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Schematic diagram of the optical path of the Polaroid SX-70 camera with freeform corrector D located at the stop and freeform eyepiece lens G positioned at the viewfinder.
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Modern advanced manufacturing and testing technologies allow the application of freeform optical elements. Compared with traditional spherical surfaces, an optical freeform surface has more degrees of freedom in optical design and provides substantially improved imaging performance. In freeform optics, the representation technique of a freeform sur...
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... example of freeform surfaces used in an off-axis catadioptric Polaroid SX-70 camera was introduced by Plummer; 17 this might be the first commercial product employing optical freeform surfaces characterized by XY polynomials to improve its imaging performance, as dis- played in Fig. 2. Owing to the optical path configuration of off-axis refractive and reflective types, it had more com- pactness. However, off-axis aberrations aggravated its imag- ing quality. Thus, two freeform optical components were used to correct the off-axis aberration. A freeform corrector (D) with a fourth-order XY polynomial profile was ...
Context 2
... example of freeform surfaces used in an off-axis catadioptric Polaroid SX-70 camera was introduced by Plummer; 17 this might be the first commercial product employing optical freeform surfaces characterized by XY polynomials to improve its imaging performance, as dis- played in Fig. 2. Owing to the optical path configuration of off-axis refractive and reflective types, it had more com- pactness. However, off-axis aberrations aggravated its imag- ing quality. Thus, two freeform optical components were used to correct the off-axis aberration. A freeform corrector (D) with a fourth-order XY polynomial profile was ...
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... In the design of optical systems, freeform surfaces are widely used in military, aerospace, automobile, and illumination applications to meet the requirements of correcting aberrations, effectively simplifying structures, and improving image quality [1][2][3][4][5] . The final performance of an optical system depends on several factors. ...
For optical surfaces, the distance between the wavefront at ideal design position and that at real surface testing position along the wavefront propagation direction is an important parameter. It determines the on-axis curvature deviation and best-fit sphere radius of the surface under testing, and thus, affects the optical distance, effective focal length, and tolerance design of the optical system. We define the distance as wavefront optical spacing (WOS or spacing d). The analytical form of the WOS can be utilised in critical tolerance balancing, and its test results can aid in optical system redesign. Aiming at a computer-generated hologram (CGH) interferometric test, in this study, we propose the WOS concept and deduce the coupling relation between the surface error and spacing d, particularly in freeform surface conditions. A cat-eye CGH interferometric method was presented to test the spacing error within a precision of several microns. The simulation and error budget demonstrate that this method can measure the WOS of freeform surfaces. The experimental results indicate that the metrology accuracy is 10.2 ± 4.3 μm (P = 95%) (absolute accuracy), 4.5 μm (repeatability), and 2.1 ppm (relative accuracy).
... In surface representation, Zernike polynomials have emerged as a means of describing the shape of freeform optical surfaces [128][129][130][131][132]. State-of-the-art lens design programs, such as Zemax and CODE V, empower optical designers to use Zernike polynomials to represent freeform surfaces, which are called Zernike surfaces. ...
The Zernike polynomials are a complete set of continuous functions orthogonal over a unit circle. Since first developed by Zernike in 1934, they have been in widespread use in many fields ranging from optics, vision sciences, to image processing. However, due to the lack of a unified definition, many confusing indices have been used in the past decades and mathematical properties are scattered in the literature. This review provides a comprehensive account of Zernike circle polynomials and their noncircular derivatives, including history, definitions, mathematical properties, roles in wavefront fitting, relationships with optical aberrations, and connections with other polynomials. We also survey state-of-the-art applications of Zernike polynomials in a range of fields, including the diffraction theory of aberrations, optical design, optical testing, ophthalmic optics, adaptive optics, and image analysis. Owing to their elegant and rigorous mathematical properties, the range of scientific and industrial applications of Zernike polynomials is likely to expand. This review is expected to clear up the confusion of different indices, provide a self-contained reference guide for beginners as well as specialists, and facilitate further developments and applications of the Zernike polynomials.
... Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. performance and downsize optical systems, which gain popularity in the optical industry due to their high shape flexibility [1][2][3]. Therefore, freeform optics are widely employed in various optical products, such as camera systems, scanners, head-mounted displays, and components used in aerospace and biomedical engineering [4][5][6]. ...
Diamond turning based on a fast tool servo (FTS) is widely used in freeform optics fabrication due to its high accuracy and machining efficiency. As a new trend, recently developed high-frequency and long-stroke FTS units are independently driven by a separate control system from the machine tool controller. However, the tool path generation strategy for the independently controlled FTS is far from complete. This study aims to establish methods for optimizing tool path for the independent control FTS to reduce form errors in a single step of machining. Different from the conventional integrated FTS control system, where control points are distributed in a spiral pattern, in this study, the tool path for the independent FTS controller is generated by the ring method and the mesh method, respectively. The machined surface profile is predicted by simulation and the parameters for the control point generation are optimized by minimizing the deviation between the predicted and the designed surfaces. To demonstrate the feasibility of the proposed tool path generation strategies, cutting tests of a two-dimensional sinewave and a micro-lens array were conducted and the results were compared. As a result, after tool path optimization, the peak-to-valley form error of the machined surface was reduced from 429 nm to 56 nm for the two-dimensional sinewave by using the ring method, and from 191 nm to 103 nm for the micro-lens array by using the mesh method, respectively.
... The free-form optical surface is commonly used as it has better performance and compactness because of the recent advances in optical design and fabrication [1][2][3]. The high-precision free-form optical surface metrology remains difficult because the free-form optical surface has more degrees of freedom for correcting optical aberrations, which means that high-precision free-form optical surface metrology is still a challenge [4][5][6]. ...
In order to verify the estimated wave-front ability of the phase retrieval, a method utilized in the measurement of the aspherical optical surfaces using the phase retrieval technology is described. This technique is based on the algorithm as a solution for the measurement of the aspherical optical surfaces, whose principle is sampling a number of the given defocus images and obtaining the phase information by solving the wave-front with Fourier optical diffractive theory and mathematics optimization. We set up an experimental arrangement used to measure the aspherical optical surfaces using the improved phase retrieval. In addition, we introduced the method of optical alignment in detail, which is very important for high-precision measurements. We obtained an agreement among the error distributions, the peak value, and the root-mean-square value of a ZYGO interferometer, which demonstrates that the improved phase retrieval method can effectively estimate the wave-front and the aberrations of aspherical optical surfaces.
... The genetic algorithm (GA) is used for optimization calculation [13]. Free-form surfaces are used for surface optimization [14,15]. In this paper, an off-axis three-mirror reflective system is designed. ...
Off-axis reflective optical systems have been widely used due to the nature of miniaturization and no obscuration. However, it is difficult to control the desired system structure during the designation and optimization, especially to maintain the compact system structure. In this paper, a constructing method of off-axis reflective optical systems is proposed to achieve the compact feature. The structure construction combines the constraints of the aberration and the system structure. Multiple parameters of aberration (optical performance) and the mirror coordinates (system structure) are simultaneously optimized to obtain the initial structure using the genetic algorithm. The initial structure is compact, unobscured, and remains less difficult to optimize. A compact off-axis three-mirror reflective system was designed with an entrance pupil diameter of 90 mm, a focal length of 405 mm, and a field of view of 3∘×3∘. Each mirror is expressed by an XY polynomial to achieve optimized optical performance.
... Using free-form surfaces, the imaging quality of the optical imaging system can be greatly improved; the illumination uniformity of the optical illumination system can be evidently improved; and the transmission efficiency of the information transmission system can also be remarkably improved. With the recent advances in optical design and fabrication, the free-form optical surface is commonly used because of its better performance and compactness [1][2][3]. ...
In this paper, we demonstrate the use of the modified phase retrieval as a method for application in the measurement of small-slope free-form optical surfaces. This technique is a solution for the measurement of small-slope free-form optical surfaces, based on the modified phase retrieval algorithm, whose essence is that only two defocused images are needed to estimate the wave front with an accuracy similar to that of the traditional phase retrieval but with less image capturing and computation time. An experimental arrangement used to measure the small-slope free-form optical surfaces using the modified phase retrieval is described. The results of these experiments demonstrate that the modified phase retrieval method can achieve measurements comparable to those of the standard interferometer.
... The use of free-form surface can make the design and manufacture of optical elements have greater freedom and flexibility. The free curved surface has a greater degree of freedom in aberration correction and control of light direction, which can eliminate various aberrations of optical system, simplify optical system, make its structure more compact and have higher optical performance [1][2]. ...
... De nombreuses méthodes et comparaison existent dans la littérature, avec des cas d'usage [71][72][73][74][75][76]. Plusieurs articles de revue essayent de donner une vue globale pour se repérer dans l'ensemble des techniques disponibles [71,77]. Je ne présente ici qu'une vue d'ensemble des avantages et les inconvénients des principales méthodes. ...
... Avec les méthodes locales, en revanche, il est possible que de ne modifier que certaines portions d'un dioptre. Par conséquent, ces dernières sont intéressantes pour une modification ponctuelle d'un dioptre [78], ou pour gérer des dioptres avec de très fortes pentes [77]. ...
Suite au travail réalisé au CEA-Leti sur les capteurs courbes, et l’obtention de systèmes ultra compacts grâce à cette technologie, ce travail de thèse explore l’utilisation de microécran courbes dans des systèmes visuels pour les rendre plus compacts. Une étude théorique des apports de la courbure aux systèmes visuels ainsi qu’aux systèmes freeform est développée. La courbure permet à la fois de simplifier la correction de l’aberration de courbure de champ, mais aussi de la distorsion. Par ailleurs, la courbure permet aussi d’augmenter le flux lumineux transmis depuis le microécran au système optique, avec des gains allant jusqu’à 20 % dans les cas favorables. Par rapport aux systèmes optiques freeforms, la courbure permet de libérer des degrés de libertés dans la conception des systèmes, ce qui peut améliorer la compacité du système final, sa qualité image ou en simplifier la fabrication. L’un des avantages significatifs, c’est que ces apports ne s’excluent pas l’un l’autre.Suite à ces études théoriques, deux systèmes optiques sont conçus, dont l’un est fabriqué et caractérisé. Le premier système est un viseur à Réalité Augmentée, qui peut être intégré dans un appareil photographique, et composé de trois prismes freeforms collés. Ce système démontre les apports de la courbure à la fois en qualité image, en volume et en flux lumineux. Le second système, celui qui est fabriqué, est un viseur électronique à symétrie de révolution qui démontre les apports de la courbure en compacité ainsi qu’en difficulté de fabrication. Une caractérisation de ce second système est réalisée, qui inclus une mesure de contraste ainsi qu’un test visuel.
... An important factor in designing with freeform optical elements is the mathematical representation of the optic. For freeform surfaces, the various local and global mathematical representations strongly influence the resultant design [48]. Representation also has ramifications for ease of fabrication and testing such as by minimizing sag departure [49]. ...
Freeform optics enable irregular system geometries and high optical performance by leveraging rotational variance. To this point, for both imaging and illumination, freeform optics has largely been synonymous with freeform surfaces. Here a new frontier in freeform optics is surveyed in the form of freeform gradient-index (F-GRIN) media. F-GRIN leverages arbitrary three-dimensional refractive index distributions to impart unique optical influence. When transversely variant, F-GRIN behaves similarly to freeform surfaces. By introducing a longitudinal refractive index variation as well, F-GRIN optical behavior deviates from that of freeform surfaces due to the effect of volume propagation. F-GRIN is a useful design tool that offers vast degrees of freedom and serves as an important complement to freeform surfaces in the design of advanced optical systems for both imaging and illumination.
... In recent years, the advent in computer-based optical design enabled the simulation of complex components and led to tremendous growth in the use of freeform optics for new applications [7]. These include multifocal corrective eyewear [8,9], telescopes [10][11][12], beam shaping [13], ultra-short projection lenses [14,15], panoramic imaging [16], solar energy concentration [17], and photolithography [18]. ...
... Yet these methods are limited to characteristic scales of up to tens of micrometers in depth, and up to several mm 2 in area [20]. The fabrication of larger components relies on machining approaches such as grinding, milling, and turning, followed by polishing or finishing [7,[21][22][23][24]-processes that remain complex, expensive, and time-consuming. Additive manufacturing is a natural candidate when seeking to construct arbitrary three-dimensional configurations. ...
Freeform optical components enable advanced manipulation of light that is not possible with traditional optical systems. However, their fabrication relies on machining processes that are complex, time-consuming, and require significant infrastructure. Here we present the ability to shape liquid volumes and solidify them into desired freeform components, enabling rapid prototyping of freeform components with high surface quality. The method is based on controlling the minimum energy state of the interface between a curable optical liquid and an immersion liquid, by dictating a geometrical boundary constraint. We provide an analytical solution for the resulting topography given a predefined boundary and demonstrate the fabrication of freeform components with sub-nanometer surface roughness within minutes. Such a fabrication capability, that allows for rapid prototyping of high-quality components, has the potential to answer an unmet need in the optical design industry—allowing researchers and engineers to rapidly test freeform design concepts. It can be further envisioned to be expanded to an industrial scale, allowing for mold-less fabrication of freeform optics. © 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement.
