Primary Chromatic Aberrations Research Articles

Extending the depth of field with chromatic aberration for dual-wavelength iris imaging.

We propose a method of extending the depth of field to twice that achievable by conventional lenses for the purpose of a low cost iris recognition front-facing camera in mobile phones. By introducing intrinsic primary chromatic aberration in the lens, the depth of field is doubled by means of dual wavelength illumination. The lens parameters (radius of curvature, optical power) can be found analytically by using paraxial raytracing. The effective range of distances covered increases with dispersion of the glass chosen and with larger distance for the near object point.

Методы расчета и исследование первичной хроматической аберрации RGRIN-линз

Методы расчета и исследование первичной хроматической аберрации RGRIN-линз

Chicago aberration correction work

The author describes from his personal involvement the many improvements to electron microscopy Albert Crewe and his group brought by minimizing the effects of aberrations. The Butler gun was developed to minimize aperture aberrations in a field emission electron gun. In the 1960s, Crewe anticipated using a spherical aberration corrector based on Scherzer's design. Since the tolerances could not be met mechanically, a method of moving the center of the octopoles electrically was developed by adding lower order multipole fields. Because the corrector was located about 15 cm ahead of the objective lens, combination aberrations would arise with the objective lens. This fifth order aberration would then limit the aperture of the microscope. The transformation of the off axis aberration coefficients of a round lens was developed and a means to cancel anisotropic coma was developed. A new method of generating negative spherical aberration was invented using the combination aberrations of hexapoles. Extensions of this technique to higher order aberrations were developed. An electrostatic electron mirror was invented, which allows the cancellation of primary spherical aberration and first order chromatic aberration. A reduction of chromatic aberration by two orders of magnitude was demonstrated using such a system.

Primary chromatic aberrations of a diffractive lens on finite substrate

In this report, we present an analysis for the primary chromatic aberrations of a diffractive lens on a spherically curved substrate having nonunity refractive index. This analysis facilitates achieving an optimal thin lens layout during structural design of the diffractive lens with prespecified targets for primary chromatic aberrations. Sets of nomographs that provide ready estimates for these aberrations are also given.

Adjustable hybrid diffractive/refractive achromatic lens

We demonstrate a variable focal length achromatic lens that consists of a flat liquid crystal diffractive lens and a pressure-controlled fluidic refractive lens. The diffractive lens is composed of a flat binary Fresnel zone structure and a thin liquid crystal layer, producing high efficiency and millisecond switching times while applying a low ac voltage input. The focusing power of the diffractive lens is adjusted by electrically modifying the sub-zones and re-establishing phase wrapping points. The refractive lens includes a fluid chamber with a flat glass surface and an opposing elastic polydimethylsiloxane (PDMS) membrane surface. Inserting fluid volume through a pump system into the clear aperture region alters the membrane curvature and adjusts the refractive lens’ focal position. Primary chromatic aberration is remarkably reduced through the coupling of the fluidic and diffractive lenses at selected focal lengths. Potential applications include miniature color imaging systems, medical and ophthalmic devices, or any design that utilizes variable focal length achromats.

Modelling the primary chromatic aberrations and secondary spectrum of conceptual thick-lens modules

A virtual thick-lens module comprising three air-spaced thin lenses is proposed, which is able to have the identical primary chromatic aberrations and secondary spectrum for just real thick lenses, or groups or components within any thick lens, hence it is capable of studying the chromatic aberration behaviours of conceptual lenses without their detailed structures. The three thin-lens powers are first evaluated to match the required first-order quantities. Then the chromatic aberration coefficients of each thin lens are solved to satisfy the given system aberrations associated with the reference optical configuration. When the incident rays are changed, each thin lens will induce new chromatic aberrations according to the thin-lens formulae. The new system aberrations are obtained by adding those individual thin-lens aberrations together. The module can be directly applied to finite and infinite conjugates, focal and afocal lenses, as well as telecentric and non-telecentric lenses. Evaluations of the chromatic aberration variations of three different types of lenses are demonstrated.

Suppression of primary chromatic aberration by genetic algorithm in an advanced telephoto lens

This paper proposes a new method for finding a suitable glass combination set for an advanced telephoto lens via a genetic algorithm (GA). Normally, glass properties, inclusive of index and Abbe number, play a significant role in the elimination of primary chromatic aberration. So many optical glasses (over 300 different refractive types) have been developed hitherto that it is difficult to choose a state-of-the-art glass combination quickly. According to the newly developed GA operations in this paper, however, several suitable glass combinations can be found quickly through a unique sequence of function selection, crossover and mutation. An advanced telephoto lens design is employed in this research, which has the characteristic of being more sensitive to axial aberrations than lateral chromatic aberrations. The GA operations are described in the macro of the optical software program, CODE V. The simulation results in this research show that the primary chromatic aberration is efficiently eliminated after the application of GA. The main goal of this research is that during optimization, error function could be minimized only if primary aberrations are well under control in our first step; in a telephoto lens, the secondary spectrum of longitudinal chromatic aberration and lateral chromatic aberration caused by distortion play a role in chromatic aberration control as well; however, optimization with a combination of both primary chromatic aberration and secondary chromatic aberration will complicate the process with a lot of working variables. The GA method introduced in this paper might efficiently eliminate the primary chromatic aberration first by finding the best glass combination and its trend and then simplifying the following optimization process for all optical systems.

Primary aberration changes produced by arbitrary movements of paraxial rays

A general algorithm is proposed for evaluating variations of primary monochromatic and chromatic aberrations of single surface or thin-lens components when the paraxial marginal and chief rays are arbitrarily moved. Compared to the earlier algorithm, optical invariants of the original and the new optical configurations could be different, which is common when the object distances are changed or for zoom lenses with different f-numbers on zooming. According to the positions of object and pupil, four special cases arise which lead to the need for four separate sets of coefficients, and a new parameter which is always determinate is used to indicate which set is to be chosen.

Eliminating chromatic aberration in Gauss-type lens design using a novel genetic algorithm

Two different types of Gauss lens design, which effectively eliminate primary chromatic aberration, are presented using an efficient genetic algorithm (GA). The current GA has to deal with too many targets in optical global optimization so that the performance is not much improved. Generally speaking, achromatic aberrations have a great relationship with variable glass sets for all elements. For optics whose design is roughly convergent, glass sets for optics will play a significant role in axial and lateral color aberration. Therefore better results might be derived from the optimal process of eliminating achromatic aberration, which could be carried out by finding feasible glass sets in advance. As an alternative, we propose a new optimization process by using a GA and involving theories of geometrical optics in order to select the best optical glass combination. Two Gauss-type lens designs are employed in this research. First, a telephoto lens design is sensitive to axial aberration because of its long focal length, and second, a wide-angle Gauss design is complicated by lateral color aberration at the extreme corners because Gauss design is well known not to deal well with wide-angle problems. Without numbers of higher chief rays passing the element, it is difficult to correct lateral color aberration altogether for the Gauss design. The results and conclusions show that the attempts to eliminate primary chromatic aberrations were successful.

Correction and alignment strategies for the beam separator of the photoemission electron microscope 3 (PEEM3)

A high-resolution aberration-corrected photoemission electron microscope (PEEM3) will be installed on an undulator beamline at the Advanced Light Source at the Lawrence Berkeley National Laboratory. The aim of this instrument is to provide a substantial flux and resolution improvement by employing an electron mirror for correcting both the third-order spherical aberration and the primary chromatic aberration. In order to utilize this concept of correction, a beam separator is a prerequisite. Crucial to achieving a resolution of 5nm for the high-resolution mode, and a 16-fold increase in throughput at the same resolution as its predecessor, PEEM2, specified as 20nm at 2% transmission, for the high flux mode is the double-symmetric design of the beam separator, which eliminates all the second-order geometric aberrations. Nonetheless, substantial tuning capabilities must be incorporated into the PEEM3 design to compensate for both systematic and random errors. In this article, we investigate how to correct for nonsystematic imperfections and for systematic uncertainties in the accuracy of the magnetic fields and focus on how degradation of the resolution and the field of view can be minimized. Finally, we outline a tentative correction strategy for PEEM3.

Outline of an ultracorrector compensating for all primary chromatic and geometrical aberrations of charged-particle lenses

A novel ultracorrector is outlined which compensates for the primary and secondary first-order chromatic aberrations and all third-order geometrical aberrations of electron optical systems with a straight axis. Owing to the imposed symmetry conditions on the fields and the paraxial fundamental rays, the corrector does not introduce aberrations with 2-fold symmetry. The chromatic aberrations are corrected by means of crossed electric magnetic quadrupoles while the third-order geometrical aberrations are eliminated by octopoles. By placing these elements at distinct positions within the corrector, it is possible to successively eliminate the third-order aberrations in such a way that each subsequent correction does not affect the aberrations corrected in the preceding correction steps.

Outline of an Ultracorrector Compensating for all Primary Chromatic and Geometrical Aberrations of Charged-Particle Lenses

A novel ultracorrector is outlined which compensates for the primary and secondary first-order chromatic aberrations and all third-order geometrical aberrations of electron optical systems with a straight axis. Owing to the imposed symmetry conditions on the fields and the paraxial fundamental rays, the corrector does not introduce aberrations with 2-fold symmetry. The chromatic aberrations are corrected by means of crossed electric magnetic quadrupoles while the third-order geometrical aberrations are eliminated by octopoles. By placing these elements at distinct positions within the corrector, it is possible to successively eliminate the third-order aberrations in such a way that each subsequent correction does not affect the aberrations corrected in the preceding correction steps.

Lens Design for the Near IR … Correction of Primary Chromatic Aberration

The dispersion characteristic of conventional optical glass types will vary as a function of the wavelength region being considered. In the 1.0 to 1.5 µm region, the dispersion of traditional crown and flint glass types is found to be nearly the same. This results in a unique condition when attempting a lens design solution for this spectral region. A typical example is described here that will be helpful in understanding this phenomenon.

Hybrid diffractive-refractive telescope

Telescopes, microscopes, and similar compound systems often require achromats for objectives, since the longitudinal chromatic aberration from a singlet objective is so large that eyepieces cannot easily correct it. Such achromats can limit large-aperture systems because the curvatures required of their components are much stronger than the curvatures of singlets with the same net optical power. The hybrid diffractive-refractive telescope formed by combining a diffractive eyepiece with an unachromatized refractive objective is shown to eliminate the need for such bulky objectives, since a diffractive eyepiece is capable of correcting the large longitudinal chromatic aberrations of singlet refractive objectives. By splitting the holographic eyepiece into two elements, paraxial lateral color may also be corrected. First-order design considerations in these hybrid telescopes are presented, and a practical hybrid telescope layout is developed in which 1) primary chromatic aberration is eliminated, 2) paraxial lateral color is corrected, and 3) a useful eye relief is obtained.© (1990) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Glass chart for analyzing secondary color correction

A new glass chart procedure is presented for analyzing first-order, primary, and secondary chromatic aberration in centered refractive lens systems that do not have to be thin or closely spaced.

Multimodule optical systems*

Earlier work on modular optical-design techniques is extended to lens systems that consist of an arbitrary number of modules; the work is generalized to include finite-conjugate systems (copy lenses) and afocal systems as well as infinite-conjugate systems (camera lenses). All such modular designs have the property that third-order spherical aberration and astigmatism are identically zero. Equations are derived for obtaining zero values for the remaining third-order monochromatic aberrations as well as the primary chromatic aberrations. Several examples are given.

Primary aberrations of Fresnel lenses*

Mathematical expressions derived for the primary aberrations of a thin, flat Fresnel lens (grooved on both surfaces, in general) as functions of the constructional parameters are convenient for the analytic design of optical systems containing one or more Fresnel lenses. In general. such systems have five primary monochromatic aberrations of the Seidel type plus a sixth that is identically zero for ordinary lenses. The new aberration (called line coma to distinguish it from ordinary circular coma) bears the same relation to sagittal and tangential coma that Petzval curvature bears to sagittal and tangential astigmatism. Moreover line coma is independent of stop position, whereas Petzval curvature varies with stop position unless the line coma is corrected. The primary chromatic aberrations and the aberration contributions of Fresnel aspherics are the same as for ordinary lenses. Specific applications of the theory are discussed.

Compensating Optical Systems Part1: Broadband Holographic Reconstruction

The primary chromatic aberrations of a reconstructed holographic image can be compensated by a dispersive lens placed at the quasi-achromatic (QA) point of a hologram. The conditions for obtaining this compensation are derived. Three experimental systems that employ this compensation are discussed. Two of these are in line and use either a zone plate lens or flint glass lens as the dispersive element centered at the QA point. In the third system, an off-axis hologram is followed by an off-axis zone plate lens positioned at the offset QA point.

On the Primary Chromatic Coefficients of a Lens System

Expressions are derived for the primary longitudinal and transverse chromatic aberrations of a lens system as summations of terms over all the singlet components of the system. Each term in these summations is the product of the partial dispersion of the glass of the lens with a certain coefficient which is easily calculated from the data of a paraxial trace, and specifies the contribution made by the lens to the corresponding primary chromatic aberration of the final image. The coefficients are called the primary chromatic coefficients of the system. In addition, the coefficients provide a rapid means of analyzing the complete secondary spectrum of the system, and afford a clear guide to the adjustment of the primary chromatic aberrations insofar as it is desired to do this by the selection of different glass types.