Automated freeform imaging system design with generalized ray tracing and simultaneous multi-surface analytic calculation

Design and discussion of off-axis reflective double-pass optical systems

In most off-axis reflective optical systems, light beams only pass each optical element once. A double-pass structure can increase the number of beam reflections while using the same number of elements as conventional systems, which can be advantageous for some optical systems, with benefits that include high system compactness and cost-friendliness. In this paper, a design method for off-axis reflective double-pass optical systems is proposed that enables effective control of the overlap of a beam that passes through the double-pass surface twice. Furthermore, we designed and analyzed various geometric folding structure double-pass optical systems that include three-mirror reflections to explore their optimization potential and volume control capabilities. Subsequently, the effect of the double-pass structure on the optical system's performance is investigated using the system volume as an indicator. The results obtained show that when a system inherently requires a longer total optical length to enable better aberration correction, a double-pass structure may reduce the system volume. Finally, we discuss the impact of the double-pass configuration on the optical system's position sensitivity and surface shape sensitivity.

Optical design mode based on fast automatic design process for freeform reflective imaging systems with modest FOV

Traditional optical design methods require designer intervention in the system's evolution from the starting point to the final design. Trial-and-error during design optimization improves system performance step by step but requires much time and effort. A new optical design framework, end-to-end fast automatic design, is proposed and achieved for the freeform reflective optics in this paper, which promotes a new optical design mode. Compared with the traditional mode through improving performance after each trial, an optical system with good image quality can be directly obtained in the end-to-end design process with simple input and no human involvement within a short time. If there is still the possibility for performance improvement of the obtained system, the designer can vary the input parameters repeatedly to obtain multiple systems with good image quality. Finally, the desired system is selected from these systems. Compared with the step-by-step trials in traditional optimization, this new optical design mode involves high-speed trials of the end-to-end automatic design process, reducing the dependence on experience and skill. In this paper, an end-to-end fast automatic design method for freeform imaging systems is developed based on a new design route. Using an initial plane system as an input, a freeform system with excellent image quality can be designed automatically within 1-2 min. After several trials of the end-to-end fast design process, three high-performance freeform systems are designed successfully that consider volume control, beam obscuration, and mirror interference.

Cooled infrared coaxial four-mirror system design with a low F-number

A low F-number and 100% cold stop efficiency are beneficial for improving the performance of optical systems and have a wide range of applications in various thermal imaging scenarios. The cooled infrared coaxial four-mirror system can meet these two requirements, improve system integration, and reduce adjustment costs and difficulties. However, the secondary obstruction caused by the central hole of the third mirror will generate potential stray light. A structure model is proposed in which the primary mirror and the quaternary mirror are processed on the same mirror blank. In this model, a method is given to calculate system parameters using the obstruction ratio and magnification of each mirror. To evaluate the performance of the method, two design examples with different F-numbers (1.4, 1.0) were constructed. The influence of initial structural constraints on the exit pupil position and secondary obstruction was analyzed based on the design objectives of the examples. The aberrations were optimized by targeting the spot. In the optimization process, the incident coordinates and directions of the restricted edge field rays in the tertiary mirror and the quaternary mirror were limited to achieve control of the obstruction caused by the holes in the center of the mirrors. In the results, the RMS spot radius of the two design examples is smaller than the Airy disk radius, and the axial beam wavefront deviation RMS values are 0.026λ and 0.024λ, respectively. Moreover, the obstruction caused by the central holes of the mirrors is controlled within the given field of view. The results show that the proposed model and method can be used to design a low F-number cooled infrared coaxial four-mirror system and have good application prospects.

Aplanatic freeform-mirror-based optical systems

The exact partial differential equation to design aplanatic freeform-mirror-based optical systems is presented. The partial differential equation is not limited by the number of freeform surfaces or their orientations. The solutions of this partial differential equation can be useful as initial setups that can be optimized to meet higher criteria. One of these solutions is tested as an example of the initial setup, and the results are as expected by the theory.

Automated design of freeform imaging systems for automotive heads-up display applications

The freeform imaging system is playing a significant role in developing an optical system for the automotive heads-up display (HUD), which is a typical application of augmented reality (AR) technology. There exists a strong necessity to develop automated design algorithms for automotive HUDs due to its high complexity of multi-configuration caused by movable eyeballs as well as various drivers' heights, correcting additional aberrations introduced by the windshield, variable structure constraints originated from automobile types, which, however, is lacking in current research community. In this paper, we propose an automated design method for the automotive AR-HUD optical systems with two freeform surfaces as well as an arbitrary type of windshield. With optical specifications of sagittal and tangential focal lengths, and required structure constraints, our given design method can generate initial structures with different optical structures with high image quality automatically for adjusting the mechanical constructions of different types of cars. And then the final system can be realized by our proposed iterative optimization algorithms with superior performances due to the extraordinary starting point. We first present the design of a common two-mirror HUD system with longitudinal and lateral structures with high optical performances. Moreover, several typical double mirror off-axis layouts for HUDs were analyzed from the aspects of imaging performances and volumes. The most suitable layout scheme for a future two-mirror HUD is selected. The optical performance of all the proposed AR-HUD designs for an eye-box of 130 mm × 50 mm and a field of view of 13° × 5° is superior, demonstrating the feasibility and superiority of the proposed design framework. The flexibility of the proposed work for generating different optical configurations can largely reduce the efforts for the HUD design of different automotive types.

Freeform optical system design with differentiable three-dimensional ray tracing and unsupervised learning

Optical systems have been crucial for versatile applications such as consumer electronics, remote sensing and biomedical imaging. Designing optical systems has been a highly professional work due to complicated aberration theories and intangible rules-of-thumb, hence neural networks are only coming into this realm until recent years. In this work, we propose and implement a generic, differentiable freeform raytracing module, suitable for off-axis, multiple-surface freeform/aspheric optical systems, paving the way toward a deep learning-based optical design method. The network is trained with minimal prior knowledge, and it can infer numerous optical systems after a one-time training. The presented work unlocks great potential for deep learning in various freeform/aspheric optical systems, and the trained network could serve as an effective, unified platform for generating, recording, and replicating good initial optical designs.

Power set of mirror-based non-symmetric stigmatic optical systems

The set of all possible stigmatic systems made by mirrors is presented. The derivation of the set is analytical, and it is based on the Fermat principle. The properties of the set are properties that all possible stigmatic systems made by mirrors share. The set is tested here with a practical example of optical design, and the results are as expected by theory. This example works with a large field of view rather than a single field, and the volume of the example is several times less than similar systems reported in the literature.

Calculation of aberration fields for freeform imaging systems using field-dependent footprints on local tangent planes

Aberration theory is a fundamental understanding of the optical aberrations and remains the best way to guide optical system design. The nodal aberration theory, which can be used to describe the aberration fields of freeform imaging systems, is limited by the small field of view (FOV) of the imaging system. In this paper, we propose a method to predict the induced aberration of Fringe Zernike terms with field-dependent footprints. The footprint of each field point is calculated in its corresponding local tangent plane of the optical surface; therefore, a more accurate prediction of the induced aberrations of Fringe Zernike terms can be achieved. Both the FOV and highly tilted architecture of freeform imaging systems are considered when calculating the footprints. Two examples are presented to verify the effectiveness of the proposed method, which we believe can provide good guidance for the design of freeform imaging systems with a relatively large FOV.

Analytical equations for a nonconfocal stigmatic three-freeform-mirror system

This paper presents a novel method, to the best of our knowledge, to design three-freeform-mirror systems from scratch. The technique consists of getting an initial setup, before optimization, which is directly obtained from the set of all possible stigmatic three-freeform-mirror systems. Then, deformation coefficients are added to each surface and optimized to reduce aberration produced by additional fields. The method has been tested and the results are as expected.

Designing reflective imaging systems with multiple-surfaces-integrated elements using a Gaussian function freeform surface

We propose a design scheme and method of a freeform off-axis reflective imaging system with multiple mirrors integrated into one element. The use of a multiple-surfaces-integrated element, described by the Gaussian basis functions freeform surface with local and nonsymmetric properties, significantly decreases the system complexity, as well as reduces the assembly and fabrication difficulty, and achieves high imaging performance. The design theory and process including the initial system design, surface conversion, and system optimization are demonstrated in detail. Three design examples are demonstrated to validate the effect and feasibility of the proposed method, and good imaging performance is obtained.

Off-axis reflective imaging system design with a conicoid-based freeform surface

In this paper, we propose an off-axis reflective system design method based on a non-rotational symmetric conicoid-based freeform (CBF) surface description. The base description avoids complicated calculation of decenter and tilt when using the conventional conic expression, thus simplify the system modeling and optimization process, and it can reduce the number of coefficients that needed to represent mild freeform surfaces. A design method that includes the automatic initial system searching, preliminary optimization with rotationally symmetric surface deviation and fine-tuning with non-symmetric surface deviation is proposed. Two three-mirror systems have been designed to demonstrate the feasibility and conveniences of the proposed method.

"First time right" - calculating imaging systems from scratch -INVITED

Freeform optics can be used to greatly extend the functionalities, improve performance, and reduce the volume and weight of optical systems. Today, the design of imaging systems largely relies on efficient ray tracing and optimization algorithms. Such a "step-and-repeat" approach to optical design typically requires considerable experience, intuition, and eventually "trial-and-error" guesswork. This time-consuming process applies especially to freeform optical systems. In this work, we present a deterministic direct optical design method for freeform imaging systems based on differential equations derived from Fermat’s principle and solved using power series. The method allows calculating all optical surface coefficients that ensure minimal image blurring for each individual order of aberrations. We demonstrate the systematic, deterministic, scalable, and holistic character of our method with several catoptric and catadioptric design examples.