Longitudinal Aberration Research Articles

Exact formula to relate optical path differences and transversal aberration components.

An exact equation to relate the optical path differences (OPD) with its transversal aberration components (TAC) is determined. The OPD-TAC equation reproduces the Rayces formula and introduces the coefficient for the longitudinal aberration. The defocus orthonormal Zernike polynomial (Z DF) is not a solution for the OPD-TAC equation since the obtained longitudinal defocus depends on the ray height on the exit pupil, meaning that it cannot be interpreted as a defocus. In order to find an exact expression for OPD defocus, first, a general relationship between the wavefront shape and its OPD is established. Second, an exact formula for the defocus OPD is established. Finally, it is proved that only the exact defocus OPD is an exact solution of the exact OPD-TAC equation.

A wave-optical model for chromatic confocal sensing using multimode fibre incoherent illumination

This paper presents a wave-optical model for chromatic confocal signals based on multimode optical fibre data acquisition. It is shown that the emitted light from a multimode fibre can be modelled as a point source grid. The confocal signal can be obtained by incoherent summation of the intensities of the reflected fields in the detector plane. In this manner, this two-dimensional wave-optical model encompasses the temporal incoherence of the light source due to the usage of a broadband light source and the spatial incoherence due to the application of a multimode fibre. In fact, this model enables the modelling of different degrees of coherence. Therefore, to our knowledge, it represents the most thorough modelling tool for chromatic confocal signals. Physical parameters such as the spectral distribution of the polychromatic light source, the lateral distribution of point sources on the grid, and the strength of longitudinal aberrations, and their influences on the chromatic confocal signal have been evaluated in detail. Consideration of all these parameters results in simulated chromatic confocal signals, which almost perfectly match the experimentally recorded chromatic confocal signals. The results obtained will be very useful for the development of a deeper understanding of chromatic confocal sensing, to optimise the setup parameters with regard to a particular application and to reinterpret the results, possibly in combination with artificial intelligence algorithms, in order to increase the measurement precision and to reduce the demands imposed on the manufacturing quality of the optical elements.

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.

Influence of aberrations and roughness on the chromatic confocal signal based on experiments and wave-optical modeling

This paper addresses the effect and influence of wave optical aberrations and surface roughness on the chromatic confocal signal and resulting measurement errors. Two possible approaches exist for implementing chromatic confocal imaging based on either refraction or diffraction. Both concepts are compared and an expression for the expected chromatic longitudinal aberrations when using a diffractive optical element is derived. Since most chromatic confocal sensors are point sensors, the discussion on wave-optical aberrations is focused on spherical aberrations. Against common belief, the effect of spherical aberrations cannot be eliminated in the calibration process using for instance a piezo mounted mirror. It will be shown in the following that even a diffraction limited system with peak to valley spherical aberration smaller than 0.25 wavelength suffers from measurement errors. Experimental results will be shown to highlight this important issue. In order to develop a deeper understanding of the underlying physics, a wave-optical simulation environment has been realized. This wave-optical model furthermore enables the investigation of the influence of roughness. Herethereto the correct choice of numerical aperture when investigating a rough surface is based on a heuristic approach. Using the wave-optical simulations an explanation for the increased noise when employing a low numerical aperture to examine rough surfaces will be derived. Furthermore, a formula is presented to support the selection of the correct numerical aperture with regards to the roughness parameters of the surface under investigation.

Spherical aberration of camera-like eyes

The longitudinal and transverse spherical aberrations are estimated for the reduced camera-like eyes of gastropod mollusks and humans, and by comparing the latter with the diffraction limit, its effect on the resolving power in the center of the retina is analyzed. It is shown that these two types of aberration remain unchanged in the mollusk because of the constant diameter of the pupil and it increases in the human eye with an increase in the pupil diameter. Furthermore, the longitudinal aberration is always greater than the transverse value, and the difference between them decreases with increasing pupil diameter. The magnitude of the spherical aberration is comparable to the value of the diffraction limit of resolution of the mollusk’s eye and begins to exceed the value of the diffraction limit of the resolving power of the human eye with a pupil diameter of more than 4.6 mm.

Tolerance Analysis of Focus-adjustable Head-mounted Displays

Since the recent slowdown in the smartphone market, studies for wearable devices are briskly being carried out to find new markets, such as virtual reality devices. In this paper, a head-mounted display (HMD) which provides expanded virtual images before human eyes by enlarging images of a small display was designed, and the tolerance analysis method for a focus-adjustable HMD based on afocal optical systems was studied. There are two types of HMDs: a see-through type that allows the user to view the surroundings, and a see-close type where the user can only view the display screen; the former is used in this study. While designing the system, we allowed a lens within the system to be shifted to adjust its focus from +1 to −4 D (diopters).The yield of the designed systems was calculated by taking the worst-case scenario of a uniform distribution into account. Additionally, a longitudinal aberration was used rather than MTF for the tolerance analysis with respect to system performance. The sensitivity of the designed system was calculated by assigning a certain tolerance, and the focus lens shift was calculated to adjust the image surface variations resulting from the tolerance. The smaller the tolerance, the more expensive the unit price of the products. Very small tolerances may even be impossible to fabricate. Considering this, the appropriate tolerance was assigned; the maximum shift of the focus lens in which the image surface can be adjusted was obtained to find the changes in aberration and a good yield.

Design and analysis of miniature high-resolution omnidirectional gaze optical imaging system

A miniature high-resolution omnidirectional gaze optical imaging system comprising one optical low-pass filter and 5 lens elements with just one aspheric surface was successfully designed. The total tracking length of the system is 14.7 mm and fit on a 5MPx 2/3in CCD with 2448 × 2050 pixel of 3.45 μm for the full 360° × 200° imaging. We introduced the difficulties in the design of ultrawide field of view system and proposed specific computations to overcome them by aberration theories, furthermore making a simulated analysis and performance evaluation using ZEMAX optical design software. The result shows that an admirable corrected field curvature along with a low F-theta distortion, and a perfect lateral and longitudinal color aberration correction were achieved; relative illumination of all field is over 68%; when the ambient temperature changes from −40 to 70 ℃, the modulation transfer function performs in a steady range at 75 lp/mm; all of these will promote the wide-field lens application in medical, automotive, and stereo vision.

Spherical aberration in electrically thin flat lenses.

We analyze the spherical aberration of a new generation of lenses made of flat electrically thin inhomogeneous media. For such lenses, spherical aberration is analyzed quantitatively and qualitatively, and comparison is made to the classical gradient index rod. Both flat thin and thick lenses are made of gradient index materials, but the physical mechanisms and design equations are different. Using full-wave three-dimensional numerical simulation, we evaluate the spherical aberrations using the Maréchal criterion and show that the thin lens gives significantly better performance than the thick lens (rod). Additionally, based on ray tracing formulation, third-order analysis for longitudinal aberration and optical path difference are presented, showing strong overall performance of thin lenses in comparison to classical rod lenses.

Growth references for Japanese individuals with Noonan syndrome.

Noonan syndrome (NS) is a clinically and genetically heterogeneous syndrome characterized by distinctive facial features, short stature, congenital heart diseases, and other comorbidities. NS-specific growth charts are essential for NS care, but currently no such charts are available for Asian populations. We conducted a nationwide survey by collaborating with three academic societies in Japan. We obtained the data of 356 clinically diagnosed NS subjects from 20 hospitals. The Lambda-Mu-Sigma method was used for establishing growth charts. A total of 308 subjects (males: 159 and females: 149) were analyzed after excluding 48 subjects because of missing auxological data (26 subjects), presence of complications affecting growth (5 subjects), and extreme longitudinal growth aberrations which lay more than three standard deviation scores from the mean in this population (17 subjects). Genetic analyses were performed in 150 patients (48.7%); 103 (68.7%) were reported to have some abnormalities in the known causative genes. Cardiovascular diseases were found in 256 patients (83.1%). The NS-specific height, weight, and BMI charts were constructed with 3,249 mixed longitudinal and cross-sectional measurements. Growth standards for Japanese individuals with NS were established. These charts are expected to be used in various clinical settings.

Simulation studies of plasma lens experiments at Daresbury laboratory

Experiments are planned to study plasma lensing using the VELA and CLARA Front End accelerators at Daresbury Laboratory. This paper presents results of 2-dimensional particle-in-cell simulations of the proposed experiments. The variation in focusing strength and emittance growth with beam and plasma parameters are studied in the overdense (plasma density much greater than bunch density) regime for the VELA beam. The effect of spherical and longitudinal aberrations on the beam emittance was estimated through numerical and theoretical studies. Simulation results show that a focusing strength equivalent to a magnetic field gradient of 10 T m−1 can be achieved using VELA, and a gradient of 247 T m−1 can be achieved using CLARA Front End.

Design of telephoto superachromatic focusing objective used for measuring laser beam divergence

When measuring the laser beam divergence in the range of 350–1600nm, the focal plane position of focusing objective for different wavelengths needs to recalibrate. The measuring procedures are cumbersome, and the measurement error is introduced easily in the measurement result. In this paper, to solve the above-mentioned problem and obtain long focal length focusing objective with short total measuring system length, the wide wavelength band telephoto superachromatic objective with less than 3/4 telephoto ratio is introduced. The longitudinal aberration curve of the objective shows that the spherical aberration curves of different wavelength almost intersect in one point at 0.707 apertures, and the focal shift curve of the objective shows that the maximum focal shift of the system is only 99.5μm.

Longitudinal thermooptical aberration of the image in reflective telescopes

An analytical description of the dependence of the longitudinal thermal aberration of Gregorian and Cassegrain telescopes is obtained in the form of a sum of the components introduced by the thermal regime of each element of the telescope. Using a specific example, a technique is presented for determining the allowable ranges of temperature variation of the telescope housing and of the platform for attaching the primary mirror within which the thermal stability of the telescope in a steady-state thermal regime is ensured.

光谱共焦显微镜的线性色散物镜设计

As the nonlinearity between the Axial Chromatic Aberration(ACA)and the wavelength of a dispersive objective would lower the overall performance of a chromatic confocal microscope,the dependence of the ACA of an optical system on the lens assembly was studied and the transfer principle of ACA was derived.Based on ACA transfer principle,a dispersive objective configured with a negative and a positive lens groups was proposed,in which both the negative and positive lens groups could generate the linear ACA with specified focal power distribution.Optimized result indicates that the dispersive objective based on the proposed configuration has small longitudinal aberration,a large ACA,and a long working distance.The ACA of dispersive objective is 1mm in 430-710nm.The relative nonlinearity of ACA is about 4.6% and the deviation of sensitivity is less than 1/3 that of a whole,superior to traditional ones.With designed dispersive objective,the chromatic confocal microscope can achieve an axial resolution of 0.3μm and a lateral resolution of 5μm,which satisfies the requirements of precise measurement.

비대칭 오차요인이 있는 편심 광학계에서의 종수차 계산

줌렌즈에서 특정 렌즈군을 이동하여 손떨림 보정을 하는 광학적 방법에서는 광학계 설계단계에서 디센터(decenter)를 고려하여 설계한다. 이 때 여러 가지 광학설계 소프트웨어들은 디센터를 포함한 비대칭 오차요인이 있는 경우에 여러 가지 광학 성능들을 쉽게 계산할 수 있지만, 편심 광학계에 대한 정확한 분석이 부족하여 종수차 계산시에는 일부 계산오차가 생긴다. 특히 왜곡의 경우에는 비정상적으로 계산되는데, 이는 비대칭 오차요인이 있는 편심 광학계에서는 근축광선 추적이 제대로 되지 않기 때문이다. 본 논문에서는 이러한 손떨림으로 인한 디센터나 틸트(tilt)와 같은 비대칭 요인이 발생하는 줌렌즈에서 편심 광학계에 대한 근축광선 추적식을 새로이 유도하고, 이를 이용하여 비대칭 요인을 갖는 결상계의 종수차를 정확히 계산하는 방법을 제안한다. 이러한 편심 광학계에 대한 종수차 계산 방법은 줌렌즈의 손떨림 보정에 실제로 사용할 수 있다. When the optical image stabilization is implemented by moving one of the lens groups in a zoom system, decentration should be considered in the optical design process. Although it is partially possible to calibrate optical performances in an optical system with non-symmetrical elements by using a lot of commercial software, the results of calibrating longitudinal aberrations have some calibration errors because of the lack of precise consideration of decentered optical systems. In particular, the amount of distortion in paraxial ray tracing is different from the experimental value because paraxial ray tracing in the optical system is not useful. In this paper, in order to solve this problem being from various commercial lens design software, the set of equations of paraxial ray tracing in a zoom lens system with the non-symmetrical elements like decentration or tilt are theoretically induced. Then, the methods to calibrate the equations of longitudinal aberrations by using these equations in a non-symmetrical optical system are presented. The method of calibrating longitudinal aberrations can in practice be used to correct hand shaking effects in a zoom lens system.

Removing chromatic aberration by digital image processing

Chromatic aberration is a form of aberration in color optical devices that produces undesirable color fringes along borders within images. It is becoming a more critical problem these days as digital cameras are getting smaller, while the number of picture elements is increasing. We propose a novel method for detecting and eliminating chromatic aberration using image processing. We first analyze the color behavior on edges that do not show chromatic aberration and propose a range limitation for color difference signals. When pixels violate the preceding condition, they can be considered as color fringes caused by chromatic aberration. Corrected pixel values are generated to eliminate the chromatic aberrations. The proposed algorithm corrects both lateral and longitudinal aberration in an image, and experimental results are provided to demonstrate its efficacy.

Geometrical and optical properties of an afocal two-mirror system

This paper establishes a connection between the mathematical expressions for the longitudinal aberrations of the normals of the surfaces that form an afocal two-mirror system (ATMS) corrected for spherical aberration for an axial pencil of rays and presents a generalized global solution of the ATMS. An algorithm is developed for calculating oblique meridional pencils of rays transmitted through an ATMS.

Adding a Maksutov-like corrector to a refractor apochromat improves the color correction of the apochromat

After the more than six decades since D. D. Maksutov introduced his aplanatic, catadioptric camera with the meniscus corrector plate and spherical-mirror objective, the system and its variants are well familiar within the design community. But it would have achieved limited enthusiasm had it not been for the singlet corrector's propensity for achromatization, since no balancing aberration is available in the objective. However, the refractor-objective apochromat possesses balancing, chromatic residuals that may be coupled with a Maksutov-like corrector plate to provide improved correction for chromatic aberration. The combination may be further optimized to generate a chromatic error of longitudinal aberration that is only a small fraction of that of the progenitor refractor objective alone. Examples are provided with one and two corrector elements. Caveats are discussed.

Acousto-optic processing of images in visible and ultraviolet light

The paper concerns processing of optical images by means of tunable acousto-optic filters. Experimental and theoretical research showed that longitudinal chromatic aberrations cause a suffcient decay of the spatial resolution in the devices. It is shown that a proper choice of an optical cheme of an imager reduces the longitudinal aberrations all over the tuning range of the filters.

Design of a hybrid infrared apochromatic optical system beyond normal temperature

The principle and design method of employing diffractive optical element to athermalize an infrared optical system are discussed. An analysis is made on the diffractive optical elements dispersion characteristics and its superiority in correcting the second spectrum. A hybrid infrared optical system，as a practical application example，which has realized apochromatism and works beyond normal temperature, is presented. The parameters of the system are as follows: the focal length is 100mm，relative aperture is 1/2，field of view is 6°，and the working waveband is 8—11μm. In the system，only two materials，namely silicon and germanium, are used. The image quality of the system achieves the diffractive limit within the temperature range of -80—200℃. At about 0.7 aperture，three longitudinal aberration curves of the system intersect at one point，and the apochromatism of the optical system is achieved.

Advanced numerical studies of the neutralized drift compression of intense ion beam pulses

Longitudinal bunch compression of intense ion beams for warm dense matter and heavy ion fusion applications occurs by imposing an axial velocity tilt onto an ion beam across the acceleration gap of a linear induction accelerator, and subsequently allowing the beam to drift through plasma in order to neutralize its space-charge and current as the pulse compresses. The detailed physics and implications of acceleration gap effects and focusing aberration on optimum longitudinal compression are quantitatively reviewed using particle-in-cell simulations, showing their dependence on many system parameters. Finite-size gap effects are shown to result in compression reduction, due to an increase in the effective longitudinal temperature imparted to the beam, and a decrease in intended fractional tilt. Sensitivity of the focal plane quality to initial longitudinal beam temperature is explored, where slower particles are shown to experience increased levels of focusing aberration compared to faster particles. A plateau effect in axial compression is shown to occur for larger initial pulse lengths, where the increases in focusing aberration over the longer drift lengths involved dominate the increases in relative compression, indicating a trade-off between current compression and pulse duration. The dependence on intended fractional tilt is also discussed and agrees well with theory. A balance between longer initial pulse lengths and larger tilts is suggested, since both increase the current compression, but have opposite effects on the final pulse length, drift length, and amount of longitudinal focusing aberration. Quantitative examples are outlined that explore the sensitive dependence of compression on the initial kinetic energy and thermal distribution of the beam particles. Simultaneous transverse and longitudinal current density compression can be achieved in the laboratory using a strong final-focus solenoid, and simulations addressing the effects of focusing aberration in both directions are presented.