CN102122070B - Design method of reflective optical integrator based on planar mirror array - Google Patents

Abstract

The invention belongs to the technical field of optical device design, and relates to a reflective optical integrator design method based on a plane mirror array, including: determining the center of the planar unit of the integrator; determining the direction of each planar unit of the integrator; determining the direction of the integrator array in the Y direction The position parameters and direction parameters on the X direction; determine the position parameters and direction parameters of the integrator array in the X direction; establish the integrator model; design the machining path according to the designed integrator model, and carry out ultra-precision turning. The reflective integrator designed by the method of the present invention is simpler in structure than the traditional transmissive integrator, and has better stability, and has more excellent uniform distribution of light intensity under the condition of the same incident light energy.

Description

A Design Method of Reflective Optical Integrator Based on Plane Mirror Array

technical field

The invention belongs to the technical field of optical device design, and in particular relates to an optical integrator.

Background technique

Integral lighting is to integrate chaotic light into uniform light through an optical system, or to achieve brightness improvement and uniformity, and can be widely used in green energy, space technology and other fields. The optical integrator is the most important optical device in integrating illumination. According to the law of light propagation, optical integrators can be divided into refraction type (transmission type) and reflection type. Refractive optical integrators, such as microlens arrays, are generally used in coaxial systems. The disadvantage of coaxial systems is that the optical path is long, resulting in a large outline of the optical system. The light uniformity of the light beam is achieved by using a microlens array. However, due to the use of the lens, some shortcomings of the lens will be introduced, such as large aberrations and serious light loss. These shortcomings will affect the light beam on the receiving surface. uniformity. The reflective integrator adopts an off-axis method, which reduces the length of the optical path and occupies a small space. More importantly, the integrator uses a reflector instead of a refractor, thereby reducing the influence of aberrations on the optical path, and also reducing the absorption loss of the light radiation energy by the refraction material, and increasing the energy utilization rate.

Due to the complex shape and structure of the reflective integrator, the processing is not easy to realize, so it is rarely used at present. However, with the development and maturity of ultra-precision technology, especially the development of single-point diamond cutting technology with tool servo, it provides a powerful tool for the processing of optical devices with complex shapes, and provides a guarantee for the application of reflective integrators. Therefore, in view of the many application advantages of reflective integrators, it is necessary to carry out research on the design of reflective integrators.

Contents of the invention

The purpose of the present invention is to propose a simple and feasible design method of reflective integrator. The present invention adopts a planar array composed of multiple planes to design a reflective integrator, and converges the light parallel to the optical axis to a square plane through the reflection of the integrator, and realizes good uniform illumination. Technical scheme of the present invention is as follows:

A reflective optical integrator design method based on a plane mirror array, the reflective optical integrator includes a plane mirror array, the center of the plane at the center of the plane mirror array is the coordinate origin, and the opposite direction of the incident parallel light is Z axis, establish a Cartesian coordinate system, the parallel light along the Z axis is reflected by the integrator, and then reaches the receiving surface; the structural parameters of the integrator include the side lengths of each plane unit along the X and Y axes, and the sides of the receiving surface The length 2d and the focal length f of the integrator, the position parameters of each plane unit include the coordinates of the center point of the unit, the rotation angles around the X-axis and Y-axis respectively, and the coordinates of the rotation center around the X-axis and Y-axis, and its design method include:

The first step. Determination of the center of the planar unit of the integrator:

(1) Determine the focal length f of the paraboloid according to the distance between the receiving surface and the reflecting surface, thereby obtaining the equation of the paraboloid: X ² +Y ² =4fZ,

(2) Determine the side length of the integrator unit located at the origin of the coordinates according to the size of the receiving surface, the values of the two are equal,

(3) Divide the paraboloid in (1) into a series of grids on the XOY surface, the boundary lines of the grids are parallel to the X axis and the Y axis, and each point on the grid is used as the center of the integrator unit on the XOY surface The projection of the integrator unit at the origin is (0, 0, 0). According to the ray tracing and the position of the point on the grid, the position of each integrator unit center is determined. For each integrator unit center, respectively according to From the second step to the fourth step below, iteratively calculate the position parameter and direction parameter of each plane unit corresponding to it along the Y direction and the X direction;

从而确定平面单元的方向；Step 2. For the center of each integrator unit, set its coordinates on the XOY plane as X ₀ and Y ₀ respectively, and its tangent vector on the paraboloid is K[k ₁ , k ₂ ], k ₁ =-X ₀ /(2f), k ₂ =-Y ₀ /(2f), and the direction of the normal vector of the plane unit is perpendicular to the direction of the paraboloid tangent, and the normal vector [a, b, c],

To determine the direction of the planar unit;

The third step. Determine the position parameter and direction parameter of the integrator array on the Y direction: Let A _i be the edge point of the previous plane unit and the current plane unit on the Y direction, then A _i is known; A _{i+ 1} is the point where the current plane unit is connected to the edge point, A _i =A, according to A _i (X _i , Y _i , _Zi ) and the center of the integrator unit, it can be determined that the center of the plane unit in the Y direction is in the Z direction coordinate value Z ₁ = a*(X ₀ -X _i )+b*(Y ₀ -Y _i )+Z _i , and then obtain the coordinate value P ₁ of the center of the plane unit in the Y direction according to the normal vector of the plane unit (X ₁ , Y ₁ , Z ₁ ), thus obtaining the position parameter and direction parameter of the plane unit in the Y direction.

The 4th step. Determine the position parameter and the direction parameter of the integrator array on the X direction: Let B _i be the edge point of the previous plane unit and the current plane unit on the X direction, then B _i is known; B _{i+ 1} is the point where the current plane unit is connected to the edge point, Bi ₌ B, according to _Bi (X _i , Y _i , _Zi ) and the center of the integrator unit, it can be determined that the center of the plane unit in the X direction is in the Z direction Coordinate value Z ₂ ＝a*(X _i -X ₀ )+b*(Y _i -Y ₀ )+Z _i , and then obtain the plane center coordinate value P ₂ (X ₂ , Y ₂ , Z ₂ ), so that the position parameter and direction parameter of the plane unit in the X direction are obtained;

Step 5. Build the integrator model:

(1) Determine the position parameters of the integrator: According to the position and direction of the integrator unit in the X direction and the Y direction, the rotation angle a 0 of the plane array in the X and Y directions can be calculated respectively: ₀ = π/2-arccos(-a ) and b ₀ =π/2-arccos(-b), wherein, a ₀ represents the rotation angle of the plane around the Y axis; b ₀ represents the rotation angle of the plane around the X axis;

(2) Determine the structural parameters of the integrator: obtain the rectangular side lengths d ₁ =d/cos(a) and d ₂ =d/cos(b) of the planar unit on the X-axis and Y-axis respectively, where d ₁ represents the plane The length of the unit in the X-axis direction; d ₂ represents the length of the plane unit in the Y-axis direction;

(3) Obtain the integrator model along the positive direction of the X-axis according to the method above, and carry out the symmetrical extension of the integrator model about the Y-axis in the X direction to obtain an integrator model symmetrical about the Y-axis;

(4) Remove the planar array located near the center of the integrator on the integrator model that is symmetrical about the Y axis, to achieve the purpose of off-axis reflection;

Step 6. Design the processing path according to the designed integrator model, and perform ultra-precision turning processing.

Conventional refractive optical integrators require a converging lens to converge the light beams of the second microlens array in order to achieve uniform light. Compared with the refraction-type optical integrator, the reflective-type optical integrator designed in the present invention does not need a converging lens, and can directly form a uniform illumination distribution on the receiving surface, and only needs one reflector to realize the function of the refraction-type integrator. The reflective integrator designed by the present invention is simpler in structure than the traditional transmissive integrator, and has better stability. Under the same incident light energy, it has more excellent uniform distribution of light intensity, especially the light at the edge of the receiving surface. The intensity distribution is more stable. Moreover, due to the reduction of aberrations and transmission losses, the energy reaching the receiving surface has also been greatly improved.

Description of drawings

Fig. 1 is the overall structural diagram of the integrator of the present invention.

Figure 2 design the overall flow chart.

Figure 3 Planar cell at the center of the integrator.

Figure 4 Integrator elements along the X direction.

Figure 5 Integrator unit along the Y direction.

Figure 6. Three-dimensional contour plot of the integrator.

Figure 7 (a) Integrator model along the positive direction of the X axis; (b) Integrator model symmetrical about the Y axis; (c) Remove the planar array near the center of the integrator on the integrator model.

Detailed ways

The integrator designed by the present invention is composed of a plane reflector array, as shown in FIG. 1 . Taking the center of the plane at the center of the integrator as the origin of the coordinates, and taking the opposite direction of the incident parallel light as the Z-axis, establish a rectangular coordinate system as shown in Figure 1. The position parameters of the integrator include the coordinates of the center point of the unit, the side lengths of each planar unit along the X-axis and the Y-axis, the side length of the receiving surface and the focal length of the integrator. The orientation parameter of each plane unit includes the rotation angle of the plane unit around the X axis and the Y axis and the coordinates of the rotation center around the X axis and the Y axis.

Figure 1 is the overall structural diagram of the integrator. The parallel light along the Z axis reaches the receiving surface after being reflected by the integrator. In order to achieve uniform light of the integrator, the key is to accurately calculate the position of each unit, that is, determine the size of the planar array unit according to the size of the receiving surface, and rotate the planar array around the X-axis and Y-axis at a specific angle to realize the integrator The uniform light effect. Referring to Fig. 2, the main steps of designing the integrator of the present invention are as follows.

1. Determination of the integrator cell located at the origin of the coordinates. It needs to be determined according to the focal length of the integrator and the size of the receiving surface.

2. Complete the calculation of the integrator unit parameters in the Y-axis direction, mainly determine the center coordinates of the integrator unit, the rotation angle around the X-axis in the Y-axis direction, the coordinates of the rotation center and the side length of the integrator unit.

3. Complete the calculation of the integrator unit parameters in the X-axis direction in turn, mainly determine the center coordinates of the integrator unit, the rotation angle around the Y-axis in the X-axis direction, the coordinates of the rotation center and the side length of the integrator unit.

4. Establish a model in 3D software according to the center of the integrator unit, the rotation angles with the X-axis and Y-axis respectively, the coordinates of the rotation center and the side length of the integrator to complete the establishment of the processing model.

5. After determining the three-dimensional model of the integrator, the real object of the integrator can be processed according to the ultra-precision turning technology, and the surface roughness can be controlled within the range of tens of nanometers.

The specific implementation steps of the determination of the center of the integrator plane unit mentioned in the implementation process of the present invention are:

(1) Determine the focal length f of the paraboloid according to the distance between the receiving surface and the reflecting surface, thereby obtaining the equation of the paraboloid: X ² +Y ² =4fZ,

(2) Determine the side length of the integrator unit located at the origin of the coordinates according to the size of the receiving surface, the values of the two are equal,

(3) Divide the paraboloid in (1) into a series of grids on the XOY plane. The boundary lines of the grids are parallel to the X-axis and the Y-axis. The points on the grid are the projections of the center of the plane array on the XOY plane. That is to say, the coordinates of the center of the plane array in the X and Y directions have been determined. The center of the integrator unit at the initial origin is (0, 0, 0). In order to determine the position of the center of other integrator units, it is necessary to determine the coordinates of the center of the plane unit of the integrator in the Z direction. Once the center coordinates of the integrator unit are determined, the location parameters of the integrator unit are also determined.

The specific implementation steps of the position parameter and the direction parameter determination method of the planar unit of the integrator on the Y-axis direction mentioned in the implementation process of the present invention are:

(1) Determine the direction of the plane unit, the method is to determine according to the tangent direction of the paraboloid at this point, and the direction of the normal vector of the plane unit is perpendicular to the tangent direction of the parabola. According to the known X ₀ and Y ₀ of the center of the plane unit of the integrator, the normal vector K[k ₁ , k ₂ ] at the point plane can be obtained, as follows:

k ₁ =-X ₀ /(2f) (1)

k ₂ =-Y ₀ /(2f) (2)

After normalization, the normal vector K'[a, b, c] of the plane is obtained.

$\mathrm{<span\; class="notranslate">\; a</span>}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; /</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span>$

$\mathrm{<span\; class="notranslate">\; b</span>}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; /</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 4</span>}<span\; class="notranslate">\; )</span>$

$\mathrm{<span\; class="notranslate">\; c</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; /</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 5</span>}<span\; class="notranslate">\; )</span>$

In this way, the normal vector of the plane unit is obtained, thereby determining the direction of the plane unit.

(2) Establish a continuous relationship with the previous plane unit to ensure the continuity of the integrator. Let A _i be the edge point of the previous plane, and A _i+1 be a point connected to it, so it satisfies:

A _i =A _i+1 (6)

According to A _i (X _i , Y _i , _Zi ) and O(X ₀ , Y ₀ , Z ₀ ), the coordinate value Z of the plane center P in the Z direction can be determined:

Z ₁ ＝a*(X ₀ -X _i )+b*(Y ₀ -Y _i )+Z _i (7)

Solving the equations (4), (5), (6) and (8), you can get its center coordinate value P ₁ (X ₁ , Y ₁ , Z ₁ ), so you can get the position parameter P ₁ of the plane and the orientation parameter K'.

The specific implementation steps of the position parameter and the direction parameter determination method of the integrator unit on the X-axis direction mentioned in the implementation process of the present invention are:

(1) According to the known X ₀ and Y ₀ of the center of the plane unit of the integrator, the normal vector K[k ₁ , k ₂ ] at the point plane can be obtained,

k ₁ =-X ₀ /(2f) (8)

k ₂ =-Y ₀ /(2f) (9)

After normalization, the normal vector K'[a, b, c] of the plane is obtained.

$\mathrm{<span\; class="notranslate">\; a</span>}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; /</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 10</span>}<span\; class="notranslate">\; )</span>$

$\mathrm{<span\; class="notranslate">\; b</span>}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; /</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 11</span>}<span\; class="notranslate">\; )</span>$

$\mathrm{<span\; class="notranslate">\; c</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; /</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 12</span>}<span\; class="notranslate">\; )</span>$

This determines the direction K' of the planar unit.

(3) In order to ensure the continuity of the integrator unit, it is necessary to establish the relationship between the position coordinates of this plane unit and the previous plane unit. Let B _i be the edge point of the previous surface, and B _i+1 is a point connected to it, so it satisfies:

B _i =B _i+1 (13)

From the _Bi (X _i , Y _i , _Zi ) and O ₂ (X ₀ , Y ₀ , Z ₀ ) of the previous plane, the coordinate value of the surface center P ₂ of the desired plane in the Z direction can be determined:

Z ₂ ＝a*(X _i -X ₀ )+b*(Y _i -Y ₀ )+Z ₀ (14)

According to formulas (11), (12), (13), and (15), the center coordinate value P ₂ (X ₂ , Y ₂ , Z ₂ ) can be obtained. In this way, the position parameter P ₂ and the direction parameter K' of the requested plane unit are obtained.

The specific implementation steps of the integrator model determination method mentioned in the implementation process of the present invention are:

(1) Determine the position parameters of the integrator. According to the position and direction of the integrator unit in the X direction and the Y direction, the rotation angle of the plane array in the X and Y directions can be calculated respectively:

a ₀ ＝π/2-arccos(-a) (15)

b ₀ ＝π/2-arccos(-b) (16)

Where a ₀ represents the rotation angle of the plane around the Y axis; b ₀ represents the rotation angle of the plane around the X axis.

(2) Determine the structural parameters of the integrator, the length of the rectangular side of the plane unit on the X-axis and Y-axis:

d ₁ =d/cos(a) (17)

d ₂ =d/cos(b) (18)

Among them, d ₁ represents the length of the plane in the X-axis direction; d ₂ represents the length of the plane in the Y-axis direction. The integrator profile shown in Figure 7(a) can be obtained.

(3) Obtain the integrator model along the positive direction of the X-axis according to the above method, as shown in Figure 7(a), if the integrator is symmetrical about the Y-axis in the X-direction, an integrator model that is symmetrical about the Y-axis is obtained 7(b).

(4) Remove the planar array located near the center of the integrator on the integrator model to achieve the purpose of off-axis reflection, as shown in Figure 7(c).

The method of using the reflective integrator of the present invention in solar simulator design is as follows: determine the overall size of the reflective integrator according to the size of the incident light aperture, and obtain the overall profile of the integrator according to the principle of the integrator. In the solar simulator, the light source is a short-arc xenon lamp, which needs to be converged to an off-axis parabola through a condenser, collimated by an off-axis parabola to obtain parallel light, and then incident on a reflection integrator to achieve uniformity of light.

In order to compare the performance of the two integrators, the simulation of the two integrators in the present invention adopts the same energy of incident light, both of which are 21×21mm square parallel light, and the power of each light is 1W/cm ² . From the comparison of the receiving surfaces of the two integrators, the reflective integrator has better irradiance uniformity distribution than the transmissive integrator, and the maximum power of the receiving surface is 1.49×10 ² W/cm ² , while the maximum power of the refraction integrator under the same conditions is only 0.215W/cm ² . It can be seen by comparison that the reflective integrator designed by the present invention is simpler in structure than the traditional transmissive integrator, and has better stability. The light intensity distribution at the edge of the receiving surface is more stable. Moreover, due to the reduction of aberrations and transmission losses, the energy reaching the receiving surface has also been greatly improved.

Claims (1)

1. A reflective optical integrator design method based on a plane mirror array, this kind of reflective optical integrator comprises a plane reflector array, with the center of the plane at the center of the plane reflector array as the origin of coordinates, with the reflection of parallel light incident The direction is the Z axis, and a rectangular coordinate system is established. The parallel light along the Z axis is reflected by the integrator and reaches the receiving surface; the structural parameters of the integrator include the side lengths of each plane unit along the X and Y axes, the receiving surface The side length 2d and the focal length f of the integrator, the position parameters of each plane unit include the coordinates of the center point of the unit, the rotation angles around the X-axis and the Y-axis respectively, and the coordinates of the rotation center around the X-axis and the Y-axis, which Design methods include: The first step. Determination of the center of the planar unit of the integrator: (1) Determine the focal length f of the integrator according to the distance between the receiving surface and the reflecting surface, so as to obtain the equation of the paraboloid: X ² +Y ² =4fZ, (2) Determine the side length of the integrator unit at the origin of the coordinates according to the size of the receiving surface, and the values of the two are equal. (3) Divide the paraboloid in (1) into a series of grids on the XOY surface, the boundary lines of the grids are parallel to the X axis and the Y axis, and each point on the grid is used as the center of the integrator unit on the XOY surface The projection of the integrator unit at the origin is (0, 0, 0). According to the ray tracing and the position of the point on the grid, the position of each integrator unit center is determined. For each integrator unit center, respectively according to From the second step to the fourth step below, iteratively calculate the position parameter and direction parameter of each plane unit corresponding to it along the Y direction and the X direction; Step 2. For the center of each integrator unit, set its coordinates on the XOY plane as X ₀ and Y ₀ respectively, and its tangent vector on the paraboloid is K[k ₁ ,k ₂ ], k ₁ =-X ₀ /(2f), k ₂ =-Y ₀ /(2f), and assuming that the direction of the normal vector of the plane unit is perpendicular to the direction of the tangent of the paraboloid, the normal vector of the corresponding plane unit [a,b, c], $a=-k_1/{(k_1^2+k_2^2+1)}^{1/2},$ $b=-k_2/{(k_1^2+k_2^2+1)}^{1/2},$ $c=1/{(k_1^2+k_2^2+1)}^{1/2},$ To determine the direction of the planar unit; The third step. Determine the position parameter and direction parameter of the integrator array on the Y direction: Let A _i be the edge point of the previous plane unit and the current plane unit on the Y direction, then A _i is known; A _{i+ 1} is the point where the current plane unit is connected to the edge point, A _i =A, according to A _i (X _i ,Y _i ,Z _i ) and the center of the integrator unit, the center of the plane unit in the Y direction can be determined in the Z direction coordinate value Z ₁ =a*(X ₀ -X _i )+b*(Y ₀ -Y _i )+Z _i , and then obtain the center coordinate value P ₁ of the plane unit in the Y direction according to the normal vector of the plane unit (X ₁ , Y ₁ , Z ₁ ), thus obtaining the position parameter and direction parameter of the plane unit in the Y direction; The 4th step. Determine the position parameter and the direction parameter of the integrator array on the X direction: Let B _i be the edge point of the previous plane unit and the current plane unit on the X direction, then B _i is known; B _{i+ 1} is the point where the current plane unit is connected to the edge point, Bi ₌ B, according to _Bi (X _i , Y _i , _Zi ) and the center of the integrator unit, the center of the plane unit in the X direction can be determined in the Z direction Coordinate value Z ₂ =a*(X _i -X ₀ )+b*(Y _i -Y ₀ )+Z _i , and then obtain the plane center coordinate value P ₂ (X ₂ , Y ₂ , Z ₂ ), so that the position parameter and direction parameter of the plane unit in the X direction are obtained; the fifth step. Build the integrator model: (1) Determine the position parameters of the integrator: According to the position and direction of the integrator unit in the X and Y directions, the rotation angle a of the plane array in the X and Y directions can be calculated respectively ₀ =π/2-arccos(-a ) and b ₀ =π/2-arccos(-b), where a ₀ represents the rotation angle of the plane around the Y axis; b ₀ represents the rotation angle of the plane around the X axis; (2) Determine the structural parameters of the integrator: obtain the rectangular side lengths d ₁ =d/cos(a) and d ₂ =d/cos(b) of the plane unit on the X-axis and Y-axis respectively, where d ₁ represents the plane The length of the unit in the X-axis direction; d ₂ represents the length of the plane unit in the Y-axis direction; (3) Obtain the integrator model along the positive direction of the X-axis according to the above method, and expand the integrator model symmetrically about the Y-axis in the X-direction to obtain an integrator model that is symmetrical about the Y-axis; (4) Remove the planar array located near the center of the integrator on the integrator model that is symmetrical about the Y axis, so as to achieve the purpose of off-axis reflection; Step 6. Design the processing path according to the designed integrator model, and perform ultra-precision turning processing.

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