Optical Design Software Research Articles

Improving neural-network-based prediction models for misalignment in off-axis three-mirror anastigmat telescopes

The performance of a telescope system heavily relies on the precise alignment of the mirrors. The off-axis three-mirror anastigmat (TMA) telescope presents unique challenges due to its complex optical design. Each optical element within the off-axis TMA telescope is inherently introduced with theoretical eccentricity and tilt. Furthermore, the incorporation of freeform surfaces and other optical elements with intricate surface features typically leads to low initial alignment accuracy of the optical path. With this low initial alignment accuracy and the noise of the measurements, the prediction of the misalignment of the telescope is getting harder. A fully connected neural network architecture is proposed as a misalignment calculation method for an off-axis TMA telescope system with a freeform surface. Random training data is created by using optical design software. The sensitivity of the mirrors to the wavefront error is quantified and incorporated into the loss function of the neural network to improve prediction accuracy. Adding the noisy measurement samples to the training data creates a noise-immune neural network model. Simulation results show that our model can successfully predict misalignment of the mirrors with noisy measurement values.

Comparative Study on the Interest in Non-Uniform Rational B-Splines Representation versus Polynomial Surface Description in a Freeform Three-Mirror Anastigmat

Novel freeform optical design methods can be classified in two categories, depending on whether they focus on the generation of a starting point or the development of new optimization tools. In this paper, we design a freeform three-mirror anastigmat (TMA) and compare different surface representations using either a differential ray tracer as a new optimization tool or a commercial ray tracer (ANSYS-ZEMAX OpticStudio). For differential ray tracing, we used FORMIDABLE (Freeform Optics Raytracer with Manufacturable Imaging Design cApaBiLitiEs), an optical design library with differential ray tracing and Non-Uniform Rational B-Splines (NURBS) optimization capabilities, available under the European Software Community License (ESCL). NURBS allow a freeform surface to be represented without needing any prior knowledge of the surface, such as the polynomial degree in polynomial descriptions. OpticStudio and other commercial optical design software are designed to optimize polynomial surfaces but are not well-suited to optimize NURBS surfaces, requiring a custom optical design library. In order to demonstrate the interest in using NURBS representation, we designed and independently optimized two freeform telescopes over different iteration cycles; with NURBS using FORMIDABLE or with XY polynomials using OpticStudio. We then compared the resulting systems using their root mean square field maps to assess the optimization quality of each surface representation. We also provided a full-system comparison, including mirror freeform departures. This study shows that NURBS can be a relevant alternative to XY polynomials for the freeform optimization of reflective three-mirror telescopes as it achieves more a uniform imaging quality in the field of view.

Switching in microseconds: design of a 5 × 5 non-blocking free space optical switch at 1550nm with a piezo-actuator and beam-steering lens system

Modern data center networks (DCNs) require optical switches with ultra-low loss, ultra-fast reconfiguration speed, high throughput, and high extinction ratio performances. In this work, we propose the design of a 5 × 5 optical switch at 1550 nm based on a piezo-actuator serving as a translating input optical source, and a beam-steering system built of spherical lenses to complete the switching behaviour. An ultra-fast actuator switching speed is estimated as 1.55 μs latency for a single connection with a demo circuit. We further simulate the beam-steering system end-to-end in a commercial optical design software CODE V and demonstrate a theoretical 2.16 dB insertion loss for a single connection in the switch at optimum alignment.

Tailored detection efficiency for linear variable filter-based sensors: applying simulation models of spectral characteristics in optical design

To accurately model the specific detection characteristics of spectral sensors based on linear variable filters (LVFs) within an optical design tool, it is essential to consider crucial position-variable spectral properties, such as peak transmittance, central wavelength, half width, or slope steepness. In this context, we propose a straightforward approach, integrating a dynamic link library (DLL) containing all position-dependent spectral properties of the LVF into a commercial optical design software. Exemplary investigations are conducted for an LVF with a detection range of 450–850 nm. For ease of use, the measured position-, wavelength-, and angle-dependent transmission properties of the LVF have been described through a simple yet highly accurate model system. Moreover, to highlight the essential value of this simulation for specific applications, an efficiency-enhancing spectral module is simulated, which is an LVF-mirror arrangement characterized by a multiple-reflected beam path. The introduced optical design tool demonstrates its particular strength by enabling the optimization of the highest detection efficiency for either the short- or long-wavelength range.

Optical modeling of systematic uncertainties in detector polarization angles for the Atacama Cosmology Telescope

We present an estimate of the Atacama Cosmology Telescope (ACT) detector polarization angle systematic uncertainty from optics perturbation analysis using polarization-sensitive ray tracing in CODE V optical design software. Uncertainties in polarization angle calibration in CMB measurements can limit constraints on cosmic birefringence and other cosmological parameters sensitive to polarization leakage. Our framework estimates the angle calibration systematic uncertainties from possible displacements in lens positions and orientations, and anti-reflection coating (ARC) thicknesses and refractive indices. With millimeter displacements in lens positions and percent-level perturbations in ARC thicknesses and indices from design, we find the total systematic uncertainty for three ACT detector arrays operating between 90 and 220 GHz to be at the 10th of degree scale. Reduced lens position and orientation uncertainties from physical measurements could lead to a reduction in the systematic uncertainty estimated with the framework presented here. This optical modeling may inform polarization angle systematic uncertainties for current and future microwave polarimeters, such as the CCAT Observatory, Simons Observatory, and CMB-S4.

A Novel Analytical Interpolation Approach for Determining the Locus of a Zoom Lens Optical System

In an optical system with multiple lens groups and increased zoom magnification levels, achieving a smooth zoom locus is increasingly difficult. Traditional methods for calculating zoom loci often involve complex and time-consuming formulas. Consequently, we utilized the Padé approximation in optical design software to compute the zoom locus analytically, irrespective of the number of zoom positions (nodes). The initial data were used to assign orders to rational function polynomials, facilitating Padé approximation. If the image surface extended beyond the depth of focus (DOF), a node was added, with adjustments made until it fell within the DOF range. Furthermore, Padé approximation was performed to prevent singularities. The loci of all lens groups in the optical system can be expressed in a rational function format. Specifically, the numerator and denominator polynomial degrees were 20° and 1°, respectively, with their sum being the total number of nodes. In addition, we calculated the zoom locus by increasing the numerator sequence to minimize the occurrence of the singularity and added the node automatically to enable zoom locus calculation in all optical systems. Accordingly, we could make fast calculations, unlike conventional methods, using complex and time-consuming simultaneous equations. Therefore, we could express the locus of the compensated group in the form of a smooth function, as presently shown.

Analysis of the impact of temperature on the spectral shift in ultraviolet hyperspectral imaging spectrometers.

The imaging spectrometer's high performance in practical applications may be compromised by environmental factors, particularly temperature variations, posing a challenge to its stability. Temperature fluctuations can induce spectral shift, directly impacting the accuracy of spectral measurements, subsequently influencing the precision of radiometric measurements. To address this issue, this study investigates a dual-channel UV imaging spectrometer. This instrument boasts a wavelength calibration accuracy of 0.01 nm. This paper conducts an in-depth analysis of the various mechanisms through which temperature changes influence the spectral line offset in the imaging spectrometer, integrating actual orbital temperature data to discuss the instrument's temperature load settings. The impact of temperature on spectral shift is examined using finite element analysis and optical design software. Estimations of spectral shift were made based on temperature variations. Simulation results indicated that the maximum deviation of spectral shift is estimated at 0.018 nm under a temperature condition of 16 ± 1°C. Under a more controlled orbital temperature condition (16 ± 0.3°C), the maximum deviation of spectral shift decreased to 0.01 nm. Experimental data revealed that at 16 ± 1°C, the maximum deviation of spectral shift did not exceed 0.01 nm. This effectively corroborates our theoretical analysis. The relationship between temperature and spectral shift offers a crucial theoretical foundation for calibrating spectral measurements and managing the thermal conditions of the instrument.

Semi-analytical finite ray-tracing through the quadratic symmetric GRIN lens.

The propagation of light within a gradient index (GRIN) media can be analyzed with the use of differential equations for a given non-homogenous refractive index profile. Numerical methods are often necessary to perform ray-tracing in GRIN media; however, analytical solutions exist for several types of GRIN lenses. In this paper, paraxial and non-paraxial differential equations are derived to calculate the ray path in a GRIN lens. It is shown that the paraxial equation has an analytical solution for a GRIN media with a quadratic profile within the paraxial region. The analytical solution can be obtained by using Legendre polynomials or by the Frobenius method involving a power series. Using the Legendre or Frobenius solution, one can calculate the refractive indices along the ray path. A new recursive relationship is proposed to map the trajectory of light at finite heights. To illustrate the finite ray-tracing method utilizing a non-paraxial differential equation, two lenses (with spherical and elliptical iso-indicial contours) are considered. The lenses' back focal distances, for rays entering the lenses at varying finite heights, are calculated. For each lens, its spherical aberration is estimated. The effective focal length and the shape of the principal surface are also obtained. The accuracy of the results is then compared to the numerical ray-tracing using an optical design software, Zemax OpticStudio. The predicted spherical aberration for the spherical lens differs from numerical ray-tracing by less than λ14 at the marginal zone, while the error for the effective focal length is less than λ100.

Off-the-shelf optical systems design enabled by an evolution strategy: front stop case

Commercial off-the-shelf optics enable economic and rapid solutions in the photonics industry and academia. However, the design of optical systems with off-the-shelf optics is a time-consuming task for experienced optical designers and hopeless for novice designers. In this paper, we propose an automatic optical design tool to generate optical systems using only off-the-shelf optical components without human assistance. Our solution is based on an evolution strategy (ES) that performs a discrete combinatorial optimization following optical design-based methodologies that satisfy user-defined specifications. Unlike the conventional methods, the algorithm decreases the design process time and provides optical designers with several optical solutions from where to choose and adapt for targeted applications. In this work, the ES is described and tested with front stop optical configurations. We demonstrate the broad solution domain of the algorithm through the generation of optical systems with F-numbers within a range F/1 to F/90 and field of views up to 300 mm at the image plane. To analyze the solution domain and the characteristics of the solution, we used the design specifications of 29 commercially available scan lenses and compared the performance of different ES parameters. The compatibility of our algorithm with (standard) commercially available optical design software unlocks automatic design tools for off-the-shelf optical systems.

Optimizing the Effectiveness of Magnetic Lenses by utilizing the Electron Optical Design (EOD) Software

This paper introduces a computational analysis that discusses an approach for optimal synthesis in the design of magnetic lenses, specifically focusing on the analytical method. A widely employed approach for magnetic lens design involves utilizing an analysis optimization procedure, which makes use of the finite element method and is supported by Munro programs. In this study, this approach has been employed to explore magnetic lenses using the Electron Optical Design (EOD) software. The study offers insights into the role of the air gap in magnetic lens design, highlighting its importance in optimizing objective and projector properties. The analysis reveals that variations in the air gap (S) significantly influence the performance of magnetic lenses. Decreasing the air gap when it is set to (3) leads to substantial improvements in objective optical properties and focal length. Conversely, increasing the air gap when it is set to (12) enlarges the half-width of the axial magnetic field while reducing the maximum magnetic field value. These findings underscore the importance of carefully optimizing the air gap to achieve desired lens performance. The focal length is determined using this input data and coefficients of aberration (spherical and chromatic) of the objective. The study focuses on the influence of a crucial geometric parameter, specifically the air gap (S), on both objective and projector properties. Its importance stems from its capability to pinpoint the suitable geometry for magnetic lenses, thereby facilitating their efficient application.

Design and Performance Analysis of Automobile Headlamp Based on Light-Emitting Diode

As a vital component of the automobile headlamp, its design is not only related to power loss but also affects the appearance of the automobile. Most importantly, its design directly affects the night lighting effect and driving safety. Compared with the traditional headlamp light source, light-emitting diode (LED) light source has the advantages of long lifespan, small size, fast response, flexible design, flexible control, and so on. Based on this, this study designs high-power white LED automobile headlamps, adopts the commonly used reflector design technology, and puts forward the design scheme of the lighting group system. This scheme relies on a reflector for light distribution, without needing a baffle or lens with light distribution patterns. The optical design software TracePro and the three-dimensional design software PROE are used to simulate and design the reflectors of low and high beams, respectively. The simulation results of the reflector of the low beam show that more than 490000 rays of light reach the filament shield, with a light utilization rate of over 95%. The horizontal cut-off line and 15° light and dark cut-off lines are clearly visible, and the front window material is closed. Considering this factor, the illumination distribution of the low beam meets relevant national regulations. The high beam reflector simulation results reveal that over 960000 light rays reach the filament shield, with a more than 95% light utilization rate. The light spot is symmetrical. If the front window material is polycarbonate and not coated, the absorption and scattering of light are ignored, and the transmittance of the beam through the two optical surfaces achieves 90%.

Method for algebraic calculation of initial design parameters of a two-element telecentric f-theta lens.

A method for the algebraic calculation of paraxial design parameters of a telecentric f-theta lens is described. Moreover, a third-order aberration analysis is performed for a telecentric f-theta lens composed of two optical elements. The method can be used to calculate the starting optical design of telecentric f-theta lenses, which can be used, for example, in laser material processing, optical imaging systems, and optical metrology. The initial design parameters then can be used for further optimization in optical design software.

Automatic Method of Exploring the Landscape of Freeform Dioptric Optical Problems, Working in the Infrared Region

We present an automated method of finding different freeform dioptric starting systems, working in the infrared region, for further optimization in commercial optical design software. Our developed method couples the simultaneous multiple surface (SMS) method, introduced by Benítez and Miñano, with automatic optimization in Zemax OpticStudio. The method allows an optical designer to explore the merit function (MF) landscape of freeform optical problems. In this article, we apply our method to a size, weight, and power (SWaP) problem, and we compare our designed system with a system found in the literature that has the same aperture of F/1.2. Then, we increase the aperture of the system up to F/0.9, taking advantage of the use of freeform surfaces.

Beam shaping for two-dimensional laser array by a computational model

The application of two-dimensional array laser source is more and more popular. Currently, many methods have been proposed for the collimation of laser beams; however, there is still a lack of research for the collimation of array laser sources so far. This paper presents a collimating method for array laser source. Through the calculation of the lens surfaces, the shape of the illumination spot on the target can be directly controlled, and the diameter of the lens can be directly constrained by setting the initial point coordinates. In this method, the edge-ray principle is used to simplify the extended light source model. The size and intensity distribution of the light spot irradiated by the light source to the target position were simulated by establishing a ray tracing model. The whole process was calculated using MATLAB software. The corresponding lens model can be obtained by fitting discrete coordinate points using Solid Works. Finally, the optical design software ZEMAX is used for simulation test. After shaping the laser light source with a luminous diameter of 1 mm, a circular and uniform spot is obtained at 100 m. For the point light source model, the divergence angle of 0.28° is achieved. Furthermore, an annular spot is also realized by setting the laser irradiation range, which provide a new solution for customized laser lighting.

Advances in CODE V design in terahertz imaging system

The band of terahertz (THz) spans from microwave to infrared bands, which belongs to the transition band from macro-electronics to micro-photonics, possessing peculiarities different from electromagnetic waves in other bands. THz technology with the characteristics of high penetration, broadband, high resolution and transient are employed in various fields, such as space remote sensing, nondestructive detection biomedical imaging and near-field microscopy. These broad applications, in turn, provide incentive to further improve the basic performance of THz technology. Aiming at the application of terahertz technology in the imaging field, this novel mainly discussed the basic principle, key devices, system composition, technical advantages and future development trend of terahertz imaging system. The application status of CODE V optical design software in designing scanning lens systems for terahertz imaging, such as free-form surfaces, non-free surfaces and multi-lens groups are further discussed in this paper.

Freeform mirror validation by interferometric techniques using a spatial light modulator

The most widespread verification method for optical elements is interferometry but, in the case of freeform surfaces, a strong deviation of the slope along the surface can create areas in which the fringe density is too high for the interferometer to resolve them. The most desirable solution is to create a null or near null interferogram introducing compensating elements like a spatial light modulator (SLM) that provides the flexibility to accommodate the measurement of a wide range of free-form surfaces. This paper shows the process for a convex freeform mirror metrology. The method consists of inserting the SLM in the optical path to compensate the freeform component of the surface to be verified and to generate a null of aberrations in the interferometer. The system is previously modelled in an optical design software to calculate the required phase to be introduced in the SLM to generate the null. The arrangement of the SLM makes possible to keep its position fixed and use the same setup to measure a wide range of freeform surfaces, limited by the dynamic range of the SLM. For each specific surface, it is necessary to introduce suitable elements to compensate the base surface, reserving the SLM for the freeform component compensation. The method is illustrated with the verification of a convex freeform mirror whose freeform component is described by the astigmatism Zernike polynomial Z5.

Algebraic ray trace analysis of spatial heterodyne spectrometers.

Algebraic ray traces of various configurations of spatial heterodyne spectrometers are developed to derive general, approximate, formulas for resolving the power, fringe localization plane, and admissible off-axis angle for each configuration. Michelson, all-reflective, and field-widened configurations are considered separately. The derived formulas for each configuration are tested against exact numerical ray traces using optical design software and in general found to be in good agreement.

Extreme Refractive-, Diffractive- and Hybrid-Hyperchromats: Minimizing the Equivalent Abbe Number of a Two-Lens System

This work provides a comprehensive analysis of the maximum chromatic axial split of two-element hyperchromats, with the distance between the two lenses being a key variable. Purely refractive and diffractive systems are considered, as well as hybrid layouts combining refractive and diffractive elements. In order to achieve extreme chromatic axial splitting and accordingly a minimum equivalent Abbe number for lens combinations, a three-step procedure was used. In the first paraxial step, purely optical quantities such as focal lengths of the lenses, inter-lens distances and dispersion properties of the lenses were investigated. In the second step, which also takes place in the paraxial domain, additional geometric boundary conditions such as the radii, diameters and thicknesses of the lenses are taken into account. The results of this step serve as an input for the final optimization using optical design software, which derives practical solutions for minimum equivalent Abbe numbers with diffraction-limited image quality. As a significant result, the comparison with directly cemented lens doublets shows that the introduction of a distance between the elements allows for a much stronger chromatic decomposition for refractive, diffractive and also hybrid combinations. Quantitatively, the minimum equivalent Abbe number for refractive systems is reduced from 2.5 (without spacing) to 1.79 (with spacing). For hybrid combinations, a corresponding reduction from 0.4 to 0.29 is achieved.

Development of a flat conical chamber-based non-dispersive infrared CO2 gas sensor with temperature compensation.

In order to accurately monitor CO2 concentration based on the non-dispersive infrared technique, a novel flat conical chamber CO2 gas sensor is proposed and investigated by simulation analysis and experimental verification. First, the optical design software and computational fluid dynamics method are utilized to theoretically investigate the relationship between the energy distribution, absorption efficiency of infrared radiation, and chamber size. The simulation results show that the chamber length has an optimal value of 8cm when the cone angle is 5° and the diameter of the detection surface is 1cm, which makes infrared absorption efficiency optimal. Then, the flat conical chamber CO2 gas sensor system is developed, calibrated, and tested. The experimental results indicate that the sensor can accurately detect CO2 gas concentrations in the range of 0-2000 ppm at 25 °C. It is found that the absolute error of calibration is within 10 ppm, and the maximum repeatability and stability errors are 5.5 and 3.5%, respectively. Finally, the genetic neural network algorithm is presented to compensate for the output concentration of the sensor to solve the problem of temperature drift. Experimental results demonstrate that the relative error of the compensated CO2 concentration is varied from -0.85 to 2.32%, which is significantly reduced. The study has reference significance for the structural optimization of the infrared CO2 gas sensor and the improvement of the measurement accuracy.

Method of initial design of a two-element double-sided telecentric optical system.

An algebraic method for finding fundamental parameters of a starting design of a two-element double-sided telecentric lens is introduced in this work. The telecentric lens is formed by two objectives composed of an afocal meniscus lens followed by a cemented doublet. It is used the third-order aberration theory to find the fundamental parameters of the starting configuration of a given optical system. The method gives results which make possible to obtain a good initial design of such a telecentric lens for further optimization using optical design software. The proposed method is presented on an example of finding initial design parameters of the double-sided telecentric lens.