Off-axis Optical System Research Articles

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.

Compact off-axis reflective optical system design combining freeform mirror and freeform detector

Minimizing system size and weight without sacrificing the desired imaging performance is a crucial and challenging goal in the design of off-axis optical systems. In this paper, we propose a design concept that combines freeform mirror and freeform detector to achieve more compact off-axis optical systems. Initially, by applying nodal aberration theory, the optimal focal surface shape for off-axis systems is demonstrated to be an off-axis paraboloid or even a freeform surface, rather than the commonly assumed spherical shape. Subsequently, we show the ability of the design concept to reduce off-axis system volume through a design example of a fast and wide-field off-axis three-mirror system. Results indicate that, under the same design parameters and imaging quality, the design with a freeform detector is 80% smaller than that with a flat detector in terms of volume. Finally, the bending capability of the freeform detector presented in this paper is ensured through finite element analysis, and its surface accuracy is achievable based on the current precision level of curved detector fabrication. The proposed design concept holds promise for application in planetary science, where the imaging performance of the instrument is highly required and the size and weight are strictly limited.

Off-axis optical system for the monitoring of the Laser Metal Deposition process

The Laser Metal Deposition (LMD) is emerging among the additive manufacturing (AM) technologies of metals for its versatility. It takes advantage of the flexibility of a laser source and a powder flow to fabricate or repair components with very complex features. The challenging process conditions that characterize the processing of metallic materials (temperatures and stresses) underlie the occurrence of several defects that plague such AM processes. Thus, the necessity to develop monitoring systems that can comprehensively analyze the production phase arises. In the present work, an innovative off-axis optical system consisting of three cameras with appropriate filters is proposed for the monitoring of LMD process. The peculiarity of this system lies in the capability of monitoring the spatial evolution of the melt pool, enabling eventually a complete control of the deposition process. In fact, through the use of properly developed image processing algorithms, the system enables the tridimensional definition of the size and shape of the melt pool and at the same time the reconstruction of each deposited layer. The potential of the monitoring system was tested on a series of thin-walled components. Subsequently, the analysis results were validated by comparison with 3D scanning of the parts and analyses performed using a coaxial monitoring system.

Interfacial analysis by optical monitoring of layer level multi-material parts fabricated via Powder Bed Fusion–Laser Beam

This experimental work aims to contribute to the development of Powder Bed Fusion–Laser Beam (PBF-LB) processes for the fabrication of multi-material structures by studying the interfacial characteristics using an off-axis optical monitoring system and relating in-situ results with metallurgical and mechanical properties of built parts. The study was developed employing an innovative approach for intralayer multi-material fabrication by PBF-LB, based on the use of a partitioning system in the powder chamber.Image analysis was used to extrapolate information needed to describe possible contamination effects between powders, the size of the interface and the presence of metallurgical defects.Chemical, metallographic and statistical analyses were also carried out to study the interface between the two materials of the samples and to support the results from optical monitoring.The results showed that the optical monitoring system enables real-time verification of the required quality parameters during the joining of different materials with PBF-LB processes.

Alignment Method for Off-Axis Optical Systems Based on CGH Multi-Mirror Attitude Determination

Alignment Method for Off-Axis Optical Systems Based on CGH Multi-Mirror Attitude Determination

Design of low polarization off-axis three-mirror reflective optical systems.

Off-axis optical systems have several important advantages over on-axis ones. However, high polarization aberrations, which play important roles in many applications, become critical disadvantages of off-axis systems. Thanks to the seven free design parameters, three-mirror reflective systems have a good potential to achieve low polarization. A general method to design low polarization off-axis three-mirror reflective optical systems is proposed in this paper. Based on genetic algorithms, several off-axis three-mirror systems with both low polarization aberrations and good wave aberrations are designed. The method proposed in this paper is versatile and can be used to design other types of optical systems that demand low polarization aberrations.

Sub-ppb NaCl aerosol detection at a distance of 30 meters by femtosecond laser induced plasma spectroscopy.

In this work, sub-ppb aerosol detection is achieved by femtosecond laser filament with a single pulse energy of 4 mJ at a distance of 30 m. A concave mirror with an open aperture of 41.4 cm is employed in an off-axis optical system to focus the femtosecond laser beam and collect the fluorescence of NaCl aerosol. The simulation and experimental results show that the astigmatism can be greatly reduced when femtosecond laser beam is incident non-symmetrically on the concave mirror. Compared with the case that femtosecond laser strikes at the center of the concave mirror, the intensity of acoustic signal emitted from the optical filament is increased by 69.5 times, and the detection of limit of sodium element in aerosol is reduced by 86%, which is down to 0.32 ppb. The improved excitation scheme in this work utilizes the nonsymmetrical beam spot on the concave mirror to compensate the non-symmetry induced by the off-axis setup, reducing the astigmatism of the focusing laser beam and decreasing the sodium chloride aerosol's detection of limit.

Design of a Large Field of View and Low-Distortion Off-Axis Optical System Based on a Free-Form Surface

Free-form surfaces have good aberration correction capability and balance capability for nonrotationally symmetric imaging systems. In this study, we analyzed the quantitative relationship between X–Y polynomial combination and aberration for the efficient design of X–Y free-form optical systems. The purpose of this study was to provide an exhaustive design method for off-axis triple inverse optical systems with X–Y free-form surfaces. Finally, we designed a free-form off-axis optical system with a large field of view (FOV) and low distortion based on the off-axis triple inverse optical system without an intermediate image plane. The primary mirror (PM) of the system adopted an X–Y polynomial free-form surface to correct the aberration of different FOVs of the system and improve the image width and quality. The optical system had a focal length of 1000 mm, an F-value of 9.5, an FOV angle of 23° × 1°, a maximum distortion grid in the FOV less than or equal to −0.05%, and a full-field average wave aberration better than 0.055 λ (λ/18.2, λ = 632.8 nm). The analysis of the design results showed that the system had high-quality imaging and a compact structure. This design method can provide a technical reference for the study of such free-form off-axis systems.

Analysis and experiment of polarization characteristics of Off-axis freeform optical system

As freeform surfaces are widely used in off-axis optical systems with large apertures, large fields of view, and long focal lengths, the polarization effect caused by the system cannot be ignored. For this in mind, a polarization aberration analysis method for freeform optical system with fringe Zernike polynomial is proposed. An analytical model for the polarization aberration in this case is constructed. The influence of the surface shape on the polarization aberration is investigated. Our analysis shows that the distribution of phase aberration, diattenuation and retardance at the exit pupil introduced by the freeform surface in the system is related to the entrance pupil, incident field angle, and also closely dependent on the surface sag of the freeform surface. The introduction of freeform surfaces causes the system polarization aberration distribution to lose rotational symmetry. Finally, a freeform surface multi-angle polarization characteristic test platform was built to test the validity of the theoretical model. The polarization aberration characteristic data of the incident mirror at different angles of view at different positions were obtained and analyzed. The measured results show that the relative errors of phase aberration, diattenuation and retardance are all less than 7.2%, which is basically consistent with the theoretical simulation analysis results. The research in this paper provides a theoretical basis for guiding the design of an off-axis freeform surface polarization imaging optical system, and provides theoretical guidance for improving the polarization aberration calibration of a freeform surface optical system.

Method of optimizing deterministic small free-form surfaces for off-axis optical systems with extremely low aberration

A mapping model of arbitrarily shaped surfaces and the system image quality is constructed to examine the optimization of the residual aberration of an off-axis optical system to construct an off-axis optical system with very small aberrations. First, orthogonal surfaces are chosen within the arbitrary aperture. The mapping relationship between the orthogonal surfaces and system wavefront aberration is then established. Finally, the surfaces required for optimization are acquired by solving the mapping relationship through singular value decomposition and the Gauss–Newton algorithm. The residual aberration of the system is optimized using free-form surfaces with small deviations. In this paper, the residual aberration of an off-axis optical system with a non-circular aperture is optimized by adopting the above method, with the residual aberration of the system reducing from 0.549 nm (root-mean-square, RMS) to 0.443 nm (RMS) after adding a small free-form surface to a single lens, and to 0.393 nm (RMS) after adding small free-form surfaces to two lenses. The optical system with a circular aperture is optimized and the residual aberration of the system is reduced from 2 nm (RMS) to 0.47 nm (RMS).

Investigation of Focusing Properties on Astigmatic Gaussian Beams in Nonlinear Medium.

Ultra-short laser filamentation has been intensively studied due to its unique optical properties for applications in the field of remote sensing and detection. Although significant progress has been made, the quality of the laser beam still suffers from various optical aberrations during long-range transmission. Astigmatism is a typical off-axis aberration that is often encountered in the off-axis optical systems. An effective method needs to be proposed to suppress the astigmatism of the beam during filamentation. Herein, we numerically investigated the impact of the nonlinear effects on the focusing properties of the astigmatic Gaussian beams in air and obtained similar results in the experiment. As the single pulse energy increases, the maximum on-axis intensity gradually shifted from the sagittal focus to the tangential focus and the foci moved forward simultaneously. Moreover, the astigmatism could be suppressed effectively with the enhancement of the nonlinear effects, that is, the astigmatic difference and the degree of beam distortion were both reduced. Through this approach, the acoustic intensity of the filament (located at the tangential focal point) increased by a factor of 22.8. Our work paves a solid step toward the practical applications of the astigmatism beam as the nonlinear lidar.

Spatial Three-Mirror Off-Axis Freeform Optical System without Any Symmetry

In this manuscript, we have launched a study on the completely nonsymmetric freeform optical system with neither rotational symmetry nor planar symmetry. An off-axis three-mirror freeform optical system with nonsymmetric geometry is proposed and a direct design method is developed for the nonsymmetric freeform optical system. The design field points are sampled across the full FOV to control the imaging quality and object–image relationship. In this system, the center of the image plane is greatly away from the plane determined by the centers of the three mirrors. This nonsymmetric system with F/1.3, a focal length of 50 mm, and an 8° × 6° field of view can achieve imaging quality close to the diffraction limit. This work provides a feasible nonsymmetric system design idea for the optical community.

Increasing the measurement accuracy for wave aberrations of an optical system using the intensity distribution of a focused light beam

Subject of study. A method for enhancing the measurement accuracy for wave aberrations of an optical system by using cross-section images of a focused light beam in the presence of the image’s amplitude distortions is described. Method. The measurement procedure includes determining the wave aberrations of the optical system individually for each of the beam cross-section images recorded at different sides from the focal plane and subsequently averaging the obtained wave aberrations. Main results. The utilized method for obtaining the wave aberrations of an optical system involves analysis and processing of the aberration-distorted intensity distributions in the cross-section images of a focused light beam that are recorded in a plane before and after the focal plane. Noticeably, the presence of intensity nonuniformities in the light beam cross-sections that do not result from the wave aberrations inevitably causes measurement errors. The effect of such amplitude noise on the measurement accuracy can be suppressed manifold by recording and processing an additional image of the beam cross-section positioned at a particularly selected distance on the opposite side to the focusing plane. This is followed by averaging the wave aberrations obtained for each of these images. If the amplitude and aberrational distortions of the intensity distribution have similar profiles in one of the recording planes, they are added, and they increase the degree of nonuniformity of the total intensity distribution. However, the profiles of the amplitude and aberrational distortions of the intensity distribution in the other plane are mutually opposite, which reduces the degree of distribution nonuniformity. This effect allows the measurement errors caused by amplitude noise to be compensated by arithmetically averaging the wave aberrations obtained individually for each image. We demonstrate that the variation in the measured values of the root mean square deviation of the wave front of the beam of up to 20%–30% from the individual measurements of the wave aberrations in the presence of noise can be reduced to several percent using the proposed method. Practical significance. Amplitude distortions in the images of the cross-sections of a beam that are not caused by aberrations are ubiquitous because they are present in, e.g., high-aperture, apodized, or off-axis optical systems. Measurement of the wave aberrations of such optical systems by the standard method using one image of a focused beam does not provide accurate results. The modification of this measurement technique proposed in this paper enables the extension of its application area to the aforementioned systems while maintaining its characteristic measurement accuracy at λ/20.

Comprehensive design analysis and verification of space-based short-wave infrared coded spectrometer via curved prism dispersion.

The spaceborne dispersive spectrometer is widely used in environmental, resource, and ocean observations. The coded spectrometer has higher energy advantages than the dispersion spectrometer, so it has great application prospects. In the current study, we developed an off-axis short-wave infrared coded optical system (SICOS) based on curved prism dispersion, and we further explored the design and optimization of the SICOS structure. Finite element analyses of a space-based short-wave infrared coded spectrometer based on curved prism dispersion (SSICS-CPD), including static simulation, modal analysis, sinusoidal vibration mechanical analysis, and random vibration mechanical analysis, were carried out. Simulation results showed that the SICOS support structure had excellent mechanical and thermal stability. As off-axis optical systems cannot meet the requirements of optical position accuracy through centering processing, a point source microscope and three-coordinate measuring machines were employed to complete the high-precision and rapid assembly of the SSICS-CPD. In addition, verification tests of surface shape error, stress relief, random vibration, and optical design parameters were carried out to validate the high stability and imaging performance of the SSICS-CPD. Results showed that the average modulation transfer function in the full field was 0.43 at 16.67 lp/mm, the spectral smile was <0.2 pixels, and the spectral keystone was <0.1 pixels. The design, analysis, assembly, and verification of the SSICS-CPD provide a useful reference for the development of other spaceborne prism dispersion spectrometers.

A Method to Increase the Field of View of an Imaging Optical System

The Y field of view of an off-axis optical system is generally less than 1°. Scholars usually use a freeform surface to achieve a rectangular field of view imaging. However, it adds to the difficulty of processing, testing, assembling, and adjusting, and at the same time has the drawbacks of high manufacturing costs and long processing cycles. In view of the above problems, this paper presents a computational imaging design method for expanding the Y field of view of an off-axis optical system. This method analyzes the aberration characteristics of the optical system, creates a point spread function model based on the wavefront aberration theory and Zernike polynomials, and processes images using a spatial variation deconvolution algorithm. In this paper, we used this method to simulate an off-axis three-mirror optical system with a focal length of 260 mm, the f-number of 2.5, and a field of view of 8° × 1° and compare the images before and after processing. The results show that the processed images have a clear outline, the overall image quality is improved, the field of view is improved to 8° × 6°, and the modulation transfer function of the entire field of view is above 0.4. The off-axis optical system rectangular field of view imaging is realized without using a freeform surface.

Analysis of polarization characteristics of freeform surface optical system

Freeform surfaces are widely used in off-axis optical systems with large aperture, large field of view, and long focal length. The polarization effect caused by the non-rotationally symmetrical shape has an impact on the system’s polarization imaging quality and measurement accuracy. Based on Jones’ notation, this paper proposes a polarization aberration analysis method for fringed Zernike polynomial freeform optical systems and constructs a full-field polarisation aberration analysis model of non-rotationally symmetric freeform reflective optical systems. The light propagation vector k is added on the basis of the two-dimensional ray tracing algorithm. By tracing the full-field polarized light of the off-axis optical system in the field of view, the Jones pupil diagram is obtained. The phase aberration, diattenuation and retardance are separated by Pauli decomposition and SVD decomposition. The off-axis freeform surface optical system is designed. The analysis results show that the phase aberration of the off-axis freeform surface optical system is directly related to the surface shape of the freeform surface. The changes of the freeform surface to the diattenuation and retardance are both 56% of the diattenuation and retardance of the sistem. For deep-space telescopes and lithography systems, it is of great significance for improving system accuracy to master this change.

Distortion analysis and focal length testing of off-axis optical system

Distortion analysis and focal length testing of off-axis optical system

Polarization Aberration Analysis and Compensation of Off-Axis Optical System with Digital Micro-Mirror Device

Polarization Aberration Analysis and Compensation of Off-Axis Optical System with Digital Micro-Mirror Device

Fundamental-ray aberration analysis of off-axial optical systems: analytical formulae of first-order aberrations.

In our previous paper [Appl. Opt.59, 4466 (2020)10.1364/AO.389600], we presented a fundamental-ray aberration analysis that extends ray matrix analysis to the third-order aberration region. The analysis results shown in that paper were applicable to coaxial rotationally symmetric optical systems. This time, we have extended the fundamental-ray aberration analysis so that it can be applied to off-axial optical systems. Here we present new analysis formulae for fundamental-ray aberration analysis of the first-order aberration region. In addition, we newly present first-order aberration expansion formulae for four-element fundamental-ray aberrations and calculation formulae for the fundamental-ray aberration coefficients of the first order, which are necessary for this extension.

Optical distortion correction considering radial and tangential distortion rates defined by optical design

This paper proposes a high-accuracy distortion correction method for optical imaging distortion mapping and computational image predistortion. Due to the establishment of the predistortion is based on the distortion evaluation in the common optical design software CODE V, it can be used in the broad field of optical imaging system. Two distortion correction methods considering radial and tangential distortion rates which defined by optical design are introduced to perform distortion correction, and the forward and inverse image warping interpolation methods are adopted, separately. Simulations are conducted to verify the effectiveness in correcting complex distortion for freeform off-axis optical system. Furthermore, we implement a distortion correction experiment for an augmented reality head-mounted display that suffers from an asymmetric distortion with the maximum tangential distortion over 7%. For the first method, fast and high-accuracy image warping is achieved, and the RMS error of the approximation predistortion image is less than 1 pixel. Meanwhile, the RMS errors of the corrected imaging points are approximately 1.93 pixels vertically and 2.16 pixels horizontally when using a 5-megapixel camera. The second method considers the additional influence of the actual machining and assembly errors of the optical system, and the RMS errors of 0.89 pixels vertically and 0.85 pixels horizontally are achieved.