In the later stages of imaging optical system design, balancing the imaging performance across the full field-of-view is a major task, as the image performance over the entire image plane may vary significantly, and the performance at some field points may be very low and cannot achieve the design goal. A typical method for imaging performance balance is to adjust the optimization weights of sample field points in a repeating manner. However, as common optical design software cannot automatically adjust the weight values, the performance balance is done by the designers and the process may be very tedious and time-consuming. In this paper, we introduce an automated imaging performance balance method of complicated imaging optical systems. An out loop is introduced to automatically calculate and adjust the optimization weight of each field point based on its imaging performance after each iteration cycle. In addition, the weight is regulated by an extra factor which is calculated based on the performance change ratio of each field after the previous iteration step, in order to accelerate convergence. After a certain number of cycles, the imaging performance of the system is balanced. Human involvement is reduced to a minimum. The proposed method can be further integrated into commercial optical design software in the future.
Imaging systems which can work for both the far and near object distances is a growing trend in many applications. However, due to the mechanical movement of the zoom and compensating groups inside the system, the whole system may be very bulky. In this paper, we propose the optical design of a dual-object-distance imager enabled by polarizationsensitive flat phase element, which can be realized by polarization-multiplexing metasurface. The system contains only two co-axis phase element which offer optical power and wavefront modulation ability. By rotating the polarizer in front of the whole imager, the incident light can be altered into two orthogonal polarization states corresponding to two object distances, and whole system is compact. The starting point of the system is firstly established using confocal flat phase element. Then further optimization is conducted and the field-of-view of the system is gradually increased. The final system can operate at two different object distances: infinity and 10mm. The field-of-view for both two working modes is 30 degrees, and the entrance pupil diameter is 2.5mm. High imaging performance is achieved.
In recent years, the use of freeform optical surfaces in optical system design has experienced a significant increase, allowing systems to achieve a larger field-of-view and/or a smaller F-number. Despite these advancements, further expansion of the field-of-view or aperture size continues to pose a considerable challenge. Simultaneously, the field of computer vision has witnessed remarkable progress in deep learning, resulting in the development of numerous image recovery networks capable of converting blurred images into clear ones. In this study, we demonstrate the design of offaxis freeform imaging systems that combines geometrical optical design and image recovery network training. By using the joint optimization process, we can obtain high-quality images at advanced system specifications, which can be hardly realized by traditional freeform systems. We present a freeform three-mirror imaging system as a design example that highlights the feasibility and potential benefits of our proposed method. Zernike polynomials surface with an off-axis base conic is taken as the freeform surface type, using which the surface testing difficulty can be controlled easily and efficiently. Differential ray tracing, image simulation and recovery, and loss function establishment are demonstrated. Using the proposed method, freeform system design with increased field-of-view and entrance pupil size as well as good image recovery results can be realized. The proposed method can also be extended in the design of off-axis imaging systems consisting phase elements such as holographic optical element and metasurface.
KEYWORDS: Imaging systems, Education and training, Design and modelling, Machine learning, Ray tracing, Chemical elements, Optical components, Systems modeling, Holographic optical elements, Distortion
Imaging systems consisting of flat phase elements can achieve more compactness and lighter-weight. In this paper, we propose a design framework of off-axis reflective imaging system consisting of flat phase elements based on deeplearning. Differential ray tracing for off-axis systems consisting of flat phase elements is used. Supervised and unsupervised learning are combined to improve the generalization ability of the deep neural network for a wide range of system and structure parameter values. Single or multiple systems can be generated directly after the design requirements are inputted into the network, and can be taken as good starting points for further optimization. The design efficiency can be significantly improved, and the dependence on the advanced design skills is dramatically reduced.
Retinal projection display (RPD) is considered as a better solution for near-eye displays (NEDs). It can be used for the augmented-reality (AR) and virtual-reality (VR) applications. In this paper, we propose the RPD system with extended eyebox solution based on freeform holographic elements, realizing the 3×3 viewpoints array in two-dimensional directions on the pupil plane. The viewpoints spacing is 3mm, the FOV of each viewpoint is close to 40°×40°, and the eye relief is 25 mm, which can effectively overcome the eyebox limitation of the conventional RPD system. Detailed procedures of the design and analysis process of RPD system with extended eyebox will be demonstrated in this paper.
A typical and widely used configuration of freeform imaging system is freeform off-axis three-mirror systems. However, as the system configuration and surface shape have no rotational symmetry, the assembly process will be very difficult. In this paper, we designed off-axis three-mirror systems in which the primary and tertiary mirrors are integrated into one single element. The two mirrors use different portions of a single mirror, which is represented by one mathematical expression. The design process of the system is demonstrated in detail, and three different kinds of light folding geometry are explored. The system design using different types of freeform surface is also explored and the imaging performance is compared. Finally, tolerance analysis which considers the local and random nature of surface error and actual manufacturing difficulty of the freeform surface is conducted.
The compound eye optical system has attracted much recent attention, owing to its large field-of-view, compact structure, and rapid imaging capabilities. We designed a compact image scanner (cross-section 36.5 mm × 17 mm) based on the compound eye system. A single imaging unit is mainly composed of two freeform mirrors and a flat mirror, and its field-of-view in object space reaches 10 mm. The modulation transfer function of the system is greater than 0.6 at 12 cycles/mm corresponding to Nyquist spatial frequency of 600 dots per inch in depth-of-field of 0~4 mm. Furthermore, a larger field-of-view is achieved by splicing multiple imaging units with 1-mm overlap in object space. An object-side telecentric system is used to obtain constant magnification at different object distances and the distortion (<1 μm) is controlled by freeform mirrors. The final image is obtained by image splicing. The imaging quality of the scanner is further improved by eliminating stray light.
Using freeform optical surface in an imaging optical system is a revolution in the field of optical design. Introducing machine learning into freeform imaging optical design will significantly reduce the human effort and even beginners in optical design will be able to perform difficult design tasks. Machine learning has been successfully applied to the immediate generation of starting points with various system specifications for the design of freeform reflective imaging systems. However, the parameters used in the network training, which are the key points in the whole design framework, are determined without proper guidance, which may significantly affect the actual performance of the networks. In this paper, a comprehensive exploration of the training parameters of the neural network used for starting points generation of freeform reflective systems is conducted. The parameters include the number of layers, the number of nodes in the layers, the type of activation function, the type of loss function, the type of optimization algorithm, and the value of learning rate. A detailed comparison and analysis of different training parameters are demonstrated on the training results and the imaging performance of validation output systems with large amount of random system specifications input. Using the obtained results designers can choose proper parameters accordingly and get desired neural networks with shorter training time and better performance. The results also offer insight in the design of imaging systems with other system configurations and more advanced system specifications.
As a kind of radial basis functions, the Gaussian function has local feature and therefore has an excellent surface description ability. In this paper, we proposed the design strategy of freeform unobscured three-mirror system using Gaussian radial basis functions surface type and demonstrate a design example. A novel and high-accuracy surface fitting algorithm of Gaussian radial basis functions is proposed for the freeform surface fitting. Successive optimization strategy is employed for the system after surface fitting. The final example system works at the long wave infrared band and has an 8°×6° field-of-view with an F-number of 1.9.
Freeform optical surfaces can be characterized as nonsymmetric surfaces and they can offer much more degree of freedom for optical design. This kind of optical surface can be seen as a revolution in the optical design and plays a key role in the next generation of high-performance optical systems. Another trend in imaging optics is to use phase elements (such as diffractive elements and metasurface). In specific, the flat or planar phase element can effectively reduce the weight and volume of the total system. Easier-alignment of the system can also be achieved. In this paper, the point-by-point design method are applied to the design of three kinds of nonsymmetric imaging systems: consisting of only geometric freeform surfaces, only flat phase elements, and both of them (the generalized case). The entire design process begins from an initial system using simple geometric planes. Both the geometric freeform surfaces and the phase profiles or functions are generated point-by-point based on specific design requirements. The design results can be taken as good starting points for further optimization. The dependence on existing starting points is significantly reduced and advanced design skills are not required. In addition, three typical three-mirror folding geometries are employed and designed using the proposed method for all the three kinds of systems under same system specifications. The imaging performance and system volume of the different systems after final optimization are analyzed and compared. The results offer insight on the selection of optimal system folding geometry and types of imaging element for the nonsymmetric system design tasks.
In this paper, we demonstrated the design method of freeform unobscured reflective imaging systems using the point-bypoint Construction-Iteration (CI) method. Compared with other point-by-point design methods, the light rays of multiple fields and different pupil coordinates are employed in the design. The whole design process starts from a simple initial system consisting of decentered and tilted planes. In the preliminary surfaces-construction stage, the coordinates as well as the surface normals of the feature data points on each freeform surface can be calculated point-by-point directly based on the given object-image relationships. Then, the freeform surfaces are generated through a novel surface fitting method considering both the coordinates and surface normals of the data points. Next, an iterative process is employed to significantly improve the image quality. In this way, an unobscured design with freeform surfaces can be obtained directly, and it can be taken as a good starting point for further optimization. The benefit and feasibility of this design method is demonstrated by two design examples of high-performance freeform unobscured imaging systems. Both two systems have good imaging performance after final design.
Access to the requested content is limited to institutions that have purchased or subscribe to SPIE eBooks.
You are receiving this notice because your organization may not have SPIE eBooks access.*
*Shibboleth/Open Athens users─please
sign in
to access your institution's subscriptions.
To obtain this item, you may purchase the complete book in print or electronic format on
SPIE.org.
INSTITUTIONAL Select your institution to access the SPIE Digital Library.
PERSONAL Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.