Axial Chromatic Aberration Research Articles

Variation of the visual acuity--luminance function with background colour.

The relationship between visual acuity (VA) and background colour is a question that still creates a certain amount of confusion even today, although most authors agree that colour background does not basically affect VA, or at best, values that are only slightly better are obtained with monochromatic yellow light. The object of this paper is to try to clarify if, when the axial chromatic aberration (ACA) has been compensated for, certain differences due exclusively to colour persist or not. In order for this, the VA-luminance functions with red, green, blue and white backgrounds have been measured for two emmetropic observers, before and after compensating for the ACA. The results show that after the compensation, the curve corresponding to red is above the one corresponding to blue, with the one corresponding to green in between. The achromatic function (white background) practically overlaps with the green one. This behaviour is consistent with that shown recently for contrast sensitivity functions (CSFs). However, the asymptotic values are identical for the three colours, and so, it is understandable that no significant differences are normally found when only a standard measurement of VA is taken using the typical illumination from an optotype projector.

Resolving power of the human visual system to monochromatic stimuli.

The resolving power in monocular, foveal vision was found to depend on the size of a white light source made of two white rectangles separated by vertical black bar. The question arises whether the wavelength of light influences this dependence. An experiment was done on three subjects using six monochromatic lights the range 450-625 nm, and white light for control measurements. The diagram of the dependence of the minimal angle of resolution on the source size takes the shape of a biphasic curve, i.e. decreasing and constant function. The wavelength was found to have no impact on the curve shape or values. The data points obtained for white light coincide with those for monochromatic lights. The results confirm a thesis that all three colour mechanisms in the human visual system are stimulated and are active in spatial summation processes, but to a degree conditioned by a spectral sensitivity of the particular colour apparatus. It was confirmed that all colour mechanisms have potentially the same acuity but the axial chromatic aberration causes observed reduction of acuity.

Three-dimensional image sensing by chromatic confocal microscopy

In the image of a confocal microscope, only those parts of an object appear bright that are located in the focal plane of the objective. Because of an axial chromatic aberration deliberately introduced into the microscope objective, the location of the focal plane depends on the wavelength used. By using a white-light source and examining an object with a depth variation less than the axial range of the chromatic focus, we find that all parts of the object appear sharp and bright in the image, but according to its height they appear in different colors. A camera with black-and-white film sequentially combines, with three selected chromatic filters, intensity and tone of color of each object point. For each tone of color one can assign a height by using a calibration curve. This assignment could be made unequivocal by the selection of filters with adequate chromatic transmission.

Effect of Color on Contrast Sensitivity with Two Different Accommodative Stimuli

We studied the influence of color and accommodation on the contrast sensitivity function (CSF). At the same time, we measured the effect of axial chromatic aberration (ACA) on the CSF. The CSF's of two observers were determined using red, green, blue, and white light, at 5- and 0.5-m viewing distances. At 5 m the CSF's were measured with natural vision and also with lenses which compensated the ACA. Results show that the effect of ACA on the CSF is to reduce the sensitivity to blue with respect to the red. The difference in sensitivity between these two colors is between 50 and 150% and varies with the frequency and the subject. When the ACA is compensated the influence of the color on the CSF is very small, in our experiment, and this result is discussed in relation to the compensating effects of chromatic adaptation of the color mechanisms. In near vision, the CSF's were measured with natural vision and also with the lenses required to give the same accommodative stimulus for all colors. We discuss the effect of accommodation on the CSF. For both far and near the results are compared with the CSF with white light.

AXIAL CHROMATIC ABERRATION OF SINGLE-POLE LENS

The axial chromatic aberration coefficient of single-pole lens is studied. Using the paraxial ray equation the axial chromatic aberration of exponential field model, which represented as a first approximation the field of single-pole lens, was analytically expressed.

Chromatic aberration of three-cylinder electrostatic lenses

Accurate calculations of the axial chromatic aberration coefficients of geometrically symmetric three-cylinder tripotential electrostatic lenses are presented for two different center electrode lengths. This is an extension of the first-order properties and the third-order spherical aberration coefficients published by Harting and Read.

CHROMATIC ABERRATION OF SINGLE-POLE PROJECTOR LENSES

The chromatic aberration of magnetic projector lenses is divided into axial aberration and chromatic field aberration. Analytical expressions for chromatic aberration coefficients of the spherical field model which is useful for the study of single-pole magnetic lenses are given.

Correction of axial chromatic aberration improves the contrast transfer in bright-field phase contrast imaging

Abstract The modulation transfer function of an electron microscope having a corrected axial chromatic aberration of first order and first degree as well as a corrected spherical aberration of third order is determined by the sperical aberration of fifth order, the almost totally controllable aperture aberrations of first to fourth order, and by the axial chromatic aberration of first order and of second degree. We calculated the contrast transfer function for axial parallel illumination for a corrected objective lens system considering a time-dependent change of the electron energy as well as considering a Gaussian energy distribution. These influences render a phase contrast transfer function, which is limited by an envelope function that is mainly determined by the chromatic aberrations. Contrast transfer functions and their envelope functions have been calculated for the case of the chromatically and spherically corrected electron microscope, as it has been investigated earlier by Scherzer, Koops and Rose. Discussion of the modulation transfer functions for the different correction states obtained show, that the correction of the axial chromatic aberration of first order and first degree to a value of

Axial chromatic aberration: linear or power function of wavenumber?

Axial chromatic aberration: linear or power function of wavenumber?

New Feasible Concepts of Aberration Correction for Realizing High-Resolution Electron Microscopes

The imaging performance of the light optical lens systems has reached such a degree of perfection that nowadays numerical apertures of about 1 can be utilized. Compared to this state of development the objective lenses of electron microscopes are rather poor allowing at most usable apertures somewhat smaller than 10-2 . This severe shortcoming is due to the unavoidable axial chromatic and spherical aberration of rotationally symmetric electron lenses employed so far in all electron microscopes.The resolution of such electron microscopes can only be improved by increasing the accelerating voltage which shortens the electron wave length. Unfortunately, this procedure is rather ineffective because the achievable gain in resolution is only proportional to λ1/4 for a fixed magnetic field strength determined by the magnetic saturation of the pole pieces. Moreover, increasing the acceleration voltage results in deleterious knock-on processes and in extreme difficulties to stabilize the high voltage. Last not least the cost increase exponentially with voltage.

Axial chromatic aberration of the human eye: frequency or wavelength?

The axial chromatic aberration of the human eye is nearly perfectly described by a linear function when expressed in terms of frequency rather than wavelength. Since linear functions are simple to work with and more readily understood, there are advantages for the expression of these data in terms of frequency.

Chromatic aberration of symmetric two-cylinder electrostatic lenses

Accurate calculations of the axial chromatic aberration coefficients of symmetric two-cylinder bipotential electrostatic lenses for three different gap values (0.10D, 0.50D, and 1.0D) are presented. This is an extension of the first-order properties and the third-order spherical aberration coefficients published by Harting and Read.

Computer programs for designing multipole electron and ion optical systems

New computer programs have been developed for designing multipole electron and ion beam systems. The charge density method is used to calculate the axial field distribution for electrostatic quadrupole and octopole lenses and deflectors, dipole deflectors, and rotated magnetic quadrupole lenses. The programs are described and some comparisons against analytic models are presented. An existing finite element program is used so that electrostatic round lenses may also be included in the analysis. An optical properties program uses a new compact aberration theory developed by the authors to calculate the first‐order focusing and deflection properties, third‐order geometrical and first‐order chromatic aberrations, for any combination of the elements already mentioned. The desired focusing is obtained by using an iterative least squares routine to focus the round and quadrupole lenses. An analysis of crossed electrostatic and magnetic quadrupole lenses is presented showing how the first‐order axial chromatic aberration coefficient can be reduced to less than 0.1 mm, making the size of the chromatic disk negligible.

Correction for chromatic aberration in microscope projection photolithography

We have measured the ultraviolet dispersion of several microscope objectives and we find that all of them are limited by axial chromatic aberration when used for polychromatic exposure of photoresist. We show how to measure and correct for the ultraviolet focus shift, and estimate the corrected resolution. Certain lenses are able to produce micron features over millimeter fields.

Correction of chromatic aberrations in GRIN endoscopes

A gradient-index (GRIN) endoscope can be constructed by substituting for the usual objective and relay sections suitable cylindrical index-distribution rod lenses. Currently available GRIN lenses exhibit large amounts of chromatic aberration. Axial color arises mostly from the relay lens, while lateral color is due to the objective lens. A negative lens cemented to a shortened GRIN relay lens can simultaneously correct axial and lateral chromatic aberrations with commercially available components. This correction system reduces the requirements for mechanical centration better than do color correctors that are incorporated into the ocular design. Monochromatic aberrations are also considered.

A modified achromatizing lens.

A lens which compensates for the axial chromatic aberration of the human eye is described and tested. Such a lens is useful in optical stimulators to render refocusing for different wavelengths unnecessary.

Human axial chromatic aberration found not to decline with age.

Millodot (1976) reported a dramatic decline in the amount of axial chromatic aberration of the human eye with age. The present study represents a failure to replicate that finding using a more standard procedure. No difference in chromatic aberration was found between a young and an older group of observers. Also, the chromatic aberrations of two observers which had been measured 25 years previously showed no decline when these measurements were repeated, even though their ages at first and second testing straddled the period over which Millodot reported the most change in chromatic aberration.

Changes in perceived color due to chromatic interactions

Studies of chromatic induction have generally examined either (a) the effects of a chromatic surround on a neutral test field, or (b) the effects of one spectral hue on another. To investigate how colors interact in other regions of color space an experiment was designed using fifteen test stimuli scattered through C.I.E. color space. The perceived hue of each stimulus was matched on its own and in the presence of five inducing stimuli. Matching was done both with and without a lens to correct axial chromatic aberration, which was found to be a significant prereceptoral factor influencing perceived colour. With chromatic aberration corrected the overall pattern of chromatic changes can be explained neither by receptor processes alone, nor by opponent channel processes alone. But a reasonable fit can be obtained if changes are allowed to take place in both levels of the system.

Lenses for correcting chromatic aberration of the eye

Optical systems for correcting the axial chromatic aberration of the eye are studied theoretically. Compact (cemented) doublets or triplets for this cannot avoid introducing unwanted transverse color. A new airspaced system is described which avoids this problem. Experimental results confirmed that this lens performed well over a 14-deg field of view.

Computerized optimization of electron-beam lithography systems

An optimization program has been developed for designing combined focusing and dual-channel deflection systems with low aberrations for electron beam lithography. The program can handle any combination of magnetic and electrostatic lenses and deflectors, and uses the damped least squares method for minimizing a weighted sum of squares of aberrations, subject to specified physical constraints. The program has been used to optimize the design of several types of lithography system. The results show that, in many cases, the program can yield designs with extremely low aberrations. For example, a system with one magnetic lens and two deflectors has been found which, at the corners of a 5 mm scan field with 5 mrad aperture, has only 0.19 μm overall aberration before dynamic corrections; by adding an electrostatic retarding field, this can be reduced to 0.12 μm. By adjusting the strengths and positions of the deflectors, several of the aberrations can be individually eliminated, including field curvature. It is also shown that electrostatic subfield deflectors can be added without significantly increasing the aberrations, and a pure electrostatic focusing and deflection system for ion beam lithography has been designed which is limited almost entirely by axial chromatic aberration.