Freeform hyperspectral imager design in a CubeSat format

Comprehensive performance domain tolerance analysis methodology for freeform imaging spectrometers

In recent years, attention has been directed towards cost-effective and compact freeform Schwarzschild imaging spectrometers with plane gratings. The utilization of tolerance analysis serves as a potent approach to facilitate the development of prototypes. Conventional tolerance analysis methods often rely solely on the modulation transfer function (MTF) criterion. However, for a spectrometer system, factors such as the keystone/smile distortion and spectral resolution performance also require consideration. In this study, a tailored comprehensive performance domain tolerance analysis methodology for freeform imaging spectrometers was developed, considering vital aspects such as the MTF, keystone/smile distortion, and spectral resolution. Through this approach, meticulous tolerance analysis was conducted for a freeform Schwarzschild imaging spectrometer, providing valuable insights for the prototype machining and assembly processes. Emphasis was placed on the necessity of precise control over the tilt and decenter between the first and third mirrors, whereas the other fabrication and assembly tolerances adhered to the standard requirements. Finally, an alignment computer-generated hologram (CGH) was employed for the preassembly of the first and third mirrors, enabling successful prototype development. The congruence observed between the measured results and tolerance analysis outcomes demonstrates the effectiveness of the proposed method.

Design method for eliminating spectral line tilt in a multiple sub-pupil ultra-spectral imager (MSPUI)

A multiple sub-pupil ultra-spectral imaging system designed with a single spectrometer and detector can simultaneously detect multiple-channel spectra with ultra-high spectral resolution. However, due to using a prism in the system's front end, the nonlinear dispersion introduces spectral line tilt in the imaging spectra. This phenomenon can lead to bias in the final spectral data. To eliminate this issue, we propose a new design by introducing a second prism to correct this spectral tilt in the system. The angle of spectral line tilt generated by the nonlinear dispersion of the first prism is derived. It provides the theoretical basis for characterizing the second complementary prism. Finally, a UV multiple sub-pupil ultra-spectral imaging system is designed. The system employs two pupil separation prisms and one flat panel array to segment the pupil in three channels, each operating within spectral ranges of 180∼210 nm, 275∼305 nm, and 370∼400 nm, respectively. The spectral resolutions in all three channels are better than 0.1 nm. The corrected spectral line tilt is less than 1/3 of a pixel in the two channels with pupil separation prisms. At a Nyquist frequency of 30 lp/mm, the modulation transfer functions of all three channels are greater than 0.7, ensuring imaging quality. The design results indicate that the method proposed in this paper, utilizing complementary prisms, can effectively correct the spectral line tilt caused by the nonlinear dispersion of the pupil separation prisms. This design approach can be a reference for developing multiple sub-pupil ultra-spectral imaging systems.

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.

Freeform surfaces that enable high-quality Offner-type imaging spectrometers with holographic grating

In this paper, the impact of introducing freeform surfaces into the recording and imaging paths of holographic gratings on system performance is quantitatively investigated, and the performance boundaries of various systems are demonstrated. These performance parameters encompass numerical aperture, spectral resolution, spectral band, and slit length, among others. The results indicate that introducing a freeform surface in the recording path can significantly improve performance, surpassing the introduction of a freeform surface in the imaging path. Besides, the performance improvement is several times that brought by an aspherical surface. Therefore, by incorporating a freeform surface in the recording path and using simple spherical elements in the imaging path, a series of high-performance and low-cost imaging spectrometers can be achieved. Additionally, a high-quality imaging spectrometer with holographic grating is introduced, where all surfaces are freeform.

Off-axis four-mirror telescope with a wide field of view and a long focal length using double integrated mirrors

An off-axis four-mirror optical system has the advantages of a wide field of view (FOV) and a small telephoto ratio. However, it will bring difficulties in assembly and detection. Here we report an off-axis four-mirror free-form telescope with a long focal length and a wide field of view based on two integration mirrors. The initial structure of a coaxial four-mirror optical system is established based on the Seidel aberration theory. A Zernike Fringe free-form surface is introduced to correct aberrations. By gradually increasing the entrance pupil diameter and the FOV, we finally obtain an off-axis four-mirror telescope with a FOV of 0.4∘×20∘, an F-number of 11.5, a long focal length of 2000 mm, and a volume of 360×400×600m m 3. In addition, four mirrors remain coaxially aligned, remarkably facilitating detection and adjustment. The proposed off-axis four-mirror telescope, with double integration mirrors, holds great potential for application in aerospace remote sensing observations.

Exit pupil quality analysis and optimization in freeform afocal telescope systems

Afocal telescopes are often used as foreoptics to existing imaging systems to allow for application flexibility. To properly combine an afocal telescope with an existing imaging system, the exit pupil of the afocal telescope and the entrance pupil of the imaging system must be coincident. Additionally, the exit pupil of the afocal telescope must be well-formed; that is, it must be the correct size and shape to mitigate pupil-matching challenges. This work introduces processes for designing freeform afocal telescopes with an emphasis on understanding how to analyze and control the exit pupil quality of such systems. The included 3-mirror design examples demonstrate the advantages of using freeform surfaces in afocal systems and quantify the tradeoffs required to improve the exit pupil quality.

Design of compact off-axis freeform imaging systems based on optical-digital joint optimization

Using a freeform optical surface can effectively reduce the imaging system weight and volume while maintaining good performance and advanced system specifications. But it is still very difficult for traditional freeform surface design when ultra-small system volume or ultra-few elements are required. Considering the images generated by the system can be recovered by digital image processing, in this paper, we proposed a design method of compact and simplified off-axis freeform imaging systems using optical-digital joint design process, which fully integrates the design of a geometric freeform system and the image recovery neural network. This design method works for off-axis nonsymmetric system structure and multiple freeform surfaces with complicated surface expression. The overall design framework, ray tracing, image simulation and recovery, and loss function establishment are demonstrated. We use two design examples to show the feasibility and effect of the framework. One is a freeform three-mirror system with a much smaller volume than a traditional freeform three-mirror reference design. The other is a freeform two-mirror system whose element number is reduced compared with the three-mirror system. Ultra-compact and/or simplified freeform system structure as well as good output recovered images can be realized.

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.

Implementation of a null test for freeform optics using a high-definition spatial light modulator

We report the implementation of an interferometric null test using a high-definition spatial light modulator (SLM) as a reconfigurable alternative to a computer-generated hologram. We detail the alignment process chain, including novel techniques using the SLM to project alignment fiducials on the test part. To validate the alignment protocol, we measure a mild off-axis conic with the SLM-based system and cross-validate with conventional interferometry within 30 nm root-mean-square (RMS) surface figure. Finally, we report the null test of a 65 mm clear aperture concave freeform with 91 μm peak-valley sag departure from the base sphere. The measured surface figure of the freeform is within 40 nm RMS compared to the measurement with a commercial metrology instrument.

Multi-material freeform gradient-index spectrometers

With the advent of 3D printing optical elements, new techniques for manufacturing gradient-index (GRIN) optics have been realized that blend multiple materials in the deposition process. A method to achieve spectral splitting using multi-material GRIN optics is presented. The GRIN is additionally used to generate optical power, allowing for planar entrance and exit surfaces. It is shown that this simultaneous focusing and spectral splitting is not feasible with a two-material GRIN. A comparative design study is then conducted using three and four-material GRIN. A four-material design with optimized materials is also presented to showcase the potential for this new design form.

Design Method of Freeform Off-Axis Multi-Mirror Optical Systems

A data point calculation method that does not require the use of Fermat′s principle and a simple and general design method of starting points of freeform off-axis multi-mirror optical systems are proposed in this paper, which aim to promote the realization of high-performance reflective systems containing freeform surfaces. Taking a planar system and the required parameters as the input, a good starting point for a freeform off-axis multi-mirror system can be automatically obtained using the proposed method. The design of a freeform off-axis five-mirror system with a low F-number is taken as an example to show the effectiveness of the proposed method. The method can also be used for the design of freeform reflective systems with other numbers of mirrors.

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.

Freeform optics: introduction

This feature issue of Optics Express highlights 28 state-of-the-art articles that capture a snapshot of the recent developments in the field of freeform optics. As an introduction, the editors provide an overview of all published articles, which cover a broad range of topics in freeform optics. The wide variety of applications presented here demonstrates that freeform optics is a growing and vibrant field with many more innovations to come.