Levels Of Defocus Research Articles

Phase retrieval for high-numerical-aperture optical systems.

We describe a phase retrieval approach for intensity point-spread functions of high-numerical-aperture optical systems such as light microscopes. The method calculates a generalized pupil function defined on a spherical shell, using measured images at several defocus levels. The resultant pupil functionsreproduce measured point-source images significantly better than does an ideal imaging model. Availability of pupil function information will facilitate new approaches to aberration correction in such systems.

Short-wavelength acuity: optical factors affecting detection and resolution of blue–yellow sinusoidal gratings in foveal and peripheral vision

Previous studies have indicated that peripheral achromatic grating resolution is limited by the sampling density of the neural array (sampling limited), and largely unaffected by large amounts of optical defocus and significant changes in luminance. Under certain conditions, peripheral short-wavelength sensitive (SWS) grating acuity is also sampling limited. We wished to determine how the sampling-limited nature of SWS-driven grating resolution was affected by changing optical defocus and stimulus luminance. Using SWS-cone isolation techniques, detection and resolution acuity were measured for sinusoidal gratings under varying levels of stimulus mean luminance and optical defocus in the fovea and at 20° eccentricity. From 1.4 down to 0.3 cd/m 2 peripheral detection acuity was superior to resolution acuity, accompanied by observations of aliasing: there was little change in resolution performance throughout this range. For defocus up to 3–4 dioptres, peripheral detection acuity was superior to resolution but fell steadily: resolution performance remained flat throughout the same range. Unlike achromatic acuity, foveal resolution performance displayed some robustness to defocus but to a lesser degree than the periphery. Peripheral SWS-driven resolution remains sampling limited for large changes in stimulus luminance and optical defocus, and should thus be useful as a clinical test of SWS-driven ganglion cell density.

Steady‐state VEP and behavioural measures of visual acuity in infants and children with Down syndrome

Purpose: Children with Down syndrome (DS) have reduced behavioural visual acuity (VA). This may reflect sensory deficits, or alternatively, a loss of performance in later mechanisms responsible for behavioural responses. This study compared acuity measured using visual‐evoked potentials (VEP), with behavioural tests, in children with DS. The goal was to determine whether reduced VA could be detected in VEP recordings from the first stages of the response pathway.Methods: The subject group contained 34 children with DS and 35 controls, aged 3 months to 14 years. VA was measured using steady‐state, swept VEP (Norcia and Tyler, 1985). VA was also measured using behavioural techniques.Results: Visual acuity was analysed using a subject group (DS vs controls) × test type (behavioural vs VEP) anova with age as a covariate. A significant effect of subject group was observed (F1,59 = 8.632, p < 0.001) and a significant interaction between subject group and test type (F1,59 = 5.169, p = 0.027). The DS group showed reduced VA compared with the controls in both VEP and behavioural tests, but the deficit was more pronounced with behavioural testing. Reduced VA in the DS group was still seen when analysis was restricted to children who accommodate accurately (F1,26 = 8.047, p = 0.009).Conclusions: Reduced VEP acuity in the DS group supports the idea of an underlying sensory deficit in the DS visual system. Increased reduction with behavioural techniques implies additional losses at later stages of processing. Accommodative inaccuracy does not fully explain reduced VA in DS. Children with DS who do not have significant levels of defocus still exhibit reduced VA when compared with controls.

Contrast sensitivity and the Stiles–Crawford effect

We investigated the influence of the Stiles–Crawford effect (SCE) of the first kind on the contrast sensitivity function using the apodisation model of the SCE. The SCE was measured for the right eyes of two subjects using an increment threshold technique involving a two-channel Maxwellian-viewing system. Filters made of photographic film neutralised or doubled the SCE. Contrast sensitivities were measured with a 6 mm pupil diameter, defocus to ±2D, and three SCE conditions (normal, neutralised and doubled). Modulation transfer functions were derived after measuring transverse aberrations with a vernier alignment technique, and were used to predict contrast sensitivity functions (CSFs). The measured CSFs were, in general, reasonable matches with the predicted CSFs. In particular, both demonstrated definite undulations (“notches”) as defocus level increased. The influences of the SCE-modifying filters were generally of similar magnitude and direction to predictions, thus supporting the apodisation model of the SCE. The magnitudes of SCE influence between SCE-neutralised and SCE-doubled conditions were usually small at about 0.2–0.3 log unit, with a maximum influence of 0.5 log unit. Influences of the SCE were greater for myopic than for hypermetropic defocus. As measured by the CSF and an apodisation model, this study is in agreement with previous theoretical work and one experimental study in indicating that the SCE plays a minor role in improving spatial visual performance.

Spherical and irregular aberrations are important for the optimal performance of the human eye.

Contrast sensitivity measured psychophysically at different levels of defocus can be used to evaluate the eye optics. Possible parameters of spherical and irregular aberrations, e.g. relative modulation transfer (RMT), myopic shift, and depth of focus, can be determined from these measurements. The present paper compares measured results of RMT, myopic shift, and depth of focus with the theoretical results found in the two eye models described by Jansonius and Kooijman (1998). The RMT data in the present study agree with those found in other studies, e.g. Campbell and Green (1965) and Jansonius and Kooijman (1997). A new theoretical eye model using a spherical aberration intermediate between those of the eye models described by Jansonius and Kooijman (1998) and an irregular aberration with a typical S.D. of 0.3-0.5 D could adequately explain the measured RMT, myopic shift, and depth of focus data. Both spherical and irregular aberrations increased the depth of focus, but decreased the modulation transfer (MT) at high spatial frequencies at optimum focus. These aberrations, therefore, play an important role in the balance between acuity and depth of focus.

Schematic eye models for simulation of patient visual performance.

To determine if model eyes can simulate the visual performance of normal human eyes under conditions of varying low myopic blur, pupil size, and contrast. High and low contrast Bailey-Lovie logMAR visual acuity (VA) of three normal eyes of three subjects were measured for four artificial pupil sizes and ten levels of myopic defocus. Simulated visual acuities were then determined for three model eyes--the Indiana Eye with no spherical aberration, the Indiana Eye with average spherical aberration, and the Kooijman Eye--by generating optically aberrated VA charts for each testing condition using Visual Optics Lab software by Sarver and Associates, Inc, and having the subjects read high resolution printouts of these charts using a 3-mm pupil and optimal spectacle correction. The correlation between real VA and simulated VA was then plotted and a regression line calculated. Slopes for the Indiana Eye, Indiana Eye with spherical aberration, and Kooijman Eye were 0.98, 0.98, and 1.01 for high contrast, and 0.92, 0.67, and 0.75 for low contrast, respectively. The r2 values were 0.73, 0.74, and 0.77, for high contrast, and 0.69, 0.40, and 0.50 for low contrast, respectively. Under low contrast conditions the Indiana Eye VA was significantly closer to the real VA than that of the other two models (P<.0003). Visual performance can be simulated by eye models. The simple single surface Indiana Eye with no spherical aberration best modeled both high and low contrast visual acuity.

Measuring contrast sensitivity with inappropriate optical correction*

Spatial frequency-selective minima (notches) in the contrast sensitivity function (CSF) because of defocus can mimic those that occur with ocular disease. We examined the influence of measurement conditions on CSF shape in simulated clinical testing. CSF notches occurred with almost all levels of defocus for all subjects. Multiple notches were found under some conditions. Notches were found with defocus as small as 0.50 D. Effects of induced astigmatism depended on the orientation of the target. Notches were apparent in defocus conditions after stimulus size and room illuminance were modified and when subjects had insufficient accommodation to compensate for hypermetropic defocus. The equivalent of notches was not noted with the Pelli-Robson chart. As defocus-induced CSF notches may be mistaken for functional loss, careful refractive correction should be conducted prior to clinical or experimental CSF measurement, even at low spatial frequencies.

Measuring contrast sensitivity with inappropriate optical correction

Spatial frequency-selective minima (notches) in the contrast sensitivity function (CSF) because of defocus can mimic those that occur with ocular disease. We examined the influence of measurement conditions on CSF shape in simulated clinical testing. CSF notches occurred with almost all levels of defocus for all subjects. Multiple notches were found under some conditions. Notches were found with defocus as small as 0.50 D. Effects of induced astigmatism depended on the orientation of the target. Notches were apparent in defocus conditions after stimulus size and room illuminance were modified and when subjects had insufficient accommodation to compensate for hypermetropic defocus. The equivalent of notches was not noted with the Pelli–Robson chart. As defocus-induced CSF notches may be mistaken for functional loss, careful refractive correction should be conducted prior to clinical or experimental CSF measurement, even at low spatial frequencies.

Measuring contrast sensitivity with inappropriate optical correction

Spatial frequency-selective minima (notches) in the contrast sensitivity function (CSF) because of defocus can mimic those that occur with ocular disease. We examined the influence of measurement conditions on CSF shape in simulated clinical testing. CSF notches occurred with almost all levels of defocus for all subjects. Multiple notches were found under some conditions. Notches were found with defocus as small as 0.50D. Effects of induced astigmatism depended on the orientation of the target. Notches were apparent in defocus conditions after stimulus size and room illuminance were modified and when subjects had insufficient accommodation to compensate for hypermetropic defocus. The equivalent of notches was not noted with the Pelli–Robson chart. As defocus-induced CSF notches may be mistaken for functional loss, careful refractive correction should be conducted prior to clinical or experimental CSF measurement, even at low spatial frequencies.

Simultaneous multiplane imaging with a distorted diffraction grating

We describe a simple technique for simultaneously imaging multiple layers within an object field onto a single camera. The approach uses a binary diffraction grating in which the lines are distorted such that a different level of defocus is associated with each diffraction order. The design of the gratings is discussed, and their ability to image multiple object planes is validated experimentally. Extension of the technique for spherical-aberration correction is described, and it is shown how the gratings can be used as part of a wave-front-sensing system.

Effects of defocus and pupil size on human contrast sensitivity

Defocus lowers the contrast sensitivity function (CSF), producing a complex function with local dips and peaks. Previously, we were able to predict the shape of the CSF with large pupils from measured transverse aberrations with hypermetropic defocus but not with myopic defocus (Atchison et al., 1998c, J. Opt. Soc. Am. A. 15, 2536). As there is no reason that myopic defocus should be more difficult to predict than hypermetropic defocus, we modified the procedure to try to improve CSF predictions with myopic defocus. Also, we extended the study to consider a range of pupil sizes. CSFs were measured for three subjects at three defocus levels (in-focus, -2D and +2D) and three pupil sizes (2 mm, 4 mm and 6 mm). Using a diffraction optics model, transverse aberration measures and in-focus CSF measures, we predicted the defocused CSFs. The predicted defocused CSFs were lower than the in-focus CSF as expected, and had complex shapes that varied with defocus and pupil size and between subjects. While a few predictions were poor, generally, the overall magnitude and shape of the defocused CSFs were well predicted and similarly so for myopic and hypermetropic defocus. Some further improvements in technique are indicated.

Effects of defocus and pupil size on human contrast sensitivity

Defocus lowers the contrast sensitivity function (CSF), producing a complex function with local dips and peaks. Previously, we were able to predict the shape of the CSF with large pupils from measured transverse aberrations with hypermetropic defocus but not with myopic defocus (Atchison et al., 1998c, J. Opt. Soc. Am. A.15, 2536). As there is no reason that myopic defocus should be more difficult to predict than hypermetropic defocus, we modified the procedure to try to improve CSF predictions with myopic defocus. Also, we extended the study to consider a range of pupil sizes. CSFs were measured for three subjects at three defocus levels (in-focus, −2D and +2D) and three pupil sizes (2mm, 4mm and 6mm). Using a diffraction optics model, transverse aberration measures and in-focus CSF measures, we predicted the defocused CSFs. The predicted defocused CSFs were lower than the in-focus CSF as expected, and had complex shapes that varied with defocus and pupil size and between subjects. While a few predictions were poor, generally, the overall magnitude and shape of the defocused CSFs were well predicted and similarly so for myopic and hypermetropic defocus. Some further improvements in technique are indicated.

Optical system modeling for digital image restoration

Defocused digital images may be effectively restored if the imaging system's optical transfer function (OTF) is known. In this paper, Wiener filtering based on known OTFs is applied to noisy, defocused images to characterize the conditions for useful restoration for a range of noise and defocus levels. Restoration mean-square-error is measured over these ranges as a function of a constant noise/object power spectrum ratio in the Wiener filter equation.

Letter contrast sensitivity function of the eye

To provide empirical data of letter CSF for various levels of defocus under controlled conditions of luminance and age. Corrected distance visual acuities were tested at different levels of contrast and defocus. An experiment was conducted using the Medmont visual acuity tester on 10 young subjects and under normal room lighting. Empirical data of visual acuity were obtained for 7 levels of contrast (5, 10, 15, 25, 40, 60, 80%) and defocus levels of 0, +1 and +2D. A mathematical model was derived (R2=0.995) and this can be used to estimate visual acuity at various contrast levels for defocus of < or =+2D. This information is useful for the clinician as normative data and for further development of optical models to predict visual performance of the eye.

Defocussed TEM contrast from small helium bubbles in copper

The theoretical defocussed contrast of the TEM images of bubbles is computed using simulations based on the two-beam dynamical theory of electron diffraction. The bubble parameters used are chosen to be typical of the small (∼ 2 nm in diameter) bubbles found in gas-bubble superlattices. Simulated images are calculated for single equilibrium bubbles, for isolated columns of equilibrium bubbles and for single overpressured bubbles in copper. The calculated images are found to depend strongly on many parameters: the depth, pressure and radius of bubbles; foil thickness; diffracting vector; excitation error; defocus level, small deviations from the Bragg angle and number of bubbles included in the column. Representative examples are presented and comparisons made with experiment. It is concluded that simulations provide a very useful framework for guiding the broad choice of imaging parameters and provide a basis for the interpretation of the complicated imaging behavior often encountered in practice. Various methods for measuring bubble radii from TEM micrographs are assessed.

Psychophysical measurements of the foveal optical modulation transfer function of the human eye at various levels of defocus

The dependence of the foveal optical modulation transfer function of the human eye [O(f)] on the level of defocus was derived by utilizing two simple psychophysical methods based on contrast sensitivity measurements. O(f) was determined at 0.0−+2.0 DS of defocus for monochromatic green gratings using 1 and 5 mm pupils, and for achromatic gratings using 8 mm pupil by measuring contrast sensitivity as a function of spatial frequency for gratings whose retinal illuminance increased but area decreased in proportion to spatial frequency squared. The experiments using 8 mm pupil were repeated by using another method based on comparison of contrast sensitivity measured with and without spatial noise. On double logarithmic co‐ordinates the experimentally determined O (f) was found to decrease slowly at low spatial frequencies up to a corner frequency fc and then more steeply with increasing spatial frequency. The empirical O(f) for 5 and 8 mm pupil was modelled as O(f) = e−(f/fc)n, where n indicates how sharply O(f) is bending at the corner frequency fc. The corner frequency and the exponent n were different for the two conditions and varied as a function of defocus. The two experimental methods used yielded similar results, and were validated by the fact that at 1 mm pupil empirical O(f) could be described as an ideal optical system suffering only from diffraction and defocus.

Psychophysical measurements of the foveal optical modulation transfer function of the human eye at various levels of defocus

The dependence of the foveal optical modulation transfer function of the human eye [O(f)] on the level of defocus was derived by utilizing two simple psychophysical methods based on contrast sensitivity measurements. O(f) was determined at 0.0−+2.0 DS of defocus for monochromatic green gratings using 1 and 5 mm pupils, and for achromatic gratings using 8 mm pupil by measuring contrast sensitivity as a function of spatial frequency for gratings whose retinal illuminance increased but area decreased in proportion to spatial frequency squared. The experiments using 8 mm pupil were repeated by using another method based on comparison of contrast sensitivity measured with and without spatial noise. On double logarithmic co-ordinates the experimentally determined O (f) was found to decrease slowly at low spatial frequencies up to a corner frequency fc and then more steeply with increasing spatial frequency. The empirical O(f) for 5 and 8 mm pupil was modelled as O(f) = e−(f/fc)n, where n indicates how sharply O(f) is bending at the corner frequency fc. The corner frequency and the exponent n were different for the two conditions and varied as a function of defocus. The two experimental methods used yielded similar results, and were validated by the fact that at 1 mm pupil empirical O(f) could be described as an ideal optical system suffering only from diffraction and defocus.

Determination of the fold of the core protein of hepatitis B virus by electron cryomicroscopy.

Hepatitis B virus, a major human pathogen with an estimated 300 million carriers worldwide, can lead to cirrhosis and liver cancer in cases of chronic infection. The virus consists of an inner nucleocapsid or core, surrounded by a lipid envelope containing virally encoded surface proteins. The core protein, when expressed in bacteria, assembles into core shell particles, closely resembling the native core of the virus. Here we use electron cryomicroscopy to solve the structure of the core protein to 7.4 A resolution. Images of about 6,400 individual particles from 34 micrographs at different levels of defocus were combined, imposing icosahedral symmetry. The three-dimensional map reveals the complete fold of the polypeptide chain, which is quite unlike previously solved viral capsid proteins and is largely alpha-helical. The dimer clustering of subunits produces spikes on the surface of the shell, which consist of radial bundles of four long alpha-helices. Our model implies that the sequence corresponding to the immunodominant region of the core protein lies at the tip of the spike and also explains other properties of the core protein.

Factors influencing interocular blur suppression

An Important feauture of monovision correction is the ability of the binocular system to suppress blur from the defocused eye (interocular blur suppression). We conducted a study with three subjects and found that interocular blur suppression improved with higher levels of monocular defocus (addition powers in monovision) but was not affected by the eye defocused (sighting dominant or non-domninant) or by pupil size. The selection and management of monovision patients may be assisted by an understading of the understanding of the underlying suppression preocesses.

Effects of optically induced blur on the refractive status of young monkeys

In each of eight rhesus monkeys, one eye was defocused with a —9 D contact lens beginning before 1 month of age for periods of 2–3 months. At the end of the rearing period, interocular comparisons showed that one subject had developed a relative axial myopia (3.0 D), however, five monkeys had developed a relative axial hyperopia (2.0–3.5 D). After discontinuing the contact-lens rearing procedure, the induced refractive errors diminished over time in all subjects. These results indicate that the defocus threshold for form-deprivation myopia is relatively high and that substantial levels of optical defocus which do not exceed this threshold typically produce axial hyperopia. The recovery data suggests that monkeys have an emmetropization mechanism which is sensitive to optical defocus, but the failure of this mechanism to compensate for the refractive errors simulated during the lens-rearing procedures suggests that this mechanism has a limited operating range.