New equations for spectacle induced ocular deviations: responses to some typical questions.
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Eyeglasses↗
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Results for “Optics and Refraction”
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Magnification, blur, and ray state at the retina for the general eye with and without a general optical instrument in front of it: 1. Distant objects.
PURPOSE: To derive general equations that characterize rays, magnification, and blur at the retina in the case of distant object points for a naked eye and for an eye looking through an arbitrary optical instrument. The eye and optical instrument may be astigmatic and noncoaxial. METHOD: The derivation is based on linear optics and makes use of the concept of the augmented ray transference of an optical system. Because the transference completely characterizes the linear optics, the analysis can claim completeness. RESULTS: Equations are presented for position and direction of rays at the retina from distant object points. They lead naturally to the definition of six properties that characterize blur, shape, size, orientation, and position of images of distant objects viewed by the naked eye and by the eye looking through an instrument. By way of example, the general equations are applied to the simple examples of a thin contact lens and a thin spectacle lens in particular. CONCLUSION: The analysis provides a framework, complete as far as linear optics is concerned, for the analysis of light arriving at the retina through any instrument from a distant point. In so doing, it unifies and generalizes concepts like blur and spectacle magnification, which, in the past, have been treated separately.
Contact Lenses↗
Magnification, blur, and ray state at the retina for the general eye with and without a general optical instrument in front of it: 2. Near objects.
PURPOSE: To derive general equations that characterize rays, magnification, and blur at the retina in the case of near object points for the naked eye and for the eye in combination with a general optical instrument. METHOD: The paper draws on results obtained via linear optics in an accompanying paper. RESULTS: Equations are presented that completely characterize the state of rays at the retina from objects at any distance. They allow quantification of blur, size, shape, orientation, and magnification at the retina. CONCLUSION: The analysis provides a framework, complete in linear optics, for the analysis of light arriving at the retina of a general eye through any instrument from any object point.
Contact Lenses↗
Perceived segment misalignment in anisometropic spectacle corrections.
In anisometropic bifocals or trifocals, the magnification difference between left and right lenses will often distort the perceived alignment of the segments. The effect is most noticeable with the segment tops in bifocals or the dividing line between near and intermediate fields in trifocals. The perceived misalignment occurs because off-axis image points are displaced unequal amounts in right and left fields, which forces the lines of sight to diverge to achieve fusion. Hence, the left and right segments will appear at different levels even though they may be perfectly aligned in the spectacle lenses. This article explains why the perceived misalignment occurs, how it can be determined and quantified, and how it can be reduced or eliminated.
Eyeglasses↗
Near image size magnification for optical instruments in general.
A previous article derives expressions for coefficients and magnifications for an arbitrary optical instrument in front of an arbitrary eye and for near object points. The purpose of this note is to correct an error in the interpretation of a parameter in that article, to show that the expression derived there for near image size magnification holds only under particular conditions, and to modify the expression so that it holds in general.
Accommodation, Ocular↗
Evaluation of enhanced corneal compensation in scanning laser polarimetry: comparison with variable corneal compensation on human eyes undergoing LASIK.
PURPOSE: To investigate the potential advantages of an enhanced corneal compensation algorithm (ECC) compared with variable corneal compensation (VCC), in scanning laser polarimetry. METHODS: One eye of 15 healthy ametropic subjects was imaged immediately before and 7 days after uncomplicated LASIK surgery. Anterior segment birefringence was assessed at each measurement session. For post-LASIK calculations, either actual post-LASIK corneal retardation (VCC and ECC groups), or the pre-LASIK corneal retardation (VCC* and ECC* groups) was used. RESULTS: The typical scan score-value was higher for ECC both before and after LASIK (P < 0.01), and it was not influenced by LASIK in either compensation method. Both the axis and the magnitude of corneal birefringence altered after LASIK (P < 0.01). After LASIK, with VCC* all eyes showed uncompensated birefringence, but with ECC* none did. LASIK had no effect on retinal nerve fiber layer measurements in VCC and ECC methods. In VCC* the LASIK-induced retinal nerve fiber layer thickness change was significant (P < 0.01) in the temporal, superior, and nasal quadrants. After LASIK, the number of significantly altered sectors along the TSNIT plot showed no difference when comparing VCC and ECC, VCC and ECC*, or ECC and ECC*. In contrast, significantly more sectors were altered in VCC* than in either VCC or ECC* (P < 0.001). CONCLUSIONS: The new ECC software is more effective than VCC in neutralization of atypical polarization pattern and the uncompensated corneal retardation.
Adult↗
Paraxial propagation of astigmatic wavefronts through noncoaxial astigmatic optical systems.
PURPOSE: The paraxial propagation of astigmatic wavefronts through a noncoaxial system is described. METHODS: The augmented stepalong method (ASAM) for vergences is extended to tilted and decentered elements. RESULTS: Equations for the case of tilted and decentered elements are presented in the framework of vergence calculations. All effects according to the perturbation of a centered system can be derived from the vergences provided by the calculations for the unperturbed system. In particular, the shift in image space rendered by the pertubation is simply the sum of additional decenter and tilt terms to the unperturbed system. CONCLUSIONS: Previous work on the description of the propagation of astigmatic wavefronts has been generalized to noncoaxial systems. This completes the wavefront picture built on the paraxial augmented stepalong method.
Astigmatism↗
Two models of the partially focused clear zone compound eye.
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Animals↗
Parabolic refractive X-ray lenses.
Parabolic refractive X-ray lenses are optical components, especially suitable for third-generation synchrotron radiation sources. This article describes the status of the development of our lenses and illustrates the possibilities for micrometre and submicrometre focusing and for X-ray imaging in absorption and phase contrast. The parabolic lens profile ensures distortion-free imaging of high quality. First characteristics of Be lenses are given. A microscope based on Be lenses is expected to have a lateral resolution below 80 nm.
Journal Article↗
Effects of acoustic heterogeneity in breast thermoacoustic tomography.
The effects of wavefront distortions induced by acoustic heterogeneities in breast thermoacoustic tomography (TAT) are studied. Amplitude distortions are shown to be insignificant for different scales of acoustic heterogeneities. For wavelength-scale, or smaller, heterogeneities, amplitude distortion of the wavefront is minor as a result of diffraction when the detectors are placed in the far field of the heterogeneities. For larger-scale heterogeneities at the parenchyma wall, by using a ray approach (geometric optics), we show that no refraction-induced multipath interference occurs and, consequently, that no severe amplitude distortion, such as is found in ultrasound tomography, exists. Next, we consider the effects of phase distortions (errors in time-of-flight) in our numerical studies. The numerical results on the spreads of point sources and boundaries caused by the phase distortions are in good agreement with the proposed formula. After that, we demonstrate that the blurring of images can be compensated for by using the distribution of acoustic velocity in the tissues in the reconstructions. The effects of the errors in the acoustical velocities on this compensation also are investigated. An approach to implement the compensation using only TAT data is proposed. Lastly, the differences in the effects of acoustic heterogeneity and the generation of speckles in breast TAT and breast ultrasound imaging are discussed.
Acoustics↗
Measurement of the optical thickness of transparent tissue layers.
The method of Duc de Chaulnes was employed to determine the mechanical and optical thickness, as well as the refractive index, of transparent tissue layers in living specimens. To this end the reproducible accuracy of the method and its dependence on the adjustment in focusing and on the numerical aperture of the objective was evaluated on test specimens using the procedures of transmitted light, phase-contrast (PC), and differential interference contrast (DIC) microscopy. The best working conditions were then applied to the actual measurements.
Animals↗
Crystalline lens accommodation and anterior chamber depth.
Using paraxial equations, the change in dioptric power of the crystalline lens required to image objects at given distances from the eye, on the retina, is calculated. This shows that the depth of the anterior chamber affects crystalline lens accommodation more than other variables. The relationship between anterior chamber depth and presbyopia, and a possible geographical aspect, are discussed.
Accommodation, Ocular↗
Optical matrices of lenticular polyindicial schematic eyes.
The optical matrices for modified schematic eyes are derived. The primary modification is to replace the usual isoindicial or bi-indicial crystalline lens with a polyindicial lens so as to more closely approximate the living human lens. Further modifications are made to simulate the accommodated state. The use of optical matrices to solve an optometric problem is demonstrated.
Accommodation, Ocular↗
The futile search for the square of the sphero-cylinder.
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Humans↗
Explanation for the observation of isogyres in crystalline lenses viewed between crossed polarizers.
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Animals↗
Comparison of aberrations in different types of progressive power lenses.
Recently, computer numerically controlled machines have permitted the manufacture of progressive power lenses (PPLs) with different designs. However, the possible differences in optical performance among lens designs are not yet well established. In this work, the spatially resolved aberrations, at 20 relevant locations, of three PPLs with different designs were measured with a Hartmann-Shack wavefront sensor. The wavefront aberration (WA), its root mean square error (RMS) and the point-spread function were obtained. Spatially resolved plots are shown for all aberrations, astigmatism alone, and for higher order aberrations. The average RMS of all zones is also compared, and the standard deviation is used as a parameter to evaluate the level of hard-soft design. We find differences in the spatial distribution of the aberrations but not in the global RMS, indicating that current PPLs are rather similar to a waterbed, with the aberrations being the water: they can be moved but they cannot be eliminated.
Accommodation, Ocular↗
Ray tracing through a schematic eye containing second-order (quadric) surfaces using 4 x 4 matrix notation.
Ray tracing is used in ophthalmology for evaluation of the optical properties of the eye. We demonstrate an algebraic method for tracing a bundle of rays through the optical system of an eye containing aspheric surfaces. Restricting to second-order surfaces (quadric surfaces) such as ellipsoids, paraboloids or hyperboloids, a surface is described by a 4 x 4 matrix. In this case, the normal vector can be derived analytically and the ray-surface intersection is calculated by solving a quadratic equation. We applied this straightforward matrix-based strategy to the spherical 4-surface Le Grand schematic eye, and the Le Grand eye modified by Kooijman containing four aspheric surfaces. We calculated the spot diagram for the focal plane as well as a pre- and post-focal plane for both model eyes, and found that the optical quality of the aspheric model characterized by the ray scatter in the spot diagram at the focal plane is much better than that of the spherical model. This calculation strategy may be helpful for evaluating the image distortion of decentred or tilted spherical or aspheric artificial intra-ocular lenses.
Cornea↗
The exponential-mean-log-transference as a possible representation of the optical character of an average eye.
Considering a set of eyes, how does one define an average whose optical character represents an average of the optical characters of the eyes in the set? The recent proposal of the exponential-mean-log-transference was based on a conjecture. The purpose of this note is to provide justification by proving the conjecture and defining the conditions under which it fails.
Eye↗