PERIODIC OPTIMIZATION METHOD FOR DIFFRACTIVE OPTICAL ELEMENT

Abstract

A periodic optimization method for a diffractive optical element includes converting coordinates of individual target spots of a target spot array into angular spectrum coordinates, selecting an initial period, calculating diffraction orders of individual target spots, rounding the diffraction order, calculating the coordinates of actual projection spots by using the rounded diffraction orders, calculating evaluation indicator of period optimization, adjusting the period, and repeating the steps, and comparing the evaluation indicators to determine an optimal period for the diffractive optical element. With the periodic optimization method, an actual spot array is made to match a target spot array to the greatest possible extent with a small amount of calculations, thereby improving the design quality and accuracy of a diffractive optical element.

Claims

1. A periodic optimization method for a diffractive optical element which is used to project structured light of spot array, characterized in that the method comprises the following steps: (1) calculating diffraction angles (θ.sub.xi, θ.sub.yi) of individual target spots A of a target spot array in X direction and Y direction based on coordinates (x.sub.i, y.sub.i) of the target spots A of the target spot array in X direction and Y direction and a distance a between the diffractive optical element and a target plane, where i is an integer, θ.sub.xi=arctan(x.sub.i/√{square root over ((y.sub.i).sup.2+(α).sup.2)}), and θ.sub.yi=arctan(y.sub.i/√{square root over ((x.sub.i).sup.2+(α).sup.2)}); (2) selecting initially a period d.sub.j of the diffractive optical element, wherein the period is determined by a product of a pixel size and a number of pixels, and the number of pixels is a positive integer; (3) calculating diffraction orders (m.sub.i, n.sub.i) of the individual target spots A.sub.i in X direction and Y direction, wherein m.sub.i=sinθ.sub.xi/sinΔθ, n.sub.i=sinθ.sub.yi/sinΔθ, sinΔθ=λ/d.sub.j, λ is a wavelength of a light source; (4) rounding the diffraction orders (m.sub.i, n.sub.i) to obtain rounded diffraction orders (m.sub.i′, n.sub.i′); (5) calculating coordinates (x.sub.i′, y.sub.i′) of actual projection spots A.sub.i′ in X direction and Y direction by using the rounded diffraction orders (m.sub.i′, n.sub.i′); (6) calculating an evaluation indicator of period optimization based on the coordinates of individual target spots A.sub.i and those of their corresponding actual projection spots A.sub.i′; (7) adjusting the period d.sub.j to d.sub.j+1, and repeating the above steps (3)-(6) to calculate the evaluation indicator of period optimization with the period d.sub.j+1; and (8) determining an optimal period of the diffractive optical element according to the evaluation indicators of period optimization, wherein the evaluation indicator of period optimization is selected from a group consisted of: a distance mean between the individual target spots A.sub.i and their corresponding actual projection spots A.sub.i′, a maximum distance between the individual target spots A.sub.i and their corresponding actual projection spots A.sub.i′, a sum of distances between individual target spots A.sub.i and their corresponding actual projection spots A.sub.i′, and a maximum absolute difference of abscissas and/or ordinates between individual target spots A.sub.i and their corresponding actual projection spots A.sub.i′.

2. (canceled)

3. The periodic optimization method for the diffractive optical element of claim 1, wherein the distance mean is any one selected from a group consisted of arithmetic mean, geometric mean, harmonic mean, weighted mean and root mean square.

4. The periodic optimization method for the diffractive optical element of claim 1, wherein a minimum value of the evaluation indicators of period optimization is obtained by comparing the evaluation indicators of period optimization obtained, and the period corresponding to the minimum value is determined as the optimal period.

5. The periodic optimization method of the diffractive element of claim 4, wherein genetic algorithm is used to obtain the minimum value.

6. The periodic optimization method for the diffractive optical element of claim 1, wherein, in the step (7), the period d.sub.j is adjusted to the period d.sub.j+1 by fixing the pixel size and increasing the number of pixels by a pixel number increment.

7. The periodic optimization method for the diffractive optical element of claim 1, wherein, on the premise that the pixel size adapts to the processing accuracy, the period d.sub.j is adjusted to the period d.sub.j+1 by increasing the product of the pixel size and the number of pixels by a product increment.

8. The periodic optimization method for the diffractive optical element as claimed in claim 1, wherein, in the step (4), rounding is carried out with any method selected from a group consisted of rounding to the nearest integer, rounding down, rounding up, odd digit rounding, and even digit rounding.

9. The periodic optimization method for the diffractive optical element of claim 8, wherein the period d.sub.j+1 is less than or equal to the size of the diffractive optical element.

10. The periodic optimization method for the diffractive optical element of claim 3, wherein a minimum value of the evaluation indicators of period optimization is obtained by comparing the evaluation indicators of period optimization obtained, and the period corresponding to the minimum value is determined as the optimal period.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0032] Other features, objects, and advantages of the invention will become more apparent by reading the following detailed description of non-limitative embodiments with reference to the following drawings.

[0033] FIG. 1 is a flowchart of a periodic optimization method for diffractive optical element according to the present invention;

[0034] FIG. 2 is a chart showing the target spot array and its coordinates;

[0035] FIG. 3 is the calculation data table for achieving the target spot array shown in FIG. 2 by using the periodic optimization method for diffractive optical element of the present invention; and

[0036] FIG. 4 is a chart showing absolute difference of coordinates obtained from the data in FIG. 3.

DETAILED DESCRIPTION

[0037] The invention will be further described in detail in conjunction with drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the related invention, but not to limit the invention. In addition, it should be noted that, for the convenience of description, only the parts related to the invention are shown in the drawings.

[0038] Diffractive optical elements used for light-split spot array projection are generally designed in the form of periodic dense arrangement. A diffractive optical element has a microstructure surface, which comprises a number of microstructure pattern units arranged adjacent to each other in the form of an array. Every one of the microstructure pattern units has the same microstructure pattern (phase). That is, each microstructure pattern unit can modulate the phase of the incident light, so as to project the light-split spot array on the target plane. The size of the microstructure pattern unit is called period of the diffractive optical element. Processing accuracy of the diffractive optical element determines pixel size of the diffractive optical element. The period and the pixel size of the diffractive optical element determine the number of pixels of a single microstructure pattern unit. Period of a diffractive optical element determines an angular resolution of diffractive light: sinΔθ=λ/d, wherein Δθ is the angular resolution, λ is the wavelength of the incident light, and d is the period. The greater the period d is, the smaller the angular resolution Δθ is; and the smaller the angular resolution Δθ is, the finer adjustment of the position of the spots of the projected light-split spot array the diffractive optical element can achieve. It is easy for those skilled in the art to understand that the diffractive optical element used for projecting light-split spot array can also be designed to have one single period for divergent light. In such a case, the size of the diffractive optical element is the period size of the diffractive optical element. The present invention intends to cover both the design with periodic dense arrangement and the design with one single period.

[0039] With a certain processing accuracy, that is, with a predetermined pixel size, the larger the period is, the more pixels a single microstructure pattern unit can have, and the more flexible the design of the diffractive optical element can be, such that the more flexible modulation of incident light can be carried out to generate more complex and finer projection patterns. However, the larger the number of pixels is, the more difficult the design of the diffractive optical element is, and the longer it takes for the computer aided program to calculate. Being limited by size of a product, the period of the diffractive optical element cannot be expanded indefinitely. Therefore, it is necessary to optimize the period of the diffractive optical element.

[0040] FIG. 1 is a flowchart of a periodic optimization method for diffractive optical element according to the present invention.

[0041] Detailed description of steps of the periodic optimization method for diffractive optical element according to the present invention will be given below with reference to FIG. 1.

[0042] In step 101, diffraction angles (θ.sub.xi, θ.sub.yi) of individual target spots A.sub.i of a target spot array in X direction and Y direction are calculated based on coordinates (x.sub.i, y.sub.i) of the target spots A.sub.i of the target spot array in X direction and Y direction and a distance a between the diffractive optical element and a target plane, where i is an integer, θ.sub.xi=arctan(x.sub.i/√{square root over ((y.sub.i).sup.2+(α).sup.2 (a).sup.2)}), and θ.sub.yi=arctan(y.sub.i/√{square root over ((x.sub.i).sup.2+(α).sup.2)}).

[0043] Generally, angular spectrum resolution is calculated in the design of a diffractive optical element, and so in step 101, the coordinates of the target spot array are converted from plane coordinates to angular spectral coordinates.

[0044] In step 102, a period d.sub.j of the diffractive optical element is selected initially, wherein the period is determined by a product of a pixel size and a number of pixels, and the number of pixels is a positive integer.

[0045] In step 103, diffraction orders (m.sub.i, n.sub.i) of the individual target spots A.sub.i in X direction and Y direction of individual target spots A.sub.i are calculated based on the obtained diffraction angles (θ.sub.xi, θ.sub.yi) and the period d.sub.j of the diffractive optical element selected initially, wherein m.sub.i=sinθ.sub.xi/sinΔθ, n.sub.i=sinθ.sub.yi/sinΔθ, sinΔθ=λ/d.sub.j, λ is a wavelength of a light source, and JO is the angular resolution which is determined by the period d.sub.j.

[0046] In step 104, the diffraction orders (m.sub.i, n.sub.i) are rounded to obtain rounded diffraction orders (m.sub.i′, n.sub.i′). In fact, diffraction orders are integer, so the calculated diffraction orders (m.sub.i, n.sub.i) need to be rounded.

[0047] In step 105, coordinates (x.sub.i′, y.sub.i′) of actual projection spots A.sub.i′ in X direction and Y direction are calculated by using the rounded diffraction orders (m.sub.i′, n.sub.i′). In step 105, the spots on the angular spectrum are converted to spots on the plane where the target spot array lies, so that the coordinates (x.sub.i′, y.sub.i′) of the actual projection spots A.sub.i′ in the X direction and Y direction can be compared with the coordinates (x.sub.i, y.sub.i) of the corresponding target spots of the target spot array.

[0048] In step 106, an evaluation indicator of period optimization is calculated based on the coordinates of individual target spots A.sub.i and those of their corresponding actual projection spots A.sub.i′.

[0049] Since the period d.sub.j of the diffractive optical element is limited by the actual size of the diffractive optical element, in step 109, it is judged whether the period exceeds the limit value of the actual size of the diffractive optical element. If not, proceed to the following steps.

[0050] In step 107, the period d.sub.j is adjusted to period d.sub.j+1, and the above steps 103˜106 are repeated to calculate the evaluation indicator of period optimization with the period d.sub.j+1.

[0051] In step 108, an optimal period of the diffractive optical element is determined according to the evaluation indicators of period optimization.

[0052] Next, taking a 3×3 array as an example of the target spot array, an embodiment of the periodic optimization method for diffractive optical element according to the present invention is described in details.

[0053] FIG. 2 is graph showing a 3×3 spot array and its coordinates; FIG. 3 is a calculation data table showing how the periodic optimization method of diffractive optical element according to the invention is carried out to achieve the 3×3 spot array shown in FIG. 2. In this embodiment, the distance between the diffractive optical element and the target plane is 700 mm, the pixel size is 0.23 μm, and the wavelength of light source is 0.94 μm.

[0054] The coordinates (x.sub.i, y.sub.i) of the target spots in FIG. 3 are respective coordinates of individual target spots of the 3×3 spot array. Diffraction angles (θ.sub.xi, θ.sub.yi) of the target spots in FIG. 3 are calculated with the formulas θ.sub.xi=arctan(x.sub.i/√{square root over ((y.sub.i).sup.2+(α).sup.2)}) and θ.sub.yi=arctan(y.sub.i/√{square root over ((x.sub.i).sup.2+(α).sup.2)}), where a is the distance between the diffractive optical element and the target plane, which is 700 mm in this embodiment.

[0055] In this embodiment, the period of the diffractive optical element is initially selected to be 621.23 μm. The period of the diffractive optical element is determined by the product of the pixel size and the number of pixels. The known pixel size is 0.23 μm, and then the number of pixels is 2701.

[0056] Then, based on the diffraction angles (θ.sub.xi, θ.sub.yi) of the target spots, the initially selected period 621.23 μm and the known wavelength of light source 0.94 μm, the diffraction orders (m.sub.i, n.sub.i) of the target spots in FIG. 3 are calculated with the formulas m.sub.i=sinθ.sub.xi/sinΔθ, n.sub.i=sinθ.sub.yi/sinΔθ, sinΔθ=λ/d.sub.j.

[0057] Then, the calculated diffraction orders (m.sub.i, n.sub.i) of the target spots are rounded to obtain the rounded diffraction orders (m.sub.i′, n.sub.i′). In this embodiment, odd digit rounding is used. Since the diffraction order starts from Order 0, an odd digit is corresponding to an even number of diffraction orders. In the data table shown in FIG. 3, the odd digit rounding is to round off the decimal of a diffraction order with an even integer and to round up the diffraction order with an odd integer. Practice has proved that the diffractive optical element designed in this way has better light effect, lower non-uniformity of the spot array, and more uniform light spots in the light field. In this embodiment, the odd digit rounding method is a preferred rounding method.

[0058] The diffraction angles (θ.sub.xi′, θ.sub.r′) in FIG. 3 are the diffraction angles of the actual projection spots calculated based on the rounded diffraction orders (m.sub.i′, n.sub.i′), and thus based on the diffraction angles (θ.sub.xi′, θ.sub.yi′) of the actual projection spots, coordinates (x.sub.i′, y.sub.i′) of the actual projection spots on the target plane can be further calculated.

[0059] In this embodiment, the position difference between the target spots and the actual projection spots is evaluated by calculating the absolute difference between the coordinate (x.sub.i, y.sub.i) of each target spot and the corresponding coordinate (x.sub.i′, y.sub.i′) of the actual projection spot in X direction and Y direction, respectively. The data of the absolute difference of coordinates in FIG. 3 are the data calculated.

[0060] FIG. 4 is a chart showing the absolute differences of coordinates obtained based on the data in FIG. 3. The maximum of the absolute differences of coordinates is selected as the evaluation indicator of period optimization for the diffractive optical element.

[0061] Thus, calculation of the evaluation indicator of period optimization, that is, the absolute difference of coordinates between the target diffraction spots and the actual projection spots is fulfilled with a initially selected period of the diffractive optical element of 621.23 μm.

[0062] Then, the period of the diffractive optical element is adjusted to d.sub.j+1. With a period of d.sub.j+1, the calculation of the above absolute difference of coordinates is repeated, and the maximum absolute difference of coordinates obtained with each selected period is taken as the evaluation indicator of period optimization for the diffractive optical element, until the period d.sub.j+1 is greater than or equal to the actual size of the diffractive optical element or it exceeds the preset threshold. The above preset threshold can be set according to the experience of those skilled in the art. For example, a lower threshold limit can be corresponding to the minimum number of pixels that can meet the requirement of the design flexibility to achieve uniform light splitting modulation of incident light, and an upper threshold limit can be corresponding to a number of pixels which will not significantly increase the time required for computer aided software to calculate the phase distribution of diffractive optical elements, so as to ensure the efficiency of designing diffractive optical elements.

[0063] The maximum value of the absolute difference of coordinates obtained with every selected period are compared, and the selected period corresponding to the minimum value of the maximum value of the absolute difference of coordinates is taken as the optimal period. In this embodiment, genetic algorithm is used to obtain the minimum value. The diffractive optical element designed with this optimal period can make the actual light-split spot array projected by the diffractive optical element match the target light-split spot array as much as possible.

[0064] It should be noted that in the embodiment described with reference to FIGS. 2-4, although the evaluation indicator of period optimization is the maximum absolute difference of coordinates, in fact, the evaluation indicator of period optimization can be any of the following: a distance mean between the individual target spots A.sub.i and their corresponding actual projection spots A.sub.i′, or a maximum distance between the individual target spots A.sub.i and their corresponding actual projection spots A.sub.i′, or a sum of distances between individual target spots A.sub.i and their corresponding actual projection spots A.sub.i′, or a maximum absolute difference of abscissas and/or ordinates between individual target spots A.sub.i and their corresponding actual projection spots A.sub.i′.

[0065] Moreover, when the distance mean is used as the evaluation indicator of period optimization, the distance mean can be any of the arithmetic mean, geometric mean, harmonic mean, weighted mean, and root mean square.

[0066] In the embodiment described with reference to FIGS. 2-4, the minimum value is calculated with genetic algorithm, but the invention is not limited to this, but rather other algorithms that can obtain the minimum value are also within the protection scope of the invention. The minimum value here is the minimum of the maximum absolute difference between the calculated coordinates and the target coordinates. The smaller this value is, the closer the calculated coordinates are to the target ones.

[0067] The period of the diffractive optical element is determined by the product of the pixel size and the number of pixels. The pixel size is usually determined by the processing accuracy. Therefore, when adjusting the period, the period d.sub.j is adjusted to the period d.sub.j+1 by fixing the pixel size and increasing the number of pixels by a pixel number increment. On the premise that the pixel size adapts to the processing accuracy, the period d.sub.j can also be adjusted to the period d.sub.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, i.e. the period, should adapt to the product size specification, and should not be too large or too small. The adjustment range is limited by the actual size of a diffractive optical element.

[0068] In the embodiment described with reference to FIGS. 2-4, the diffraction orders (m.sub.i, n.sub.i) of the target spots are rounded using the odd digit rounding method, which is the preferred rounding method for this embodiment. In other embodiments, even digit rounding can be used for rounding as needed, that is, the decimal of a diffraction order with odd integer digits can be rounded off, and a diffraction order with an even integer can be rounded up. The calculated diffraction orders can also be rounded with a method of rounding to the nearest integer, rounding down, or rounding up.

[0069] According to the periodic optimization method for diffractive optical element of the invention, the actual light-split spot array projected by the diffractive optical element can match the target light-split spot array as much as possible with a small amount of calculation, and design quality and accuracy of the diffractive optical element can be improved.

[0070] The above description is merely an illustration of the preferred embodiments of the present application and the applied technical principles. Those skilled in the art should understand that the scope of the invention involved in the present application is not limited to the technical solution formed by the specific combination of the above technical features, but also covers other technical solutions formed by any combination of the above technical features or their equivalent features without departing from the inventive concept. For example, the technical solution is formed by replacing the above features with (but not limited to) the technical features with similar functions disclosed in the present application.