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Semiconductor near-infrared lasers have been widely used in lidar systems. However, various source types have different shapes and divergence angles, causing more difficulties for long-distance detection. In this paper, an optical collimation system is designed for a long-range lidar system with a shaped laser source (the wavelength is 905 nm, the emitted spot size is 50 µm long by 10 µm wide, and the divergence angles are 33°and 15°, respectively, which are unconventional). On the basis of the traditional method of aspheric lens setting, a pair of asymmetric aspherical lenses were designed using an extended polynomial. The simulation results show that the spot shapes are all close to circular from 100 mm to 30 m and the spot size always remains the same value. The corrected optical system is put into the designed lidar system for verification. It results show that the average divergence angles in the long and short axis directions are 0.06°and 0.07°, which satisfy the project requirements. This optical system designed provides a collimation scheme and expands the application of vehicle-mounted lidar in the field of long-range detection. [ABSTRACT FROM AUTHOR]

Aspheric surfaces are widely used in advanced optical instruments. Measuring the aspheric surface parameters (ASPs) with high accuracy is vital for manufacturing and aligning optical aspheric surfaces. This paper provides a review of various techniques for measuring ASPs and discusses the advantages/disadvantages of these approaches. The aim of this review is to contribute to advancements in the fabrication and testing of aspheric optical elements and their practical applications in diverse fields.

The position accuracy of the polishing tool affects the surface quality of the polished aspheric surface. The contact deformation among the polishing tool, abrasives, and aspheric part can cause a displacement, which, in turn, will cause a position error of the polishing tool, which will lead to a significant change in the polishing force. In order to resolve this error, this paper proposed a method of normal displacement compensation for a computer numerical controlled (CNC) polishing system by controlling the polishing force. Firstly, the coupling principle between the polishing force and the position of the polishing tool is expounded, and the relationship between normal displacement and deformation is analyzed. Based on Hertz’s theory, a model of normal displacement is established. Then, on the basis of the decoupled polishing system developed, a normal displacement compensation method was proposed. Finally, a group of comparative experiments was carried out to verify the effectiveness of the proposed method. Compared with no displacement compensation, when the part was polished with the normal displacement compensation method, the value of roughness decreased from 0.4 µm to 0.21 µm, and the unevenness coefficient of surface roughness decreased from 112.5% to 19%. The experimental results show that the polishing quality is improved greatly, and the aspheric surfaces can be polished more uniformly with the method proposed in this paper.

Semiconductor near-infrared lasers have been widely used in lidar systems. However, various source types have different shapes and divergence angles, causing more difficulties for long-distance detection. In this paper, an optical collimation system is designed for a long-range lidar system with a shaped laser source (the wavelength is 905 nm, the emitted spot size is 50 µm long by 10 µm wide, and the divergence angles are 33°and 15°, respectively, which are unconventional). On the basis of the traditional method of aspheric lens setting, a pair of asymmetric aspherical lenses were designed using an extended polynomial. The simulation results show that the spot shapes are all close to circular from 100 mm to 30 m and the spot size always remains the same value. The corrected optical system is put into the designed lidar system for verification. It results show that the average divergence angles in the long and short axis directions are 0.06°and 0.07°, which satisfy the project requirements. This optical system designed provides a collimation scheme and expands the application of vehicle-mounted lidar in the field of long-range detection.

The aspheric surface is a commonly used method to improve the imaging quality of the fisheye lens, but it is difficult to determine the position and initial value. Based on the wave aberration theory of the plane-symmetric optical system, a method of using an aspheric surface to design a fisheye lens is proposed, which can quickly determine the appropriate aspheric surface to improve the imaging performance. First, the wave aberration of each optical surface of the fisheye lens is calculated and its aberration characteristics are analyzed. Then, a numerical evaluation function is reported based on the aberration distribution of the fisheye lens on the image plane. According to the functional relationship between the evaluation function and the aspheric coefficient, the position of the aspheric surface and the initial value of the aspheric coefficient can be calculated. Finally, the adaptive and normalized real-coded genetic algorithm is used as the evaluation function to optimize the fisheye lens using an aspheric surface. The proposed method can provide an effective solution for designing a fisheye lens using an aspheric surface. [ABSTRACT FROM AUTHOR]

To obtain a continuous range of clear vision for pseudophakic eyes, a design of intraocular lens (IOL) with extended depth of focus (EDoF) was proposed. The IOL was optimized with a multi-configuration approach based on a pseudophakic eye model and the optical performances of the designed IOL were analyzed. The modulation transfer function (MTF) values remain above 0.2 at 50 lp/mm for object distance ranging from 0.35 m to infinity in both photopic vision and mesopic vision over a field of 4°. The optical performances remain stable when the pupil diameter changes from 2.25 mm to 5 mm. Besides, the presented theoretical analyses show the designed IOL has good optical performances for polychromatic light and corneal asphericity. The above shows that the IOL exhibits an excellent ability for pseudophakic eyes to see the object in a continuous range of distance.

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With the development of science and technology, aspherical surface has become an indispensable component in optical system. However, the aspheric surface has more complex optical properties than the spherical surface, so it restricts the rapid development of aspheric surface. In this paper, the main problem of aspherical machining is analyzed, which is"Trajectory control", and the unique optical properties of aspherical surface are analyzed, a trajectory control algorithm based on genetic-BP neural network is proposed to solve the trajectory control in aspheric forming. The method is proved to be feasible and effective. [ABSTRACT FROM AUTHOR]

The surface accuracy and quality of the mirror blank determine the performance of the optical mirror, so it is essential to explore a simple and effective way to process the mirror blank. Gas jet forming is a simple and efficient way of forming optical surfaces. However, the key to accurately forming mirror blanks is establishing the relationship between the gas jet parameters and the resulting surface shape. Therefore, several experiments were carried out in this study to develop the relevant models to investigate the above issues. The experimental data analysis found that the surface tension of the viscous fluid being processed impacts the shape of the surface formed by the gas jet. Therefore, the new model for predicting the surface shape of gas jets was developed by refining the Blanks and Chandrasekhara model by adding surface tension. The prediction error of the new model for the depth of the surface formed by the gas jet is in the range of 0.0497–0.833 mm, much smaller than the uncorrected model. [ABSTRACT FROM AUTHOR]

To obtain a continuous range of clear vision for pseudophakic eyes, a design of intraocular lens (IOL) with extended depth of focus (EDoF) was proposed. The IOL was optimized with a multi-configuration approach based on a pseudophakic eye model and the optical performances of the designed IOL were analyzed. The modulation transfer function (MTF) values remain above 0.2 at 50 lp/mm for object distance ranging from 0.35 m to infinity in both photopic vision and mesopic vision over a field of 4°. The optical performances remain stable when the pupil diameter changes from 2.25 mm to 5 mm. Besides, the presented theoretical analyses show the designed IOL has good optical performances for polychromatic light and corneal asphericity. The above shows that the IOL exhibits an excellent ability for pseudophakic eyes to see the object in a continuous range of distance. [ABSTRACT FROM AUTHOR]

The aspheric surface is a commonly used method to improve the imaging quality of the fisheye lens, but it is difficult to determine the position and initial value. Based on the wave aberration theory of the plane-symmetric optical system, a method of using an aspheric surface to design a fisheye lens is proposed, which can quickly determine the appropriate aspheric surface to improve the imaging performance. First, the wave aberration of each optical surface of the fisheye lens is calculated and its aberration characteristics are analyzed. Then, a numerical evaluation function is reported based on the aberration distribution of the fisheye lens on the image plane. According to the functional relationship between the evaluation function and the aspheric coefficient, the position of the aspheric surface and the initial value of the aspheric coefficient can be calculated. Finally, the adaptive and normalized real-coded genetic algorithm is used as the evaluation function to optimize the fisheye lens using an aspheric surface. The proposed method can provide an effective solution for designing a fisheye lens using an aspheric surface.

A serious challenge faced by manufacturers of large-aperture aspheric optical components of glass ceramics is the long processing time. Ultrasonic vibration–assisted grinding (UVG) allows one to effectively shorten the subsequent polishing process by several times, which is essential for grinding of aspheric components. However, the surface creation mechanism of UVG-treated glass ceramics is rarely studied. Herein, rotary ultrasonic vibration–assisted vertical grinding (RUVG) and parallel grinding (RUPG) are applied to polish the aspheric glass ceramics. Particular attention is paid to the surface formation mechanism of UVG-processed ceramics. The single-grain kinematic functions are created and the contact characteristics between the grinding wheel and aspheric surface are analyzed for the two UVG methods in terms of contact area, velocity, and trajectory. In addition, aspheric grinding texture is simulated and comparative experiments are conducted correspondingly. According to the results, the rotary ultrasonic vibration mainly influences the microscopic grinding marks. Besides, the aspheric surface form accuracy of Pt and RMS value in RUVG is 2.16 and 3.71 times lower than those in RUPG, respectively, whereas the surface roughness–related parameters (mean deviation Sa and maximum height of profile Sz) in RUVG are 6.36% and 4.56% higher than those in RUPG. This indicates that RUVG is more suitable for high precision and efficiency grinding of the aspheric surface than RUPG due to the fact that the polishing depth is primarily determined by surface form accuracy rather than surface roughness. Thus, the current research enables an in-depth understanding of surface generation mechanism in rotary ultrasonic vibration–assisted grinding, pointing out its benefits in the high-efficiency aspheric surface manufacturing. [ABSTRACT FROM AUTHOR]

An in-situ measurement device combining contact probe and capacitive displacement sensor is developed. An aspherical measurement and compensation machining software is also developed. The single point diamond ultra precision cutting experiments for C3604 brass spherical and aspherical surface are carried out. The in-situ measurement and compensation machining experiments are also carried out. After compensation machining, the spherical surface form accuracy PV reaches 231.4 nm, and the aspheric surface form accuracy PV reaches 206.3 nm. Compared with the off-line measurement results, the difference between the results is 3.0 nm, 7.0 nm respectively, the measuring accuracy of the in-situ measurement system and the validity of compensation machining are verified.

The Zemax optical simulation program was used to design a multilens configuration and further optimize the design of a lens module using six plastic lenses and 12 aspheric surfaces. The lens module with 13 million pixels was designed for application in a cellphone camera module. The basic specifications of the design with six plastic lenses were established and matched with those of an OV13853 complementary metal oxide semiconductor (CMOS) chip, and the minimum imaging circle radius of the designed optical lens module based on OV13853 was 3.029 mm. The optimized mirror aspheric coefficients of surfaces #1–#12 of the designed lens module and the aspheric coefficients of each mirror surface were increased to the 18th order. The optimal parameters for the designed lens module, including the radiuses, thicknesses, conics, and materials used, are presented in this paper. The modulation transfer function (MTF) curves, the ranges of field curvature, the maximum horizontal chromatic aberration, and the maximum range of Seidel aberration were also found. [ABSTRACT FROM AUTHOR]

Elliptical elements are essential optical surfaces for modifying optical systems. For polishing the whole elliptical surface using doughnut-shaped MCF polishing tool with variable tilt angle, an experimental investigation was conducted in this work. Firstly, a flat workpiece was polished to determine the polishing feasibility. It was found that the middle portion of the polishing tool had optimal ability to remove materials, and the surface roughness Sa at the material removal peak was changed from 134 nm to 17.5 nm within 50 min of polishing. A smoother surface could be obtained using MCF2 slurry and MCF3 slurry, but the use of MCF1 slurry resulted in a rough surface. Then, the effects of working gap h, revolution speed of MCF polishing tool and polishing time on the polishing results were tested to study the polishing characteristics. Sa 9.6 nm and glossiness 278 Gu were obtained, and form error improved from 2.3 μm to 1.3 μm. Finally, the MCF polishing tool was dried to observe the microstructure of the MCF polishing tool after polishing. Abrasive particles were distributed evenly after polishing. It was seen that the abrasive particles were grabbed by the ferric clusters, and the α-celluloses were interleaved between the clusters. [ABSTRACT FROM AUTHOR]

A method for designing double aspheric lenses enabling minimal Fresnel losses in the class of stigmatic lenses is considered. Minimization of the Fresnel losses is provided by ensuring equal ray-deviation angles on both aspheric surfaces of the lens. The design of the lens is reduced to the integration of an explicit ordinary differential equation. Simple analytical approximations for the lens profiles are also presented.

With the development of science and technology, in the fields of national defense, aerospace, medical treatment, automobile, and so on, the demands for ultra-precision parts and molds with complex surfaces such as aspheric or free-form surface are becoming more and more common and demanding. Bonnet polishing technology, which uses a new polishing tool and special form of motion, is a high-precision and high-efficiency optical component processing method. This method is especially suitable for the processing of aspherical and free-form surfaces and has broad application prospects. This paper first introduced the basic principle and development process of bonnet polishing technology. Then the key technology and its state-of-the-art bonnet polishing technology were analyzed. Finally, the development of bonnet polishing technology was summarized and prospected. [ABSTRACT FROM AUTHOR]

In order to meet the needs of users for large-field of view angle and high resolution of virtual reality head-mounted displays, the initial structure of the optical system was calculated by using reverse design method, and the optical design software was used for simulation analysis optical structure of coaxial large field of view virtual reality head-mounted display. The results show that three aspheric lenses are used in each channel, and the full field angle is 90°, the exit pupil diameter is 8mm, the exit pupil distance is 13mm, the modulation transfer function is greater than 0.3 at Nyquist frequency of 10.581p/mm, and the maximum distortion is 6.1%, respectively. Compared with the reference, the resolution is higher, the distortion is reduced and aberration balance is reasonable. The design provides a reference for optimizing the optical structure of large field of view head-mounted display. [ABSTRACT FROM AUTHOR]

This study investigated a novel methodology called equivalent-sphere swing grinding (ESSG) for the cup wheel grinding of large revolving aspheric and spherical surfaces. The method is proposed to improve the machining efficiency and reduce the complexity of machine tools. Different from the traditional single-point grinding of aspheric surfaces, the ESSG method developed a novel multipoint grinding process to increase the material removal rate (MRR) and reduce the wear of single abrasive grain. A structure with few axes and a wheel spindle with multi degrees of freedom simplifies the machine tools and improves the machine dynamic stiffness. The grinding process was modeled, and the feasibility for grinding aspheric and spherical surfaces was verified. The criteria for ESSG-based grinding method were established, and the wheel position and posture models were derived. The cup wheel posture was proved to have multiple options for grinding a revolving surface, in which the optimal posture can achieve the maximum number of abrasive particles involved in grinding and maximize MRR under the same wheel wear. The numerical trajectory control parameters were calculated, and a hierarchical grinding method is proposed. An experiment was conducted on a developed grinding machine prototype. The results indicate that the proposed methodology can efficiently grind paraboloid surfaces and can be extended to grinding other revolving aspheric and spherical surfaces. [ABSTRACT FROM AUTHOR]

The uniformity of material removal can affect the profile accuracy and surface quality of the polished curved surface. In the aspheric surface polishing, the Archimedes spiral path may result in poor consistency of material removal due to the changes of the surface curvature and the projection path interval. Firstly, under the constant process parameters, the material removal characteristic is inconsistent throughout the aspheric surface due to the curvature change characteristics of the surface. Secondly, the projection path interval variations on the surface may lead to the inconsistency of the adjacent paths overlapping. In this study, a new path called optimized Archimedes spiral path is proposed to ensure the uniform material removal depth in aspheric surface polishing. The path generation method takes into account the effect of the surface curvature variations on material removal and the effect of the path interval on the adjacent paths overlapping. First, the model of material removal profile is proposed based on the Preston equation. Subsequently, a path interval search algorithm based on material removal profile is developed to generate the optimized Archimedes spiral path. Lastly, a group of comparative experiments between the traditional path and the optimized path was conducted to verify the effectiveness of the proposed path generation method. Compared with the traditional path, the fluctuation of the material removal depth attributed to the optimized path is reduced by 49.7%. It indicates that the proposed path generation method is effective for improving the uniformity and consistency of material removal depth in aspheric surface polishing. Furthermore, the surface roughnesses of the two workpieces polished by the traditional path and optimized path are 0.9493 μm and 0.8893 μm, respectively. The reduction in surface roughness indicates that the uniform material removal depth can improve surface quality. [ABSTRACT FROM AUTHOR]

Elliptical elements are essential optical surfaces for modifying optical systems. For polishing the whole elliptical surface using doughnut-shaped MCF polishing tool with variable tilt angle, an experimental investigation was conducted in this work. Firstly, a flat workpiece was polished to determine the polishing feasibility. It was found that the middle portion of the polishing tool had optimal ability to remove materials, and the surface roughness Sa at the material removal peak was changed from 134 nm to 17.5 nm within 50 min of polishing. A smoother surface could be obtained using MCF2 slurry and MCF3 slurry, but the use of MCF1 slurry resulted in a rough surface. Then, the effects of working gap h, revolution speed of MCF polishing tool and polishing time on the polishing results were tested to study the polishing characteristics. Sa 9.6 nm and glossiness 278 Gu were obtained, and form error improved from 2.3 μm to 1.3 μm. Finally, the MCF polishing tool was dried to observe the microstructure of the MCF polishing tool after polishing. Abrasive particles were distributed evenly after polishing. It was seen that the abrasive particles were grabbed by the ferric clusters, and the α-celluloses were interleaved between the clusters.

Aiming at the problems of the current head-mounted display with large volume, large weight, and small field of view, in order to meet the user's demand for light and small head-mounted displays, the Ranston eyepiece was used as the initial structure, and then was optimized by using ZEMAX software. Image quality evaluation and tolerance analysis were then carried out. The result shows that each channel in the binocular system uses only two lenses, the maximum field of view of the optical structure is 80°, the total length is 54. 24mm, the maximum distortion is less than 4. 7%, the weight of the two lenses is less than 11. 5 g. Compared with related research, the field angle and the number of pixels are increased, the volume is reduced, and the modulation transfer function is improved. The head-mounted display has certain market prospects, and can provide a reference for the optical design of the light and small head-mounted display. [ABSTRACT FROM AUTHOR]

With the continuous development of cataract surgery and intraocular lens(IOL), the evaluation of visual quality after IOL implantation has become a research hotspot, and aberration is an important factor that affecting visual quality. After more than 60y of development, IOL has made great improvement in optical design. Due to the fact that conventional spherical IOL has a positive spherical aberration and cannot correct the positive spherical aberration existing in the normal human cornea, it is improved to an aspherical IOL having a negative spherical aberration and a zero spherical aberration. The former can correct the cornea positive spherical aberration, improve the contrast sensitivity and improve visual quality. However, if the optical position does not match, the formation of other higher-order aberrations will have greater impact on visual effects. Although the latter is well tolerated to tilt and decentration, it still cannot compensate for the positive aberration from the cornea. The advent of the non-constant aberration IOL provides a new way for cataract surgeons to solve this problem. In this paper, the concept of aberration, the design principle and advantages and disadvantages of different kinds of aspheric IOL, as well as the observation of clinical application effect of non-constant aberration aspheric IOL are discussed.

For the aspheric optical surface finished with a doughnut-shaped MCF (magnetic compound fluid) polishing tool, the performance of the polishing tool depends mainly on the properties of the MCF slurry. Therefore, understanding the effect of each MCF slurry component on the polishing characteristics is crucial to developing novel polishing techniques. In this paper, the polishing principle was depicted and the corresponding polishing jig was constructed with a six-degree-of-freedom manipulator. The conical surfaces, which were considered as special aspheric surfaces, were experimentally polished under proper polishing conditions to examine the effects of the carbonyl iron particles (CIPs) concentration and the sizes of the abrasive particles (APs) on the polishing ability to remove material/tool marks and improve work surface qualities. Theoretical analyses were also performed to gain a more comprehensive understanding of the behaviors of CIPs and APs in the magnetic field. The results were shown as follows: (1) The CIPs concentration affected positively the magnetization of the MCF slurry, leading to better performance in the removal rate of material/tool marks when a higher CIPs concentration of was applied. The best surface quality was attained with a CIPs concentration of 45 wt%. (2) Larger APs were beneficial for obtaining higher removal rates of material/tool marks. The APs with 1 μm in diameter were preferred for achieving a better surface quality. (3) Ferric clusters were formed along the magnetic line of force and their orientations changed periodically to stir the APs with the magnet revolution. (4) The Aps, at a given working gap, can squeeze the work-surface. The squeezing action was much more intense when larger APs and the MCF slurry with a higher magnetization were employed. (5) The material removal model suggested that the material was removed due to the APs and the relative motion between the work-surface and APs. • The orientations of ferric clusters are changed together with the magnetic line of force. • MCF slurry with 45 wt% in CIPs concentration results better surface quality. • Abrasive particles can be stirred and squeeze the work-surface during polishing. • Abrasive particles with 1 μm in diameter are preferred rather than other sizes. [ABSTRACT FROM AUTHOR]

In order to understand the physical meaning of the best-fitting sphere of aspheric surface, based on the optical design idea of the aberration theory, the relationship between the curvature radius of the best-fitting sphere and the spherical aberration for the full aperture aspheric surface is set. The result is consistent with the traditional calculation method, which gets mainly from the geometric or algebraic. This formula explains the physical meaning of the best-fitting sphere of aspheric surface from the longitudinal spherical aberration: the curvature center of the best-fitting sphere moves compare with the vertex curvature center of the aspheric surface, and the amount of movement is one quarter of the longitudinal spherical aberration which the object is at the center of the vertex curvature of the aspheric mirror. Furthermore, the best-fitting sphere and asphericity for the annular aperture aspheric surface are also solved successfully. These formulas not only can help understand the best-fitting sphere from optics, but also calculation for off-axis aspheric surface is more convenient. The full aperture can be regarded as an annular aperture aspheric surface with zero inner diameter, the best-fitting spherical surface curvature radius and asphericity have unified calculation formulas for different aperture shapes of aspheric surfaces. All letters of the final expressions come from the parameters of aspheric surface itself, and each term is a clear physical quantity. Calculation is faster; concepts are easier to be understood. This is quite helpful for engineering. [ABSTRACT FROM AUTHOR]

Aspheric elements have become essential optical surfaces for modifying optical systems due to their abilities to enhance the imaging quality. In this work, a novel method employing a doughnut-shaped magnetic compound fluid (MCF) polishing tool, and an industrial robot was proposed for polishing aspheric surfaces. Firstly, investigations on the MCF tool, including the formation process and geometry, were conducted to form an appropriate polishing tool. The distribution of abrasive particles was observed using SEM and EDX mapping. Thereafter, a conic workpiece constructed from 6061-aluminum alloy was selected as the workpiece, which was used to discover the effects of the parameters on the polishing ability of aspheric surfaces. Finally, a polishing experiment was conducted with an aspheric element under the optimized conditions. The obtained results are shown as follows. (1) A relatively regular MCF tool was obtained when the eccentricity (r), amount of MCF slurry supplied (V), revolution speed of the MCF carrier and magnet (n c and n m , respectively) were given at appropriate values. (2) Abrasive particles entrapped in or attached to the clusters were observed abundantly on the MCF tool sample. (3) The surface profile of the conic workpiece after 60 min of polishing indicated that material was removed evenly, and an annular polishing area was attained. Meanwhile, a higher material removal rate and better surface roughness were achieved with a smaller working gap (h) and larger volume of the MCF slurry supplied (V). (4) The roughness (Ra) of the aspheric surface decreased from 49.81 to 10.77 nm after 60 min of polishing. The shape retention obtained a Pearson correlation coefficient (Pcc) of 0.9981, which demonstrated that this novel method is appropriate for polishing aspheric elements. • Aspheric surfaces are polished by a doughnut-shaped magnetic compound fluid tool. • A perfect MCF tool are obtained by researching the formation process and geometry. • The material removal rate affects deeply to the surface topography. • The h = 1 mm and V = 1.5 ml are perfect for polishing. • The roughness Ra 10.77 nm and high shape retention (pcc: 0.9981) are achieved. [ABSTRACT FROM AUTHOR]

As a new polishing method, bonnet polishing is suitable for polishing the curved surface due to its advantages in flexibility and adaptability of the polishing tool. In the polishing process, the contact state between the bonnet and the curved surface always changes. The traditional polishing tool path with equal interval will inevitably lead to over-polished areas and unpolished areas. In this article, a new tool path for bonnet polishing, which is called the revised Archimedes spiral polishing path, is proposed to ensure the physical uniform coverage of the curved surface in bonnet polishing. The path generation method is based on the modified tool–workpiece contact model and the pointwise searching algorithm. To prove the effectiveness of the revised path, two aspheric workpieces were polished along the traditional Archimedes spiral polishing path and the revised path, respectively. The roughnesses of the two workpieces are 10.94 and 10 nm, and the profile tolerances are 0.4097 and 0.2037 μm, respectively. The experimental results show that the revised path achieves lower roughness and surface tolerance than the traditional Archimedes path, which indicates that the revised path can achieve uniform physical coverage on the surface. [ABSTRACT FROM AUTHOR]

In this paper, we propose and experimentally demonstrate a tunable liquid lens integrated with an aspherical surface for spherical aberration and distortion compensation. Through optimizing the aspherical surface's morphology, the spherical aberration and distortion can be significantly reduced. The root mean square spot size at focus is distinctly reduced from 55. 7 μ m to 2. 095 μ m after performing optimum optimization. The tunable liquid lens is integrated with the aspheric surface with 6 mm clear aperture and 19.2 mm minimum focal length and demonstrate the improvement in optical performance over the conventional lens without an aspheric surface over a focal length range. Its applications in microscope system and tunable-focus eyeglasses are foreseeable. [ABSTRACT FROM AUTHOR]

In the process of large aspheric optical surfaces fabrication, the distortion of the removal function is a big problem that affects the producing efficiency and accuracy, due to the misfit between the tool and the aspheric surface in the contact region. Consequently, this paper aims to find out the influence factors and the distortion rule of aspheric removal function in the computer-controlled optical surfacing. Firstly, based on the analysis of the sub-aperture polishing technology for the large aspheric optical surfaces, the local asphericity of aspheric surface and the viscoelasticity of polishing tool are supposed to be the main sources. After that, a method to calculate the local asphericity considering the misfit between the tool and the aspheric surface is proposed based on the least square method, and the viscoelasticity of the polishing tool is obtained through viscoelastic experiment. Subsequently, combining the results of the local asphericity of aspheric surface and the viscoelasticity of polishing tool, the prediction of the distortion rule of aspheric removal function is presented. Finally, the comparative experiment is carried out, and the removal function on different regions of the aspheric surface is obtained. The experimental result indicated that the distortion of the removal function is consistent with the theoretical result. Through this study, the distortion rule of aspheric removal function in the computer-controlled optical surfacing with pitch tool is finally mastered, which provides a theoretical guidance for the computer-controlled optical surfacing process optimization. [ABSTRACT FROM AUTHOR]

Elastic deformation machining method is a simple machining method in manufacturing aspheric surfaces process. In this method, the top surface of workpieces will deform and be in contact with the mold surface once vacuum is applied, while the bottom of workpiece is polished to flatness with the vacuum pressure is maintained stability. The machining process is finished when the thickness of workpiece is polished to size as required. When the vacuum is turned off and the workpiece is released from the mold, the bottom surface of the workpiece will be shaped into the aspheric surface as the top surface returns to its original flat surface form due to material elasticity. During machining, the form accuracy of aspheric surface is dependent on the value of vacuum pressure and contact between workpiece and mold surface. Therefore, the study of behavior of the glass in contact with the mold surface is necessary to determine the suitable mold surface. In this paper, the simulation results of the glass in contact with the mold in the different pressure values have been carried out. Based on the simulation and experiment results, the appropriate pressure values and mold surface are established for machining process by elastic deformation machining method. In order to improve the precision of form surface produced in elastic deformation machining, the mold profile is modified by selecting the finite element analysis results of workpiece in the case of vacuum pressure P = −95 kPa and the conic constant K = −3. [ABSTRACT FROM AUTHOR]

A flexible interferometry is proposed to test concave optical aspheric and free-form surfaces. It employs a flexible aberration generator (FAG) consisting of a movable reflective sphere (MRS) and two counter-rotating optical wedges (CROW). The FAG is able to generate low-order Zernike aberrations to compensate the inherent aberrations of the test surface by the rotation of wedges in CROW and translation (or tilt) of the MRS. For some surfaces with mild departure, the FAG would result in a resolvable interferogram by the different aberrations compensation and the flexible test is thus achieved. The practical calibration for FAG is also reported. After calibration, experiment results showing the validity of the flexible test are presented by testing an ellipsoidal mirror and an off-axis paraboloidal mirror. [ABSTRACT FROM AUTHOR]

Compared to a conventional optical lens with spherical surfaces, an aspheric lens has many merits. However, due to the nonlinearity in its mathematical expression, its characterization is quite difficult. In this paper, we proposed a new method to construct discrete orthogonal polynomials by the binomial expansion of irrational part into even order terms. The proposed method utilizes last two polynomials to compute conic constant and subsequently applies it to separate desired coefficients. The least squares method is employed to retrieve coefficients of discrete orthogonal polynomials in fitting. Simulation and experiment were performed to test the method. The results indicate that the method is not only able to retrieve accurate parameters, but also has fast convergence speed. [ABSTRACT FROM AUTHOR]

Unlike traditional machinery manufacturing generally using simple features of workpiece as the alignment reference, optical manufacturing, which prioritizes shape tolerances of the machining surface over position tolerances between workpiece geometry features, chooses the machining surface itself as the alignment reference. Thus, the manual alignment of workpiece in optical manufacturing could be very time-consuming when the machining surface is aspheric. Workpiece localization technology is able to automate the workpiece alignment and improve its efficiency. However, there are no relevant reports about application of this technology in the field of optical manufacturing. In this work, the workpiece localization problem for aspheric surface in magnetorheological finishing (MRF) is investigated from aspects of measurement and algorithm. The probe radius error is compensated by applying the polynomial fitting method. A new localization algorithm is proposed in order to improve the computational efficiency for the localization of aspheric surface. Simulation and experiment results verify the validity of the proposed methods. The accurate and efficient workpiece localization in MRF has been achieved and applied in real application which proves its practicability. [ABSTRACT FROM AUTHOR]

An aspheric surface lens is presented to realize collimating illumination with low Fresnel loss based on Fresnel equations and Snell's law. The smooth 2D contour of refractive optical surface is constructed from a set of cubic Bézier segments, whose control points are computed by deCasteljau algorithm. Simulation results show that the optical efficiency of 90.82% is achieved under a divergence angle of ±2.87° for an extended light-emitting diode (LED) source with chip size of 1 mm × 1 mm and the Fresnel loss is only 8.76%, whose optical efficiency has improved 14.3% than traditional collimating lens. By employing this proposed surface construction method, the largest divergence angle of collimating lens for point source is only 0.26° with 15 feature points on each refractive surface, while more than 2° for the traditional method. Therefore, the beams are well controlled with fewer feature data points. Tolerance analyses are also conducted in detail. [ABSTRACT FROM AUTHOR]

Because of the material characteristic of high hardness and high abrasion resistance of SiC ceramics, grinding wheel wear is an essential problem which must be taken seriously and be solved in grinding process, especially in grinding of large-scale aspheric surface. In this paper, a ground aspheric surface form error model in large-scale aspheric surface grinding process of SiC ceramics is built without considering any other conditions but just radius wear of the grinding wheel. In this model, volume grinding ratio is employed to combine the wear volume of the grinding wheel and the removed volume of SiC ceramics. Experiments are conducted to corroborate the feasibility of the model, and the results reveal that the forecast error between the predicted value and the experimental value is less than 15 %. Considering the assumptions and interference of other factors, the form error model is acceptable. [ABSTRACT FROM AUTHOR]

The use of optical coherence tomography (OCT) for noncontact three-dimensional aspheric lens profiling and retrieval of aspheric surface parameters is demonstrated. Two commercially available aspheric lenses with different focal length-to-diameter ratio have been imaged using OCT, and the measured optical path length distribution has been least square fitted with the aspheric lens surface retrieving the radius of curvature, aspheric constant, and conic constants. The refractive index of these lenses has also been measured referencing with a standard Zerodur glass flat. The fitted aspheric surface coefficients of the lenses are in close agreement with the manufacturer's values, thus, envisaging the potential of OCT in rapid screening, testing of aspheric lenses, and other micro-optical components such as those used in illumination optics. [ABSTRACT FROM AUTHOR]

As a newly developed aspheric machining technology, elastic deformation molding process (EDMP) can convert complex aspheric surface machining to simple flat surface machining and has been successfully applied to aspheric surface machining. But during the machining process, workpiece made of brittle materials sometimes fractured, which seriously affected the reliability of the new machining method. In this paper, fragment analysis of fractured workpiece and finite element analysis of thermal stress have been carried out. Water leakage was observed during machining process which caused a high temperature difference inside workpiece, and the corresponding maximum thermal stress was up to 7 MPa near the boundary of contact area. Considering the tensile stress caused by elastic deformation in attaching process, the total tensile stress on attached surface of workpiece has exceeded the admissive bending strength of workpiece material which caused random fracture. Sealing measures like the use of silicone rubber sealant can effectively improve the stability of elastic deformation molding process. [ABSTRACT FROM AUTHOR]

Aiming to develop a prototype swing arm profilometer for several meter-class aspheres, we first present detailed error analysis including error motions of the swing rotary table and the part rotary table, and misalignment of the axes of the two rotary tables. The induced probing error in the normal direction of the reference sphere is calculated by considering the error motions in the coordinate transformation. A surface reconstruction algorithm is then proposed to separate the error motions of the part rotary table by stitching multiple traces. The error motions are optimally recognized and then removed from the trace measurement based on the least squares principle. We model the objective function by relating the normal error to the rigid body transformation of each trace. The basic idea is to minimize the inconsistency of all intersection points of different traces simultaneously. Finally the algorithm is verified through simulations. It shows that error motions of sub-milliradian scale are even tolerant with the surface reconstruction algorithm. [ABSTRACT FROM AUTHOR]

Aspheric ultraprecision machining is increasingly important to the manufacturing industry. The performance of aspheric optical components manufactured by mass-production is largely dependent on the form error of molds and dies. It is believed that productivity of a machining process could be improved if the form error is predictable. In this study, the response surface methodology (RSM) was employed to derive predictive models of rough and compensation cuttings for an aspheric convex mold, with an outer aperture of ϕ 12 mm and curve height of 0.6 mm. Two control factors, the depth of cut and spindle speed, were selected for study. The 2 K factorial design with four center points was adopted. Two linear models for both rough and compensation cuttings were derived experimentally based on the form errors obtained. The models adequacy was examined through ANOVA (analysis of variance) results for the surface responses. It was found that the linear model of rough cutting is adequate, reflected by the significant regress coefficients and the high R 2 value. However, the model of compensation cutting was found to be inadequacy. [ABSTRACT FROM AUTHOR]

Elastic deformation molding method is a newly developed aspheric machining technology which can convert complex aspheric surface machining to simple flat surface machining. Two key problems of the machining principle of the new method are analyzed, according to which the corresponding measures are studies and adopted. Then, the complete machining process flow of the new method is established. An aspheric surface machining experiment is carried out based on the machining process flow, and a parabolic surface with a diameter of 45 mm on quartz glass is finished. The profile error of the machined surface is PV 0.68 μm and the surface roughness is R 0.75∼1.12 nm, which shows that the established machining process flow of the elastic deformation molding method can realize ultra-precision and low-cost machining of aspheric surfaces. [ABSTRACT FROM AUTHOR]

The elastic deformation machining method has been demonstrated to be a novel optical manufacturing approach which can greatly reduce and simplify the production of large aspheric lens. Upon completion of the machining process, the workpiece under process will be shaped into a desired surface form of mold. The method allows the lapping and polishing of aspheric optical surfaces using a large lapping or polishing tools. The subject of this study is to determine the surface shape of the finished glass workpiece after the lapping process of the elastic deformation machining process associated with molding. The experimental and finite element analysis (FEA) results were compared with the shape of the molded surface form. The form accuracy between the optical glass and mold is within 1.6 μm (within radius 32 mm). The conclusions show that the method proposed is effective for machining the aspheric optical glass with proper elastic deformation machining parameters. [ABSTRACT FROM AUTHOR]

Three-dimensional (3D) profile measurement is an indispensable process for assisting the manufacture of various optic, especially aspheric surfaces. This work presents the measurement error calibration of a 3D profile measurement system, namely PMI700. Measurement errors induced by measuring tool radius, alignment error and the temperature variation were analyzed through geometry analysis and simulation. A quantitative method for the compensation of tool radius and an alignment error compensation model based on the least square method were proposed to reduce the measurement error. To verify the feasibility of PMI700, a plane and a non-uniform hyperboloidal mirror were measured by PMI700 and interferometer, respectively. The data provided by two systems were high coincident. The direct subtractions of results from two systems indicate RMS deviations for both segments were less than 0.2 λ. [ABSTRACT FROM AUTHOR]

The subaperture stitching algorithm as a key step of annular subaperture interferometric testing (ASIT) is used to sew all subaperture data together to get the full aperture information. The core part of stitching algorithm is that using the stitching model to eliminate the relative misalignment errors between the adjacent subapertures to realize the stitching treatment. Obviously, the stitching accuracy is mainly determined by the performance of the stitching model. Different stitching model for existing annular stitching algorithms are briefly discussed in this paper. Based on Zernike annular polynomials (ZAP), a more accurate and stabile stitching model for ASIT is proposed. By combining standard deviation and correlation coefficient of overlapping area, we can comprehensively evaluate the stitching performance. In addition, the fitting performance of the ZAP is evaluated in some pertinent cases: different obscuration ratios and noises. By comparing the results of proposed method with that of the classical auto-collimation method, it demonstrates that the accuracy and practicability of the proposed stitching model. [ABSTRACT FROM AUTHOR]

Cross and parallel grinding modes are two typical general grinding modes for aspheric surface in vertical wheel spindle grinding system. In this paper, roughness, surface profile, form accuracy, and wheel wear of the ground aspheric surface utilizing the cross and parallel grinding methods are compared and investigated. Firstly, the maximum undeformed chip thickness of aspheric surface was analyzed in the two grinding modes. And then, the precision grinding of monocrystal silicon for aspheric surface and wheel wear experiments was carried out with the same grinding parameters. Experimental results revealed that the cross grinding mode was advantageous over parallel grinding in terms of achieving precision aspheric surface with a roughness (Ra) of 20.1 nm, form accuracy (PV) of 235 nm, and a steady surface. The change of the maximum undeformed chip thickness in grinding process caused the increased surface roughness from the edge to the center. And without considering the influence of the wheel arc profile form error, better form accuracy was obtained by cross grinding. Besides, the wheel wear modes were significantly different in the two grinding modes. This study gives an indication of the strategy to follow to achieve high-quality ground aspheric surfaces on brittle materials. [ABSTRACT FROM AUTHOR]

Aspheric surfaces have become widely used in various fields ranging from imaging systems to energy and biomedical applications. Although many research works have been conducted to address their manufacturing and measurement, there are still challenges in form characterization of aspheric surfaces considering a large number of data points. This paper presents a comparative study of 3D measurement and form characterization of an aspheric lens using tactile and optical single scanning probing systems. The design of the LNE high precision profilometer, traceable to standard references is presented. The measured surfaces are obtained from the aforementioned system. They are characterized with large number of data points for which a suitable process chain is deployed. The form characterization of the aspheric surfaces is based on surface fitting techniques by comparing the measured surface with the design surface. A comparative study of registration methods and non-linear Orthogonal Least-Squares fitting Methods is presented. Experimental results are analyzed and discussed to illustrate the effectiveness of the proposed approaches. [ABSTRACT FROM AUTHOR]

Due to the existence of imprecise fitting of subapertures' overlap zone, the accumulation of adjustment errors is significant during the measurement of aspheric surface by stitching interferometry. Theoretical analysis indicates that the effect and the appearance of three-direction adjustment errors accords with that of Seidel aberration, of which the axial error leads defocus, third-order spherical aberration and higher-order errors of wave front distribution. Based on the analysis we have made, a correction model has been established, and the estimated values of adjustment errors have been acquired. By correcting the higher-order aberration in the model, fitting precision of subapertures' overlap zone can be improved. Experiment for comparison shows that, after fitting, the value of both residual error and uncertainty of measurement become smaller than those values obtained by traditional correction method of three-direction adjustment error, which proves that the stitching precision of proposed method is higher. [ABSTRACT FROM AUTHOR]

Annular subaperture stitching interferometry (ASSI) is increasingly used for precision metrology of aspheric surfaces. The stitching model is a critical factor for stitching algorithms in ASSI. An optimized stitching model is proposed, which describes the alignment errors of adjacent subapertures based on an off-axis model and wave aberration theory. To keep the stitching errors from transmitting and accumulating, a simultaneous optimization algorithm is presented. The residual difference of overlapped regions of adjacent subapertures is utilized to evaluate the stitching accuracy. Finally, the comparative numerical simulations and experiments are carried out. It shows that the optimized stitching model has a better performance and validity. [ABSTRACT FROM AUTHOR]

Elastic deformation machining is a fabrication method that exploits the elastic deformation properties of materials under stress. Coupled with plane lapping machining process, this new fabrication method is suitable for machining complex aspheric surfaces. Upon completion of the machining process, the workpiece under process will be shaped into a desired surface form. The elastic deformation machining has several advantages over traditional fabrication methods, i.e., high machining compatibility and high fidelity of material property during machining process. The subject of this study is to determine the surface shape of the finished glass workpiece after the lapping process of the elastic deformation machining. The experimental results were compared with theoretical calculations. In the case when the vacuum pressure is 50 kPa, the maximum deviation value between the deformation curves from the theoretical calculation and the experiment results is within 62 μm. In order to improve the precision of form surface, the vacuum pressure is modified from 50 to 42 kPa. This reduction corresponds to a change of workpiece thickness when it is lapped. The results of the change of vacuum pressure show that the form accuracy produced is improved significantly and agrees very well with theoretical calculations. The maximum deviation in this case is 1.6 μm. The study indicates that the experimental plane lapping setup that exploits the material elasticity property can be utilized to fabricate aspheric lenses with axisymmetric surface and low complexity. [ABSTRACT FROM AUTHOR]

Abstract: We formulate the fourth order correction to a paraxial Gaussian beam propagating through a non-spherical surface system that is rotationally symmetric. First we represent the Gaussian beam by a complex-source-point spherical wave (CSPSW). Next we examine the evolution of the CSPSW through the non-spherical surface system by applying a Fresnel–Kirchhoff diffraction integral. We find a ray-optical solution to the diffraction integral in terms of both the conic constant and the aspheric coefficient of fourth order. Then we numerically evaluate the quality factor of the fourth order-corrected beam propagating through either an aspheric mirror or a thin lens made up of two non-spherical surfaces. The fourth order formulas derived here can be useful in determining the quality factor of the Gaussian beam degraded by a rotationally symmetric system of non-spherical surfaces. [Copyright &y& Elsevier]