CN116841024A - Free-form surface optical system design method with addition of turning manufacturing constraint - Google Patents

Abstract

The invention provides a free-form surface optical system design method added with turning manufacturing constraint, which is used for solving the technical problems that the processing difficulty of a free-form surface is ignored in the traditional free-form surface design method, so that the processing difficulty of the free-form surface is high and the surface type processing precision cannot meet the requirement. The design method of the optical system provided by the invention comprises the following steps: according to the analytic expression of the free-form surface, calculating to obtain a reference aspheric busbar equation of the free-form surface; uniformly sampling data points in the rho direction and the theta direction on the free curved surface to obtain the deviation RMS value of the sampled data points relative to the reference aspheric surface; adding the deviation RMS value of the sampled data points from the reference aspheric surface as a manufacturing constraint to an evaluation function of the optical design; the method can be used for completing the design of the free-form surface optical system by setting the target value of the corresponding evaluation function to zero and selecting the weight of the target value, and effectively reduces the processing difficulty of the free-form surface on the premise of meeting the imaging requirement.

Description

A design method for free-form optical systems with added turning manufacturing constraints

Technical field

The invention relates to a free-form surface processing method, and in particular, to a free-form surface optical system design method that adds turning manufacturing constraints.

Background technique

Free-form surfaces are complex optical elements whose surface topography lacks translational or rotational symmetry. Compared with traditional spherical and aspherical mirrors, free-form surfaces will introduce new degrees of design freedom to optical design. Using free-form surfaces instead of traditional spherical and aspherical mirrors to design reflective optical imaging systems will allow the optical system to gain many advantages, including simplification of the system structure, reduction in the number of optical components, improvement of imaging quality, and expansion of the imaging field of view. wait. However, since the free-form surface does not have rotational symmetry, the machining accuracy of the free-form surface will be limited in actual processing.

In the traditional free-form surface design method, the indicators of the optical system need to be constrained according to the design requirements, such as imaging quality, structural parameters of the optical system, etc. Currently, only the imaging quality of the optical system is usually considered, while the free-form surface in the system is ignored. processing difficulty. This is likely to cause the processing of the free-form surface to be very difficult after the optical system is designed, and may even lead to the surface processing accuracy not meeting the requirements because the surface processing is too difficult.

Contents of the invention

The purpose of the present invention is to solve the technical problem of neglecting the processing difficulty of the free-form surface in the traditional free-form surface design method, resulting in high processing difficulty of the free-form surface, which in turn causes the surface processing accuracy of the free-form surface to fail to meet the requirements, and proposes an additive method. Design method of free-form optical system with manufacturing constraints for turning.

In order to achieve the above objects, the technical concept of the present invention is as follows:

Based on the single-point turning processing method, the machinability and processing difficulty of different surface shapes of free-form surfaces are analyzed. When controlling the turning process based on the fast tool servo system, the workpiece needs to be placed on the C-axis for high-speed rotation. When turning a free-form surface, the C-axis rotation angular speed is usually set to rotate at a constant speed. In addition, the feed speed in the sports. When the height change of the surface along the radial direction is relatively small, the z-direction movement of the tool head during processing will be smaller, which will bring two benefits: when the same number of points are selected on the spiral of a cycle, The linear interpolation error in the tangential direction is smaller; when the reciprocating motion amplitude in the z direction is relatively small, the motion accuracy of the linear axis is higher. Therefore, when the deviation of the free-form surface relative to the reference aspheric surface is lower, it means that the processing difficulty of the free-form surface is also lower.

Based on the above concepts, the technical solutions provided by the present invention are as follows:

A free-form surface optical system design method that adds turning manufacturing constraints is special in that it includes the following steps:

1】According to the analytical expression f(ρ, θ) of the free-form surface, calculate the reference aspherical bus equation of the free-form surface. Its specific expression is:

Among them, ρ represents the polar diameter in the cylindrical coordinate system, θ represents the polar angle in the cylindrical coordinate system, and h(ρ) represents the height of the reference aspheric surface corresponding to the polar diameter ρ in the cylindrical coordinate system;

2] Uniformly sample the data points in the ρ direction and θ direction on the free surface, where M times are sampled in the ρ direction and N times are sampled in the θ direction; combined with the reference aspherical bus equation of the free surface obtained in step 1], M*N is obtained The deviation RMS value ∈ of a sampled data point relative to the reference aspheric surface, its expression is:

Among them, j represents the number of sampling times in the ρ direction, j=1,2...M; i represents the number of sampling times in the θ direction, i=1,2...N; ρ _j represents the number corresponding to the sampling data point in the ρ direction. Polar diameter; θ _i represents the polar angle corresponding to the sampling data point in the θ direction, M is an integer greater than or equal to 1, and N is an integer greater than or equal to 12;

3] Add the deviation RMS value ∈ of M*N sampling data points relative to the reference aspheric surface as a manufacturing constraint to the evaluation function of the optical design;

4] Set the target value of the evaluation function corresponding to the manufacturing constraints to zero, and select the weight of the evaluation function corresponding to the manufacturing constraints to complete the design of the free-form optical system.

Further, step 2]-step 3] are specifically:

2] At the maximum diameter r _max of the free-form surface corresponding to the ρ direction on the free-form surface, uniformly sample the data points in the θ direction N times; combined with the reference aspherical bus equation of the free-form surface obtained in step 1], obtain N sampled data points The average value of the deviation value ∈′ relative to the reference aspheric surface, its expression is:

where z _i represents the height of the sampling data point;

3] Add the average value ∈′ of the deviation values of N sampling data points relative to the reference aspheric surface as a manufacturing constraint to the evaluation function of the optical design.

Further, in step 3], the evaluation function adopts the evaluation function in ZEMAX software.

Compared with the prior art, the beneficial effects of the present invention are as follows:

1. The present invention provides a free-form surface optical system design method that adds turning manufacturing constraints. The reference aspheric surface and the deviation RMS value relative to the reference aspheric surface are determined based on the free-form surface, thereby quantitatively describing the difficulty of free-form surface turning processing. , on this basis, the deviation RMS value of the free-form surface is added as a manufacturing constraint to the design process of the free-form surface. Compared with the traditional free-form surface design method, the present invention enables the designed free-form surface to meet the imaging requirements, Effectively reduces the difficulty of processing free-form surfaces.

2. The invention provides a free-form surface optical system design method that adds turning manufacturing constraints. It is simple to operate and highly practical, and can be widely used in mirror processing of free-form surfaces.

3. The invention provides a free-form surface optical system design method that adds turning manufacturing constraints. At the maximum diameter r _max of the free-form surface corresponding to the ρ direction on the free-form surface, the data points in the θ direction are uniformly sampled, which can simplify ZEMAX. form of operands in the software, thereby speeding up optimization.

Description of the drawings

Figure 1 is a schematic diagram of the linear interpolation error caused by the movement of the tool according to the control point in free-form surface turning processing;

Figure 2 is a schematic diagram of the simulation results of the deviation RMS value of 1000 random free-form surfaces and the RMS value of the linear interpolation error of processing.

Figure 3 is a schematic structural diagram of a free-form off-axis three-reflection system without manufacturing constraints;

Figure 4 is a schematic structural diagram of a free-form off-axis three-reflection system with added manufacturing constraints;

Figure 5 shows the spot array diagram and MTF curve of each field of view of the free-form off-axis three-mirror system without manufacturing constraints, where (a) is the spot array diagram and (b) is the MTF curve;

Figure 6 shows the spot array diagram and MTF curve of each field of view of the free-form off-axis three-mirror system with manufacturing constraints added, where (a) is the spot array diagram and (b) is the MTF curve;

Figure 7 is the deviation value distribution diagram of the free-form surface off-axis three-mirror system without manufacturing constraints. (a) is the deviation value distribution diagram of the primary mirror in the free-form surface off-axis three-mirror system without manufacturing constraints. (b) (c) is the deviation value distribution diagram of the third mirror in the free-form off-axis three-mirror system without manufacturing constraints;

Figure 8 is the deviation value distribution diagram of the free-form surface off-axis three-mirror system with added manufacturing constraints. (a) is the deviation value distribution diagram of the primary mirror in the free-form surface off-axis three-mirror system with added manufacturing constraints. (b) (c) is the deviation value distribution diagram of the third mirror in the free-form off-axis three-mirror system with manufacturing constraints added.

Figure 9 is a columnar comparison diagram of the deviation RMS values of the primary mirror, secondary mirror and third mirror in the free-form off-axis three-mirror system without manufacturing constraints and the free-form off-axis three-mirror system with manufacturing constraints added;

Figure 10 is a columnar comparison diagram of the RMS values of the machining linear interpolation errors of the primary mirror, secondary mirror and third mirror in the free-form off-axis three-mirror system without manufacturing constraints and in the free-form off-axis three-mirror system with manufacturing constraints added.

Detailed ways

In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments These are some embodiments of the present invention, rather than all embodiments. The components of the embodiments of the invention generally described and illustrated in the figures herein may be arranged and designed in a variety of different configurations.

A design method for free-form surface optical systems that adds turning manufacturing constraints, specifically including the following steps:

1] Based on the characteristics of free-form surface turning processing, according to the analytical expression f(ρ, θ) of the free-form surface, the reference aspherical bus equation of the free-form surface is calculated, and its specific expression is:

Among them, ρ represents the polar diameter in the cylindrical coordinate system, θ represents the polar angle in the cylindrical coordinate system, and h(ρ) represents the height of the reference aspheric surface corresponding to the polar diameter ρ in the cylindrical coordinate system.

2] In the present invention, the deviation RMS value ∈ of the free-form surface is used to evaluate the processing difficulty of the free-form surface. Therefore, the data points in the ρ direction and the θ direction on the free-form surface are uniformly sampled, in which the ρ direction is sampled M times, and the θ direction is sampled M times. Sampling N times; combined with the reference aspherical bus equation of a certain free-form surface obtained in step 1], the deviation RMS value ∈ of M*N sampled data points relative to the reference aspherical surface is obtained, and its expression is:

Among them, j represents the number of sampling times in the μ direction, j=1,2...M; i represents the number of sampling times in the θ direction, i=1,2...N; ρ _j represents the number corresponding to the sampling data point in the ρ direction. Polar diameter; θ _i represents the polar angle corresponding to the sampling data point in the θ direction, M is an integer greater than or equal to 1, and N is an integer greater than or equal to 12.

In order to verify the deviation RMS value ∈ of the free-form surface, the processing difficulty of the free-form surface can be measured. This embodiment takes a quadratic surface as the base surface and a free-form surface with an additional term of 7th order XY polynomial as an example. In this embodiment, the normalized radius of the free-form surface is selected as 1mm, and its surface shape expression is:

Among them, R ₀ represents the radius of curvature of the base surface of the free-form surface, r ₀ represents the diameter of the free-form surface, k represents the conic coefficient, i represents the degree of x in the XY polynomial, j represents the degree of y in the XY polynomial, and m represents the degree of x in the XY polynomial. The maximum degree of , n represents the maximum degree of y in the XY polynomial, x ⁱ y ^j represents a certain polynomial, A _{i, j} represents the coefficient of the x ⁱ y ^j polynomial.

Randomly select 1,000 sets of XY polynomial coefficients to construct 1,000 free-form surface expressions. The base curvature radius R ₀ of the free-form surface, the cone coefficient k, and the range of the XY polynomial coefficients are determined in order to make the constructed free-form surface representational. is reasonable, and the specific range is shown in Table 1.

Table 1 The base curvature radius R ₀ of the free-form surface, the cone coefficient k and the range of the XY polynomial coefficient

The deviation RMS value ∈ and the processing linear interpolation error RMS value based on these 1000 free-form surfaces were calculated respectively. Among them, the deviation RMS value ∈ is calculated according to formula (2), and the source of the linear interpolation error is that the actual trajectory of the tool is controlled according to the number of control points, and there is a deviation from the ideal surface. As shown in Figure 1, the control of the tool The points are _si and _si+1 . The ideal trajectory of the tool is the curve between _si and si ₊₁ , while the actual trajectory of the tool is the straight line between _si and _si+1 . Because the two trajectories There will be machining errors, which are called linear interpolation errors. The parameters of the machining simulation are that the machining diameter is 20mm, the number of selected control points is 200, and the spiral spacing is 10um. Therefore, based on the control point coordinates, the linear interpolation error distribution of the free-form surface and the linear interpolation error RMS value can be calculated. .

As shown in Figure 2, the relationship between the deviation RMS value ∈ of 1000 random free-form surfaces and the linear interpolation error of processing is shown. According to the simulation experiment results, it can be seen that the two are positively correlated. That is, when the deviation from the RMS value ∈ is larger, it means that the linear interpolation error of processing is also larger, that is, the difficulty of processing is greater.

In summary, it is completely feasible to use the deviation RMS value ∈ of the free-form surface to evaluate the processing difficulty of the free-form surface. In design, the smaller the deviation RMS value ∈ of the free-form surface, the lower the processing difficulty of the free-form surface. Therefore, in order to make the processing of the free-form surface in the optical system less difficult, it is only necessary to make the deviation RMS value ∈ of the free-form surface smaller.

When the deviation RMS value is added to the merit function as a manufacturing constraint, a large number of data points need to be sampled and calculated according to its definition. The method of realizing constraints in the evaluation function is through operands. Too many sampling points will lead to too many operands, which will lead to slower optimization of the optical system, which is not conducive to software implementation. Therefore, in this embodiment, the number of operands is reduced by reducing sampling points, thereby speeding up the optimization of the optical system. Specifically, at the maximum diameter r _max of the free-form surface corresponding to the ρ direction on the free-form surface, for the data points in the θ direction Sampling N times uniformly, usually N is selected from 20-30, and the specific number is determined based on the maximum diameter r _max of the free-form surface corresponding to the ρ direction.

Since the angle of the sampling data point θ _i =i/n·2π, according to the expression of the free surface, the height z _i of the sampling data point is:

z _i =f (r _max , θ _i ) (4)

Then the average value ∈′ of the deviation values of N sampled data points relative to the reference aspheric surface is:

3] In the subsequent optical design process, the average value ∈′ of the deviation values of the N sampling data points relative to the reference aspheric surface is added to the evaluation function of the optical design as a manufacturing constraint. In this embodiment, the evaluation function in the ZEMAX software is used to add manufacturing constraints. In other embodiments of the present invention, other software can also be used to add manufacturing constraints. In the ZEMAX software, the SSAG operand is used to limit the sag height of the sampling data points. Therefore, when adding manufacturing constraints, it is necessary to sample the sag height of the free-form surface sampling data points, and then calculate the manufacturing based on the average sag height difference between adjacent sampling data points. constraints, and then add the obtained manufacturing constraints to the evaluation function using ZEMAX software.

4] Set the target value of the evaluation function corresponding to the manufacturing constraints to zero, and select the weight of the evaluation function corresponding to the manufacturing constraints to complete the design of the free-form optical system.

Among them, the weight selection criteria of the evaluation function corresponding to the manufacturing constraints are related to the specific optical system. If the weight is too high, the imaging constraints in the evaluation function will be smaller, resulting in the imaging quality of the final optical system not meeting the design requirements. If the weight is too small, the processing performance of the free-form surface will not be significantly improved, so in actual design, it takes several attempts to get the appropriate weight.

Taking the free-form off-axis three-mirror optical system as an example, the effect of the free-form surface optical system design method with added turning manufacturing constraints provided by the present invention will be further explained below.

A free-form off-axis three-mirror optical system without added manufacturing constraints is used as the initial structure, and the optical system is redesigned by adding manufacturing constraints based on the initial structure. By comparing the imaging effects of the two optical systems before and after adding manufacturing constraints and the simulated processing errors, the impact of manufacturing constraints on the design of free-form optical systems is demonstrated.

Among them, Figure 3 is a schematic structural diagram of the initial structure of a free-form off-axis three-mirror system without added manufacturing constraints. The system parameters of the imaging system are: the entrance pupil diameter is 40mm, the F number is 4, and the full field of view (FOV) is 4×4. Based on the initial structure, the maximum diameters of the primary mirror, secondary mirror and third mirror are 20mm, 15mm and 25mm respectively. Sampling is carried out at the maximum aperture of the three mirrors, and an evaluation function is constructed based on the sagittal height difference of adjacent sampling data points. The weight is designed to be 0.01, and then a new optical system is re-optimized, that is, a free-form off-axis surface with manufacturing constraints added. The three-reverse system is shown in Figure 4. It can be seen that the various parameters of the free-form off-axis three-mirror system with added manufacturing constraints have not changed, such as the entrance pupil diameter, F number, and field of view size, but the system structure has changed, such as the distance between the mirrors and the deflection angle of the mirrors. and the surface topography of freeform surfaces.

As shown in Figure 5, the spot diagram and MTF curve of each field of view of the free-form off-axis three-mirror system without manufacturing constraints are shown. (a) in Figure 5 is the spot diagram, and (a) in Figure 5 is the spot diagram. (b) is the MTF curve. As shown in Figure 6, the light spot diagram and MTF curve of each field of view of the free-form off-axis three-mirror system with added manufacturing constraints are shown. Among them, (a) in Figure 6 is the light spot diagram. Figure 6 (b) is the MTF curve. By comparing the spot diagrams of the two systems, it can be seen that after adding manufacturing constraints, the spot radius RMS imaged by the system increases slightly, but it is still within the Airy disk. The MTF curves of each field of view of both optical systems remain at about 0.7 at 90lp/mm, which is not much different from the diffraction limit MTF curve. Therefore, comparing the imaging quality of the two optical systems, it can be seen that after adding manufacturing constraints, the imaging quality of the optical system is slightly reduced, but the diffraction limit can still be reached.

In addition, the reference aspheric surface equation of the free-form surface can be calculated according to formula (1), so that the distribution of the sagittal height deviation values of the primary mirror, secondary mirror and third mirror in the two optical systems relative to the reference aspheric surface can be obtained. As shown in Figure 7, it is the deviation value distribution diagram of the free-form surface off-axis three-mirror system without adding manufacturing constraints. (a) in Figure 7 shows the deviation value distribution diagram of the primary mirror, and (b) in Figure 7 shows the deviation value distribution diagram of the secondary mirror. The deviation value distribution diagram of the mirror, (c) in Figure 7 shows the deviation value distribution diagram of the three mirrors. As shown in Figure 8, it is the deviation value distribution diagram of the free-form surface off-axis three-mirror system with added manufacturing constraints. (a) in Figure 8 shows the deviation of the primary mirror in the free-form surface off-axis three-mirror system with added manufacturing constraints. Value distribution diagram, (b) in Figure 8 shows the deviation value distribution diagram of the secondary mirror in the free-form off-axis three-mirror system with manufacturing constraints added, (c) in Figure 8 shows the free-form surface off-axis with manufacturing constraints added Distribution of deviation values of three mirrors in a three-mirror system. It can be seen that in the free-form off-axis three-mirror system with added manufacturing constraints, the deviation values of all mirrors relative to the reference aspheric surface are smaller, which means that all free-form surfaces are closer to the reference aspheric surface.

According to formula (2), the deviation RMS values ∈ of the primary mirror, secondary mirror and third mirror in the two optical systems are calculated respectively. The results are shown in Figure 9. In addition, at the maximum aperture of the free-form surface, 200 points were selected in a single circle to simulate the linear interpolation error distribution during turning processing, and then the RMS value of the linear interpolation error distribution was calculated, as shown in Figure 10. Comparing the deviation RMS value ∈ and the processing linear interpolation error RMS value of the two optical systems, it can be seen that compared with the optical system without manufacturing constraints, after adding manufacturing constraints to the optical design, the processing error of the free-form optical system And the processing difficulty has been reduced.

Therefore, the present invention adds the manufacturing constraints of the free-form surface to the design process of the free-form surface, so that when designing the optical system using optical design software, not only the imaging quality of the system, but also the processing difficulty of the surface shape can be taken into consideration. The optical system designed in this way can effectively reduce the processing difficulty of each free-form surface mirror while ensuring the imaging quality of the optical system.

The above are only preferred embodiments of the present invention and are not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and changes. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention shall be included in the protection scope of the present invention.

Claims (3)

1. The free-form surface optical system design method for adding the turning manufacturing constraint is characterized by comprising the following steps of:

according to the analytic expression f (rho, theta) of the free-form surface, calculating to obtain a reference aspheric busbar equation of the free-form surface, wherein the specific expression is as follows:

wherein ρ represents the polar diameter in the cylindrical coordinate system, θ represents the polar angle in the cylindrical coordinate system, and h (ρ) represents the height of the reference aspheric surface corresponding to ρ in the polar diameter in the cylindrical coordinate system;

uniformly sampling data points in the rho direction and the theta direction on the free curved surface, wherein the directions are sampled M times and the theta direction is sampled N times; combining the reference aspheric busbar equation of the free-form surface obtained in the step 1), obtaining deviation RMS value epsilon of M x N sampling data points relative to the reference aspheric surface, wherein the expression is as follows:

where j represents the number of ρ -direction sampling times, j=1, 2 … M; i represents the number of θ -direction sampling times, i=1, 2 … N; ρ _j Representing the polar diameter corresponding to the rho direction sampling data point; θ _i Representing a polar angle corresponding to a theta-direction sampling data point, wherein M is an integer greater than or equal to 1, and N is an integer greater than or equal to 12;

adding the deviation RMS value epsilon of M.N sampling data points relative to the reference aspheric surface as a manufacturing constraint to an evaluation function of the optical design;

and 4, setting the target value of the evaluation function corresponding to the manufacturing constraint to be zero, and selecting the weight of the evaluation function corresponding to the manufacturing constraint to complete the design of the free-form surface optical system.

2. The method for designing a free-form surface optical system with addition of turning manufacturing constraints according to claim 1, wherein the steps 2 to 3 are specifically:

2, maximum caliber r of free curved surface corresponding to rho direction on free curved surface _max Uniformly sampling data points in the theta direction for N times; combining the reference aspheric busbar equation of the free-form surface obtained in the step 1 to obtain an average value E' of deviation values of N sampling data points relative to the reference aspheric surface, wherein the expression is as follows:

wherein z is _i Representing the height of the sampled data points;

the average value e' of the deviation values of the N sampled data points from the reference aspheric surface is added as a manufacturing constraint to the evaluation function of the optical design.

3. A free-form surface optical system design method adding turning manufacturing constraints according to claim 1 or 2, characterized in that:

in the step 3), the evaluation function is an evaluation function in ZEMAX software.