A free-form surface design method for large-field-of-view projection system

Abstract

The present invention belongs to the field of optical design. In order to solve the problem that the existing free-form surface design method of the projection system cannot directly design the imaging of the full-aperture free-form surface, a free-form surface design method for a large-field-of-view projection system is proposed. The method sets a reference point, defines the starting point of the characteristic light, selects K characteristic light rays in each sampling field of view, and determines the reference point on the free-form surface Ω to be determined under each sampling field of view; solves the characteristic data points on the free-form surface Ω to be determined under each sampling field of view according to Malus's law; fits the obtained characteristic data points to obtain the expression corresponding to the free-form surface Ω, uses the calculated free-form surface as the initial structure, and optimizes it in combination with a refractive lens group to obtain the initial system of the free-form surface large-field-of-view projection system. The scheme can calculate the characteristic data points of the unknown free-form surface under the full field of view and full aperture, has fewer calculation steps, simplifies the calculation process, improves the calculation efficiency, and reduces the complexity of the refractive lens group.

Description

Technical Field

[0001] The invention belongs to the field of optical design, and in particular relates to a free-form surface design method for a large-field-of-view projection system. Background Art

[0002] Free-form surfaces are non-rotationally symmetric optical surfaces that can provide more degrees of freedom for optical design, and have the advantages of improving imaging quality and reducing the number of optical components. In off-axis optical systems, in order to avoid obstruction or to meet the constraints of the size and weight of the optical system, the symmetry of the optical system is broken. When the system symmetry is destroyed, the performance of the optical system will drop significantly, and the use of free-form surfaces can restore the optical performance of the off-axis system. Therefore, free-form surfaces are often used in off-axis display systems.

[0003] In order to realize imaging of a certain field of view and aperture size, the imaging optical system needs to control the light at different aperture positions in different fields of view in the imaging system. However, the existing free-form surface direct design method used in projection systems cannot directly design free-form surfaces for full-aperture imaging. [1] Based on the principle of differential geometry and Snell's reflection law, a catadioptric ultra-short-focus projection objective was designed. Since only the light at the center of the exit pupil is considered in the design of the reflector, the optical system designed by this method can only have the main light to complete the imaging within the full field of view, and cannot image the full aperture, that is, it is only suitable for small aperture systems; secondly, this method does not consider the refractive lens group when designing the reflector of the projection objective, so the designed reflector may not match the refractive lens group.

[0004] [1] Li Runzhi, Yang Bo, Zhang Jingjing, et al. Design of ultra-short focal length projection lens using catadioptric imaging[J]. Optical Technology, 2018, 044(003): 305-309. Summary of the invention

[0005] The purpose of the present invention is to solve the problem that the free-form surface for full-aperture imaging cannot be directly designed in the prior art, and to provide a solution that can directly calculate the free-form surface reflector of a large-field-of-view projection system under full field of view and full aperture.

[0006] A free-form surface design method for a large-field-of-view projection system, the projection system comprising: a DMD chip, a 4K galvanometer, an equivalent prism, a protective glass, a refractive lens group, a free-form surface reflector, and a projection screen in sequence along the optical axis direction;

[0007] The working process of the projection system includes: light is emitted from the DMD chip, passes through the 4K galvanometer, equivalent prism, protective glass, refractive lens group in sequence, and forms an image before the free-form surface reflector, and finally is reflected by the free-form surface reflector to the projection screen to form a clear image;

[0008] The design steps include:

[0009] Step S1, establishing an initial structure, which includes the refractive lens group and the free-form surface reflector;

[0010] Step S2, defining the free-form surface reflector as the desired free-form surface Ω, keeping the refractive lens group unchanged; determining the exit pupil size and position of the refractive lens group, selecting K characteristic rays in each sampling field of view, and defining the starting point of the characteristic rays at the exit pupil position;

[0011] Step S3, determining the reference point on the free-form surface Ω to be determined in each sampling field of view;

[0012] Step S4, according to Malus's law, solve the characteristic data points P on the free surface Ω to be solved under each sampling field of view ｉｊ (i=1,2,…,M,j=1,2,…,K-1);

[0013] Step S5, wait for all feature data points P in the field of view to be ij All the solutions are completed, and the expression corresponding to the free-form surface Ω is obtained by fitting. The calculated free-form surface reflector is combined with the refractive lens group to obtain the initial system of the free-form surface large field of view projection system;

[0014] The i is the serial number of the sampling field of view, M is the total number of the sampling fields of view, j is the serial number of the characteristic data points under each sampling field of view, K is the total number of the characteristic data points under each sampling field of view, and P ij is the jth feature data point under the i-th sampling field of view.

[0015] The above-mentioned characteristic rays and the starting points of the characteristic rays are selected by the following method:

[0016] The characteristic ray is defined as the ray emitted from the exit pupil of the refractive lens group; the starting point of the characteristic ray is defined as the exit pupil of the refractive lens group. The exit pupil is sampled in polar coordinates, and the number of sampling points increases with the increase of the exit pupil radius; K data points are uniformly sampled on the pupil, and each corresponding field of view has K different characteristic rays; M different fields of view are sampled, and a total of M×K characteristic rays are emitted from the exit pupil, and the starting point of the corresponding characteristic ray is S ij (i=1,2,…,M,j=1,2,…,K).

[0017] The i is the serial number of the sampling field of view, M is the total number of the sampling fields of view, j is the serial number of the characteristic data points under each sampling field of view, K is the total number of the characteristic data points under each sampling field of view, S ｉj is the starting point of the jth characteristic ray under the i-th sampling field of view.

[0018] This method achieves relatively uniform distribution of characteristic light within the full aperture.

[0019] The above reference points are determined in the following way:

[0020] In the i-th sampling field of view, the chief ray emitted from the exit pupil of the refractive lens group is used as the reference ray R i0 (i=1,2,…,M), reference light R i0 The intersection point with the free surface Ω is taken as the reference point P i0 (i=1,2,…,M); reference light R i0 At the reference point P i0 After reflection, it reaches the ideal target point T i ;

[0021] The reference surface Ω' is defined as a surface that enables the optical system to achieve perfect imaging when the numerical aperture NA < 0.1. The reference surface Ω' is used to replace the desired free-form surface Ω to obtain the reference point P for each field of view. i0 .

[0022] The reference surface Ω' is selected in the following manner:

[0023] When the numerical aperture NA is less than 0.1, an initial aspheric reflector is constructed in the optical software according to the given field angle and object-image conjugation conditions, and is used as the reference surface Ω'.

[0024] The setting of reference points makes the shape of the desired free-form surface controllable.

[0025] The characteristic data points on the above free-form surface Ω are obtained by the following calculation method:

[0026] Define the characteristic data point as the intersection of the characteristic light and the free surface to be determined; in the same field of view, from S ij All characteristic light rays emitted converge at the same point T after being reflected by the free-form surface reflector. i , in the i-th sampling field of view, according to the coordinates of the reference point P i0 , calculate the optical path length OP of the reference light:

[0027] OP=n|S i0 P i0 |+n|P i0 T i |

[0028] Where n is the refractive index of the medium. If the system is in air, then n = 1; T i is the ideal target point, which can be solved through the object-image relationship.

[0029] All characteristic rays in the sampling field of view have the same optical path, and find other K-1 characteristic data points P in the field of view.ij (j=1,2,…,K-1), which satisfies the following conditions:

[0030] n|S ij P ij |+n|P ij T ｉ |=OP

[0031] Repeat the above steps for M sampling fields to obtain the feature data points P of all fields of view ij (i=1,2,…,M,j=1,2,…,K-1). The method achieves the technical effect of the optical system forming a perfect image under the full field of view and full aperture; and while keeping the refractive lens group unchanged, the reflector is directly constructed, which can reduce the complexity of the refractive lens group.

[0032] The expression corresponding to the above free surface Ω is:

[0033]

[0034] where z n (x,y) is the nth Zernike polynomial, k ｎ are the coefficients of the nth Zernike polynomial.

[0035] Compared with the prior art, the free-form surface design method for a large-field-of-view projection system provided by the present invention sets reference points and calculates characteristic data points of an unknown free-form surface under full field of view and full aperture according to Malus's law, thereby directly calculating a reflector of the large-field-of-view projection system, which simplifies the calculation process and has high calculation efficiency. During the calculation process, the method directly constructs a reflector while keeping the refractive lens group unchanged, which can reduce the complexity of the refractive lens group. The calculated reflector is used as the initial structure and is optimized in combination with the refractive lens group, so that a system with a large field of view and good imaging quality can be easily obtained. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Figure 1 :Flowchart of a free-form surface design method for a large field of view projection system;

[0037] Figure 2 : Schematic diagram of a method for determining the exit pupil size and position of a refractive lens group in a free-form surface large field of view projection system;

[0038] Figure 3 : Schematic diagram of exit pupil sampling in polar coordinates;

[0039] Figure 4 : Schematic diagram of reference point selection method;

[0040] Figure 5 : Schematic diagram of feature point calculation method;

[0041] Figure 6 : Partial schematic diagram of the optical path of the free-form surface large field of view projection system;

[0042] Figure 7 : Schematic diagram of the optical path of the free-form surface large field of view projection system;

[0043] Figure 8 : Partial schematic diagram of the initial structure light path of the free-form surface large field projection system;

[0044] Fig. 9 : Schematic diagram of the initial structure light path of the free-form surface large field projection system;

[0045] Fig.10 : Partial schematic diagram of the optical path of the free-form surface large field of view projection system after direct design;

[0046] Fig.11 : Schematic diagram of the optical path of the free-form surface large field of view projection system after direct design;

[0047] Fig.12 : Partial schematic diagram of the optical path of the optimized free-form surface large field of view projection system;

[0048] Fig.13 : Schematic diagram of the overall optical path of the optimized free-form surface large field of view projection system;

[0049] Fig.14 : Schematic diagram of the optimized free-form surface large field of view projection system point diagram;

[0050] Fig.15 : Schematic diagram of the MTF curve of the optimized free-form surface large field of view projection system;

[0051] Fig.16 : Schematic diagram of grid distortion of the optimized free-form surface large field of view projection system. DETAILED DESCRIPTION

[0052] The present invention will be further described below in conjunction with the accompanying drawings and embodiments:

[0053] Embodiment 1:

[0054] A free-form surface design method for a large field of view projection system, such as Figure 6 The projection system shown in the figure comprises: a DMD chip, a 4K galvanometer, an equivalent prism, a protective glass, a refractive lens group and a free-form surface reflector in sequence along the optical axis direction;

[0055] Flowchart as Figure 1 As shown, the design steps include:

[0056] Step S1, establishing an initial structure, which includes the refractive lens group and the free-form surface reflector;

[0057] Step S2, defining the free-form surface reflector as the desired free-form surface Ω, keeping the refractive lens group unchanged; determining the exit pupil size and position of the refractive lens group, selecting K characteristic rays in each sampling field of view, and defining the starting point of the characteristic rays at the exit pupil position;

[0058] Step S3, determining the reference point on the free-form surface Ω to be determined in each sampling field of view;

[0059] Step S4, according to Malus's law, solve the characteristic data points P on the free surface Ω to be solved under each sampling field of view ij (i=1,2,…,M,j=1,2,…,K-1);

[0060] Step S5, wait for all feature data points P in the field of view to be ij All the solutions are completed, and the expression corresponding to the free-form surface Ω is obtained by fitting. The calculated free-form surface reflector is combined with the refractive lens group to obtain the initial system of the free-form surface large field of view projection system;

[0061] The i is the serial number of the sampling field of view, M is the total number of the sampling fields of view, j is the serial number of the characteristic data points under each sampling field of view, K is the total number of the characteristic data points under each sampling field of view, and P ij is the jth feature data point under the i-th sampling field of view.

[0062] In step S1, the free-form surface reflector in the initial structure is an arbitrary curved surface, and its specific position is selected according to the total length limit in the design requirements;

[0063] In step S2, the exit pupil size and position of the refractive lens group may be determined by the following method:

[0064] like Figure 2 As shown, the exit pupil is the image formed by the aperture stop passing through the rear optical system, so the chief ray R of all fields of view i0 The intersection point S of the extended lines on the image side i0 That is, the position of the center of the exit pupil XP, the marginal rays R on all the meridian planes of the field of view im At the intersection point S of the image side extension line i1 , S i2 , whose vertical height is the exit pupil size. The characteristic light and the starting point of the characteristic light are selected by the following method:

[0065] like Figure 2 and Figure 3 As shown, the characteristic ray is defined as the ray R emitted from the exit pupil XP of the refractive lens group. ijThe starting point of the characteristic light is defined as the exit pupil of the refractive lens group. The exit pupil is sampled in polar coordinates, and the number of sampling points increases with the increase of the exit pupil radius; K data points are uniformly sampled on the pupil, and there are K different characteristic light rays in each corresponding field of view; M different fields of view are sampled, and a total of M×K characteristic light rays are emitted from the exit pupil, and the starting point of the corresponding characteristic light ray is S ij (i=1,2,…,M,j=1,2,…,K).

[0066] The i is the serial number of the sampling field of view, M is the total number of the sampling fields of view, j is the serial number of the characteristic data points under each sampling field of view, K is the total number of the characteristic data points under each sampling field of view, S ij is the starting point of the jth characteristic ray under the i-th sampling field of view.

[0067] In step S3, the reference point may be determined in the following manner:

[0068] like Figure 4 As shown, in the i-th sampling field of view, from the exit pupil center S of the refractive lens group i0 The main ray emitted is used as the reference ray R i0 (i=1,2,…,M), reference light R i0 The intersection point with the free surface Ω is taken as the reference point P i0 (i=1,2,…,M); reference light R i0 At the reference point P i0 After reflection, it reaches the ideal target point T i ;

[0069] The reference surface Ω' is defined as a surface that enables the optical system to achieve perfect imaging when the numerical aperture NA < 0.1. The reference surface Ω' is used to replace the desired free-form surface Ω to obtain the reference point P for each field of view. i0 .

[0070] The reference surface can be selected in the following ways:

[0071] When the numerical aperture NA is less than 0.1, an initial aspheric reflector is constructed in the optical software according to the given field angle and object-image conjugation conditions, and is used as the reference surface Ω'.

[0072] In step S4, the characteristic data points on the free surface Ω can be obtained by the following calculation method:

[0073] like Figure 5 As shown, ideally, in the same field of view, from S ij All the characteristic light rays emitted are reflected by the free-form surface reflector and converge at the same point T. i In the i-th sampling field of view, according to the coordinates of the reference point P i0, the optical path length OP of the reference light can be calculated:

[0074] OP=n|S i0 P i0 |+n|P i0 T i |

[0075] Where n is the refractive index of the medium. If the system is in air, then n = 1. |S i0 P i0 | is the starting point S of the reference ray i0 To reference point P i0 The length of |P i0 T i | is the reference point P i0 To the ideal target point T i Length.

[0076] Since the optical path is constant, all characteristic rays in the sampling field of view should have the same optical path, and other K-1 characteristic data points P can be found in the field of view. ij (j=1,2,…,K-1), which satisfies the following conditions:

[0077] n|S ij P ij |+n|P ij T i |=OP

[0078] Among them, |S ij P ij | is the starting point S of the characteristic light ij To the feature data point P ij The length of |P ij T i | is the feature data point P ij To the ideal target point T i Length.

[0079] Repeat the above steps for each sampling field to obtain the characteristic data points P of all fields of view ij (i=1,2,…,M,j=1,2,…,K-1).

[0080] In step S5, the expression corresponding to the free surface Ω is:

[0081]

[0082] where z n (x,y) is the nth Zernike polynomial, k n are the coefficients of the nth Zernike polynomial.

[0083] The free-form surface design method for a large-field projection system further includes optimizing the free-form surface reflector obtained in step S5. Specifically, the free-form surface reflector obtained in step S5 and the reflective part in the initial structure constitute a large-field projection system, which is optimized as an initial system.

[0084] like Figure 6 and Figure 7 As shown, an embodiment of the present invention provides a free-form surface design method for a large-field-of-view projection system 100. The free-form surface large-field-of-view projection system 100 comprises a DMD chip 110, a 4K galvanometer 120, an equivalent prism 130, a protective glass 140, a refractive lens group 150 and a free-form surface reflector 160 arranged in sequence along the main optical axis.

[0085] Embodiment 2:

[0086] Based on the first embodiment, the refractive lens group 150 includes eleven lenses arranged in sequence along the projection direction, arranged in sequence from the object side to the image side:

[0087] The first lens 1 has a convex surface facing the object side and a convex surface facing the image side;

[0088] The second lens 2 has a convex surface facing the object side and a convex surface facing the image side;

[0089] The third lens 3 and the fourth lens 4 are cemented lenses, wherein the third lens has a convex surface facing the object side and a convex surface facing the image side; the fourth lens 4 has a concave surface facing the object side and a concave surface facing the image side; the convex surface of the third lens facing the image side and the concave surface of the fourth lens facing the object side are cemented together;

[0090] The fifth lens 5 and the sixth lens 6 are cemented lenses, wherein the fifth lens has a concave surface facing the object side and a concave surface facing the image side; the sixth lens has a convex surface facing the object side and a convex surface facing the image side; the concave surface of the fifth lens facing the image side and the convex surface of the sixth lens facing the object side are cemented together;

[0091] The seventh lens 7 has a convex surface facing the object side and a convex surface facing the image side;

[0092] The eighth lens 8 has a convex surface facing the object side and a convex surface facing the image side;

[0093] The ninth lens 9 has a convex surface facing the object side and a concave surface facing the image side;

[0094] The tenth lens 10 has a concave surface facing the object side and a concave surface facing the image side;

[0095] The eleventh lens 11 has a concave surface facing the object side and a convex surface facing the image side;

[0096] The eleven lenses have a total of twenty mirror surfaces, the convex surface of the first lens facing the object side is the first mirror surface, and the convex surface of the first lens facing the image side is the second mirror surface;

[0097] The convex surface of the second lens facing the object side is the third mirror surface, and the convex surface of the second lens facing the image side is the fourth mirror surface;

[0098] The convex surface of the third lens facing the object side is the fifth mirror surface, the cemented surface of the third lens and the fourth lens is the sixth mirror surface; the concave surface of the fourth lens facing the image side is the seventh mirror surface;

[0099] The concave surface of the fifth lens facing the object side is the eighth mirror surface, the cemented surface of the fifth lens and the sixth lens is the ninth mirror surface; the convex surface of the sixth lens facing the image side is the tenth mirror surface;

[0100] The convex surface of the seventh lens facing the object side is the eleventh mirror surface, and the convex surface of the seventh lens facing the image side is the twelfth mirror surface;

[0101] The convex surface of the eighth lens facing the object side is the thirteenth mirror surface, and the convex surface of the eighth lens facing the image side is the fourteenth mirror surface;

[0102] The convex surface of the ninth lens facing the object side is the fifteenth mirror surface, and the concave surface of the ninth lens facing the image side is the sixteenth mirror surface;

[0103] The concave surface of the tenth lens facing the object side is the seventeenth mirror surface, and the concave surface of the tenth lens facing the image side is the eighteenth mirror surface;

[0104] The concave surface of the eleventh lens facing the object side is the nineteenth mirror surface, and the convex surface of the tenth lens facing the image side is the twentieth mirror surface;

[0105] The characteristic light emitted from the exit pupil of the refractive lens group is reflected by the reflector 160 and then forms an image on the target surface 200. The parameters of the free-form surface large field of view projection system are shown in Table 1.

[0106] Table 1 Parameters of free-form surface large field of view projection system

[0107] parameter index Throw Ratio 0.19 F number (object square NA) 1.7(0.294) Band 450nm:550nm:623nm=1:6:3 DMD pixel size 5.4μm Field of view (2ω) 160° focal length 1.8mm

[0108] The free-form surface design method of the large-field-of-view projection system 100 comprises the following steps:

[0109] Step S'1, establishing an initial structure, the initial structure including a refractive lens group 250 and an initial aspheric reflector 260, the initial reflector being a desired free-form surface;

[0110] Step S'2, defining the initial reflector 260 as the desired free-form surface Ω, keeping the refractive lens group 250 unchanged; determining the exit pupil size and position of the refractive lens group, and defining the starting point of the characteristic light, and selecting K characteristic light rays in each sampling field of view;

[0111] Step S'3, determine the reference point P on the free surface Ω to be determined under each sampling field of view i0 (i=1,2,…,M);

[0112] Step S'4, according to Malus's law, solve the characteristic data points P on the free surface Ω to be solved under each sampling field of view ij (i=1,2,…,M,j=1,2,…,K-1);

[0113] Step S'5, wait for all feature data points P in the field of view to be ij All solutions are completed, and the expression corresponding to the free surface Ω is obtained by fitting.

[0114] Step S'6, optimizing the large-field-of-view projection system formed by the free-form surface Ω to obtain the free-form surface large-field-of-view projection system 100.

[0115] In step S'2, a total of 9 fields of view are selected for design, namely (0, 1.749), (0, 4.665), (0, 7.581), (2.595, 1.749), (2.595, 4.665), (2.595, 7.581), (5.184, 1.749), (5.184, 4.665), (5.184, 7.581). 300 characteristic rays are taken for each field of view, so a total of 2700 characteristic rays are selected, corresponding to the characteristic rays of different aperture positions in different fields of view.

[0116] Figure 8 and Fig. 9 It is a light path diagram of the initial structure composed of the refractive lens group 250 and the initial reflector 260 in step S'1. It can be seen from the figure that the light beams of each field of view are not converged on the target surface 200, and the field of view angle does not meet the requirements, and the intersection point of the light beams on the target surface deviates from the ideal target point.

[0117] Fig.10 and Fig.11 This is the optical path diagram of the directly designed free-form surface large-field-of-view projection system in step S'5, which is composed of the refractive lens group 350 and the free-form surface reflector 360. It can be seen from the figure that each field-of-view light beam roughly converges to the ideal target point on the target surface 200, and the field-of-view angle has met the requirements, indicating that the free-form surface reflector 360 obtained by the design method of the present invention can improve the large-field-of-view imaging requirements of the optical system.

[0118] Fig.12 and Fig.13 1 is a light path diagram of an optimized free-form surface large field projection system 100 composed of a refractive lens group 150 and a free-form surface reflector 160. The optical system structural parameters are shown in Tables 2 to 4.

[0119] The expression corresponding to the free-form surface reflector 160 is:

[0120]

[0121] where z n (x,y) is the nth Zernike polynomial, k n is the coefficient of the nth Zernike polynomial. The Zernike polynomial coefficients are shown in Table 3, where the normalized radius is 100.

[0122] Table 2 Optical system structural parameters

[0123] Mirror number type Vertex curvature radius R(mm) Thickness(mm) Semi-caliber Optical Materials OBJ Physical surface Infinity 0.303 9.184 / flat Infinity 1.1 9.485 / / flat Infinity 0.8 9.485 / flat Infinity 16 12.357 H-ZF4A / flat Infinity 5.5 12.357 / flat Infinity 2 14.374 H-K51 / flat Infinity 1 14.374 First mirror standard 56.725 7 15.382 H-K50 Second mirror standard -32.349 0.2 15.382 The third mirror standard 35.072 4.717 14.190 H-FK61 The fourth mirror standard -1265.706 0.2 14.190 The fifth mirror standard 45.615 11.07 12.893 BAF2 The Sixth Mirror standard -23.735 6.529 12.893 H-TF8 The Seventh Mirror standard 34.232 1.493 12.893 The Eighth Mirror standard -72.138 4.008 7.961 H-ZF52 Ninth Mirror standard 45.602 2.5 7.961 H-FK61 The tenth mirror standard -39.968 0.2 7.961 / Aperture Infinity 0.2 7.518 Mirror 11 standard 172.87 3.132 8.324 H-ZF52A Mirror No. 12 standard 63.305 27.598 8.324 Mirror Thirteen standard -68.279 8.241 20.872 H-QF56 Mirror 14 standard -51.998 0.202 20.872 Mirror No. 15 standard 27.211 9.942 21.033 H-FK61 Mirror 16 standard 155.74 11.892 21.033 Mirror 17 Aspheric -18.675 4.318 18.382 E48R Mirror 18 Aspheric 20.532 27.304 18.382 Mirror 19 Aspheric -23.883 11.666 28.156 E48R Mirror 20 Aspheric -27.208 1.601 28.156 / Free-form surface / -287.464 86.23 MIRROR

[0124] Table 3 Zernike polynomial coefficients of free-form reflectors

[0125]

[0126]

[0127] Table 4 Eccentricity and tilt of free-form reflector

[0128] Surface number X-axis eccentricity(mm) Y axis eccentricity(mm) X-axis tilt (°) Y-axis tilt (°) 28 0 -5.975 7.741 0

[0129] Fig.14 To optimize the spot diagram of the free-form surface large field of view projection system 100, which represents the diffuse spot size on the projection screen, the spot size of most fields of view is smaller than a pixel size on the projection screen.

[0130] Fig.15 The modulation transfer function MTF of the optimized free-form surface large field of view projection system 100 in the visible light band is shown in the figure. As can be seen from the figure, the system MTF under each field of view is greater than 0.4 at 0.48lp / mm, indicating that the optimized free-form surface large field of view projection system has a higher imaging quality.

[0131] Fig.16 This is a grid distortion diagram of the optimized free-form surface large field of view projection system 100. It can be seen from the diagram that the system distortion is within the acceptable range for the human eye.

[0132] The method sets a reference point and directly calculates the reflector of the large-field-of-view projection system according to Malus's law. Compared with other free-form surface direct design methods, the method can calculate the characteristic data points of the unknown free-form surface under the full field of view and full aperture, and the calculation steps are fewer, which simplifies the calculation process. During the calculation process, the method directly constructs the reflector while keeping the refractive lens group unchanged, which can reduce the influence of the refractive lens group on the calculation and improve the calculation efficiency. The method enables the free-form surface reflector to bear a larger optical focal length and aberration balance, thereby reducing the complexity of the refractive lens group. The calculated free-form surface reflector is used as the initial structure and is optimized in combination with the refractive lens group, so it is easy to obtain a system with a large field of view and good imaging quality.

[0133] The parts of this technical solution that are not described in detail belong to the common knowledge of those skilled in the art.

Claims

1. A free-form surface design method for a large field of view projection system. The projection system (100) comprises: The system comprises, in sequence along the optical axis direction, a DMD chip (110), a 4K galvanometer (120), an equivalent prism (130), a protective glass (140), a refractive lens group (150), and a free-form surface reflector (160); The invention is characterized in that it comprises the following design steps: Step S1, establishing an initial structure, which includes the refractive lens group and the free-form surface reflector; Step S2, defining the free-form surface reflector as the desired free-form surface Ω, keeping the refractive lens group unchanged; determining the exit pupil size and position of the refractive lens group, selecting K characteristic rays in each sampling field of view, and defining the starting point of the characteristic rays at the exit pupil position; Step S3, determining the reference point on the free-form surface Ω to be determined in each sampling field of view; Step S4, according to Malus's law, solve the characteristic data points P on the free surface Ω to be solved under each sampling field of view ij (i=1,2,...,M,j=1,2,...,K-1); Step S5, wait for all feature data points P in the field of view to be ij All the solutions are completed, and the expression corresponding to the free-form surface Ω is obtained by fitting. The calculated free-form surface reflector is combined with the refractive lens group to obtain the initial system of the free-form surface large field of view projection system; The i is the serial number of the sampling field of view, M is the total number of the sampling fields of view, j is the serial number of the characteristic data points under each sampling field of view, K is the total number of the characteristic data points under each sampling field of view, and P ij is the jth feature data point under the i-th sampling field of view; The characteristic light and the starting point of the characteristic light are selected by the following method: The characteristic ray is defined as the ray emitted from the exit pupil of the refractive lens group; the starting point of the characteristic ray is defined as the exit pupil of the refractive lens group; the exit pupil is sampled in polar coordinates, and the number of sampling points increases with the increase of the exit pupil radius; K data points are uniformly sampled on the pupil, and each corresponding field of view has K different characteristic rays; M different fields of view are sampled, and a total of M×K characteristic rays are emitted from the exit pupil, and the starting point of the corresponding characteristic ray is S ij (i=1,2,...,M,j=1,2,...,K); S ij is the starting point of the jth characteristic light in the i-th sampling field of view; In the i-th sampling field of view, the principal ray emitted from the exit pupil of the refractive lens group is used as the reference ray R i0 (i=1, 2, ..., M), reference light R i0 The intersection point with the free surface Ω is taken as the reference point P i0 (i=1, 2, ..., M); reference light R i0 At the reference point P i0 After reflection, it reaches the ideal target point T i ; The reference surface Ω′ is defined as the surface of the optical system that perfects the imaging when NA < 0.

1. The reference surface Ω′ is used to replace the desired free surface Ω to obtain the reference point P of each field of view. i0 ; The characteristic data points on the free surface Ω are obtained by the following calculation method: In the same field of view, from S i0 All the characteristic rays emitted converge at the same point T i , in the i-th sampling field of view, according to the coordinates of the reference point P i0 , calculate the optical path length OP of the reference light: OP=n|S i0 P i0 |+n|P i0 T i | Where n is the refractive index of the medium. If the system is in air, then n = 1. T i For the ideal target point, solve it through the object-image relationship; All characteristic rays in the sampling field of view have the same optical path, and find other K-1 characteristic data points P in the field of view. ij (j=1, 2, ..., K-1), which satisfies the following conditions: n|S ij P ij |+n|P ij T i |=OP Repeat the above steps for M sampling fields to obtain the feature data points P of all fields of view ij (i=1,2,...,M,j=1,2,...,K-1).

2. The free-form surface design method for a large-field-of-view projection system according to claim 1, characterized in that: The reference surface Ω′ is selected in the following manner: When the numerical aperture NA is less than 0.1, an initial aspheric reflector is constructed in the optical software according to the given field angle and object-image conjugation conditions, and is used as the reference surface Ω′.

3. The free-form surface design method for a large-field-of-view projection system according to claim 1, characterized in that: The expression corresponding to the free surface Ω is: where z n (x, y) is the nth Zernike polynomial, k n are the coefficients of the nth Zernike polynomial.

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