Fundamental ray aberration analysis: extension of ray matrix analysis to the third-order region using a four-element fundamental ray vector
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Abstract:
We have developed a new fundamental ray aberration analysis that extends conventional ray matrix analysis to the third-order region using a four-element fundamental ray vector. This analysis method can analyze the factors in the generation of the Seidel aberration coefficients by separating them into the transform characteristics of rays unique to the optical system and paraxial trace values representing the conjugate relationship. In establishing this analysis, we first introduce the fundamental ray aberration, and we present calculation formulae for the fundamental ray aberration coefficients of a co-axial rotationally symmetric optical system. Numerical examples employing these analysis results are shown, and it is confirmed that the causes of the Seidel aberration coefficients can be analyzed.We report a novel calculation model for dense spot pattern multi-pass cells consisting of two common identical spherical mirrors. A modified ABCD matrix without the paraxial approximation was developed to describe the ray propagation between two spherical mirrors and the reflection on the mirror surfaces. The intrinsic aberration from the spherical curvature creates a set of intricate variants with respect to a standard Herriot circle spot pattern. A series of detailed numerical simulations are implemented to verify that the input and output beams remain the same and, hence, retrace the same ray pattern. The set of exotic spot patterns obtained with a high fill factor improves the utilization efficiency of the mirror surfaces and produces a longer total optical path length with a low mirror cost.
Curved mirror
Geometrical optics
Reflection
Mirror image
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Compact description of substrate-related aberrations in high numerical-aperture optical disk readout
Optical disks are read out by focusing a beam of high numerical aperture (NA) through the substrate. Deviations of the thickness from the nominal value result in spherical aberration; tilting the substrate results in coma. Exact analytical expressions for the rms aberration per micrometer thickness mismatch (for spherical aberration) and per degree tilt (for coma) are derived. The paraxial estimates for these sensitivities proportional to NA4 (spherical aberration) and NA3 (coma) underestimate the exact values by a factor of approximately 2 for the value NA = 0.85, corresponding to the new Blu-ray disk format. Expansion of the aberration function in Zernike aberrations shows that the exact aberration functions are well described by the lowest-order Zernike spherical aberration (A40) and coma (A31) term for all but the very highest NA values.
Coma (optics)
Contrast transfer function
Optical aberration
Aperture (computer memory)
Numerical aperture
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We present an approach to the problem of the calculation of basic paraxial parameters and the third-order aberration coefficients of thin refractive tunable-focus lenses. It is shown that aberration coefficients of the third order of the thin refractive tunable-focus lens can be completely characterized by three functions that depend only on refractive indices of fluids forming the tunable-focus lens and do not depend on the position and size of the object and the position of the entrance pupil.
Thin lens
Position (finance)
Geometrical optics
Third order
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The purpose of this study was to develop a technique to calculate the effects of laser corneal reshaping on the spherical aberration of a model eye. Our model indicates that spherical corrections of high myopia (> 5 D) by laser corneal reshaping are expected to significantly increase the amount of primary spherical aberration of the eye.
Optical aberration
Geometrical optics
Gaussian optics
Spherical wave
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Conventional lenses made from optical glass or plastics have fixed properties (e.g. focal length) that depend on the index of refraction and geometrical parameters of the lens. We present an approach to the problem of calculation of basic paraxial parameters and the third order aberration coefficients of compound optical elements analogical to classical lenses which are based on refractive tunable-focus lenses. A detailed theoretical analysis is performed for a simple tunable-focus lens, a generalized tunable-focus lens, a generalized tunable-focus lens with minimum spherical aberration, and three-element tunable-focus lens (a tunable-focus doublet).
Simple lens
Geometrical optics
Gradient-index optics
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Citations (30)
For reshaping aperture size and correcting low-order aberration of laser beams with large aspect ratios, a simplified analytical method is proposed to design an anamorphic refractive shaping system, which is composed of double-plane symmetric lenses. The simplified method enables performing a global study of aberrations via calculating the analytical primary wave aberration function under paraxial approximation. The aberration balance is analyzed with a three-lens laser collimating system and a compact four-lens laser expanding system. Lens bending and conic surfaces are introduced to decrease ray errors. Through the simplified analytical method, anamorphic refractive shaping systems for laser beams with large aspect ratios can be adequately analyzed and conveniently designed.
Collimated light
Aperture (computer memory)
Geometrical optics
Chromatic aberration
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Citations (4)
In general, the work of optical design is to minimize Seidel aberrations. If the lens designer lacks the fundamental theory of aberrations, he may face tedious aberrations correction processes. However, nowadays powerful lens design software can give a quick answer to this specific purpose. The purpose of this paper is to present the analytical calculations of the first primary aberration, i.e., spherical aberration, by paraxial and meridional raytracing. By analyzing the spherical aberration of the singlet, a rigid concept of how the aberration is calculated by computer from the basic ray tracing technique is given. Thus helping to obtain a better structure of first order lens design.
Geometrical optics
Optical aberration
Tracing
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Citations (1)
Light Reflection at Plane Mirrors Refraction of Light Refraction by Planes, Plates and Prisms Paraxial Refraction at Planes, Plates and Prisms Refraction and Reflection at Spherical Surfaces Thin Lenses Rotationally Symmetrical Systems Astigmatic Lenses Thick Lens Systems Stops, Pupils and Ports Numerical Aperture, f-Number and Resolution Magnifiers and Microscopes Telescopes Cameras and Projectors Ophthalmic Instruments Dispersion and Chromatic Aberration Trigonometric Ray Tracing Monochromatic Aberrations.
Chromatic aberration
Monochromatic color
Reflection
Geometrical optics
Achromatic lens
Aperture (computer memory)
Prism
Snell's law
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Citations (46)
Abstract The geometrical aberration of an optical system is usually measured through wavefront aberration. We propose a very direct experimental ray-tracing measurement method in this paper. Two fiber point-light-sources are used to simulate an arbitrary incident ray in space, the diffracting wavefronts of the two fibers pass through the lens under test and interfere on two photographic planes. The outgoing ray intersects the photographic planes at the extrema of their phase maps, thus can be traced by connecting the two intersections. We measure four kinds of geometrical aberrations of the lens and compare them with Zemax simulation results. This method provides a new solution for the geometrical aberration measurement of an optical system.
Zemax
Optical aberration
Geometrical optics
Caustic (mathematics)
Ray
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We present an analytical method for systematic optical design of a double-pass axicon that shows almost no astigmatism in oblique illumination compared to a conventional linear axicon. The anastigmatic axicon is a singlet lens with nearly concentric spherical surfaces applied in double pass, making it possible to form a long narrow focal line of uniform width. The front and the back surfaces have reflective coatings in the central and annular zones, respectively, to provide the double pass. Our design method finds the radii of curvatures and axial thickness of the lens for a given angle between the exiting rays and the optical axis. It also finds the optimal position of the reflecting zones for minimal vignetting. This method is based on ray tracing of the real rays at the marginal heights of the aperture and therefore is superior to any paraxial method. We illustrate the efficiency of the method by designing a test axicon with optical parameters used for a prototype axicon, which was manufactured and experimentally tested. We compare the optical characteristics of our test axicon with those of the experimental prototype.
Axicon
Vignetting
Catadioptric system
Conic section
Aperture (computer memory)
Sawtooth wave
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Citations (12)