍射光学元件的周期优化方法，其中，所述周期d j+1小于等于衍射光学元件的尺寸。
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