The 14-meter off-axis deployable space telescope, Single Aperture Large Telescope for Universe Studies (SALTUS), is designed to serve as an exceptionally large far-infrared observatory in space. SALTUS aims to observe thousands of faint astrophysical targets, including the earliest galaxies, protoplanetary disks in different stages of evolution, and various solar system objects. Its architecture incorporates a radiatively cooled, unobscured 14-meter aperture and cryogenic instruments, enabling both high spectral and spatial resolution with unprecedented sensitivity across a wavelength range that is largely inaccessible to current ground-based or space observatories. The innovative SALTUS optical system, featuring a large inflatable off-axis primary mirror, offers exceptional sensitivity, angular resolution, and imaging performance at farinfrared wavelengths over a wide ±0.02° × 0.02° field of view. SALTUS' compact design allows it to fit within existing launch fairings and be easily deployed in orbit.

Incoherent digital holography is a technology that can acquire 3D information from incoherent objects. Since it does not require a laser, incoherent digital holography enables speckle-free imaging with a relatively small and lowcost optical setup. However, like conventional holography, it suffers from the twin-image problem. Additionally, when imaging objects with multiple colors or at varying distances, it becomes difficult to distinguish between color and distance due to the nature of incoherent holography. In this paper, we introduce the use of a dual-focus checkerboard lens and dual cameras to address these issues.

Waveguide AR glasses with gratings can reduce the size and weight of augmented reality products. Typically, the optical system includes both geometric optic and wave optic components; therefore, a multi-domain solution is needed for designing and optimizing the system. Furthermore, achieving sufficient uniformity, chromaticity, and efficiency while maintaining desired field of view is also a challenge. The key for waveguided AR design is the feasible design flow and comprehensive simulation as well as optimization tools that can handle multi-domain, multi-target problems. We successfully integrated wave optics phenomenon into geometrical optics results to complete an optimized waveguide AR glasses design by using Synopsys RSoft RCWA tool DiffractMOD, and LightTools Spatial BSDF interface.

We demonstrate birefringent resonances in high-index tungsten disulfide (WS₂) metasurfaces which enhance light-matter interaction and achieve an unprecedented birefringence. Our results overcome fundamental limit of birefringent devices and unfold an avenue for creating ultimate thin polarization optical devices.

A device is built to create virtual scenarios to realize intelligent perceptual tests of machine vision. The device consists of multiple projectors and uses light field superposition to build a multi-channel scenario projector, based on which any application scenario can be virtually reproduced on a two-dimensional plane. Currently, the device can cover 430~700 nm, and the effective number of controllable pixels is more than 1 million. We perform spectral segmentation of different channels, which can enhance the freedom of spectral combination for 2D scene reproduction. The application of the above multi-channel projector for intelligent perception is investigated using number plate character recognition as a case study. An image dataset of license plate character recognition for testing and evaluation was designed, and experiments on license plate character perception were carried out to demonstrate the application of the multi-channel projector in intelligent perception. The multi-channel projector-based test device and the basic test procedure, with reasonable scene matching and customization, can be used for testing and evaluating the intelligent perception performance of machine vision systems in a variety of scenes.

In this investigation, a polarization multiplexing technique is applied to optical testing, especially shearing interferometers, low coherence interferometers and a clocking motion interpreter. Polarization multiplexing techniques possess the snapshot capability in interferometers and polarization imaging devices, and can enhance the measurement speed compared to the conventional optical techniques, which needs a timely-mannered procedure. Experimental results show the various application of the polarization multiplexing technique and give some insight to be used in optical testing area.

We consider the design of cascaded phase diffractive optical elements (DOEs) operating at several different wavelengths. The problem of DOE design is formulated as the problem of minimizing a certain error functional that depends on the functions of diffractive microrelief height of the cascaded DOE and evaluates its performance at different design wavelengths. Explicit expressions are obtained for the Fréchet derivatives of the error functional. The presented expressions for the derivatives of the error functional constitute the basis for gradient design of cascaded multiwavelength DOEs in various problems including the beam shaping and optical classification problems. As particular example, we consider the calculation of cascaded DOEs focusing radiation of three different wavelengths into different letter-shaped areas.

Virtual and augmented reality systems are actively developing and modernizing, and their application is increasingly finding itself in new areas. The role of AR is especially high in learning and navigation processes, medicine and travel. However, modern AR systems are far from perfect - the image quality and ergonomics of existing solutions are imperfect. The paper considers a theoretical variation of an AR system with a reduced number of components using a freeform mirror surface. Through iterative calculations with further approximation by a power polynomial and Bezier curves, the resulting AR system is modeled in Zemax. The use of Bezier curves by CAD-modeling gives an advantage over integrated surfaces, but the amount of residual transverse aberration Δy'_max = 12 arc-min twice the tolerance Δy'_max ≤ 5 arc-min, and the exit pupil size is 10% less than stated (54 mm against the nominal 60 mm) with a tolerance of 1.5%. Thus, the use of the ray mapping method for the calculation of imaging systems is promising, but requires further improvement of the algorithm calculation process.

A polarization-independent diffractive optical element (DOE) consisting of dual photonic crystal (PhC) slabs was proposed for unidirectional light transmission at telecom wavelengths. Employing rigorous coupled wave analysis (RCWA) together with genetic algorithm (GA), the contrast ratios of designed DOE with 10nm precision at normal incidence from opposite directions reached to 33.6 dB and 32.2 dB with transmittance differences of 84.57% and 87.63% at wavelengths of 1310 nm and 1550 nm, respectively. The presented DOE showed great promising for applications in optical communication.

At present, the space-borne optical camera installed on satellite platform used for space targets monitoring usually adopts optical system having fixed length and therefore the corresponding field of view cannot be changed either. However, searching for targets of interest needs large field of view but powerful details resolving capability depends on long focal length instead. In order to realize searching within large field of view and high-resolution imaging within small field of view by using one optical system, zooming is an ideal choice. Nowadays, optical zooming is the most popular zooming technique and by introducing zooming group and compensating group at the same time, not only the focal length could be changed but also the focal plane could be stabilized. However, mechanical moving elements based traditional optical zooming has obvious drawbacks, for example relatively low zoom speed, possible disturbance to platform stability and reliability decreasing. Therefore, optical zooming without macroscopic moving elements has been paid much attention and the key lies in the use of variable curvature mirror (VCM). By combining variable curvature mirror and optical leveraging effect, the slight variation of curvature radius of VCM can generate large optical zooming. On the one hand, the fewer the number of VCM used is, the bigger the saggitus variation of each variable curvature mirror will be. On the other hand, large zoom factor needs large saggitus variation but aberrations turn up correspondingly as well. Therefore, how to balance the number of variable curvature mirrors, the reasonable saggitus variation and better aberration compensation within limited volume are the key to system design. In this manuscript, first of all, the current development status of variable curvature mirror based optical zooming are systematically reviewed and our research progress on this technique is also introduced. After that, the design method is described and one typical design example is presented. At the same time the effectiveness of digital restoration in improving the imaging quality is demonstrated as well. Finally, the development tendency of variable curvature mirror based optical zooming is simply discussed.

In computer-aided design of optical systems, the choice of starting point is very important. Typically, the designer selects the initial optical design from any database available to him based on his own experience and technical specifications for designing the required optical system. To date, thousands of optical systems of various purposes and complexity have been designed. This diversity significantly complicates the process of selecting an initial circuit for its further optimization. The authors propose a method for constructing an evaluation function for the automated selection of a starting optical design. The proposed methodology combines the classification of optical systems by their type and the complexity of their structural design and includes requirements for image quality, size and weight characteristics, spectral range, manufacturing complexity, and estimation of manufacturing costs for mass production.

Single-pixel imaging is a unique technique that can image target objects over a wide band range and in low-light environments. However, this method requires a large number of structured pattern illuminations in addition to reconstruction calculations, which limits its practical application. We introduce the single-pixel techniques that we have developed: deep learning, optimization, field-programmable gate array (FPGA), and nonnegative matrix factorization (NMF)-based methods. Deep learning and optimization techniques can improve image quality, and FPGA approaches can perform real-time imaging. The NMF approach can drastically reduce the number of structured patterns and measurement time.

360 panoramic lens is a key component of the vehicle’s vision for its safe movement. Fish eye lens introduces large geometric distortions of the field edge, thus the edge image has a low resolution. Furthermore, for night driving (infrared spectral mode), conventional systems are not performing well. To solve these problems, we have proposed a new panoramic car system. In our work we analyze general characteristics and methods of panoramic visualization system introduction, as well as present a car panoramic lens scheme.

Interest in variable-focus lenses is growing due to their dynamic optical power control and reduced spatial demands for focusing and/or zooming functions. Most variable-focus lenses are limited to small apertures (< 10mm), limiting their application scenarios. In this work, we designed and fabricated a 42mm large-aperture variable-focus lens based on a liquid-membrane-liquid (LML) structure. This design surpasses the typical limitations of small aperture sizes in variable-focus lenses. Experiments show that the prototype achieves consistent optical power actuation range in [−3D, +3D], high repeatability during the actuation process, and 82.1622% transmittance using a ~630nm laser beam. After constructing an imaging system incorporating the proposed prototype, the imaging tests yield average modulation transfer function (MTF) values of 0.7904 at 17.204lp/mm spacial frequency and 0.5439 at 34.409lp/mm in the region where no obvious distortion occurs. The prototype demonstrates potential applications in fields requiring large aperture and high-quality imaging capabilities, such as wearable devices and machine vision.

Aberrations in minimalist optical imaging systems pose significant challenges to achieving high-quality imaging. Traditional Wiener filtering methods, though effective, are constrained by their dependency on precise blur kernels and noise models, and their performance degrades with spatial variations in these parameters. On the other hand, deep learning techniques often fail to fully utilize prior information about aberrations and suffer from limited interpretability. To address these limitations, we propose a novel deep attention Wiener network (DAWN). This approach integrates deep learning with Wiener filtering to enhance image restoration while reducing computational complexity. By using optical simulations to generate blur kernels and noise models that closely mirror real conditions, our method fits distinct point spread function (PSF) for different fields of view (FOV), creating a robust dataset for training. The DAWN model first employs a convolutional neural network (CNN) for feature extraction, followed by sequential Wiener filtering applied in half FOV block length steps. To further improve image restoration, a nonlinear activation free net (NAFNet) is used to correct discrepancies introduced by simulated blur kernels and noise models. The model is trained end-to-end, and to streamline the process, Wiener filtering is confined to 4 × 4 FOV blocks. A weighting matrix within the Wiener filtering layer mitigates seams between adjacent blocks. Simulation and experiment results demonstrate that our approach outperforms the mainstream image restoration methods.

We present several geometrical models for freeform optical design based on Hamilton’s characteristic functions, which can be either expressed in terms of a cost function or a generating function. These models are closed with a conservation law for luminous flux. We give an example of a near-field problem where a collimated beam is converted into a target distribution on a sphere.

Here focus on freeform lens design for irradiance tailoring on tilted target planes based on differentiable ray tracing. Leveraging the computational graph, we develop a differentiable Monte Carlo ray tracing framework featuring a 3D coordinate rotation operator. The forward calculation within this framework can simulate the irradiance distribution on a tilted target plane generated by a freeform lens, facilitating the assessment of deviations from the desired irradiance distribution. The back-propagation efficiently acquires surface parameter gradients for optimization through the Adam optimizer. The design example demonstrates that the proposed method can effectively generate a high-quality uniform irradiance distribution on a tilted receiver.

Freeform surfaces have been widely used in various imaging applications. The selection of the initial structure is particularly critical in the optical design of freeform imaging systems due to the significantly expanded solution space. Here, we introduce a method to identify an initial point for the optical design of four-mirror freeform reflective imaging systems. The initial design method for four-mirror freeform imaging systems leverages the optical property of conical surfaces and the linear-astigmatism-free condition, which is computationally simple, easily accessible and theoretically supported. The initial configurations prioritize the elimination of field-constant aberration and linear astigmatism, providing a robust foundation for subsequent optimization of freeform imaging systems. We generalize the design method for linear-astigmatism-free confocal systems to four-mirror confocal off-axis systems with “double-pass surface”. We present a design example in which the field-constant aberration and the linear astigmatism are eliminated, showcasing the effectiveness of the proposed method. The proposed approach proves capable of delivering a promising starting point for the development of four-mirror freeform off-axis reflective imaging systems.

At the present time, computer-generated holograms (CGH) are state-of-the-art components in interferometric systems for testing aspherical surfaces. When using CGH, there is a problem of assembling the control scheme. Even an error of ~ 10 microns in the exposure of scheme elements distorts the interference pattern and makes it impossible to further adjust the optical elements to control the aspherical surface. This problem is solved by the introduction of additional diffractive structures that form spatial labels for rough positioning of control scheme elements. In this paper, we give an overview of peculiarities of combination of amplitude and phase diffractive structures at designing of high precision CGHs fabricated by means of circular laser-writing system (CLWS) and direct laser thermochemical writing technology . The problem of optimizing the writing strategy and different technological steps is discussed in order to make easy alignment procedure and to reduce errors. The limiting parameters of the control scheme related to the characteristics of the created diffractive structures, limited by the features of the technological stages of manufacturing CGH, are also discussed. We also present practical results in CGHs fabrication using modernized laser-writing system at the IA&E SB RAS and combination of different types of diffractive structures.

This paper presents the design of a continuous zoom optical system operating in the long-wave infrared spectrum (8 - 12μm), compatible with an uncooled detector having a resolution of 640×480 pixels and a pixel size of 12μm. Focal length ranges from 20mm to 100mm, with corresponding aperture values varying from F/0.8 to F/1.1. In order to possess good optical performance and compactness, the optical system applied a number of diffractive and aspheric surfaces. This system consists of 5 elements with a total length of 180mm and is optimized at 8 focal positions. All configurations exhibit good optical quality, with RMS spot sizes smaller than the sensor pixel size and MTF values at Nyquist frequency close to the diffraction limit. Additionally, in order to give the system good imaging performance in the operating temperature range from -20°C to 60°C, an active mechanical compensation method was used.

Ultra-precision measurement technology is the cornerstone of ultra-precision machining and manufacturing technology, and is an essential component of the national modern advanced measurement system. chromatic confocal sensors (CCS), with their advantages of high accuracy, fast measurement speed, wide adaptability to tested surface, and non-contact measurement capability, have become an important research hotspot in the field of ultra-precision measurement. Due to the low scanning efficiency of point chromatic confocal sensors, which can only obtain height information for a single point at a time, line chromatic confocal sensors (LCCS) has developed rapidly in recent years. The LCCS can simultaneously obtain height information for thousands of points (such as 2048 points) along a line, and the three-dimensional topography of the measured surface can be obtained through several one-dimensional scans, greatly improving measurement efficiency. It has been widely applied in various advanced manufacturing fields. Firstly, the working principle of the LCCS is introduced, and the key components affecting its performance are analyzed. Then, the research progress of the LCCS is introduced, followed by the research progress of its metrological calibration. Next, the measurement applications of the LCCS are summarized. Finally, the application development of the LCCS are summarized and prospected.

A highly scalable and reconfigurable optical convolution paradigm based on wavelength routing is proposed, which leverages the unique sliding property of an arrayed waveguide grating router (AWGR) to execute the sliding window operation of convolution in the wavelength-space domains. By directly loading two input vectors onto two modulator arrays, the convolution result is instantaneously generated at a photodetector array at the speed of light propagation. This enables the entire convolution computation to be executed within one clock cycle, eliminating the necessity for preprocessing or decomposition into elementary MAC operations. The proposed optical convolution unit (OCU) has striking advantages of high scalability, high speed, and processing simplicity compared to those based on optical matrix-vector multipliers (MVM). A proof-of-concept experiment employing standalone optical components is devised to validate optical convolution computing principles with one-bit accuracy. The classification of ten handwritten digit classes sourced from the MNIST database is experimentally demonstrated, achieving a precision of 4-bit. New algorithms for data splitting and reorganization were concurrently introduced to facilitate the convolution calculation of two-dimensional image data. Notably, through Field-Programmable Gate Array (FPGA) across varying data transmission speeds of 1MHz, 5MHz, and 10MHz, inference accuracy rates of 97.32%, 96.25%, and 94.50% were respectively achieved, demonstrating the robustness and versatility of the proposed paradigm.

With the application of freeform surface, beam shaping can achieve greater flexibility and precision. Ray mapping is an efficient geometric method for freeform surface design. However, the mapping may not always be integrable, which will result in actual performance falling short of expectations. Additionally, this method often relies on fitting the surface through the calculated coordinates of discrete points, and the fitting accuracy can also affect actual performance. In this study, adaptive weighted particle swarm optimization (AWPSO) is employed to optimize freeform polynomial coefficients to improve beam shaping performance. The initial freeform structure is obtained by non-integrable ray mapping method and fitted into a surface polynomial. Then, the process of optical design is transformed into a multi-dimensional optimization problem within mathematical models. Therefore, performance improvements do not depend on time-consuming ray tracing. A challenging beam shaping example of circle to regular hexagon is given to prove the effectiveness of the method. The results show a significant improvement in the uniformity of the ray spot on the target surface, with the contour becoming sharper and smoother after optimization. From the numerical results, the potential of this method is shown to be used in more irregular beam shaping conditions.

The Chromatic Confocal Displacement Sensor, with its capacity to avoid damage to the measured surface and achieve high measurement accuracy, has been widely used in many fields such as advanced manufacturing, biomedical, aerospace, and more. The dispersive objective lens is a core component of the chromatic confocal sensor, with its optical properties directly determining the system's measurement performance. To achieve real-time dynamic error separation in dynamic measurement scenarios and ensure high-precision measurement, a dual-channel common optical path structure is proposed. In dual-channel mode, the paths of the two measurement points are the same, and the information obtained about the object is consistent, with only the relative phase delay related to the distance from the two measurement points. By subtracting the two sets of data and fitting the error, real-time dynamic error can be obtained. Using ZEMAX optical design software, a linear dispersive objective lens composed of eight full-sphere lenses was designed. The design results indicate that the system operates in the wavelength range of 500-800nm, with the image numerical aperture greater than 0.68, a working distance greater than 7mm, and axial dispersion exceeding 100μm. Using the least squares method, linear regression calculations were performed on the dispersion-wavelength linearity, yielding a linear determination coefficient R2=0.9989, indicating an excellent linear relationship.

Freeform surfaces offer more degrees of freedom (DOF) in off-axis optical system design, showing its advantages in achieving compact systems and improving system performance. Various types of freeform descriptions have been put forward and have shown their effectiveness in optical design. However, conventional surfaces focus on mathematics and their function is limited to ray tracing. In this study, we propose a novel description method for optical surfaces, where the surface contains the mathematic core and a surface manipulation encirclement, and its key ray tracing results is dynamically updated as surface coefficients. With its two-level construction, the DOF in surface representation can be extended, and with the self-updating capability, pseudo-paraxial ray tracing data can be obtained and even controlled in the optimization process. The description is fulfilled with user-defined surface type and is compatible with commercial lens design software. Two design examples are introduced, and the design results reveal that the flexibility and DOF of the proposed surface can facilitate the design process.

This study focuses on the light scattering characteristics of two-dimensional chiral photonic crystals. We have conducted an in-depth investigation into the structural features and optical properties of two-dimensional chiral photonic crystals, particularly their scattering behavior towards light. Through a combination of experimental preparation and theoretical simulation, we have analyzed in detail the scattering characteristics of two-dimensional chiral photonic crystals under different wavelengths and incident angles. The results indicate that due to the unique chiral structure of two-dimensional chiral photonic crystals, they exhibit significant anisotropy and optical rotation in light scattering, which provides new ideas for the design and optimization of photonic devices. Furthermore, we have explored the potential applications of two-dimensional chiral photonic crystals in optical communication, optical sensing, and other fields, laying a foundation for the future development of optoelectronics technology.

We design and demonstrate a high-order mode (HOM) convertor based on asymmetric dual-core fiber (ADCF) with high coupling efficiency, wide bandwidth and high stability. The two ends of the ADCF are fused with single-mode fiber and few-mode fiber respectively. A periodic power transfer in the ADCF, thereby achieving direct mode conversion from the fundamental mode to HOMs (LP₁₁, LP₂₁, LP₀₂). Taking the ADCF with a small core diameter of 8 μm as an example, the operating bandwidth (coupling efficiency in excess of 95% (LP₁₁) and 90% (LP₂₁, LP₀₂)) is 202nm, 54nm, and 60nm, respectively.

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 this paper, a whole general design and optimization process is detailedly demonstrated by taking the design and optimization of a 55mm diameter variable curvature mirror(VCM) with a cycloid-like thickness distribution as example. The finite-element analysis to the VCM under each change of main structure parameter is done and analyzed to choose the proper parameter value of each structure to obtain the optimum surface figure accuracy. Finally, the designed VCM can achieve 0.386mm central deflection and RMS 82.84nm within the effective aperture 28.4mm.

The hybrid refractive-diffractive optics system exhibits strong capabilities in achromatic and non-thermalized design, as well as information encoding. This paper introduces an innovative end-to-end design scheme for refractive-diffractive hybrid imaging optical systems, which optimizes both optical and neural network parameters simultaneously. An all-ray differentiable ray-tracing model is proposed to integrate lens and diffractive optical elements into a unified design framework, thereby maintaining precision by avoiding wave-to-ray conversion losses. The neural network is constructed based on the imaging characteristics of infrared hybrid optical systems and enhances aberration correction. The proposed method is applied to the design of a single-lens short-wave infrared imaging system, outperforming traditional discrete designs and demonstrating significant potential for infrared optical system applications.

Commercial EUV lithography projection systems are designed with six-mirror, using high order aspherical surfaces or freeform surfaces, which require high processing and inspection requirements. When designing the initial structure of the projection system, it is important to consider the balance between the system's aberration and the difficulty of processing and manufacturing. EUV lithography optical systems minimize the number of mirrors in order to improve light energy utilization. Freeform surfaces or aspherical surfaces are used to provide more degrees of freedom for optimization. For a 6-mirror projection system, there are several ways for group design. There are 2-4, 3-3 and 4-2 combinations when divided into two groups, or into 2-2-2 triple groups. According to the design parameters of the EUV lithography projection optical system, the initial structure obtained by different group methods is analyzed. And choose more reasonable initial structure for further optimization.

Using micro-structure components in the spectacle lens has enabled myopia progression control in children and teenagers. However, the optical design of these spectacle lenses has never been discussed, leading to a lack of correct understanding of the underlying optical treatment principle. In this work, the array-patterned hexagonal lenslets with two opposite addition power designs were proposed to construct the lenslet-array-integrated (LARI) spectacle lens developed for an ongoing randomized controlled clinical trial and to support the optical approach to myopia control via image blurry. We found that the phase modulation induced by the micro-structures of the lenslet array contributes to the increase of RMS wavefront aberrations, leading to the image blurry, further inspiring the novel array-patterned microstructure design with high-order phase elements (HOPE). The optical performance of both LARI and HOPE spectacle lenses was investigated by simulation and experiment.

Current mainstream phase retrieval research is only applicable to monochromatic light wavelengths and relies on experimental devices such as narrowband filters. Especially when there is high noise or frequent reflections in the system, narrowband wavelengths may cause poor signal-to-noise ratio and unexpected artifacts, thereby reducing measurement accuracy. Therefore, phase retrieval with broadband sources has received widespread attention. In this paper, we proposed a fast broadband phase retrieval model based on Zernike coefficient matrix. Firstly, a coefficient matrix was established to represent the relationship between various Zernike coefficients at different wavelengths. In addition, we have utilized time division multiplexing technology to achieve a diffraction free iterative process, greatly improving computational efficiency. The numerical simulations are carried out to verify the effectiveness of broadband phase retrieval model.

Multi-aperture optical systems provide a solution that can enhance resolution without the requirement for a large-diameter single-aperture system. However, one of the challenges of multi-aperture optical systems is the detection of the piston. The phase diversity (PD) technique can detect non-continuous co-phase errors and is often used for the detection of multi-aperture piston. The PD technique estimates the wavefront aberration of the optical imaging system and the target image by acquiring an image of the focal plane of an unknown target passing through the optical system and one or more images of known aberration (often chosen to be defocused). The PD technique is usually converted to a nonlinear optimization problem, but the optimization process may fall into local minima due to 2π piston ambiguity. Such a 2π piston ambiguity problem can be solved by using broadband light with multiple wavelengths. In this paper, a multi-wavelength phase diversity technique based on optimized grid search is used, which improves the detection range so that the piston and the final evaluation function values will be more likely to be within the correct range, and improves the solution success rate compared to the unoptimized grid search method.

Wavefront aberration is a crucial metric for evaluating the imaging quality of an optical system and enhancing the accuracy of wavefront detection is of significant importance. Noise is a critical factor that affects detection accuracy. Simulating and suppressing noise can help explore the theoretical limit of wavefront detection and improve the actual measurement accuracy. We develop a comprehensive noise model where the input is a simulated, noise-free image in units of photons, and the output is a noisy digital signal. The model considers external disturbance noise, speckle noise, and camera noise. Speckle noise is selectively added based on the light source’s coherence. Camera noise is modeled using real camera parameters and includes photon shot noise, dark shot noise, readout noise, and quantization noise. Additionally, a noise suppression algorithm based on frame averaging is designed. We introduce the concept of a noise suppression factor, calculate this factor based on the noise characteristics and system properties, and apply it to the frame-averaged noisy image on a pixel-by-pixel basis, achieving effective noise reduction. Using the established noise model, we calculate the theoretical peak-to-valley (PV) and root mean square (RMS) limit determined by noise for two typical high-precision wavefront aberration detection systems: the Ronchi lateral shearing interferometry (LSI) system and the phase-diverse phase retrieval (PDPR) system. With our proposed noise suppression algorithm, the theoretical RMS limit can be reduced to 10% of the previous value, demonstrating its effectiveness in noise suppression. Our model provides a definitive standard for the theoretical accuracy limit of optical metrology, guiding the selection of hardware and the design of wavefront detection algorithms for subsequent research.

Specially designed backlight systems can cast information from display screen to designated zone. Here we introduce an ultra-thin multi-directional backlight system. The main components of the system include microlens arrays, a Fresnel lens and a high-brightness liquid crystal display (LCD) panel. The proposed backlight system allows us to control the light propagation in a desired manner, and could be applied to three dimensional (3D) display.

High-precision wavefront measurement is a crucial technology in lithography systems. Ronchi lateral-shearing interferometry (LSI) has exhibited significant potential in wavefront measurement of the projection lenses in lithography systems due to its advantages of a common optical path, null testing, and reference-free interference. A conventional Ronchi interferometer applies two orthogonal Ronchi gratings sequentially as beam-splitting elements to obtain shear information in two directions. However, system errors from grating switching and higher-order parasitic diffraction complicate the accurate calculation of the wavefront under test. This paper proposes an LSI based on the sinusoidal amplitude grating. By altering the system's coherent modulation function, only the 0th and ±1st orders interfere, avoiding the effects of irrelevant diffraction orders. We establish an interference model of this novel LSI using scalar diffraction theory and used a combination of uniform phase shift and least squares to reconstruct the wavefront with high accuracy. This work simplifies the operating principle of Ronchi LSI, theoretically eliminating error sources such as higher-order parasitic diffraction and even-order harmonic diffraction, providing more possibilities for structural improvements in Ronchi LSI.

Extreme ultraviolet lithography uses a light source with a wavelength of about 10nm-14 nm for illumination, and almost all known optical materials have strong absorption in this band. Therefore, the extreme ultraviolet lithography optical systems used reflective design, the reflective optical elements need to be coated with multilayers film to improve reflectivity. The choice of multilayers material and thickness of reflective optics is a key factor affecting their reflectivity in this wavelength bands. Currently, Mo/Si multilayer thin-film reflectors are used in extreme ultraviolet lithography optical systems. And in the 10nm-20nm band, Nb/Si multilayer films can also be used. In this research, the influence of factors including incident angle, operating wavelength, and film thickness on the corresponding reflectance of two multilayer reflective film structures is analyzed through mathematical modeling using Mathcad.

This paper discusses adapting the Gerchberg-Saxton algorithm to design refractive free-form optical elements for custom beam tailoring, particularly to convert powerful diode laser outputs into high-quality Gaussian beams. A distinctive feature of the algorithm is its ability to design thin-profile optical elements (less than 5 wavelengths), manufacturable with high precision using industrial grayscale lithography. Experimental results are presented for transforming a 455 nm, 6 W diode laser beam into an efficient pump source for Ti:Sa lasers, demonstrating the algorithm’s potential to enhance diode laser applications in scientific and industrial settings.

The camera is an important part of the optical telescope observing system, and the performance of the camera is an important factor affecting the quality and efficiency of astronomical observations. EMCCD can achieve lower noise and higher detection sensitivity by charge multiplication techniques, and can be used to realize direct observations of very faint and weak targets, and relative to the traditional CCD/CMOS detectors, the noise level can be reduced by an order of magnitude to reach the Sub-electron level. However, facing the need for calibration of ultra-low noise at the sub-electron level, it is difficult to satisfy the currently available equipment and methods. Therefore, the study of EMCCD readout noise calibration method under high gain is of great significance for the theoretical study of EMCCD and the design of low-noise electronics. In this paper, we propose a calibration system of "cascaded integrating sphere + parallel light pipe" local illumination in dark room environment, through which we can obtain the light source under ultra-low brightness, which solves the problem of difficult to obtain the point light source, and the method of local illumination can avoid the fatigue attenuation problem under the high-fold gain, and we also refine the noise model, and propose a "gain-noise" model, which can be used to calibrate the EMCCD readout noise. The noise model is refined and the "gain-noise" fitting method is proposed, and finally the readout noise test at high gain achieves a noise calibration result of about 0.8e@600x.

The separation of transmitting and receiving means that the optical axes of the receiving and transmitting optical systems are not coaxial. It has the advantages of simple installation and adjustment, no stray light interference in the shared optical path, etc., which can effectively reduce the measurement error. Combined with the application of cooperative target, the relative measurement accuracy between two spacecraft can be effectively improved. In this paper, a design scheme of separated vision measurement system between receiving system and transmitting system based on cooperative target is proposed. Through the analysis of entrance pupil constraint, diffuse influence and imaging optical path, the structural layout of cooperative target and the parameters of visual measurement sensor are reasonably designed, so that the light spot reflected by cooperative target can be imaged completely and clearly in the receiving optical system.

In order to improve the accuracy of scanner measurement standard apparatus, a scanner measurement optimization method based on cluster analysis is proposed in the paper. The method firstly constructs a marker point layout with redundant information on the basis of the traditional scanner measurement of standard apparatus, and collects the measurement information of standard apparatus under this layout by a 3D laser scanner, and then optimizes the initial marker point layout by using a weight-based optimization strategy for the measurement results, and then performs the re-fitting of the length parameter of the standard apparatus under the optimized layout, and outputs the final standard apparatus measurement Finally, based on this optimization scheme, an experimental analysis of a 38.1 mm standard ball is carried out and compared with the CMM method with higher accuracy, which verifies that the optimized layout has an important impact on improving the measurement accuracy of the standard ball. The optimization method provides a new calibration scheme for realizing the quantity and value traceability of high-precision large-size 3D laser scanner, which is of good practicality and certain guiding significance.

This article presents a high-precision algorithm for extracting laser centroids using a four-quadrant detector (4QD), specifically designed for situations where laser position shifts happen on the nanoscale. The algorithm uses an iterative method to create a functional relationship between position changes and the differential output signals from the 4QD. We have validated the algorithm through simulations and experimental tests.

A systematic study of sub-10 femtosecond pulse laser induced damage threshold (LIDT) determination was performed for the metal mirrors, (i.e. silver mirrors, aluminum mirrors, and aurum mirrors, etc.) with different thickness of protective layers. The damage morphology of metal mirrors with different thickness protective films at fluences below the single-pulse LIDT was studied to investigate the mechanisms leading to the onset of damage. The study found that the increase in the thickness of a single protective layer has little effect on the initial location of damage, and the use of a protective layer does not necessarily increase the damage threshold of a metal mirror. The damage threshold of the metal mirror is affected by the competition between the electric field in the protective layer and the material band gap and the degree of integration of the electric field with the metal-dielectric interface. However, the metal film without additional treatment has a lower degree of integration at the metal-dielectric interface and is more susceptible to damage. Therefore, even if the thickness change of the protective layer affects the peak intensity of the electric field in the protective layer, the degree of bonding at the metal-dielectric interface is still the decisive factor in the damage threshold of the metaldielectric film. This work is helpful to find new technologies to improve the damage threshold of metal mirrors used in ultrafast high-power laser systems.

To ensure stable output of the 780 nm band laser with a large splitting ratio, a high splitting ratio depolarizing beam splitter was designed and fabricated in this paper. Initially, the double-sided depolarizing film system was designed and simulated. Subsequently, the sample was fabricated using ion beam assisted deposition. The film structure of the sample was analyzed using a TEM, and its transmittance spectrum was measured with a spectrophotometer. The spectral results showed that in the working band wider than 60 nm, the transmittance of the beam splitter was close to 98%, and the transmittance deviation is less than 0.3%. Finally, experiments were conducted to evaluate the performance of the beam splitter. The depolarizing beam splitter presented in this paper demonstrates excellent depolarization performance and is suitable for direct application in precision measurement fields such as optical test metrology and quantum sensing detection.

High-precision optical path alignment is essential in modern optical systems, especially for high-resolution imaging and precision measurement. Misalignment of the image plane can lead to image distortion, adversely affecting overall image quality. Recent research has focused on algorithmic approaches for image tilt correction, but this paper proposes a Bidirectional Rotational Symmetry Correction (BRSC) method that combines mechanical adjustment with a contour detection algorithm for effective image plane tilt correction. The mechanical adjustment process involves bidirectional symmetry rotation of the image plane to achieve precise alignment. The edge contour detection algorithm enhances image processing by fitting an elliptical contour around detected features, enabling precise measurement of the contours. Experimental validation using a point diffraction interferometer (PDI) demonstrates the effectiveness of the proposed BRSC method in correcting image plane tilt.

With the development of display technology, augmented reality (AR) devices have a wide range of application scenarios in many fields. The optical performance, volume and cost of the device are the main factors restricting the development of AR technology. As a traditional structure for optical combiner, birdbath faces challenges in achieving both a large field of view (FoV) and a lightweight, compact design. In this study, we introduce a novel off-axis configuration by replacing the polarized beam splitter (PBS) with a freeform holographic optical element (HOE). The system achieves a 46° FoV with a total thickness of 8.42mm, representing a 17.5% reduction in size compared to conventional PBS-based structures. Due to the wavefront manipulation by uniquely designed HOE, this approach significantly reduces system volume while maintaining high imaging performance. The proposed system holds potential for future AR applications where compactness, lightweight structures, and image quality are important factors.

This paper introduces an optimized mini-LED backlight local dimming algorithm. The proposed algorithm leverages grayscale dispersion degree to establish the grayscale distribution interval within each backlight partition. Subsequently, the actual grayscale of all backlight partitions is determined using the root mean square formula. This approach enables the accurate restoration of the overall grayscale distribution characteristics across natural image types. A 55-inch LCD prototype with 2304 mini-LED backlight partitions is developed to implement the proposed algorithm alongside traditional local dimming algorithms.