Axial Chromatic Aberration Research Articles

Telephoto achromatic camera based on optical–digital co-design

Due to the difficulty of correcting chromatic aberration (CA) in telephoto cameras, recent studies have combined image algorithms with simple optical structures, such as single-spherical lenses, for high-quality photography, moving away from complex optics. However, this approach often struggles to comprehensively address compounded issues arising from optical aberrations of simple optical systems, including defocus blur and multi-channel misalignment. To tackle this challenge, this manuscript presents an approach for developing a telephoto imaging system by leveraging the distinct characteristics of axial and lateral chromatic aberrations (ACA, LCA) over the visible spectrum. The optical design is limited to a specific wavelength range to preserve high-frequency information of the green channel. A cross-channel fitting method is presented to suppress the LCA. Subsequently, the powerful capabilities of deep learning are utilized to correct ACA, defocus blur, and other residual optical aberrations. Simulation experiments demonstrate the effectiveness of the proposed approach in mitigating the CA inherent in telephoto systems, thereby delivering high-quality imaging results over the whole visible waveband.

High-NA broadband achromatic metalens in the visible range

We designed a high-NA (High numerical aperture) broadband achromatic metalens consisting of elliptical TiO2-based integrated-resonant unit-cells. The phase profile for the designed metalens is constituted by incorporating the geometric phase with the transmission phase, where the geometric phase contributes to the basic phase profile of the metalens and the transmission phase is used to compensate phase profile at different incident wavelengths. With the method of finite element simulation, the results demonstrate that the metalens has an average focusing efficiency of 36.4% in the visible range from 530 nm to 850 nm. Compared with chromatic metalens, the axial chromatic aberration of achromatic metalens is reduced by 2.66 times. Furthermore, the designed metalens has a high-NA of 0.564. This work can be potentially applied in various fields, such as optical communications, microscopy imaging, and optical instruments.

Design of a Prism-Grating Wide Spectral Range Transmittance Imaging Spectrometer.

As spectroscopic detection technology rapidly advances, back-illuminated InGaAs detectors with a wider spectral range have emerged. Compared to traditional detectors such as HgCdTe, CCD, and CMOS, InGaAs detectors offer a working range of 400-1800 nm and exhibit a quantum efficiency of over 60% in both the visible and near-infrared bands. This is leading to the demand for innovative designs of imaging spectrometers with wider spectral ranges. However, the widening of the spectral range has led to the presence of significant axial chromatic aberration and secondary spectrum in imaging spectrometers. Additionally, there is difficulty in aligning the system optical axis perpendicular to the detector image plane, resulting in increased challenges during post-installation adjustment. Based on chromatic aberration correction theory, this paper presents the design of a wide spectral range transmission prism-grating imaging spectrometer with a working range of 400-1750 nm using Code V. The spectral range of this spectrometer covers both the visible and near-infrared regions, which is beyond the capability of traditional PG spectrometers. In the past, the working spectral range of transmission-type PG imaging spectrometers has been limited to 400-1000 nm. This study's proposed chromatic aberration correction process involves selecting optical glass materials that match the design requirements and correcting the axial chromatic aberration and secondary spectrum, ensuring that the system axis is perpendicular to the detector plane and easy to adjust during installation. The results show that the spectrometer has a spectral resolution of 5 nm, a root-mean-square spot diagram less than 8 μm over the full field of view, and an optical transfer function MTF greater than 0.6 at a Nyquist frequency of 30 lp/mm. The system size is less than 90 mm. Spherical lenses are employed in the system design to reduce manufacturing costs and complexity while meeting the requirements of wide spectral range, miniaturization, and easy installation.

Achromatic polymer-dispersed liquid crystal lens with diffractive–refractive hybrid structure

The focal length of liquid crystal Fresnel lens is electrically controllable, but the disadvantage is the chromatic aberration is obvious. In this paper, the electrically controlled zoom characteristics of liquid crystal lens and the basic theory of Fresnel lens achromatic are analyzed, and a diffractive–refractive hybrid lens model made of polymer-dispersed liquid-crystal (PDLC) material is proposed. Fresnel liquid crystal lenses and PDLC hybrid lenses are tested with light at R (700.0 nm), G (546.1 nm) and B (435.8 nm) wavelengths, respectively. The simulation results show that the hybrid lens provides a greater range of adjustment of the focus position. After voltage modulation, the measured light with three different wavelengths have the same focal length, which means that the axial chromatic aberration is eliminated. In addition, with the elimination of axial chromatic aberration, the zoom range of the hybrid lens is doubled by further accurately controlling the electrode, which breaks through the limitation that the traditional liquid crystal lens can only work in monochromatic light spectrum.

Multicolor high-resolution whole-brain imaging for acquiring and comparing the brain-wide distributions of type-specific and projection-specific neurons with anatomical annotation in the same brain

Visualizing the relationships and interactions among different biological components in the whole brain is crucial to our understanding of brain structures and functions. However, an automatic multicolor whole-brain imaging technique is still lacking. Here, we developed a multicolor wide-field large-volume tomography (multicolor WVT) to simultaneously acquire fluorescent signals in blue, green, and red channels in the whole brain. To facilitate the segmentation of brain regions and anatomical annotation, we used 4′, 6-diamidino-2-phenylindole (DAPI) to provide cytoarchitecture through real-time counterstaining. We optimized the imaging planes and modes of three channels to overcome the axial chromatic aberration of the illumination path and avoid the crosstalk from DAPI to the green channel without the modification of system configuration. We also developed an automatic contour recognition algorithm based on DAPI-staining cytoarchitecture to shorten data acquisition time and reduce data redundancy. To demonstrate the potential of our system in deciphering the relationship of the multiple components of neural circuits, we acquired and quantified the brain-wide distributions of cholinergic neurons and input of ventral Caudoputamen (CP) with the anatomical annotation in the same brain. We further identified the cholinergic type of upstream neurons projecting to CP through the triple-color collocated analysis and quantified its proportions in the two brain-wide distributions. Both accounted for 0.22%, implying CP might be modulated by non-cholinergic neurons. Our method provides a new research tool for studying the different biological components in the same organ and potentially facilitates the understanding of the processing mechanism of neural circuits and other biological activities.

Design and on-orbit verification of Tianwen-1 multispectral camera

<p indent=0mm>China’s first Mars exploration mission Tianwen-1 was successfully launched on July 23, 2020. The multispectral camera is an essential payload of Tianwen-1 and is installed on the mast of the Zhurong rover. The scientific goals of the mission are to obtain multispectral images of the landing and inspection zones, investigate the surface material composition on Mars, and obtain basic information on the chemical evolution of Mars. This article introduces the scheme and design results of the Tianwen-1 multispectral camera. To improve reliability, Tianwen-1 realizes multispectral imaging and corrects axial chromatic aberration by switching eight narrow-band filters with different thicknesses, and achieves focusing function by switching six focus compensation lenses of different thicknesses. The scientific data of on-orbit work shows that the image is clear and the spectral data are normal. The spectral reflectance data of the calibration board taken by the multispectral camera on Mars are consistent with the ground measurement data. The spectral reflectance data of the Martian surface obtained by the multispectral camera are basically consistent with the spectral reflectance data obtained by the Mars Reconnaissance Orbiter Imaging Spectrometer (CRISM) in orbit.

Single-shot 3D profilometry using a color imaging polarimeter

We demonstrate a single-shot uniaxial three-dimensional (3D) profilometry system that illuminates a sample with a color structured polarization pattern with an axial chromatic aberration. We have previously shown that real-time 3D shape measurement can be performed without the occlusion problem using a polarization camera and a monochromatic polarized pattern. Here, we show that it is possible to double the depth range of the system, with no tradeoff in depth resolution, measurement speed, or accuracy, using color pattern projection and an RGB polarization camera. We present the measurement principles of the system and show the results of a real-time 3D profilometry experiment for a sample with a deep hole.

Post hoc Correction of Chromatic Aberrations in Large-Scale Volumetric Images in Confocal Microscopy.

Over the last decade, tissue-clearing techniques have expanded the scale of volumetric fluorescence imaging of the brain, allowing for the comprehensive analysis of neuronal circuits at a millimeter scale. Multicolor imaging is particularly powerful for circuit tracing with fluorescence microscopy. However, multicolor imaging of large samples often suffers from chromatic aberration, where different excitation wavelengths of light have different focal points. In this study, we evaluated chromatic aberrations for representative objective lenses and a clearing agent with confocal microscopy and found that axial aberration is particularly problematic. Moreover, the axial chromatic aberrations were often depth-dependent. Therefore, we developed a program that is able to align depths for different fluorescence channels based on reference samples with fluorescent beads or data from guide stars within biological samples. We showed that this correction program can successfully correct chromatic aberrations found in confocal images of multicolor-labeled brain tissues. Our simple post hoc correction strategy is useful to obtain large-scale multicolor images of cleared tissues with minimal chromatic aberrations.

Relativistic theory of aberrations of electrostatic electron-optical systems

Using the central particle method, within the framework of a unified mathematical formalism, the equations of trajectories of charged particles in electrostatic electron mirrors and lenses, including cathode lenses, are obtained, taking into account relativistic effects, with an accuracy of the third order of smallness inclusive. On the basis of the obtained equations, the conditions for the spatial focusing of beams of charged particles in such systems and their coefficients of geometric aberrations of the third order and chromatic aberrations of the second order are determined with full account for relativistic effects. By means of numerical calculations, parameters of the three-electrode electrostatic mirror of rotational symmetry, which provide conditions for simultaneous elimination of spherical and axial chromatic aberrations with allowance for relativistic effects, are determined.

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.

Compound eye image scanner optimally arranged for image combining and suppressing axial chromatic aberration by wavefront coding

A compound eye optical system design allows us to construct a compact image scanner with a large field of view and a large depth of field, both of which are beneficial for use in a copier’s flatbed scanner. Our prototypes are constructed of 32 or 28 imaging units, which are ommatidia, and the representations from the imaging units are electrically combined. Since the arrangement of the imaging units is a key factor in combining the images correctly without any loss at the boundaries, we discuss two types of arrangements along with results of their prototypes: a one-line arrangement of varying magnification imaging units and a two-line staggered arrangement of telecentric imaging units. We also discuss the effectiveness of wavefront coding (WFC) in suppressing chromatic aberration, which is caused using cheap refractive imaging units, along with experimental results of applying both cubic- and quartic-phase-modulated WFC.

Теория и расчет электростатических электронных зеркал с учетом релятивистских эффектов

Using the central particle method, the equations of the trajectory of charged particles in an axisymmetric electrostatic mirror are obtained with an accuracy of the third order of smallness inclusive with account for relativistic effects. The conditions for spatial focusing and the coefficients of spatial aberrations in the Gaussian plane of the mirror image are determined with account for relativism. By means of numerical calculations, conditions for simultaneous elimination of spherical and axial chromatic aberrations are determined, taking into account relativistic effects, in an axisymmetric electrostatic mirror when the object plane of the mirror is aligned with its focal plane. It is shown that account for high particle velocities leads both to a shift in the position of the Gaussian image plane and a change in the focusing quality.

Microscope calibration protocol for single-molecule microscopy

Single-molecule microscopy allows for the investigation of the dynamics of individual molecules and the visualization of subcellular structures at high spatial resolution. For single-molecule imaging experiments, and particularly those that entail the acquisition of multicolor data, calibration of the microscope and its optical components therefore needs to be carried out at a high level of accuracy. We propose here a method for calibrating a microscope at the nanometer scale, in the sense of determining optical aberrations as revealed by point source localization errors on the order of nanometers. The method is based on the imaging of a standard sample to detect and evaluate the amount of geometric aberration introduced in the optical light path. To provide support for multicolor imaging, it also includes procedures for evaluating the geometric aberration caused by a dichroic filter and the axial chromatic aberration introduced by an objective lens.

Achromatic metasurface doublet with a wide incident angle for light focusing.

Benefiting from the excellent capabilities of arbitrarily controlling the phase, amplitude and polarization of the electromagnetic wave, metasurfaces have attracted much attention and brought forward the revolution of fields ranging from device fabrications to optical applications. Cascaded metasurfaces have been demonstrated to correct the monochromatic aberration and enable a near-diffraction-limited focusing spot over a wide incident angle. However, they can only work under the design wavelength and suffer from the axial chromatic aberration at another wavelength. Here, an achromatic metasurface doublet is proposed to eliminate the axial achromatic aberration and enable high-quality focusing with a wide incident angle at distinct wavelengths. It consists of square nanopillar arrays with spatially varying width to simultaneously realize wavelength-dependent phase controls. The constructed metasurface doublet is further verified numerically and near-diffraction-limited foci are exactly formed at the same plane with an incident angle up to 20° for design wavelengths. We expect that our proposed approach can find optical applications in the fields of holograms, photograms, microscopy and machine vision.

Spectral acquisition method based on axial chromatic and spherical aberrations of lens.

In this study, a spectral acquisition method is proposed in which axial chromatic and spherical aberrations are introduced as an error function. These aberrations lead to changes in the focal lengths as the wavelengths of the incident light changes. A coefficient matrix representing the variation in the intensity distribution of each image, formed at the focal point (the detection position) corresponding to a wavelength, is obtained by calibration. The least square method is used to reconstruct the spectrum. The numerical simulation results show that the spectral correlation coefficient and the spectral mean square error between the reconstructed spectrum and the original spectrum are 0.9997 and 0.0025, and 0.9683 and 0.0204, respectively, for the polychromatic light spectrum obtained from the mercury lamp using our experimental set-up. These results confirm the feasibility and efficiency of the proposed spectral imaging method.

Visible achromatic super-oscillatory metasurfaces for sub-diffraction focusing.

Conventional optical lenses enable precise foci but suffer from the diffraction limit due to the cutoff of spatial frequencies. Development of a super-oscillatory phenomenon offers an alternative approach to realize far-field sub-diffraction focusing. However, most super-oscillatory lenses exhibit a strong dependence on incident wavelengths, resulting in a narrow-band working frequency due to a fragile super-oscillatory field. Here, for the first time, achromatic super-oscillatory metasurfaces (ASOMs) are proposed to simultaneously steer optical fields at visible wavelengths of 473 nm, 532 nm and 632.8 nm and to achieve focusing at the same axial position with a resolution beyond the diffraction limit. These metasurface-based devices provide dispersionless phase profiles so that the material dispersion can be neglected in the optimization process. In addition, the design strategy can effectively circumvent the axial chromatic aberration observed in previously demonstrated metasurfaces. Constructed ASOMs are further verified numerically and simulated results for one ASOM with spot sizes of 0.706, 0.722 and 0.750 times the diffraction limit at the preset plane are consistent with the designs. Furthermore, benefiting from flexible and arbitrary phase modulations of the metasurface, the proposed method gives more freedom for a design of a super-oscillatory field and enables a lightweight, low-cost and compact optical element to replace the bulky doublet/triplet lens in a conventional optical system.

Chromatic aberration of plane-symmetric optical systems.

This paper presents a calculation method of chromatic aberration of such kinds of optical systems based on the aberration theory of plane-symmetric optical systems, and the analytic expressions of the axial chromatic aberration and chromatic change in the magnification at an image plane of any position are derived. The resultant expressions are used to calculate the chromatic aberration of two single-lens optical systems with a large incidence angle, and the calculation results are compared to the ones obtained from a ray-tracing program to validate the chromatic aberration expressions. The study shows that the calculation accuracy of the chromatic aberration expressions is satisfactory. The analytical analysis of chromatic aberration is helpful in the imaging analysis and design of plane-symmetric optical systems.

Multimodal label-free ex vivo imaging using a dual-wavelength microscope with axial chromatic aberration compensation.

Label-free microscopy is a very powerful technique that can be applied to study samples with no need for exogenous fluorescent probes, keeping the main benefits of multiphoton microscopy, such as longer penetration depths and intrinsic optical sectioning while enabling serial multitechniques examinations on the same specimen. Among the many label-free microscopy methods, harmonic generation (HG) is one of the most intriguing methods due to its generally low photo-toxicity and relative ease of implementation. Today, HG and common two-photon microscopy (TPM) are well-established techniques, and are routinely used in several research fields. However, they require a significant amount of fine-tuning to be fully exploited, making them quite difficult to perform in parallel. Here, we present our designed multimodal microscope, capable of performing simultaneously TPM and HG without any kind of compromise thanks to two, separate, individually optimized laser sources with axial chromatic aberration compensation. We also apply our setup to the examination of a plethora of ex vivo samples to prove its capabilities and the significant advantages of a multimodal approach.

Simple and practical approach for computing the ray Hessian matrix in geometrical optics.

A method is proposed for simplifying the computation of the ray Hessian matrix in geometrical optics by replacing the angular variables in the system variable vector with their equivalent cosine and sine functions. The variable vector of a boundary surface is similarly defined in such a way as to exclude any angular variables. It is shown that the proposed formulations reduce the computation time of the Hessian matrix by around 10 times compared to the previous method reported by the current group in Advanced Geometrical Optics (2016). Notably, the method proposed in this study involves only polynomial differentiation, i.e., trigonometric function calls are not required. As a consequence, the computation complexity is significantly reduced. Five illustrative examples are given. The first three examples show that the proposed method is applicable to the determination of the Hessian matrix for any pose matrix, irrespective of the order in which the rotation and translation motions are specified. The last two examples demonstrate the use of the proposed Hessian matrix in determining the axial and lateral chromatic aberrations of a typical optical system.

Damage Characteristics of Dynamically Induced Incipient Spall in Ultrapure Aluminum

A series of plate-impact experiments were performed to study the damage characteristics of incipient spall in ultrapure aluminum (99.999%). Surface profile measurement system based on the axial chromatic aberration was used to measure the cross section of “soft-recovered” samples and reconstruct the metallographic and 3D surface topography. Statistical analyses show that the size distribution, coalescence condition and connectivity factor of the voids are regularly affected by loading conditions. Based on this finding, the mechanisms that control the damage properties and evolution process of dynamic fracture are analyzed in detail. The results of this research offer an experimental quantitative microstructure description of the ductile fracture process.