Aberrations Of Optical System Research Articles

Optical-Digital Integrated Design Method for Near-Eye Display Imaging System

Near-eye display (NED) systems have various structures, including the freeform prism, off-axis synthesizer, and holographic optical waveguide structures. In this study, the three types of structures of NED systems were analyzed in terms of their advantages and disadvantages. Hence, an optical-digital integrated design method was proposed for the NED imaging system. In particular, a point spread function model with aberration information was developed based on the analysis of optical system aberration. Algorithm preprocessing was conducted on the image-end, and the processed image was transformed into a sharp image by the optical system and sent to the pupil. A NED optical system with a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$45^{\circ } \times32$ </tex-math></inline-formula> ° field of view, 10-mm exit pupil diameter, and 30-mm exit pupil distance was developed using the proposed method. This system can meet the NED requirements using three aspherical reflectors instead of a free-form and lens-correction group.

Absolute characterization of high numerical aperture microscope objectives utilizing a dipole scatterer

Measuring the aberrations of optical systems is an essential step in the fabrication of high precision optical components. Such a characterization is usually based on comparing the device under investigation with a calibrated reference object. However, when working at the cutting-edge of technology, it is increasingly difficult to provide an even better or well-known reference device. In this manuscript we present a method for the characterization of high numerical aperture microscope objectives, functioning without the need of calibrated reference optics. The technique constitutes a nanoparticle, acting as a dipole-like scatterer, that is placed in the focal volume of the microscope objective. The light that is scattered by the particle can be measured individually and serves as the reference wave in our system. Utilizing the well-characterized scattered light as nearly perfect reference wave is the main idea behind this manuscript.

Contribution of wave aberrations represented by Zernike polynomials to the cross-correlation function between distorted and actual speckle patterns

Speckles are sensitive to the slightest inhomogeneities of the medium, which is used in optical research methods such as speckle interferometry. However, the stochastic nature of propagation of speckle fields complicates their accurate detection and processing. For example, aberrations in the optical system result in the decorrelation of the image of speckles with the actual speckles that are observed in free space. The report will consider the main types of wave aberrations of optical system and their influence on the correlation properties of speckle patterns. The research results can be used to optimize optical systems in which speckles play a significant role, for example, in classical ghost imaging.

Imaging characteristics and image restoration method for large field circular scanning system

Large field circular scanning system obtains remote sensing images by rotating scanning, which is one of the technical ways to effectively expand the field of view of geostationary orbit optical remote sensing imaging system. However, due to its special rotation scanning imaging mechanism, the on-orbit imaging process of this system is affected by the coupling of detector rotation sampling, satellite platform vibration, optical system aberration and other factors, so the image degradation characteristics are very complex. In this paper, the on-orbit imaging characteristics of large field circular scanning system are first analyzed to provide a theoretical basis for the subsequent research of image restoration method. Secondly, aiming at the problems of annular geometric distortion and spatial blur of the system image, the image restoration method is proposed based on ring block and regularization methodology. Experimental results show that under the condition of detector rotation speed ω <0.06 rad/s, the proposed method exhibited a satisfactory processing performance.

Compact periscope-type objective based on wedge-shaped prisms with free-form surfaces

Peculiarities of the optical layout configuration of a periscope-type objective based on wedge-shaped prisms with free-form surfaces are considered. Guidelines on the correction of aberrations of the initial optical system and control of ray incidence angles on the prism surfaces in the areas where ray reflection and refraction zones overlap are formulated. The effectiveness of these guidelines is demonstrated by calculation of a compact periscope-type objective operating in a spectral interval spanning visible and near-infrared ranges. Elements of the optical layout of the objective are fabricated using advanced commercially available types of plastic.

Influence of collimator aberrations on the instrument line shape of a Fourier transform spectrometer

The influence of the aberrations of a collimator optical system on the instrument line shape (ILS) of a Fourier transform spectrometer was studied. By analyzing the wave propagation in the spectrometer, numerical distributions of intensity in images of source points visible at different angles from the center of the collimator were modeled. Thus, the shape of the function describing the angular distribution of the intensity in the interferometer was obtained. Then, the ILS of the spectrometer was derived. The influence of the aberration on the ILS was analyzed by determining the shifts of the line positions for different values of third-order aberrations and parameters of the device (field of view and diameter of the aperture). Conclusions concerning the influence of the particular aberrations are presented.

Modeling, experimental validation, and model order reduction of mirror thermal dynamics.

A large variety of optical systems and devices are highly sensitive to temperature variations and gradients induced by the absorption of thermal energy. Temperature gradients developed across optical elements, mounts, and supporting structures can lead to thermally induced wavefront aberrations and, consequently, to the reduction of optical performance. Consequently, modeling, estimation, and control of thermal dynamics are important problems that need to be carefully addressed by optical system designers. However, the development of accurate and experimentally validated models of thermal dynamics that are suitable for prediction, estimation, and control is a challenging problem. The main modeling challenges originate from model uncertainties, nonlinearities, and the fact that the thermal dynamics is inherently large-dimensional. In this manuscript, we present a synergistic modeling framework that combines first-principle heat transfer modeling, experimental validation, finite element techniques, and model order reduction techniques. We experimentally validate our approach on a recently developed 8-inch mirror prototype equipped with heaters and temperature sensors. We are able to accurately predict the temperature transients lasting for several hours. Furthermore, we apply our modeling approach to a parabolic mirror with an optimized honeycomb back structure. We investigate how the choice of mirror materials, such as aluminum, beryllium, Zerodur, and ULE, influence the ability to derive reduced-order models. Our results show that mirror thermal dynamics can be approximated by low-order state-space models. The modeling approach used in this manuscript is relevant for the prediction, estimation, and control of thermal dynamics and thermally induced aberrations in optical systems. MATLAB, COMSOL Multiphysics, and LiveLink codes used in this manuscript are available online.

Adaptive optics for dynamic aberration compensation using parallel model-based controllers based on a field programmable gate array.

Adaptive optics (AO) is an effective technique for compensating the aberrations in optical systems and restoring their performance for various applications such as image formation, laser processing, and beam shaping. To reduce the controller complexity and extend the compensation capacity from static aberrations to dynamic disturbances, the present study proposes an AO system consisting of a self-built Shack-Hartmann wavefront sensor (SHWS), a deformable mirror (DM), and field programmable gate array (FPGA)-based controllers. This AO system is developed for tracking static and dynamic disturbances and tuning the controller parameters as required to achieve rapid compensation of the incoming wavefront. In the proposed system, the FPGA estimates the coefficients of the eight Zernike modes based on the SHWS with CameraLink operated at 200 Hz. The estimated coefficients are then processed by eight parallel independent discrete controllers to generate the voltage vectors to drive the DM to compensate the aberrations. To have the DM model for controller design, the voltage vectors are identified offline and are optimized by closed-loop controllers. Furthermore, the controller parameters are tuned dynamically in accordance with the main frequency of the aberration as determined by a fast Fourier transform (FFT) process. The experimental results show that the AO system provides a low complexity and effective means of compensating both static aberrations and dynamic disturbance up to 20 Hz.

Factors influencing the applications of active heterodyne detection

Heterodyne efficiency reflects the matching states of phase and amplitude between a local oscillator (LO) beam and a received signal beam and is, therefore, an indicator of system performance. Many factors can cause sensitivity degradation or decoherence in active heterodyne detection applications, such as target speckle, atmospheric turbulence, and optical system aberrations. This paper presents a method for calculating the heterodyne efficiency by mixing LO and customized signal beams in the plane of the detector surface. Results show that the heterodyne efficiency is fixed if the amplitude distribution of the signal light obeys a certain distribution, but the phase mismatches can significantly degrade the system sensitivity. Furthermore, a high-speed camera heterodyne system was developed to evaluate the effectiveness of genetic algorithms for correcting the spatial phase mismatch in applications involving active heterodyne detection. The array detector method improves the heterodyne system sensitivity and benefits active detection applications such as Synthetic Aperture Ladar, Laser Vibrometry, and Long-range Coherent Ladar.

Starshade Imaging Simulation Toolkit for Exoplanet Reconnaissance

Starshade Imaging Simulation Toolkit for Exoplanet Reconnaissance (SISTER) is a versatile tool designed to provide accurate models of the images of exoplanet systems when observed with a starshade positioned to block the light from the host star. SISTER allows one to control a set of observational parameters including: (1) the starshade design, position, orientation, and glint properties; (2) the telescope and optical system pupil, aberrations, bandpass, and throughput including a detector model; (3) the exoplanetary system, including stellar distance and spectral type, parallax and proper motion, planet size, reflection properties, orbital parameters, and exozodiacal dust; and (4) background objects. Additionally, there is a substantial library of built-in plotting software added, but the simulations may be stored on disk and plotted with any other software. We describe SISTER’s algorithms, its operational modules, and how it can be used to generate starshade optical simulations with a high degree of fidelity. We include some imaging examples.

Reduction of spherical and chromatic aberration in axial-scanning optical systems with tunable lenses.

Optical systems with integrated tunable lenses allow for rapid axial-scanning without mechanical translation of the components. However, changing the power of the tunable lens typically upsets aberration balancing across the system, introducing spherical and chromatic aberrations that limit the usable axial range. This study develops an analytical approximation for the tuning-induced spherical and axial chromatic aberration of a general optical system containing a tunable lens element. The resulting model indicates that systems can be simultaneously corrected for both tuning-induced spherical and chromatic aberrations by controlling the lateral magnification, coma, and pupil lateral color prior to the tunable surface. These insights are then used to design a realizable axial-scanning microscope system with a high numerical aperture and diffraction-limited performance over a wide field of view and deep axial range.

Computational adaptive optics for polarization-sensitive optical coherence tomography.

Defocus aberration in optical systems, including optical coherence tomography (OCT) systems employing Gaussian illumination, gives rise to the well-known compromise between transverse resolution and depth-of-field. This results in blurry images when out-of-focus, whilst other low-order aberrations (e.g., astigmatism, coma, etc.) present in both the OCT system and biological samples further reduce image resolution and contrast. Computational adaptive optics (CAO) is a computed optical interferometric imaging technique that modifies the phase of the OCT data in the spatial frequency domain to correct optical aberrations and provide improvement of the image quality throughout the three-dimensional (3D) volume. In this Letter, we report the first implementation of CAO for polarization-sensitive OCT to correct defocus and other low-order aberrations, providing enhanced polarization-sensitive imaging contrast (i.e., intensity and phase retardation) on a 3D OCT phantom, molded plastics, ex vivo chicken breast tissue, and ex vivo human breast cancer tissue.

Macro usage for analyzing of a telescopic system aberrations in ZEMAX

The experience of optical system aberration analysis using ZEMAX software demonstrates the necessity to acquire and combine data from different text windows such as windows of Longitudinal Aberration, Ray Fan, Field Curvature and Distortion, Lateral Colour etc. This routine operation takes much time and significantly slows down the design process. Moreover, an engineer should always remember about some features of data interpretation connected with different calculation algorithms in different optical schools. It instigated us to develop a macro that forms one-window aberration summary for afocal systems with proper data interpretation according to domestic optical scientific school.

Point diffraction interferometer with tilted waves for measuring complex surfaces

Recently, much attention has been paid to optical components with complex surfaces because they can significantly optimize the aberrations of optical systems. However, a complex surface introduces several difficulties for precise measurement. To address this challenge, we propose tilted-wave point diffraction interferometer (TPDI) for measurements of complex surfaces. TPDI combines the advantages of tilted-wave interferometry and point diffraction interferometry, thus enabling high-precision measurements of complex surfaces; moreover, this method has demonstrated good efficiency and versatility. We adopt a fiber array (FA) to generate diffractive tilted waves to compensate for the local gradient of the test specimen. Unlike the classical PDI, which focuses more on the beam quality of the on-axis diffractive wave, the proposed system requires better quality for both the on-axis and off-axis diffractive waves. Therefore, the main parameters of the FA that may introduce measurement errors are analyzed, including the end face roughness of the array, the quality of diffractive wavefronts, and the initial optical path differences. Finally, the measurement result of the high-order hyperboloid verifies that our TPDI is effective and its precision of testing a complex surface is better than λ / 37 (rms, λ = 632.8 nm).

Understanding Lens Aberrations

In most textbooks, lens aberrations are usually described in the briefest possible manner, without any attempt for their proper derivation. At the same time, monographs which do go into more detail are often inaccessible to most students and non-specialists interested in deeper understanding of this topic. This article tries to fill this gap and provide an introduction to what happens when basic formulas of Geometrical Optics are extended by third-order terms in Taylor’s expansion of sin (α). The presentation is accessible to most undergraduate students as it requires only some knowledge of basic calculus and planar geometry. The resulting five aberrations are then described in detail, including a novel derivation of the exact shape of coma. A simple Mathematica program is included to facilitate numerical exploration of the magnitude of the resulting aberrations for various optical systems.

Analysis of polarization aberration of space optical system based on freeform surface

Analysis of polarization aberration of space optical system based on freeform surface

Influence of spectral characteristics of light sources on measuring space camera modulation transfer function

Modulation transfer function (MTF) measurement is a major means to evaluate the imaging quality of a space camera. The influence caused by the spectral characteristic of light source on the MTF results is not negligible, because the transmittance and color aberration of optical systems, and quantum efficiency of the space camera detectors are all spectrally related. Thus, MTF results tested by different light sources are different from each other. To address this problem, we propose a method to analyze the influence of spectral characteristics of light sources on measuring the MTF of space cameras. In addition, the devices and methods are designed to calibrate the spectral response and monochrome point spread function (PSF) of space camera. A Sigma lens (focal length: 1000mm, F number: 5.6) and a Cannon EOS 5DSR camera (pixel size: 4.14 μm) are combined into an experimental space camera, whose spectral response is calibrated with a monochromator (Omno30300, NBeT) and a spectral radiometer (FieldSpec, ASD). We calibrate the monochrome PSF of the Sigma lens with the same monochromator and a CCD (PIXIS 1024, Princeton Instruments, pixel size: 13 μm) micro-measuring system (20X objective). During the calibration of spectral response and monochrome PSF, the same collimator (focus: 5000 mm, F number: 10) is used. With using the proposed method and those calibrating data, we compute the theoretical values of the MTF of a space camera measured separately with five different light sources. The results indicate that MTF measured by a xenon lamp is greatly different from those MTFs measured by the other four light sources. Comparisons of those theoretically calculated MTFs, separately, show that the MTF measured by a tungsten halogen lamp is greater than the MTF measured by a xenon lamp at each spatial frequency. The deviation between those two lamps reaches a maximum value of 0.075 in the medium-high frequency zone. Furthermore, in order to verify those theoretical conclusions, a platform including a collimator and the previous space camera is constructed. The MTFs measured by a tungsten halogen lamp and a xenon lamp are computed with the slanted-edge method respectively. The results demonstrate that the distributions and deviations of the MTFs tested by those two lamps are identical to those theoretical results at each spatial frequency, with the maximum deviation being 0.057. The theoretical and experimental results demonstrate that the suggested method can accurately calculate the influence of spectral characteristics of light sources on measuring MTF of space cameras. The proposed method can also be adopted to investigate the influence of spectral characteristics of light sources on MTF of optical systems in the design or test stages.

Dynamic modulation transfer function measuring device for photoelectric imaging system

In the optical imaging system, the dynamic modulation transfer function (DMTF) is affected by the wave aberration of optical system, the signal resolution and transfer characteristics of detector modules, and the image blur caused by the carrier motion, which has become one of the important parameters of the photoelectric imaging system. Based on the testing principle of dynamic and static modulation transfer function of photoelectric imaging system, a DMTF measuring device was developed, in which the focal length of optical collimation system was 10 000 mm, and the speed control range of moving target was 30 mm/s~5 000 mm/s, which met the DMTF test of photoelectric imaging system with long focal length. A series of experiments were carried out, and the results show that the repeatability of DMTF measurement is better than 0.01, and the uncertainty of measurement can reach to U= 0.05 (k=2).

Aberrations of plane-symmetrical mirror systems with freeform surfaces. Part II: closed-form aberration formulas.

The aberrations of reflective optical systems with planar symmetry are investigated in the most general case, with freeform surfaces and possibly different locations of the tangential and sagittal object and image. In this second and last paper, closed-form expressions are derived for the aberrations created by an individual mirror. We study two-mirror off-axis telescopes and establish a new family of designs that we show is simultaneously free of constant coma, linear astigmatism, and quadratic distortions (including smile and keystone). Analytical expressions for the intrinsic aberrations of an astigmatic beam are also derived.

Aberrations of plane-symmetrical mirror systems with freeform surfaces. Part I: generalized ray-tracing equations.

The aberrations of reflective optical systems with one plane of symmetry are investigated in the most general case, with freeform surfaces and possibly different locations of the tangential and sagittal object and image. In this first paper in a series of two, we establish generalized ray-tracing equations including transverse aberrations up to the third order in ray coordinates. The ray-tracing treatment allows us to overcome difficulties linked to the non-existence of a suitable astigmatic wavefront reference. The obtained expressions can describe multi-mirror systems and include all induced aberration terms. As an illustration, a simple freeform off-axis mirror is analyzed.