Residual Aberrations Research Articles

Design of aspheric spectacle lenses using non-dominated sorting genetic algorithm

Significance: An effective algorithm for optimization of lens parameter can greatly eliminate the aberration and reduce the thickness, making the wearer more comfortable. Aim: We proposed a non-dominated sorting genetic algorithm (NSGA-II) for generating sets of base curves and aspheric coefficients to minimize the residual astigmatism and aberration of the lenses, while satisfying the constraints on the lens thickness and power. Approach: By simulating natural selection using the NSGA-II algorithm, the design parameters considered the inventory of the semi-finished blank. A comparison of aspheric and spherical spectacle lenses with –8 diopters was designed, simulated, processed, and measured. Results: The measured spherical and cylindrical power distributions were consistent with the simulated results with corrected oblique astigmatism and distortion. Conclusions: The aspheric spectacle lenses had the required aesthetic shape and weight reduction compared to a spherical lenses of the same power. It is verified that this paper puts forward an effective NSGA-II algorithm for the optimization of lens parameters.

Novel Chromatic Differential Confocal Matrix Sensor Using Multiband Spectral Images

In this letter, a novel chromatic differential confocal matrix (CDCM) sensor is proposed and demonstrated for accurate and fast three-dimensional (3D) profiling without mechanical scanning. In contrast to conventional chromatic confocal microscopy (CCM) methods that require spectral expansion and a peak-intensity-wavelength detection algorithm for axial positioning, our CDCM employs the intensity difference between a pair of spectral confocal images to accurately discriminate surface height. Due to the elimination of spectral expansion required by a conventional CCM, the CDCM has an at least one order of magnitude higher axial sensitivity and surface profiling efficiency than a conventional CCM. In the CDCM, axial scanning is achieved by residual chromatic aberration of an achromatic objective and by constructing a difference intensity signal between two spectral confocal images. Spectral confocal images are acquired in a parallel manner by using a digital micromirror device as an array of illumination pinholes and digitally applying the virtual detection pinhole concept. Quantitative evaluation experiments with the proof-of-principle sensor system indicate that 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">$10\times $ </tex-math></inline-formula> NA 0.25 objective, the CDCM can achieve better than <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$0.1~\mu \text{m}$ </tex-math></inline-formula> axial accuracy with an axial measurement range of approximately <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$28~\mu \text{m}$ </tex-math></inline-formula> , a lateral resolution of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$0.87~\mu \text{m}$ </tex-math></inline-formula> .

Technology for developing a high-aperture four-mirror lens with aspherical mirrors

Subject of study: Methods for optimizing the design, assembly, and alignment of a high-aperture wide-angle four-mirror axisymmetric lens are presented. Aim of study: The aim is the development of a high-tech lens design considering the relationship between the calculated tolerances for the decentering of mirrors and the technological capabilities of their fabrication, assembly, and alignment. Method: The methods include selection of an image quality criterion and calculation of its permissible decrease, distribution of the fabrication errors between the decentering errors and surface shape errors, and calculation of the tolerances based on the obtained ratios. Moreover, the motivation for choosing a lens design with a minimum number of adjustment stages based on the optimization of the calculated permissible decentering is provided considering the technological tolerances for positioning the optical elements. In addition, the possibilities of the scheme to compensate for the residual aberrations resulting from the fabrication and positioning of the mirrors are investigated. At the final stage, the method of reducing the evaluation function for the final adjustment of the optical elements in the lens is used. Main results: The design and technological solutions enabling the optimization of the requirements for the tolerances for deviation of the surface shape of the mirrors from their calculated profile, as well as decentering of the optical elements considering the technological capabilities of production, are examined. The criteria for the distribution of tolerances for permissible deviations of optical system parameters affecting the image quality are formulated. The possibility of designing a high-tech drop-in structure of a high-aperture four-mirror lens comprising a case of two blocks and a single linear adjustment stage of the second mirror to compensate for residual aberrations is demonstrated using the proposed method. Practical significance: The proposed technical solutions were tested by designing a high-resolution lens comprising four aspherical mirrors. The positive results of fabricating a lens with a high aperture and resolution allow the proposed solutions to be used for the design of multimirror axisymmetric lenses.

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).

Интерференционный метод контроля выпуклых гиперболических поверхностей с использованием дифракционного оптического элемента

Interference control methods are making it possible to evaluate with high accuracy errors in the shape of the optical part surface profile. The interference pattern processing allows obtaining a map of the surface deviations at each of its points with an accuracy of half the wavelength. An interference method is proposed for testing the convex hyperbolic surfaces, which could be introduced to control mirrors with large aperture angles in the imaginary geometric focus. The proposed auto-collimation control scheme consists of a helium-neon laser with the wavelength of 632.8 nm, a meniscus lens and a planar axisymmetric diffractive optical element to correct the meniscus spherical aberration. Numerical method is presented for calculating the optical diffraction element using a phase profile on the example of the secondary hyperbolic mirror of the Millimetron space telescope. The developed scheme was simulated in the Zemax OpticStudio program. The approximation error of the calculated phase profile was evaluated depending on the number of phase coefficients. The Fizeau interferometer optical system is proposed to implement the developed method. The influence of errors in installing a controlled mirror on the interference pattern for axial displacement, transverse displacement and tilt was determined. The residual wave aberration was evaluated in the control system

Optical design of a null test for off-axis three-mirror system based on refractive-diffractive zoom hybrid compensator

In general, the reflectors of off-axis three-mirror system have large apertures and large differences in surface shape, which means it is difficult to use one set of null compensators to test all the aspheric mirrors in the off-axis three-mirror system because of the limitation of the dynamic range of the testing equipment. In this paper, we propose a surface shape test method that combines a refractive-zoom lens group and a Spatial Light Modulator (SLM) as a null compensator to test all the aspheric surfaces of one off-axis three-mirror system. The proposed method is verified by simulating the null test process of three aspheric mirrors of one off-axis three-mirror system, with the consideration of the fabrication and alignment errors. Simulation results show that the probability that residual wave aberration is within 0.1λ RMS is 50% for the primary mirror and 40% for the secondary mirror and 80% for the tertiary mirror.

Predesign of a projector alignment system for structured light illumination systems

Structured light illumination systems can measure a target’s two-dimensional height profile. Recent advancements in computational power and algorithms have enabled the predesign of optical systems where all experimental variables are determined prior to use in the laboratory. We present a predesign process to align the projector of a custom-structured light illumination system. The predesign method uses the native optical design file to simulate the residual aberrations and can perform a trade space analysis to tailor the alignment variables to desired preferences. The presented method can predict the experimental focus position to 1.6 μm root mean square over a broad range of physical settings.

Optical Design for Aberration Correction of Ultra-Wide Spectral Range Echelle Spectrometer

The echelle grating spectrometer, with a wide spectral range and high-resolution spectral analysis, is one of the best tools for fine spectral measurement. Nevertheless, it suffers from excessive residual aberrations and a large overall size. In this study, the design and implementation of a novel asymmetric Czerny–Turner ultra-wide spectral range achromatic echelle spectrometer are described. The echelle spectrometer has three channels, and it uses an off-axis parabolic mirror to obtain collimated light without aberrations. Three sets of gratings and dispersive prisms with different coatings are utilized as cross-dispersion elements to acquire two-dimensional images containing spectral information. Suitable detectors are selected according to the requirements of each channel, and three sets of coaxial focusing lenses are designed separately to minimize the aberration. The results of the simulation analysis by ZEMAX indicate that in the entire operating band (200–1100 nm), the root mean square radius of the dispersion spots is ≤ 2.2 μm, all of which are located within the limited range of the size of the detector, thus ensuring that the system’s spectral resolution reaches 0.02 nm at 200 nm, 0.04 nm at 650 nm, and 0.1 nm at 1100 nm.

Wavefront aberrations caused by biomechanical effects after Small Incision Lenticule Extraction (SMILE) based on finite element analysis

To examine wavefront aberrations induced by biomechanical effects after Small Incision Lenticule Extraction (SMILE) surgery. The three-dimensional (3D) finite element models of the human eye were established. By loading the intraocular pressure (IOP), the displacement of the anterior and posterior surface of the cornea was calculated. Then the displacement was converted into the wavefront aberrations by wave-surface fitting. The results showed that the induced wavefront aberrations were noticeable from biomechanical effects after SMILE surgery. The induced higher-order aberrations from the anterior corneal surface included spherical aberration, y-Trefoil, and x-Tetrafoil. Spherical aberration was positively correlated with corrected diopter (D), but x-Tetrafoil and y-Trefoil remained stable. The induced wavefront aberrations from the posterior corneal surface were smaller than those from the anterior corneal surface, and some of the aberrations compensated each other. With IOP increased, defocus and x-Tetrafoil from the anterior corneal surface increased, while y-Trefoil and spherical aberration decreased. The IOP only affected defocus from the posterior corneal surface. In addition, the incision size also had a distinct impact on primary x-astigmatism and x-Trefoil from the anterior corneal surface, and it had a smaller effect on the aberrations from the posterior corneal surface. Therefore, the biomechanical effects increased residual wavefront aberrations after SMILE refractive surgery.

Theoretical study on sixth-order geometrical aberration correction

Spherical aberration correctors using hexapole fields are widely used and are pivotal in atomic-resolution imaging. Although hexapole-field correctors increase the aberration-free angular range, the angular range is limited by higher-order aberrations, such as six-fold astigmatism or sixth-order three-lobe aberration. Here, we propose two types of spherical aberration correctors to compensate for geometrical aberrations up to the sixth order. The first is a four-hexapole corrector, while the second is a two-hexapole corrector, where each hexapole has a nonuniform magnetic field. The four-hexapole corrector can increase the aberration-free angle up to almost 100 mrad. The two-hexapole corrector with a nonuniform magnetic field has a smaller aberration-free angle than that of the four-hexapole corrector, but it is more compact. The dominant residual aberration in these correctors is seventh-order spherical aberration or chaplet aberration, which is seventh-order geometrical aberration.

Research on Orbital Angular Momentum Multiplexing Communication System Based on Neural Network Inversion of Phase

An adaptive optical wavefront recovery method based on a residual attention network is proposed for the degradation of an Orbital Angular Momentum multiplexing communication system performance caused by atmospheric turbulence in free-space optical communication. To prevent the degeneration phenomenon of neural networks, the residual network is used as the backbone network, and a multi-scale residual hybrid attention network is constructed. Distributed feature extraction by convolutional kernels at different scales is used to enhance the network’s ability to represent light intensity image features. The attention mechanism is used to improve the recognition rate of the network for broken light spot features. The network loss function is designed by combining realistic evaluation indexes so as to obtain Zernike coefficients that match the actual wavefront aberration. Simulation experiments are carried out for different atmospheric turbulence intensity conditions, and the results show that the residual attention network can reconstruct the turbulent phase quickly and accurately. The peaks to valleys of the recovered residual aberrations were between 0.1 and 0.3 rad, and the root means square was between 0.02 and 0.12 rad. The results obtained by the residual attention network are better than those of the conventional network at different SNRs.

High spectral resolution compact Offner spectrometer based on the aberration-reduced convex holographic gratings recorded by spherical waves under Rowland circle mounting.

High spectral resolution, excellent imaging quality, and compact configuration have become a recent trend in push-broom imaging spectrometers. The concentric Offner imaging spectrometer has become popular due to its high optical performance and compactness. However, astigmatism is the dominant residual aberration in the Offner imaging spectrometer, which makes the meridional and sagittal images unable to be focused well and causes a deterioration in image quality and spectral resolution. In this paper, we present a compact Offner imaging spectrometer with a high resolution based on an aberration-reduced convex holographic grating (ACHG), which is recorded by spherical waves under Rowland circle mounting. The holographic aberration coefficients of ACHG and geometric aberration coefficients of the Offner imaging spectrometer are derived based on the analysis of the light-path function. Furthermore, we analyzed the relationship between holographic aberration coefficients and holographic recording parameters of ACHG under Rowland circle mounting. To balance the geometric aberration of the Offner imaging spectrometer, proper holographic aberration coefficients of the ACHG are achieved through adjusting the holographic recording parameters. The design result indicated that the Offner imaging spectrometer with ACHG provides better images than those with mechanically ruled convex grating (MRCG). Moreover, the spectral resolution is significantly improved. This lays down a theoretical basis for subsequent construction work in the Offner imaging spectrometer with holographic aberration-reduced gratings.

Miniaturized cost-effective broadband spectrometer employing a deconvolution reconstruction algorithm for resolution enhancement.

We demonstrate a miniaturized broadband spectrometer employing a reconstruction algorithm for resolution enhancement. We use an opto-digital co-design approach, by firstly designing an optical system with certain residual aberrations and then correcting these aberrations with a digital algorithm. The proposed optical design provides an optical resolution less than 1.7 nm in the VIS-channel (400-790 nm) and less than 3.4 nm in the NIR-channel (760-1520 nm). Tolerance analysis results show that the components are within a commercial class, ensuring a cost-efficient design. We build the prototype with a size of 37x30x26 mm3 and demonstrate that by applying a restoration algorithm, the optical resolution can be further improved to less than 1.3 nm (VIS-channel) and less than 2.3 nm (NIR-channel).

Direct estimation and correction of residual aberrations in the reconstructed exit-wavefunction of a crystalline specimen

Measuring residual aberrations up to second order using a crystalline specimen in transmission electron microscope is challenging. Here, we show by good examples of both experimental and simulated images that it is feasible to measure aberrations up to the second-order, using minimum amplitude contrast criterion for the exit wave function reconstructed. We propose a two-steps strategy for the task: (i) Firstly measuring defocus and two-fold astigmatism simultaneously to avoid error accumulation and to reduce the number of dimensions in parameters space. (ii) Then, with minimized misleading effects (or errors) in defocus and two-fold astigmatism, estimations of three-fold astigmatism and coma can be conducted more efficiently and effectively. Influences of other factors such as specimen structure, resolution and specimen thickness on the validity of the method are also discussed in detail. Our study provides a practical procedure for correcting residual aberrations in image wave using crystalline materials, which can then facilitate application of exit wave reconstruction technique to materials research.

Accurate and Robust Calibration of the Uniform Affine Transformation Between Scan-Camera Coordinates for Atom-Resolved In-Focus 4D-STEM Datasets.

Accurate geometrical calibration between the scan coordinates and the camera coordinates is critical in four-dimensional scanning transmission electron microscopy (4D-STEM) for both quantitative imaging and ptychographic reconstructions. For atomic-resolved, in-focus 4D-STEM datasets, we propose a hybrid method incorporating two sub-routines, namely a J-matrix method and a Fourier method, which can calibrate the uniform affine transformation between the scan-camera coordinates using raw data, without a priori knowledge of the crystal structure of the specimen. The hybrid method is found robust against scan distortions and residual probe aberrations. It is also effective even when defects are present in the specimen, or the specimen becomes relatively thick. We will demonstrate that a successful geometrical calibration with the hybrid method will lead to a more reliable recovery of both the specimen and the electron probe in a ptychographic reconstruction. We will also show that, although the elimination of local scan position errors still requires an iterative approach, the rate of convergence can be improved, and the residual errors can be further reduced if the hybrid method can be firstly applied for initial calibration. The code is made available as a simple-to-use tool to correct affine transformations of the scan-camera coordinates in 4D-STEM experiments.

Treatment of Corneal Irregularity in Radial/Astigmatic Keratotomy Patients Utilizing WaveLight Contoura.

PurposeTo demonstrate the treatment of radial keratotomy-induced corneal irregularity with topographic-guided ablation (WaveLight Contoura).MethodsThirty-two eyes of 18 patients were treated for corneal irregularity post-radial keratotomy with WaveLight Contoura topographic-guided ablation utilizing LASIK and PRK and the San Diego Protocol for reconstructing corneas. These eyes were followed for six-months. Outcomes included: measurements of vision, refraction, residual higher-order aberrations, residual lower-order and higher-order aberrations, as well as loss or gains of lines of best-corrected visual acuity.ResultsAll eyes had decreased corneal irregularity as evidenced by topographic analysis and reduction in manifest astigmatism, Contoura-measured astigmatism, higher-order aberrations, and higher-order aberrations grouped with lower-order aberrations excluding tilt (Grouped). The eyes of 5 sample patients are included in this manuscript to demonstrate the procedure, protocol, and outcomes.ConclusionTreatment with WaveLight Contoura whether as LASIK or PRK appears to be an effective treatment for corneal irregularity associated with radial/astigmatic keratotomy.

High-precision co-phase method for segments based on a convolutional neural network

In order to achieve the resolution comparable to the resolution of a monolithic primary mirror telescope and make the imaging quality of the imaging system reach or approach to the diffraction limit, the submirrors of the segments telescope should ensure co-phase splicing. To solve the problem of phase error detection, a high-precision piston error detection method is proposed based on convolutional neural network (CNN). By setting a mask with a sparse multi-subpupil configuration on the exit pupil of the imaging system, a point spread function (PSF) image dataset that is extremely sensitive to the piston error is constructed. According to the characteristics of this dataset, a high-performance CNN model is built. And the best detection range of CNN is tested. The simulation results show that a single network can accurately output the piston error of one or more submirrors in the capture range slightly less than one wavelength. When the single network is applied to the six-submirror imaging system, the detection precision of the piston error reaches an RMS value of 0.0013&lt;i&gt;λ&lt;/i&gt; (here, RMS stands for root mean square). And the method has good robustness to residual tip-tilt error, wavefront aberration, and CCD noise, light source bandwidth. The method is simple and fast, and can be widely used to detect the piston error of the segments.

Aberration measurement and correction on a large field of view in fluorescence microscopy.

The aberrations induced by the sample and/or by the sample holder limit the resolution of optical microscopes. Wavefront correction can be achieved using a deformable mirror with wavefront sensorless optimization algorithms but, despite the complexity of these systems, the level of correction is often limited to a small area in the field of view of the microscope. In this work, we present a plug and play module for aberration measurement and correction. The wavefront correction is performed through direct wavefront reconstruction using the spinning-pupil aberration measurement and controlling a deformable lens in closed loop. The lens corrects the aberrations in the center of the field of view, leaving residual aberrations at the margins, that are removed by anisoplanatic deconvolution. We present experimental results obtained in fluorescence microscopy, with a wide field and a light sheet fluorescence microscope. These results indicate that detection and correction over the full field of view can be achieved with a compact transmissive module placed in the detection path of the fluorescence microscope.

Exploiting the full potential of the advanced two-hexapole corrector for STEM exemplified at 60kV

Ultimate resolution in scanning transmission electron microscopy (STEM) with state-of-the-art aberration correctors requires careful tuning of the experimental parameters. The optimum aperture semi-angle depends on the chosen high tension, the chromatic aberration and the energy width of the source as well as on potentially limiting intrinsic residual aberrations. In this paper we derive simple expressions and criteria for choosing the aperture semi-angle and for counterbalancing the intrinsic sixth-order three-lobe aberration of two-hexapole aberration correctors by means of the fourth-order three-lobe aberration. It is noteworthy that for such an optimally adjusted electron probe the so-called flat area of the Ronchigram is explicitly not maximized. The above considerations are validated by experiments with a CEOS ASCOR in a C-FEG-equipped JEOL NEOARM operated at 60 kV. Sub-Angstrom resolution is demonstrated for a Si[112] single crystal as well as for a single-layered MoS2 crystalline film. Lattice reflections of 73 pm for silicon and 93 pm for molybdenum disulfide are visible in the Fourier transform of the images, respectively. Moreover, single sulfur vacancies can be clearly identified in the MoS2.

Implementation of the Frequency Scatter Index in Clinical Commercially Available Double-pass Systems

ABSTRACTA previous work has reported a methodology to quantify intraocular scattering using a high sensitivity double-pass instrument with a robust index, the frequency scatter index. The purpose of our study was to evaluate an adaptation of the frequency scatter index for use in clinical double-pass systems. A prospective observational study was carried out in a group of patients with nuclear cataracts (n = 52) and in a control group (n = 11) using conventional double-pass systems. The frequency scatter index and the objective scatter index were used to assess the scattering. The Spearman coefficient was calculated to assess the correlation between both indexes, obtained from the double-pass images. Simultaneous measurements were performed with a double-pass and with a Hartmann-Shack wavefront sensor in the control group. The root-mean-square wavefront error and the full width at half maximum of the double-pass image were used to quantify the residual aberrations introduced by the variations in pupil size and retinal eccentricity. Measurement in eyes with different grades of cataracts shows a strong correlation (ρ = 0.929, p < .0001) between the frequency scatter index and the objective scatter index. A certain degree of correlation was observed between the objective scatter index and the root-mean-square and between the objective scatter index and the full width at half maximum, both for measurements with a different pupillary diameter and with a different retinal eccentricity (p < .05). No relationship was observed between the frequency scatter index and the root-mean-square or between the frequency scatter index and the full width at half maximum (p > .05). We have introduced and evaluated an adaptation of a methodology proposed recently for the measurement of intraocular scattering using the double-pass technique with a robust index, which is less affected by ocular aberrations. The frequency scatter index can be applied to conventional double-pass instruments available in clinical environments.