Aberrations Of Optical System Research Articles

Out-of-focus holography at the Effelsberg telescope

Context. Out-of-focus (OOF) holography can be used to determine the aperture deformations of radio telescopes that lead to errors in the phase of the complex aperture distribution. In contrast to traditional methods, OOF holography can be performed without a reference antenna, which has a number of practical advantages. Aims. The aim of this work is to develop a standard procedure for OOF holography at the Effelsberg telescope. This includes performing OOF holography observations and the development of dedicated software, the pyoof package, to compute aberrations of the telescope’s optical system. Methods. Based on the OOF holography method developed at the Green Bank telescope, we adapted the approach to the Effelsberg 100 m telescope in order to determine the aberrations of the aperture phase distribution (phase-error maps). Results. The developed OOF holography software is presented as well as the results from observations at Effelsberg. Early results reveal gravitation-related residual deformation not contained in the previously existing aperture and pointing model, and hence we propose changes to the model to counteract aberrations in the telescope’s surface. Conclusions. The OOF holography method (observations and pyoof package) works as expected at the Effelsberg 100 m telescope and is able to validate the good performance of the existing finite element model. Test measurements show that slight improvements of the aperture efficiency and gain elevation dependence are possible but limited in the current configuration.

Measurement and optimization of writing light field uniformity in dual-galvanometer laser scanning lithography system

The light field uniformity (LFU) in lithography system is a key factor in defining the resolution across the entire micro/nano structures. In this work, a cost-effective and straightforward method based on the focused laser marking on heat-mode resist is proposed for measuring and optimizing the LFU. The factors affecting the LFU are analyzed from the perspectives of optical system aberrations and mechanical assembly error. Subsequently, marking patterns with special structures are designed based on the properties of the heat-mode resist. By analyzing the marked patterns, the LFU of the system is obtained with uniformity coefficient is 42.24%. After optimization achieved by dynamic laser power adjustment, the uniformity coefficient was notably enhanced to 96.11%. This work provides an effective method for measuring and optimizing the LFU in dual-galvanometer laser scanning lithography system.

An analytic expression for the field dependence of three-order Zernike aberrations in decentered and/or tilted optical systems

The double Zernike polynomials can describe the aperture dependence and field dependence of non-coaxial optical system aberrations simultaneously, and characterize the complex optical aberrations, which are of great value in the optical system design and alignment. In this paper, the specific analytic forms of all third-order double Zernike aberrations in decentered and/or tilted optical systems are derived based on the nodal aberration theory. This paper realizes the orthogonalization of the third-order aberrations with different aperture dependence and field dependence. The calculation process of the third-order double Zernike aberrations is presented. The ray tracing of the Cassegrain telescope verifies the analytic derivation of the double Zernike aberrations.

Third-Order Intrinsic Aberration Modification with Second-Order Accuracy Transfer of Pupil Coordinates and Extrinsic Aberration of Plane-Symmetric Optical System with a Two-Dimensional Field Light Source

A plane-symmetric optical system with a two-dimensional field light source, such as a soft X-ray and vacuum ultraviolet optical system, is widely used for synchrotron radiation source devices, microscopes and so on. Therefore, this paper studied third-order intrinsic aberration modification with second-order accuracy transfer of pupil coordinates and extrinsic aberration of these kinds of optical systems. First, we discuss the extrinsic aberration calculation method and derive the corresponding aberration expressions; in addition, we apply optical geometric relations and the polynomial fitting method to obtain a second-order accuracy transfer relationship expression of the pupil coordinates between adjacent optical surfaces and derived the modification calculation expressions of the intrinsic aberration caused by the above factor. Finally, the third-order intrinsic aberration modification with second-order accuracy transfer of pupil coordinates and extrinsic aberration expressions derived in this paper are applied to calculate ray spot diagrams of two soft X-ray and vacuum ultraviolet optical systems with meridional and sagittal field angle light sources, and these results are compared with those obtained from the ray-tracing software Shadow; this showed that the calculation accuracy of the aberration expressions is sufficient.

Fifth-order intrinsic aberration and extrinsic aberration of soft x-ray multi-element orthogonal arrangement optical system with large aperture

Fifth-order intrinsic aberration and extrinsic aberration of soft x-ray multi-element orthogonal arrangement optical system with large aperture

Theoretical analysis of a compensator of the secondary longitudinal chromatic aberration.

A theoretical analysis of an afocal compensator of the secondary longitudinal chromatic aberration is provided. Such a compensator is able to compensate for chromatic aberration of an achromatic optical system and make an apochromatic correction of the system. The parameters of the proposed chromatic aberration compensator are described and the principle is presented in examples.

An Iterative High-Precision Algorithm for Multi-Beam Array Stitching Method Based on Scanning Hartmann

The multi-beam array stitching test system (MASTS) based on the Hartmann principle is employed to measure the aberrations in large-aperture optical systems. As each small-aperture and ideal parallel beam traverses the optical system, it is converged into a spot at the focal plane of the optical system. The centroid position of the spot contains the information about the wavefront slope of the sub-aperture at that specific location in the optical system. Scanning the optical system with this small-aperture beam across the entire aperture of the optical system, we can yield the aberration information to be tested. To mitigate pointing errors induced by scanning motion and accurately obtain the aberration signals of the optical system, nine beams are integrated into a 3 × 3 multi-beam array system, and their directions are aligned to be identical. However, achieving complete alignment in the same direction for all nine beams is a challenging task, resulting in errors due to their pointing differences within the array. This paper introduces an iterative algorithm designed to obtain high-precision multi-beam pointing errors and to reconstruct the wavefront of the optical system under test. This enables a more accurate measurement of wavefront aberrations in the optical system to be tested. Firstly, simulation models were implemented to validate the algorithm’s feasibility. Additionally, a scanning optical measurement system with a multi-beam array was developed in our lab, and the iterative algorithm was applied to process our experimental data. The results were then compared with interferometer data, demonstrating that our algorithm is feasible for MASTS to measure aberrations in large-aperture optical systems with high accuracy.

Wave aberration corrections in PSF ellipticity measurements of astronomical telescopes using a multi-objective optimization.

The weak gravitational lensing (WGL) produces a shear effect on the observed galactic ellipticity that is much smaller than the endogenous ellipticity of the galaxy itself. Achieving such a high-level astronomical observation requires the superior performance of telescopes. To ensure the optical properties of telescopes to be competent in WGL detections, it is very necessary to measure point spread function (PSF) ellipticity of telescopes in labs. In this paper, a 2m off-axis telescope that would be used to detect WGL in space is analyzed and studied. A collimator whose aperture is 2m has been built to measure PSF ellipticity of the telescope. The wave aberrations of the collimator are roughly equal to those of the telescope, so they are important systematical errors and must be removed. However, it is difficult to precisely measure the wave aberrations of optical systems that have large apertures and long focal lengths. In addition, a 2m flat mirror, which is indispensable to measure wave aberrations of optical systems, has significant surface errors. In this paper, a multi-objective optimization method is proposed to eliminate the effects of wave aberrations on PSF ellipticity measurements of the telescope. By constructing an equivalent model, the wave aberrations from collimators and flat mirrors can be corrected so that PSF ellipticity measurement error is reduced to within 0.01. Measurement accuracy of PSF ellipticity of the telescopes can be improved significantly.

Non-coincidence detection of fiber optic circulators based on Hertz-level frequency-shifting heterodyne interferometry

The fiber optic circulator in the form of point diffraction is a key component for coupling fiber optical path and spatial optical path in a laser Doppler vibration measurement system. The coupling efficiency and other performance parameters of fiber optic circulator are great significant for improving measurement accuracy and working distance of vibration measurement system. The conventional circulator coincidence detection methods include energy monitoring method and far-field coincidence monitoring method, which cannot be used to quantitatively analyze the fiber mismatch factors. Therefore, the consistency of the circulator coupling efficiency cannot be guaranteed. To solve these problems, a phase detection technology based on Hertz-level frequency-shifting heterodyne interferometry is proposed. The interferometry phase information is used to calculate the relative spatial positions of optical fibers, and this technology performs quantitative detection in the fiber alignment process. The interference wavefront formed by relative spatial positions of optical fibers is simulated and validated experimentally. The curves of coupling efficiency and wavefront PV value versus different kinds of alignment errors are simulated and analyzed. By fitting the interference wavefront with the Zernike polynomials, the correspondence between different kinds of alignment errors and Zernike coefficients is obtained. The value of Z2 (Zernike coefficient) can be used as the basis for judging whether there is transverse displacement in the Y direction. Similarly, Z3 corresponds to the transverse displacement in the X direction, Z4 corresponds to the longitudinal displacement in the Z direction and Z5 corresponds to the optical axis angle. Through this correspondence relationship, the quantitative separation and analysis of fiber mismatch factors are realized. The experimental results show that the accuracy of this method for measuring lateral displacement is better than 1μm. According to the phase diagram obtained from the experiment, Zernike coefficient fitting is performed. The lateral displacement deviation, longitudinal displacement deviation, and angular deviation are calculated by the coefficients of Z2 to Z5. The fiber adjustment mechanism corrects the transverse displacement deviation, and the experimental phase diagram is shown in <xref ref-type="fig" rid="Figure14">Fig. 14</xref>. It provides a new detection method for realizing fiber alignment and mismatch correction. Compared with the existing detection methods, the phase detection method based on Hertz-level frequency-shifting heterodyne interferometry solves the quantification problem of fiber coincidence adjustment. This method has the advantages of high measurement accuracy, compact detection structure and composition, and low detection cost. This method has great potential applications in the fields of optical fiber and spatial optical device alignment, optical system aberration detection, and planar wavefront detection.

A Phase Recovery Technique Using the Genetic Algorithm for Aberration Correction in a Coherent Imaging System.

For traditional imaging systems, high imaging quality and system miniaturization are often contradictory. In order to meet the requirements of high imaging quality and system miniaturization, this paper proposes a method to correct the aberration of coherent imaging optical systems. The method is based on the idea of phase recovery and the imaging principle of a coherent imaging system to recover the aberrations at the exit pupil of the system. According to the recovered aberrations, conjugate filters are constructed to correct the image quality in the frequency domain. The imaging quality of the system is improved without changing the original optical path, and the simplicity of the system is guaranteed. To solve the pupil frequency domain aberration more accurately, this paper adopts the dual competition and parallel recombination strategy based on the genetic algorithm and introduces the disaster model. The improved genetic algorithm can effectively restrain the appearance of the "precocity" phenomenon. Finally, the paraxial imaging optical path is simulated and verified by experiments. The results show that, after aberration correction, the image sharpness is improved and the edge information is richer, which verifies the feasibility of the coherent imaging system image quality enhancement method proposed in this paper.

Simplified analysis and suppression of polarization aberration in planar symmetric optical systems.

Polarized remote sensing imaging has attracted more attention in recent years due to its wider detection information dimension compared to traditional imaging methods. However, the inherent instrument errors in optical systems can lead to errors in the polarization state of the incident and outgoing light, which is the polarization aberration of the optical system, resulting in a decrease in polarization detection accuracy. We propose a polarization aberration simplification calculation method for planar symmetric optical systems, by what only three ray samples are needed to obtain the distribution of polarization aberrations within the pupil. This method has a calculation accuracy close to traditional methods, and the sampling rate is 0.003 times that of traditional methods. Based on this, we designed a merit function that optimizes both wavefront and polarization aberrations simultaneously. It is found that diattenuation and retardance of the optical system are 62% and 58% of the original, and the polarization crosstalk term is reduced by 37% when the polarization weight factor takes an appropriate value. And at the same time, the wavefront aberration has also been well optimized.

Object-independent wavefront sensing method based on an unsupervised learning model for overcoming aberrations in optical systems.

This Letter introduces the idea of unsupervised learning into object-independent wavefront sensing for the first time, to the best of our knowledge, which can achieve fast phase recovery of arbitrary objects without labels. First, a fine feature extraction method which only depends on the wavefront aberrations is proposed. Then, a lightweight neural network and an optical feature system are combined to form an unsupervised learning model, and the neural network is promoted to be well trained by reversely outputting fine features. Simulation results prove that the proposed method can effectively overcome the aberrations (static or variable) existing in the optical system and achieve wavefront sensing of different objects with high precision and efficiency.

2D calculation of parasitic fields in misaligned multipole electron-optical systems

The effects of geometrical imperfections in electron-optical components are usually evaluated in 3D simulations. These calculations inherently take a long time, require a large amount of memory, and do not directly produce the necessary axial field functions. We present a 2D perturbation method to calculate parasitic fields in misaligned multipole systems. Our method is based on finding an equivalent potential perturbation, similarly to Sturrock’s method, but does not rely on the potential being differentiable. The method is directly applicable to both electrostatic and non-saturated magnetic problems. It does not require any 3D data and it is fully compatible with existing finite element method codes such as EOD. The proposed method produces axial field functions with an accuracy of units to a few tens of percents, depending on the number of unperturbed multipole field components used and the geometry. The results can then be used, for instance, to determine the parasitic imaging aberrations of the misaligned optical system using standard methods, in order to evaluate the effect of mechanical design tolerances.

Anatomical and optical parameters and aberrations of the optical system of the eye in anisometropic myopia

Purpose: to compare anatomical and optical parameters and aberrations of both eyes in patients with acquired and congenital anisometropic myopia.Material and methods. 22 patients (44 eyes) aged 18–35 (averagely, 25.2) with acquired and congenital anisometropic myopia were examined using the Galilei G6 optical eye system analyzer (Ziemer, Switzerland). The analysis of total, corneal and internal aberrations of the eye was carried out on an OPD-Scan III (Nidek) aberrometer.Results. In both groups with acquired and congenital anisometropic myopia, the axial length of the higher myopic eye was greater than that of the fellow eye. A greater asphericity and higher astigmatism of the cornea were revealed in higher myopic eyes of patients with congenital myopia as compared to acquired myopia. The total RMS HOA in congenital myopia was significantly greater in the higher myopic eye compared to the fellow eye (1.07 D and 0.68 D, respectively) and greater than in cases of acquired myopia. All HOA were greater in higher myopic eyes as compared to the fellow ones in cases of congenital myopia. In case of acquired myopia only the total coma appeared to be greater in the higher myopic eye. Corneal aberrations in acquired anisometropic myopia did not differ in the paired eyes. In case of congenital myopia, the total tilt was significantly greater in the higher myopic eye, and total coma and spherical aberration have lower values, even with a transition to negative ones (p < 0.05).Conclusion. The revealed differences of the wavefront of the eyes with anisometropic congenital and acquired myopia are rather a consequence of anatomical and optical differences (the axial length of the eyes and the topography of the cornea), than the cause of anisometropia.

Transverse ray aberrations determination innon-axially symmetrical optical imaging systemsusing Taylor series expansion.

Non-axially symmetrical optical systems can provide better solutions to several optical design problems. However, the determination of their aberrations is a challenge due to the great diversity of their configurations. To address this problem, this study extends previous work by the present group to determine the transverse ray aberrations in non-axially symmetrical optical imaging systems through the use of a Taylor series expansion. The expansion converts the coordinates of the incident point, which are highly composite functions, of a general ray on the image plane into polynomial functions. The various order transverse ray aberrations are then extracted directly from the corresponding terms of the polynomials. Notably, the derived expressions are exact since they are determined without any approximations. Furthermore, the proposed method can be equally applied to axially symmetrical systems provided that the object is confined on the meridional plane. Consequently, the proposed method offers a useful and generally applicable approach for the systematic analysis of the transverse ray aberrations in optical systems with the object at either finite or infinite positions.

Neural invertible variable-degree optical aberrations correction.

Optical aberrations of optical systems cause significant degradation of imaging quality. Aberration correction by sophisticated lens designs and special glass materials generally incurs high cost of manufacturing and the increase in the weight of optical systems, thus recent work has shifted to aberration correction with deep learning-based post-processing. Though real-world optical aberrations vary in degree, existing methods cannot eliminate variable-degree aberrations well, especially for the severe degrees of degradation. Also, previous methods use a single feed-forward neural network and suffer from information loss in the output. To address the issues, we propose a novel aberration correction method with an invertible architecture by leveraging its information-lossless property. Within the architecture, we develop conditional invertible blocks to allow the processing of aberrations with variable degrees. Our method is evaluated on both a synthetic dataset from physics-based imaging simulation and a real captured dataset. Quantitative and qualitative experimental results demonstrate that our method outperforms compared methods in correcting variable-degree optical aberrations.

Focal length, EFL, and the eye.

The focal length is often called the effective focal length, or efl instead, and although this is acceptable for a lens in air, it is not otherwise correct. The eye is used as an example here for an optical system where the object is in air and the image is in fluid. Welford, Aberrations of Optical Systems (1986) has paraxial equations that are consistent with historical use while also clearly defining efl. These are based on power at a surface having to be the same for light traveling in both directions (n '/f '). The focal length f ' is the actual physical distance from the 2nd principal point to the paraxial focus, and the equivalent focal length, or efl, is the focal length divided by the image index (f '/n '). Separately, when the object is in air, the efl is shown to act at the nodal point, with the lens system represented by either an equivalent thin lens at the principal point with a focal length or a different equivalent thin lens in air at the nodal point with an efl. The rationale for using effective instead of equivalent for efl is unclear, but efl is used more as a symbol than as an acronym.

Velocity map imaging with no spherical aberrations.

Velocity map imaging (VMI) is a powerful technique to deduce the kinetic energy of ions or electrons that are produced from a large volume in space with good resolution. The size of the acceptance volume is determined by the spherical aberrations of the ion optical system. Here we present an analytical derivation for velocity map imaging with no spherical aberrations. We will discuss a particular example for the implementation of the technique that allows using the reaction microscope recently installed in the cryogenic storage ring (CSR) in a VMI mode. SIMION simulations confirm that a beam of electrons produced almost over the entire volume of the source region, with a width of 8 cm, can be focused to a spot of 0.1 mm on the detector. The use of the same formalism for position imaging, as well as in a mixed mode where position imaging is in one axis and velocity map imaging is in a different axis, is also discussed.

Preparation and refractive index characterization of chalcogenide glasses with gradient refractive index

AbstractInfrared gradient refractive index (GRIN) lenses have great application value and potential in multispectral imaging systems. This study reports various chalcogenide axial GRIN glasses prepared using the hot‐pressing diffusion method. It is worth noting that the S4–S60 GRIN sample has a difference in refractive index (RI) Δn of greater than 0.3 and a diffusion depth of about 5 mm, which is the deepest diffusion depth reported in chalcogenide glass to date. In addition, the linear portion in the profile of the GRIN sample has a RI difference of 0.15 and a thickness of 1.2 mm. The effects of the temperature, concentration difference, and diffusion time on the sample diffusion process are discussed. The dispersion properties of the GRIN samples were further calculated, providing a new option for correcting chromatic aberrations in optical systems. In addition, a method for the indirect nondestructive characterization of sample RI using the Raman intensity ratio is proposed, and the reliability of the method is verified by practical experiments, which is convenient for the subsequent measurement of the GRIN profile.

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).