红外与激光工程

Design method of imaging systems using square-domain orthogonal polynomials freeform surface (invited)

Zhou Lijun, Yang Tong, Cheng Dewen, Wang Yongtian

2023, 52(7): 20230317. doi: 10.3788/IRLA20230317

[Abstract](188) [FullText HTML] (19) [PDF 4589KB](71)

Objective Compared with traditional spherical and aspherical optical surfaces, freeform optical surface offers more degrees of design freedom, and it can be used in the design of imaging systems with more advanced system specifications, better imaging performance, more compact structure and novel functions. During freeform imaging system design and optimization, high imaging performance is an important design target. In addition, the freeform surfaces should be easier to be tested and fabricated. Interferometric surface testing is one of the most accurate methods for freeform surface and it is now increasingly used. To decrease the testing difficulty, the sag difference between the freeform surface and the base sphere or base conic should be as small as possible. For rotationally symmetric systems, the sag difference can be controlled easily and efficiently by using circular-domain orthogonal polynomial surfaces such as Zernike polynomials surface and Q2D polynomials surface. However, for nonrotationally symmetric freeform systems, as rectangular field-of-view is often used, the freeform surfaces often have rectangular aperture, the ability of circular-domain orthogonal polynomial surfaces is limited. Therefore, it is necessary to establish a design method to control the testing difficulty of freeform surface with rectangular aperture. Methods A design method of imaging systems using square-domain orthogonal polynomials freeform surface is proposed. Two kinds of square-domain orthogonal polynomials of Chebyshev polynomials and Legendre polynomials are analyzed and used. The inner product of the surface sag difference using orthogonal surfaces is related to the weighted square sum of the polynomial coefficients. For Chebyshev polynomials, as its weight function is a complicated function of x and y, it is not straightforward to use this property to control the sag difference. However, the sag difference can be controlled by constraining the sum of sag difference around the margins of the rectangular aperture to be zero. In addition, piston and tilt terms in orthogonal surface description should be zero. This can be controlled by constraining linear combinations of surface coefficients to be zero during optimization. For Legendre polynomials surface type, the constraint on the aperture margin can still be used. In addition, as the weight function of Legendre polynomials is one, the square sum of the polynomial coefficients can be used directly, which can be integrated into the total merit function during optimization. Detailed mathematical equations for establishing the design constraints and merit functions can be found in Eqs. (8), (9), (15)-(18). Results and Discussions Several design examples are used to show the feasibility and effect of the proposed design method. For Chebyshev polynomials freeform surface, a freeform off-axis three-mirror system whose primary and tertiary mirrors are integrated into one surface is designed. Compared with the design using traditional XY polynomials surface without sag difference constraints, the sag difference of the freeform surfaces in the system using Chebyshev polynomials surface is effectively controlled (Fig.2-3, Tab.3). For Legendre polynomials freeform surface, three kinds of off-axis three-mirror systems are designed: a system whose primary and tertiary mirrors are integrated into one surface, a system with the traditional zig-zag structure, and a system with a cylindrical package and real exit pupil. The design constraints on the sag difference at aperture margins, and the constraints on square sum of surface coefficients are used. Compared with the design using traditional XY polynomials surface without sag difference constraints, the sag difference of the freeform surfaces in the system using Legendre polynomials surface is effectively controlled (Fig.4, Fig.6, Fig.8, Tab.4-6). Conclusions For the commonly used rectangular surface aperture in freeform imaging system, a design method of freeform imaging system using square-domain orthogonal polynomials freeform surface is proposed. Chebyshev polynomials freeform surface and Legendre polynomials freeform surfaces are used and discussed. Based on the mathematical properties of the two kinds of polynomials, the mathematical constraints on the sag difference at the margins of the rectangular aperture and the constraints on the square sum of the polynomial coefficients are derived. Several design examples are given to show the feasibility and effect of the proposed design method. The design results show that, using the proposed design method and square-domain orthogonal Chebyshev and Legendre polynomials, the surface sag difference between the freeform surface and the base surface can be reduced effectively, and the testing difficulty can be reduced. The proposed method can be used in the design and development of all kinds of freeform imaging systems, and can be easily implemented in optical design software and other computing platforms and environments.

Desensitization design of large freeform off-axis three-mirror optical system (invited)

Ren Chengming, Meng Qingyu, Qin Zichang

2023, 52(7): 20230287. doi: 10.3788/IRLA20230287

[Abstract](229) [FullText HTML] (41) [PDF 2043KB](65)

Objective Off-axis three-mirror optical systems, based on the advantages of non-obscuration and capable of achieving a large field of view (FOV), can exhibit excellent optical performance, combined with the optical freeform surface with high degrees of freedom and strong aberration correction ability. The improvement of the imaging requirements has led to the continuous increase of the aperture and focal length of the reflective optical system, the error sensitivity of the optical system increases dramatically, resulting in higher processing difficulty and alignment sensitivity, as well as substantial time and economic costs. Error sensitivity represents the sensitivity of optical system after misalignment. The tolerance accuracy of optical system with low error sensitivity is loose. By controlling error sensitivity during the optimization process, an optimal balance can be achieved between image quality and cost. Therefore, desensitization optimization is an indispensable part of the large freeform off-axis three-mirror optical system design process. Methods Low error sensitivity optical system design begins with the selection of image quality evaluation criteria that can characterize the error sensitivity. The optical path difference and wavefront error are selected as two image quality evaluation criteria, and the geometrical optics method is adopted to establish the mathematical model of ray tracing before and after misalignment (Fig.1, Fig.4). Then the mathematical relationship between the parameters of the optical system and the error sensitivity is obtained, two error sensitivity evaluation functions (S and LC) are constructed based on the mathematical relationship, and the angle optimization desensitization design method and the local curvature desensitization design method are proposed as two desensitization design methods applicable to freeform optical systems according to the evaluation functions. A desensitization design process for large freeform off-axis three-mirror optical systems is developed (Fig.5). Two proposed desensitization design methods are applied to desensitize a large freeform off-axis three-mirror optical system with a focal length of 30 000 mm, an F number of 15 and an FOV of 1°×1° (Tab.1), and the desensitization effect of the two methods is compared. Results and Discussions The initial structure of the large freeform off-axis three-mirror optical system is System 1 (Fig.7), the angle optimization desensitization design method is used to obtain System 2, and the local curvature control desensitization design method is used to obtain System 3. The modulation transfer function (MTF) of all three systems is close to the diffraction limit, and the average RMS WFE of System 1, System 2, and System 3 is 0.038λ, 0.036λ and 0.039λ respectively (Fig.8), the image quality of all three systems is in the range of 0.038× (1±5%)λ and less than 1/15λ of each FOV (Fig.8).The total length of System 1, System 2, and System 3 is9 097.23 mm, 8 862.07 mm and 9 100.00 mm (Tab.2) respectively. The three systems are identical in configuration and differ slightly in total length. Under the tilt error perturbation (tangential: 0.001°, sagittal: 0.001°), the error sensitivity (ΔRMS WFE) of System 1, System 2, and System 3 is 0.089λ, 0.073λ and 0.062λ respectively (Fig.9). The error sensitivity is reduced by 17.98% using the angle optimization desensitization design method and by 30.34% using the local curvature control desensitization design method, obviously the latter method has better desensitization effect. Conclusions In this paper, the angle optimization desensitization design method and the local curvature control desensitization design method are introduced to desensitize the large freeform off-axis three-mirror optical system. Systems designed with different methods are compared, and the results demonstrate that, under the condition of no significant differences in optical system configuration, both desensitization design methods exhibit excellent theoretical aberration correction results for the optical system, and the MTF of the systems is close to the diffraction limit. The two desensitization design methods can effectively reduce the error sensitivity of the optical system, and it is found that the local curvature control desensitization design method can achieve better desensitization performance. Applying the desensitization design method in the large freeform off-axis three-mirror optical system design process correctly can significantly improve the system robustness, and effectively reduce the manufacturing cost, which is of great significance for the design and construction of large optical systems.

Application of nodal aberration theory in aberration compensation of the imaging system (invited)

Xie Bofu, Zhang Shuai, Li Haoran, Feng Hao, Li Da, Zhao Xing

2023, 52(7): 20230343. doi: 10.3788/IRLA20230343

[Abstract](249) [FullText HTML] (45) [PDF 2253KB](66)

Objective With the flourishing development of the applied optics, there are higher and higher requirements for the imaging quality of the optical system. With multiple design degrees of freedom, the freeform surface has excellent aberration compensation capability and is widely applied in the imaging system. Thus, it is very important to select a suitable design method and successfully design a freeform surface which can effectively compensate the aberrations. Considering the design requirement of compensating aberrations, it is very appropriate to choose the design methods guided by aberration theory. Nevertheless, the optimization and design method based on classical scalar aberration theory (SAT) may not give a good result because it is mainly applicable to rotational symmetric systems and there is aberration characterization error when the SAT method is used in a non-rotational symmetric system. What's different is that the nodal aberration theory (NAT) can accurately provide the relationship between wave aberration and various terms of Zernike type freeform surfaces. So, if adopting the optimization method guided by NAT, a freeform surface with better aberration compensation ability may be attained. Methods Firstly, on the basis of the wavefront aberration distribution from Zernike type freeform given by NAT, combined with self-developed iterative solution algorithm, a freeform surface optimization and design method guided by NAT is introduced in this paper. Secondly, in order to investigate the NAT optimization method's effect, a decentered telescope system is built as an example and the proposed method is utilized to optimize the freeform surface to compensate the aberrations of the decentered telescope system. Moreover, the aberration compensation experiment for the decentered telescope system is conducted by SLM loading freeform surface phase maps. Finally, the simulation and experimental results demonstrate that the freeform surface optimized by NAT method has better aberration compensation ability compared with that optimized by SAT method. Results and Discussion Firstly, after clarifying the aberration characteristics of the decentered telescope system (Fig.4), the aberration compensation freeform surfaces are optimized and designed by NAT method and SAT method respectively. The optimized result shows that the wavefront aberrations of this system reduce sharply (Fig.5). Compared to SAT optimization method's result, the residual aberration is significantly smaller by NAT optimization (Fig.5). Secondly, according to the simulation spot shape and RMS radius at the image surface, it is also found that the spot size of the system has smaller RMS radius optimized by NAT method (Fig.6). Then, the MTF curve indicates the optimized decentered telescope system by NAT method has better imaging quality after the aberration compensation freeform surface is introduced (Fig.7). Finally, by means of the SLM loading optimized freeform surfaces phase maps, the experiment on compensating the aberration of the decentered telescope system is carried out (Fig.8). The experimental results also demonstrate that the aberration of the system could be effectively compensated by freeform surface (Fig.10), and the surface optimized by NAT method has stronger aberration compensation ability. Thus, combined with simulation and experimental results, it is concluded that the NAT optimization method has better performance in optimizing freeform surfaces for aberration compensation and image quality improvement. Conclusions Aiming at the optimization and design of the aberration compensation freeform surface for the imaging system, a NAT optimization method is investigated in this paper. In order to explore this method's effect and compare with traditional SAT optimization method, these two methods are used to optimize the freeform surfaces for compensating the aberration of the decentered telescope system. More than that, an aberration compensation experiment for the decentered telescope is also carried out through SLM loading freeform surfaces phase maps, which could realize the same wavefront modulation effect as the freeform surfaces. Both simulation and experimental results show that better aberration compensation and imaging quality improvement effect can be achieved by using the NAT optimization method. Moreover, the proposed NAT optimization method also has great potentials in many applications, such as building individual optical model of human eye, evaluating visual quality of refractive surgery and optimizing the corneal removals for refractive surgeries, which are typical research issues in optometry.

Design of cooled freeform off-axis three-mirror system with large rectangular field (invited)

Qian Zhuang, Mo Yan, Fan Rundong, Tan Hao, Ji Huiru, Ma Donglin

2023, 52(7): 20230339. doi: 10.3788/IRLA20230339

[Abstract](212) [FullText HTML] (47) [PDF 2491KB](59)

Objective A cooled off-axis three-mirror system with a large rectangular field of view based on freeform surface is designed to satisfy the requirement of infrared remote sensing using a large plane array detector. The off-axis three-mirror system is composed of one even aspherical surface and two freeform surfaces, achieving secondary imaging with a real exit pupil that matches the cold shield, resulting in 100% cold shield efficiency. The system has larger rectangular field and decent imaging quality compared to other off-axis three-mirror systems, which ensures the adaption to large-format infrared detectors with a 4 k resolution. The system has a focal length of 150 mm, working waveband of 1.5-5 μm, F-number of 5, and field of view of 30°×25°. The primary mirror is even-order aspherical surface, and the secondary and third mirror are XY polynomial surfaces. High-order aberrations are properly corrected with the adoption of freeform surfaces, so the modulation transfer function of the system at 25 lp/mm exceeds 0.4 across all fields of view, meeting the imaging quality requirements of large-format infrared detectors. Methods An off-axis three-mirror systems with large rectangular field of view is presented in this paper. The initial structure is a coaxial three-mirror system with its optical power distribution being convex-concave-concave (Fig.1). The curvatures of three mirrors are calculated by eliminating primary aberrations based on Seidel aberration theory. The off-axis three-mirror system is derived from the coaxial structure by shifting the field center. According to Nodal aberration theory, even aspherical surfaces are adopted to shift aberration contributions of surfaces to new field centers so they can compensate for each other (Fig.3). The off-axis three-mirror system with large field of view in tangential direction is further optimized with pupil shifting (Tab.1). The secondary and third mirror are then converted to XY polynomial surface to expand field of view in horizontal direction while the image quality is not degenerating. Results and Discussions The optimized off-axis three-mirror system is presented (Fig.5) with primary mirror being even aspherical surface, the secondary and third mirror being XY polynomial free-form surfaces. The system meets the requirements of the detector and the design specifications (Tab.2) and the efficiency of cold diaphragm is 100%. The modulation transfer function of the system at 25 lp/mm exceeds 0.4 across all fields of view (Fig.6). RMS radius of spot diagram for all fields of view are less than Airy disk radius (Fig.7), indicating a good imaging quality. The maximum distortion of the system is −4.88%, which is acceptable and can be corrected by specific image processing algorithm. A tolerance analysis is conducted on the system, proving a good instrumentation feasibility (Fig.9). Conclusions A cooled off-axis three-mirror system with a large rectangular field of view is presented in this paper. The field of view of the system is 30°×25°, and F-number is 5, ensuring the adaption to 4000×3400@20 μm infrared detector. Of three mirrors of the system, the primary mirror is even aspherical surface, and the secondary and third mirror are XY polynomial free-form surfaces. The system is a re-imaging structure with no obscuration and a real exit pupil matching cold shield of the detector, achieving 100% cold shield efficiency. The image quality is good when the system works in 1.5-5 μm waveband, thus the system has broad application in optical remote imaging and sensing field.

Freeform off-axis four-mirror all-aluminum infrared detection system (invited)

Gao Rong, Mao Xianglong, Li Jinpeng, Xu Zhichen, Xie Yongjun

2023, 52(7): 20230338. doi: 10.3788/IRLA20230338

[Abstract](241) [FullText HTML] (55) [PDF 3247KB](81)

Objective Infrared detection technology has the advantage of passive thermal radiation detection and continuous work day and night. It can greatly reduce the restriction of environmental factors such as the light conditions. It is widely used in ecological environment monitoring, night vision detection, precision guidance and other fields. In recent years, with the development of infrared detection technology, especially in the field of aviation and aerospace remote sensing, in order to improve the timeliness of infrared remote sensing detection and realize the large-scale deployment of infrared detection system, the demand for large-field-of-view, high-compact, lightweight and low-cost infrared detection system is becoming more and more urgent. For this purpose, a freeform off-axis four-mirror all-aluminum infrared optical detection system with a large field of view and a compact package is designed in this paper. Methods A freeform off-axis four-mirror all-aluminum infrared optical detection system is designed and built in this paper. The optical system has a real exit pupil to connect the cold aperture of a cooled infrared detector (Fig.2). The 7^th order XY polynomials is used to represent the surface of the four freeform mirrors. The full-field geometric spot radius, wave aberration, modulation transfer function, and distortion grid are analyzed (Fig.5-9). The Monte Carlo algorithm is used for tolerance analysis to determine the influence of the alignment errors of the four mirrors (Tab.3). The optical system adopts an all-aluminum optomechanical design (Fig.12), in which the aluminum freeform mirror employs a three-ear flexible support mode to reduce the rigid connection stress (Fig.13). The optical, mechanical and thermal integration analysis is carried out, and the athermal effect of the optical system is verified (Fig.14-16). The optical system is assembled, and the full-field wave aberration is measured (Fig.17-18). Results and Discussions The optimized freeform off-axis four-mirror optical system has a large field of view of 6.25°×5°. The maximal geometric spot radius over the whole field of view is 5.36 μm, which is far less than the radius of the airy spot (Fig.5-6). The full-field wavefront error is less than 0.037λ@8.85 μm, which approaches the diffraction limit (Fig.7). The minimal MTF at 20 lp/mm is 0.48 (Fig.8). Considering the conventional alignment errors of the four mirrors (Tab.3), the geometric spot radius of the optical system is expect to be less than 19.8 μm. According to the optical, mechanical and thermal integration analysis, the maximal full-field geometric spot radius is slightly changed from 5.36 μm to 5.49 μm when the working temperature is changed from 20 ℃ to 30 ℃ (Fig.16). The result proves that the all-aluminum optomechanical system potentially has the optically athermal characteristics. The prototype has a focal length of 146.2 mm and a NETD of 26.8 mK. The measured wavefront error of the prototype is less than RMS 0.7λ@632.8 nm, which meets the technical requirements (Fig.18). Conclusions A freeform off-axis four-mirror all-aluminum infrared optical system with a real exit pupil, a large field of view and a compact package is built in this paper. The optical system has a field of view of 6.25°×5°. The designed full-field geometric spot radius, wavefront error and modulation transfer function all approach the diffraction limit. The tolerance analysis of the alignment errors of the four mirrors is carried out based on the Monte Carlo algorithm, which leads to a full-field geometric spot radius of less than 19.8 μm. The optical system adopts an all-aluminum optomechanical design, which naturally possesses an optically athermal potentiality. The optical, mechanical and thermal integration analysis for a temperature rise of 10 ℃ of the optical system verifies the optical athermality of the optical system. The measured full-field wavefront error of the prototype is less than RMS 0.7λ@632.8 nm. The captured far field infrared image shows the high performance of the prototype. Compared with the traditional off-axis reflective optical system, the demonstrated optical system adopts a new configuration of "all-freeform optical surfaces + all-aluminum optomechanics". It can achieve a larger field of view with a more compact envelope. And, the system has the characteristics of lightweight, low cost and optical athermality, which has important application prospects in the field of infrared detection.

Design of compact telephoto mobile phone lens based on freeform surface (invited)

Xu Ningyan, Gao Zhishan, Chen Lu, Huang Jing, Zou Yutong, Yuan Qun

2023, 52(7): 20230322. doi: 10.3788/IRLA20230322

[Abstract](148) [FullText HTML] (32) [PDF 2987KB](74)

Objective Telephoto lens is widely used in astronomy, space optics, aerial reconnaissance, security monitoring and other fields due to its ability to image distant objects. For devices with high requirement of miniaturization and lightweight, such as telephoto lens mounted on mobile phone, the majority solution is to use one or more prisms to fold the optical path to form a periscopic-type lens. Although this approach allows the element to be placed in an ultra-thin mobile terminal, it does not solve the lengthy, voluminous and weighty problem caused by the characteristics of telephoto lens. Instead, multiple prisms are added to the system as reflective elements, making the structure even bulkier. For the purpose of designing a compact and lightweight telephoto lens, this paper explores the solution of compact system design based on the structure of off-axis three-mirror imager. The initial structure is designed by utilizing the optical properties of conical surface to achieve ideal imaging of the on-axis object. Freeform surface is applied to extend field of view (FOV) to complete the design of a compact telephoto optical system. Methods Off-axis three-mirror imager has the advantages of lightness, compactness, non-chromatic, unobstructed aperture, high reflectiveness, and low optical energy loss for all wavelengths after being coated. A compact telephoto lens design method is proposed based on the off-axis three-mirror structure. Firstly, positive-negative-positive (PNP) power distribution was decided for the purpose of compactness. Unobscured PNP reflective imagers with different layouts of elements are listed (Fig.2). Then they are analysed and compared in terms of both compactness and imaging performance. After the structure type has been determined, parameters such as distance and angle can be calculated (Fig.3). Next, the optical properties of conical surfaces whose focal points conjugate between each other are used to calculate surface parameters such as conical coefficients and vertex radius of curvature to construct the initial structure (Fig.4), which can image on-axis object ideally. Taking telephoto lens applied to smartphone as an example, after calculating initial structural parameters with the above design method, the judgment condition that ray is obscured or not is established, and an optimized design strategy is developed to construct freeform surface, extend FOV (Fig.5) and optimize the system (Fig.6). The design of a compact telephoto lens is implemented and the feasibility of the design method is verified. Results and Discussions The result (Fig.7) is a compact telephoto lens with an F-number of 5, equivalent focal length of 196 mm and FOV of ±3.8°, consisting of only three reflective mirror and volume of 26 mm × 24 mm × 10 mm. The design results show that modulation transfer function (MTF) is greater than 0.2 at 114 lp/mm for all FOV (Fig.8), relative distortion is less than 0.5% (Fig.9) and displays good performance of imaging quality (Fig.10), meeting the imaging requirements of mobile phone lens. Our design is comparable to the current market indicators of periscopic-type telephoto lens in terms of design parameters. Although the F-number is slightly larger, effective focal length is longer, and it has obvious advantages in miniaturization and light weight. Conclusions In order to achieve a compact and lightweight telephoto lens design, this paper proposes a design method for a compact telephoto system based on optical characteristics of conical surface, combined with the off-axis three-mirror structure type. With the initial structure of off-axis three-mirror with ideal imaging at on-axis object, freeform surface is used to achieve a compact, lightweight, and high image quality telephoto system based on the unobstructed judgment condition and FOV expansion optimization strategy. The solution contains only three mirrors to fold ray path and compress volume, resulting in a lighter system with fewer lenses and less optical energy loss than a refractive telephoto imager, and an unrestricted wavelength band which means non-chromatic. Additionally, conical surface is used to calculate off-axis initial structure directly without aberrations at on-axis object, and subsequently controlling optimization process in combination with unobstruction judgement, avoiding the problem of aperture obstructed in the reflective telephoto. The result is a compact telephoto lens with an F-number of 5, an equivalent focal length of 196 mm and a field of view of ±3.8°, which meets the imaging requirements and has obvious advantages in terms of miniaturization and lightness compared to periscopic-type telephoto lens, providing a new solution to the design of compact telephoto lenses.

Design methods of freeform surface diffractive optics for beam shaping (invited)

Liao Qingming, Feng Zexin

2023, 52(7): 20230430. doi: 10.3788/IRLA20230430

[Abstract](347) [FullText HTML] (40) [PDF 1819KB](126)

Significance Beam shaping plays an important role in many fields including laser material processing, medical treatment and laser fusion. The goal of beam shaping is to transform an incoming laser beam into a desired output irradiance (or intensity) distribution. Diffractive optical elements (DOEs) are one of the most promising ways for beam shaping. The design of DOEs plays a crucial role in high-quality beam shaping applications. To further promote the development of more advanced methods for designing DOEs which can better meet the requirements of different beam shaping applications, it is necessary to summarize the research progress of existing DOE design methods, discuss their advantages and disadvantages, and provide a necessary outlook. Progress This review summarizes the design methods of phase-only DOEs for beam shaping. Since the DOE microrelief height function is lineally proportional to the phase function of the optical field generated by the DOE, the DOE design problem can be directly transferred into the calculation of the DOE phase distribution. There are two design methods of geometrical optics methods and physical optics methods to realize this goal. Geometrical optics methods usually generate continuous freeform optical surfaces. However, in many cases, the beam shaping quality can be degraded due to the diffraction effects. Physical optics methods, which describe the light propagation in a more accurate way, are commonly used to design phase-only DOEs for beam shaping. However, the iterative Fourier transform algorithms (IFTAs), which are the most commonly-used approach for designing DOEs, often generate complex and irregular shapes in DOE profiles. Such DOE profiles are difficult to fabricate and could generate speckles, which significantly impair the quality of the generated irradiance distribution. In addition, traditional IFTAs often surfers from slow convergence and iteration stagnation. Composite methods that combine the geometrical and physical optics methods have been proposed to address these issues. The freeform surfaces generated from the geometrical optics methods could provide good initial values for the following IFTAs, significantly improving the convergence. The resulting optical surface profiles are more regular than those of the traditional IFTAs, which are easier to fabricate and could achieve high-quality beam shaping. Conclusions and Prospects We have summarized (some of) the design methods of DOEs for beam shaping. After a brief recall of the traditional physical optics methods and their limitations, we have paid more attention to the review of the composite methods which can generate freeform DOEs that are easier to fabricate and could achieve high-quality beam shaping. Future directions of the DOE design methods include developments of fast geometrical optics solvers and wide-angle light propagation algorithms, more considerations of different fabrication techniques, and other promising methods based on auto-differentiation.

Freeform surface design of laser beam shaping by iteration in two orthogonal directions (invited)

Ye Jingfei, Zhu Yu, Gu Youyang, Zhan Huanqiu, Cao Shuqin, Wei Jianmin, Song Zhenzhen, Cao Zhaolou, Zheng Gaige

2023, 52(7): 20230299. doi: 10.3788/IRLA20230299

[Abstract](308) [FullText HTML] (41) [PDF 3782KB](44)

Objective In many laser industrial applications, laser beam shaping is an important process to redistribute the laser energy, which is highly essential to obtain uniform or prescribed spatial energy distribution with high efficiency. At present, there are different methods for laser beam shaping, including the grouped aspheric lenses, microlens arrays, diffractive optical elements, liquid crystal spatial light modulator and freeform optical technology. Compared with other laser beam shaping methods, the method using freeform surfaces is beneficial to make the shaping optical system more simplified and more compact. In the current freeform surface construction method for laser beam shaping, the seed curve extension algorithm in one direction has the non-negligible normal vector deviation during the generation of surface sampling points. Therefore, in this paper, a method is proposed to reduce the normal errors to improve the construction precision of freeform reflector for obtaining the highly uniform spatial energy distribution in the target plane. Methods There are mainly three steps for constructing the freeform surface (Fig.2-3). At first, the incident beam and the target plane are divided in grids according to equal energy and equal area. The main purpose of this step is to obtain the one-to-one energy mapping between the light source and the target plane, which is based on the conservation of energy and Snell's law. Then, the initial constraint conditions are set according to the requirements, which are used to calculate the sampling data points of horizontal and vertical curves on the freeform surface. Finally, according to the results of previous two steps, the sample data points on the unknown freeform surface can be calculated by iteration together with normal error correction. The averaging approach of coordinates of adjacent sampling points in the orthogonal direction is applied to relieve the normal deviations, which is very useful for reducing the normal errors to obtain smooth freeform surface relatively. Results and Discussions The proposed freeform surface construction method can effectively regulate a collimated Gaussian laser beam into the square or rectangular intensity distribution with high uniformity. On the target plane for a square pattern (Fig.5), the normalized irradiance uniformity is about 88.70% in the global region. Along the lines x=0 mm and y=0 mm on the target plane, the irradiance uniformity is about U_x=88.18% and U_y=86.67% respectively. Besides, the irradiance uniformity of local region (70 mm×70 mm) is about 92%. In the similar way, for a rectangular pattern on the target plane (Fig.6), the corresponding normalized irradiance uniformity is as high as about 94.30% as well as U_x=92.96% and U_y=94.07% along the lines x=0 mm and y=0 mm, which realize the laser beam shaping with high performance. On the other hand, the irradiance uniformity can also reach about 90% when the target plane has different distances for the square pattern (Fig.7-8). This indicates that the proposed method keeps robust elegantly. Further, in the aspect of surface smoothness, fitting precision and irradiance uniformity stability over a certain manufacturing error range (Fig.10-12), the freeform surface constructed by the proposed method shows great performance compared with that constructed by the traditional design method. Conclusions The freeform surface design by iteration in two orthogonal directions with surface normal correction is proposed, which can effectively regulate a collimated Gaussian laser beam into the square or rectangular intensity distribution with high uniformity. The feature sampling points of the freeform reflector are calculated iteratively in two orthogonal directions based on energy conservation and Snell’s law. Meanwhile, the averaging approach of coordinates of adjacent sampling points in the orthogonal direction can relieve the normal deviations effectively. Therefore, it is very helpful for constructing the freeform surface more precisely. The capabilities of the presented method are demonstrated and verified by examples. Moreover, for the target plane with different distances within a certain range, the energy uniformity maintains 90% well. At the same time, the freeform surface designed by the proposed method not only has high fitting accuracy, but also has a more stable irradiance uniformity on target plane within the allowable machining error range. It means that the proposed freeform surface construction method keeps robust elegantly, which is very necessary and critical for laser beam shaping.

Simultaneous modulation of beam intensity and wavefront with freeform surfaces on the off-axis target plane (invited)

Shen Fanqi, Chen Yuqin, Yang Lin, She Jun, Chen Kai, Huang Jianming, Wu Rengmao

2023, 52(7): 20230323. doi: 10.3788/IRLA20230323

[Abstract](104) [FullText HTML] (17) [PDF 7048KB](42)

Objective Simultaneous modulation of beam intensity and wavefront with freeform surfaces is widely used in illumination optics and imaging optics. The current method of simultaneous modulation of beam intensity and wavefront is generally aimed at vertical-axis optical systems. However, the optical system generally has an off-axis layout to achieve a compact optical structure. In this paper, we proposed a method to design freeform surfaces to realize simultaneous modulation of beam intensity and wavefront on the tilted target plane. Methods Firstly, a virtual observation plane perpendicular to the optical axis is set up, and the mapping relationship between the specific irradiance distribution on the target off-axis observation plane and the corresponding irradiance distribution on the vertical axis virtual observation plane is established. Then the Monge–Ampère (MA) equation with nonlinear boundary conditions for the vertical virtual plane is established according to Snell's law, local energy conservation law, and optical path conservation constraints. Then the finite difference method is used to solve the beam control model of vertical axis layout, and the numerical solutions of beam intensity and wavefront modulation of freeform surface on the off-axis observation plane are obtained. Finally, the Monte Carlo ray tracing method is used to verify the effectiveness of the designed freeform surface. Results and Discussion The design example is to use two freeform surfaces to shape a Lambertian point source into a uniform square irradiance distribution on an off-axis target plane, the shaped beam is a divergent spherical wave, and the off-axis target surface has an inclination angle of 30 degrees. The obtained surfaces are intricate but smooth, continuous, and easy to fabricate. Researchers use 10 million rays for Monte Carlo tracing to verify the effectiveness of the designed lens. The irradiance distribution on the target plane demonstrates the effectiveness of the modulation of beam intensity, with the irradiance error RMS=0.0117. The analysis of the outgoing wavefront and the simulation results at different distances verify the effectiveness of the modulation of the beam wavefront. Conclusion Simultaneous modulation of beam intensity and wavefront is a challenging but worth exploring problem. In this paper, the efficient and accurate modulation of beam intensity and wavefront under an inclined optical path layout is realized by establishing the mapping transformation of off-axis irradiance distribution to vertical irradiance distribution. This method breaks the restriction of vertical optical path layout and obtains a flexible optical path layout, which plays an active role in promoting the wide application of freeform surface beam modulation. This method uses only two freeform surfaces to realize efficient and flexible modulation of beam intensity and wavefront, which will promote the beam control system towards the direction of comprehensive function and compact system.

Design of freeform reflector for laser light source automotive headlight

Jiang Lusong, Chen Yu, Hai Xiaohua, Peng Liwei

2023, 52(7): 20230321. doi: 10.3788/IRLA20230321

[Abstract](128) [FullText HTML] (31) [PDF 3016KB](46)

Objective Laser light source is a new type of automotive headlight light source that is efficient, compact, and long-lasting. It has attracted wide attention and research in recent years. It can provide longer and brighter illumination distance and brightness, as well as higher design freedom for heat dissipation and styling. Currently, some universities and research institutions have designed and optimized the freeform optical structure of laser headlights. However, most of the existing methods adopt sub-surface stitching or surface array to achieve the target illuminance distribution, which leads to discontinuity of the freeform surface and increases the production processing difficulty. In addition, the reflectors designed by the existing methods have low energy utilization rate. Aiming at the problems of difficult optical structure design and low energy utilization rate of laser headlights, a new freeform reflector design method based on spherical optimal transport theory is proposed, and a freeform reflector suitable for laser headlights (including low beam and high beam) is designed using this method. Methods The algorithm flow chart of freeform reflector design is shown (Fig.1). First, according to the coordinates and illuminance of the test points and boundary vertices of the test area given by the regulation GB 25991—2010, the target illuminance on the target surface is obtained by using thin plate spline interpolation method. Then, different density Delaunay triangulation is performed on the target surface. A series of rotating ellipsoids are obtained with the origin and triangulation vertices as focal points (Fig.2), which are used to form the freeform surface. Then, the reflector design algorithm based on spherical optimal transport is used to iterate and obtain the eccentricity of these rotating ellipsoids. According to the size and luminous characteristics of the light source, the area of reflection light on the target surface is determined (Fig.5). If there is light irradiating to the dark area, the position of the sampling point is adjusted (Fig.7) until no reflected light can irradiate to the dark area. Finally, SolidWorks is used to model the reflection surface entity, fit it into a continuous freeform surface, and import it into Lighttools for optical simulation to verify the reliability of the algorithm. Results and Discussions Simulation is carried out for low beam and high beam respectively. The light source used in simulation is a Lambert light source with a diameter of 1.2 mm and a divergence angle of 60° full angle. The simulation results show that the illuminance distribution on the distribution screen meets the regulation requirements, and the reflection surfaces are smooth and continuous. The illuminance of test points on low beam target surface is listed (Tab.3). The energy utilization rate of low beam system is 96.96%, and a clear bright-dark cutoff line is realized (Fig.12). The illuminance of test points on high beam target surface is listed (Tab.4). The high beam reflector is an array of three identical reflection surfaces. The energy utilization rate of high beam system is 97.80%. Conclusions This paper proposes an improved reflector design method and designs a freeform reflector for laser headlights (including low beam and high beam). The reflector can not only form a distribution that meets the regulation GB25991—2010 requirements, but also has a smooth surface shape and high energy utilization rate. It can effectively reduce the power consumption of automotive headlights, improve the heat dissipation performance of automotive headlights, extend the service life of laser light sources, and facilitate equipment production and processing. It conforms to the new development trend of energy conservation, environmental protection and efficient use of energy in future automotive industry.

Design of waveguide decoupled metasurface for augmented reality display optical engine (invited)

Chen Enguo, Chen Kangkang, Fan Zhengui, Sun Zhilin, Lin Zijian, Zhang Kaixin, Sun Jie, Yan Qun, Guo Tailiang

2023, 52(7): 20230342. doi: 10.3788/IRLA20230342

[Abstract](342) [FullText HTML] (50) [PDF 3186KB](120)

Object The optical engine design of augmented reality (AR) near-eye display is one of the research hotspots in the field of display technology. It projects virtual images to the real physical environment for display, and simultaneously enhances, merges, and complements the physical world in space. AR near-eye display optical engine has high requirements for the integration and miniaturization of optical system, and the glass-like AR near-eye display optical device is an inevitable development trend in the future. Optical metasurface is an artificial structure array composed of subwavelength unit structure periodically arranged on a two-dimensional plane. It realizes arbitrary regulation of the amplitude, phase, and polarization of the light field through the interaction of the unit structure and electromagnetic wave. At the same time, it has the characteristics of small size, high efficiency, and compact structure, and has great potential in near-eye display applications. Methods In this paper, a metasurface structure is designed as the decoupled structure of the AR near-eye display optical waveguide (Fig.1). The decoupled part adopts a waveguide with a cutting angle of 60°. By changing the angle of incident light, the incident light propagates inside the waveguide at 50°-75°. The coupled part of the metasurface has a height of 900 nm and a radius of 50-120 nm (Fig.6). The AR near-eye display optical waveguide is simplified and simulated in FDTD. The light source is placed inside the waveguide to simulate the total reflection of the incident light, and the decoupling angle is simulated by changing the incident angle. Results and Discussions When the collimated light is incident into the metasurface structure, the outgoing light deviates from the z-axis by −35° (Fig.7). The field intensity distribution is observed by placing a monitor or far-field calculation, and the deflection efficiency is calculated to reach 77%. In addition, the angle distribution of the outgoing light on the metasurface within the designed wavelength of ±30 nm is simulated, and it can be seen that the deflection angle of the device fluctuates within the designed angle of 5° (Fig.8). Since the same metasurface structure has a specific phase response to incident light at different angles, different wavefront adjustment of incident light at different angles can be realized. Waveguide with a cutting angle of 60° is adopted in the coupled part. By changing the incident light angle, the incident light can propagate in the waveguide at 50°-75°, and the variation range of the outgoing optical coupling angle is 0°-20°. There is a one-to-one correspondence between the angle change of the incident light and the angle change of the outgoing light (Fig.9). Conclusions A metasurface coupling structure for AR near-eye display optical waveguide is designed. The metasurface structure can be deflected by changing the radius and height of the structure, and the wavefront of the incident light at different angles is controlled. The results show that the deflection efficiency of light at a small incident angle can be as high as 77%. By changing the total reflection angle of the incident light in the waveguide, the coupling angle changes with the change of the incident angle, and finally the field of view angle of 20° can be achieved. The introduction of metasurface provides an effective scheme for the design of AR near-eye display optical engine, which is of great significance for the realization of light-weight and compact eyeglass for a AR module, and is expected to become a potential development direction of AR near-eye display optical engine.

Special issue—The technology of freeform optical system design

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