Off-axis System Research Articles

Off-axis freeform optical design for large curved field of view imaging

Recording neuron activities is pivotal for elucidating the functionality of the nervous system. However, the curved cortex surface of experimental mice presents a significant challenge for optical systems, particularly when a larger field of view (FOV) is required. To address this challenge, we have designed an off-axis three-mirror system that incorporates freeform surfaces on both the primary and secondary mirrors. This system achieves a large imaging FOV of 18°×9°, delivering near-diffraction-limit imaging quality across a curvature spectrum of −14.7 to −15.3mm. A manufacturability analysis indicates that the freeform surfaces are straightforward to produce, and the overall system demonstrates low sensitivity to tolerance and measurement errors. This study introduces a novel, to the best of our knowledge, solution to the field curvature constraints in optical imaging of cortical activity, providing substantial technical support for in vivo neuronal imaging endeavors.

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.

Desensitization design method of an off-axis three-mirror anastigmatic optical system based on the nodal aberration theory

A design method for an off-axis three-mirror anastigmatic optical system with low misalignment sensitivity is proposed. Based on the transformed pupil coordinate and nodal aberration theory, the analytical expressions between the optical parameters and misalignments are derived and an as-built performance evaluation model is established. The effects of mirror spacings and the off-axis magnitude value on the misalignment sensitivity are analyzed. With the desensitization design method proposed in this paper, a low-sensitivity off-axis TMA optical system can be designed. The simulation experiments show that, the misalignment sensitivity of the off-axis TMA optical system obtained by our method is approximately 60% that of the system obtained by nominal performance optimization method, and the as-built performance is about 1.49∼1.54 times that of the nominal performance optimization method.

Local slope tolerance model for optical surfaces with distortion as the evaluation criterion

Ultra-precision imaging systems support cutting-edge scientific exploration and technological innovation. The continuous development of optical freeform and aspheric surface technology offers new possibilities for high-performance optical systems but also presents significant manufacturing challenges. In this paper, we derive and discuss in detail the impact of surface manufacturing errors on the image point positions of optical systems. The analysis reveals that among the manufacturing errors, the surface slope error is the primary factor driving positional changes in image points. Based on these insights, a local slope tolerance model using distortion as the evaluation criterion is proposed. This model specifies the slope error requirements at each point on the surface, ensuring the optical system's distortion meets the acceptable threshold during manufacturing. The model’s effectiveness is validated through an off-axis three-mirror freeform optical system and a Cassegrain aspheric optical system.

Optimizing algorithm for high-precision imaging stitching systems based on spline surfaces

As optical systems continue to advance, non-uniform rational B-spline (NURBS) surfaces increasingly being considered in asymmetric optical systems due to their localized control characteristics. However, the representation of NURBS surfaces has complicated the analysis of these systems, leading to a significant computational burden. To address this challenge, we propose an optimizing algorithm for imaging optical systems based on high-precision ray tracing of NURBS surfaces. This method initiates with getting a knot grid as prior information, in conjunction with the Newton-Raphson algorithm, to obtain high-precision numerical solutions for the intersection of rays with a NURBS surface. Building upon this methodology, we introduce an optimization technique that includes shape evaluation to generate an evaluation function specific to NURBS surfaces. This approach is then applied within a rapid optimization process that accounted for the region of ray influence. Under consistent control point grids and sampling ray conditions, we present an off-axis four-mirror system to showcase that our algorithm has achieved a computational efficiency improvement of approximately 14 times compared to the previous method. This high-precision imaging design based on spline surfaces fulfills the need for efficient and accurate algorithms for NURBS surface applications in various imaging systems, providing guidance for practical applications.

Design of off-axis reflective dual-channel zoom freeform optical systems

In this work, two off-axis reflective dual-channel zoom optical systems are conceived and designed. These two systems achieve good imaging quality and compact system volume by introducing freeform surfaces. Firstly, the system models of the off-axis reflective dual-channel zoom optical systems are introduced, and the first-order analysis is carried out. Then, a design method of an off-axis reflective dual-channel zoom freeform optical system is introduced, and two examples are designed using this method. In one example, the two channels have a separate primary mirror and share a secondary mirror and a third mirror. The system achieves a zoom ratio of 2 times. The two different channels of the other system have separate third mirror and share the primary mirror and the secondary mirror. The system achieves a zoom ratio of 4 times. The two systems have good imaging performance close to the diffraction limit in the visible light band. Finally, the proposed off-axis reflective dual-channel zoom freeform optical system is analyzed and discussed.

Plane mirror-optical path coupling noise in telescope off-axis system dimensional stability measurement

The dimensional stability of the off-axis optical system affects its optical performance significantly and may even lead to its failure. Here, we report a heterodyne interferometry technology to measure the telescope’s dimensional stability. In this method, the standard plane mirror, which reflects the measurement laser, is a critical structural component. Additionally, it is one of the primary sources of the noise. The study focuses on the impact of the standard plane mirror’s positional misalignment instability on optical path noise. A mathematical model was established to depict the effects of mirror misalignment instability on the optical path, and experiments were conducted to decouple the noise. The results of the experiment show that the standard plane mirror introduces approximately 1nm/Hz1/2 at 10 mHz of optical path noise into the off-axis system, and the dimensional stability of the off-axis system is about 6.23nm/Hz1/2 at 10 mHz.

Design method for zoom systems based on magnification ratio modulation of afocal off-axis three-mirror anastigmat systems

Design method for zoom systems based on magnification ratio modulation of afocal off-axis three-mirror anastigmat systems

Design and on-orbit performance evaluation of Ethiopian earth observation satellite multispectral optical imaging payload

The Ethiopian Earth observation micro-satellite was successfully launched into a sun-synchronous orbit equipped with an optical multispectral imaging payload system. This optical multispectral imaging payload camera weighs 1.4 kg with four spectral bands: RGB and NIR, each having a unique spectral range. Furthermore, it has a field of view of 7.4°×0.3°, a relative F-number of 9.8°, and a spectral range of 0.45∼0.9μm. The present article covers the design and on-orbit performance analysis of the ETRSS-1 electro-optical imaging payload system, which is based on the COTS compact and unobscured off-axis three-mirror anastigmatic system for high-resolution imaging. Additionally, selecting an appropriate imaging sensor, optomechanical architecture, and performance characteristics for optical instruments is investigated to evaluate spatial, spectral, and radiometric requirements and the payload’s on-orbit performance and capability.

Off-Axis Integral Cavity Carbon Dioxide Gas Sensor Based on Machine-Learning-Based Optimization.

Accurately detecting atmospheric carbon dioxide is a vital part of responding to the global greenhouse effect. Conventional off-axis integral cavity detection systems are computationally intensive and susceptible to environmental factors. This study deploys an Extreme Learning Machine model incorporating a cascaded integrator comb (CIC) filter into the off-axis integrating cavity. It is shown that appropriate parameters can effectively improve the performance of the instrument in terms of lower detection limit, accuracy, and root mean square deviation. The proposed method is incorporated successfully into a monitoring station situated near an industrial area for detecting atmospheric carbon dioxide (CO2) concentration daily.

Multiphysics Coupling Simulation of Off-Axis Integrated Cavity Optical Sensing System

The optical properties of an off-axis integrated cavity system are influenced by both structural deformation and thermal deformation. In this paper, the finite element simulation and analysis software COMSOL multiphysics was used to numerically simulate the optical system. By coupling geometric optics, solid mechanics, and solid heat transfer and conducting parametric temperature scanning, a multiphysics simulation of the off-axis integrated cavity optical sensing system was achieved. The effects of different temperature conditions on the stress field, displacement field, and optical mirrors were analyzed, and changes in optical properties were assessed using ray trajectories and point diagrams. Additionally, optical simulation software was used to simulate and optimize the experimental optical path, obtaining the distribution of light spots on the detector surface. This provides a theoretical basis for the subsequent optimization of the off-axis integrated cavity optical system.

On the Association of GW190425 with Its Potential Electromagnetic Counterpart FRB 20190425A

Recent work by Moroianu et al. has suggested that the binary neutron star (BNS) merger GW190425 might have a potential fast radio burst (FRB) counterpart association, FRB20190425A, at the 2.8σ level of confidence with a likely host galaxy association, namely UGC10667. The authors argue that the observations are consistent with a long-lived hypermassive neutron star (HMNS) that formed promptly after the BNS merger and was stable for approximately 2.5 hr before promptly collapsing into a black hole. Recently, Bhardwaj et al. conclusively associated FRB20190425A with UGC10667, potentially providing a direct host galaxy candidate for GW190425. In this work, we examine the multimessenger association based on the spacetime localization overlaps between GW190425 and the FRB host galaxy UGC10667 and find that the odds for a coincident association are O(5) . We validate this estimate by using a Gaussian process density estimator. Assuming that the association is indeed real, we then perform Bayesian parameter estimation on GW190425 assuming that the BNS event took place in UGC10667. We find that the viewing angle of GW190425 excludes an on-axis system at p(θ v > 30°) ≈ 99.99%, highly favoring an off-axis system similar to GRB 170817A. We also find a slightly higher source frame total mass for the binary, namely, mtotal=3.42−0.11+0.34M⊙ , leading to an increase in the probability of prompt collapse into a black hole and therefore disfavors the long-lived HMNS formation scenario. Given our findings, we conclude that the association between GW190425 and FRB20190425A is disfavoured by current state-of-the-art gravitational-wave analyses.

Speckle noise suppression of a reconstructed image in digital holography based on the BM3D improved convolutional neural network

In digital holographic measurement, when light waves pass through inhomogeneous media or surfaces, speckle noise is generated, resulting in random, granular light and dark spots in the hologram, which greatly reduces the image quality. Therefore, in order to improve the image quality of holographic reconstruction, a noise reduction method based on the BM3D improved convolutional neural network (CNN) is proposed in this paper. Firstly, the similarity and important statistical information between blocks can be obtained by using BM3D. Then, the denoising convolutional neural network (DnCNN) is used to learn the relationship between the noise of a large number of samples and the noise image, and further purify the image to retain the details for a better denoising effect. Finally, a reflective off-axis digital holographic optical path system is constructed to collect the holograms of the test samples, and the reconstructed images are obtained by the Fresnel diffraction method to constitute a dataset with the simulated holographic reconstructed images to validate the proposed method in this paper, compared to the other methods, such as DnCNN, convolutional blind denoising network (CBDNet), BM3D, and Wiener filtering. The experimental results of qualitative and quantitative analyses show that the proposed method combines the advantages of traditional algorithms and deep learning, significantly enhances the robustness of the system, optimizes the denoising performance, and preserves the details of the reconstructed image to the greatest extent.

Design method of off-axis reflective freeform zoom optical systems

This paper presents a design method for off-axis reflective zoom optical systems. The method can be used to design off-axis zoom optical systems that include multiple mirrors. First, off-axis spherical systems for different zoom positions are solved to approximately meet the requirements for the optical power at different zoom positions, ensuring the convergence of subsequent calculations. Then, the system's optical power and aberrations are corrected by iterating the freeform surfaces point-by-point, thereby obtaining good starting points for further optimization. To illustrate the effectiveness of the method, three design examples are provided, including two off-axis three-mirror zoom optical systems and one off-axis four-mirror zoom optical system. Using the proposed method, good starting points for these systems are obtained. After optimization, the imaging quality of these three systems is close to diffraction limited.

Research on Distortion Control in Off-Axis Three-Mirror Astronomical Telescope Systems

With off-axis reflection systems with specific distortion values serving as objectives or collimators, it is possible to compensate and correct for spectral line bending in spectroscopic instruments. However, there is limited research on the precise control of distortion, which poses particular challenges in large field-of-view optical systems. This paper presents a method for controlling distortion in off-axis reflection systems. Based on Seidel aberration theory and the relationship between distortion wavefront error and primary ray error, we construct objective functions with structural constraints and aberration constraints. The initial structure with specific distortion values is then solved using a differential evolution algorithm. The effectiveness and reliability of this method are verified through the design of an off-axis three-reflection system. The method provided in this study facilitates the design of remote sensing instruments.

Design Method of Freeform Surface Optical Systems with Low Coupling Position Error Sensitivity.

Freeform off-axis reflective systems are significantly more difficult to align and assemble owing to their asymmetric surface shapes and system structures. In this study, a freeform surface system design method with low coupling position error sensitivity (FCPESM) was proposed. First, we established a mathematical model of a reflective system when it was perturbed by coupling position errors and used the clustering-microelement method to establish the coupling error sensitivity evaluation function. The evaluation function was then applied to the design process of a freeform surface off-axis three-mirror optical system. The results showed that the FCPESM optical design method can significantly relax the assembly tolerance requirements of optical systems on the basis of ensuring image performance. In this study, the reflective system was perturbed by tilt and decenter simultaneously, and the disturbance mechanism of position errors on optical systems was further improved. Through this research, freeform surface systems with both image performance and error sensitivity can be obtained, which makes freeform off-axis reflective systems with better engineering realizability.

Design of the primary mirror assembly for a space gravitational wave based on the optical path variation model

As an important component of the gravitational wave detection interferometric measurement system, the telescope’s main function is to receive and emit laser signals. Under the influence of in-orbit environmental disturbances, the telescope will experience structural deformation. This can result in changes in the propagation path of the laser within the telescope, which in turn affects the ranging accuracy. Therefore, it is necessary to suppress the optical path variation caused by the deformation of the telescope during the design phase of the telescope structure. In this paper, a calculation and analysis model of the non-geometric optical path length variation within the telescope was established using the first 36 orders of the fringe Zernike polynomials. The derivation of the geometric optical path variation within the telescope was completed, and the optical system error analysis was performed based on the internal optical path variation of the telescope as an evaluation index. The primary mirror components that meet the detection requirements were designed. The results showed that for the off-axis four-mirror optical system, under the same disturbance, the geometric optical path variation caused by the rigid displacement of the primary mirror dominates. When the environmental temperature stability is 2.8×10−6K⋅Hz−1/2 @0.1 Hz, the system’s optical path stability is reduced from the original 8.5pm⋅Hz−1/2 @0.1 Hz to 0.45pm⋅Hz−1/2 @0.1 Hz.

Characterization of polycrystalline BiFeO3 films prepared by magnetic-field-assisted 90° off-axis pulsed laser deposition

Polycrystalline BiFeO3 (BFO) films were prepared on a Pt/TiO2/SiO2/Si substate using magnetic field-assisted 90° off-axis pulsed laser deposition (PLD). We have successfully obtained polycrystalline BFO films owing to a high deposition rate derived by the confinement of the plume under a magnetic field. The obtained polycrystalline BFO films have a droplet-free surface morphology and a columnar-like microstructure. A RT ferroelectric hysteresis loop is obtained, and at the same time, the remanent polarization of 90 μC cm−2 and the reduced coercive field of 178 kV cm−1 are confirmed. Also, an evolution of the polarization switching is observed by the piezoresponse force microscopy. In this study, we provide a possible route to realize the polycrystalline film growth which has a good quality in a 90° off-axis deposition system using magnetic field-assisted PLD.

Spray characteristics of different regions downstream of a swirl cup

The spray characteristics of different regions downstream of swirl cups play a critical role in cold start and re-ignition of gas turbines. The spray measurements were performed at the fuel pressures of 0.5, 0.8, 1.0, 1.5, and 2.0 MPa and the fuel temperatures of −23, −13, −3, 7, 17 and 27 ℃, respectively. The droplet size, droplet velocity, droplet number, and instantaneous spatial spray image of sprays from an aviation kerosene Jet-A were measured using a two-component phase Doppler particle analyzer and a digital off-axis holography system. As the fuel pressure and temperature increase, the Sauter Mean Diameter (SMD) and spray non-uniformity of the Spray Shear Layer (SSL) gradually decrease. As the fuel pressure increases, the SMD and spray non-uniformity of the Central Toroidal Recirculation Zone (CTRZ) gradually decrease, and the slopes of these curves both decrease. As the fuel pressure increases, the SMD and spray non-uniformity of the CTRZ rapidly decrease at the fuel temperature of −23 ℃, while slightly decrease at the fuel temperature of 27 ℃. The droplets in the CTRZ come from 3 different sources: simplex nozzle, venturi, and outside the CTRZ. As the fuel pressure increases, the proportion of droplets recirculated from outside the CTRZ decreases. This study proposed the concept of the “pressure critical point” for the swirl cups. As the fuel temperature decreases, the proportion of droplets recirculated from outside the CTRZ increases below the critical pressure, while decreases above the critical pressure. In addition, through the models of liquid film formation and breakup on the curved cylindrical wall, a semi-theoretical model was established to predict the SMD of SSL for swirl cups. The prediction uncertainty of this model is less than 6% for all 14 conditions in this paper.

Integrated Analysis of Line-Of-Sight Stability of Off-Axis Three-Mirror Optical System

As a space camera works in orbit, the stress rebound caused by gravity inevitably results in the deformation of its optomechanical structure, and the relative position change between different optical components will affect the Line-Of-Sight pointing of the camera. In this paper, the optical sensitivity calculation of a space camera’s Line-Of-Sight pointing is realized based on the optomechanical constraint equations, and the Line-Of-Sight equations are constructed using the second type of response (DRESP2) method to realize an optomechanical integrated analysis of the camera’s Line-Of-Sight stability at the structural finite element solver level. The verification results show that the Line-Of-Sight stability error is 6.38%, meaning that this method can identify the sensitive optical elements of the optical system efficiently and quickly. Thus, the method in this paper has important significance as a reference for the analysis of the Line-Of-Sight stability of complex optical systems.