Wavefront aberrations and the depth of focus of the human eye

The depth of focus (DOF) can be defined as the variation in image distance of a lens or an optical system which can be tolerated without incurring an objectionable lack of sharpness of focus. The DOF of the human eye serves a mechanism of blur tolerance. As long as the target image remains within the depth of focus in the image space, the eye will still perceive the image as being clear. A large DOF is especially important for presbyopic patients with partial or complete loss of accommodation (presbyopia), since this helps them to obtain an acceptable retinal image when viewing a target moving through a range of near to intermediate distances. The aim of this research was to investigate the DOF of the human eye and its association with the natural wavefront aberrations, and how higher order aberrations (HOAs) can be used to expand the DOF, in particular by inducing spherical aberrations ( 0 4 Z and 0 6 Z ). The depth of focus of the human eye can be measured using a variety of subjective and objective methods. Subjective measurements based on a Badal optical system have been widely adopted, through which the retinal image size can be kept constant. In such measurements, the subject.s tested eye is normally cyclopleged. Objective methods without the need of cycloplegia are also used, where the eye.s accommodative response is continuously monitored. Generally, the DOF measured by subjective methods are slightly larger than those measured objectively. In recent years, methods have also been developed to estimate DOF from retinal image quality metrics (IQMs) derived from the ocular wavefront aberrations. In such methods, the DOF is defined as the range of defocus error that degrades the retinal image quality calculated from the IQMs to a certain level of the possible maximum value. In this study, the effect of different amounts of HOAs on the DOF was theoretically evaluated by modelling and comparing the DOF of subjects from four different clinical groups, including young emmetropes (20 subjects), young myopes (19 subjects), presbyopes (32 subjects) and keratoconics (35 subjects). A novel IQM-based through-focus algorithm was developed to theoretically predict the DOF of subjects with their natural HOAs. Additional primary spherical aberration ( 0 4 Z ) was also induced in the wavefronts of myopes and presbyopes to simulate the effect of myopic refractive correction (e.g. LASIK) and presbyopic correction (e.g. progressive power IOL) on the subject.s DOF. Larger amounts of HOAs were found to lead to greater values of predicted DOF. The introduction of primary spherical aberration was found to provide moderate increase of DOF while slightly deteriorating the image quality at the same time. The predicted DOF was also affected by the IQMs and the threshold level adopted. We then investigated the influence of the chosen threshold level of the IQMs on the predicted DOF, and how it relates to the subjectively measured DOF. The subjective DOF was measured in a group of 17 normal subjects, and we used through-focus visual Strehl ratio based on optical transfer function (VSOTF) derived from their wavefront aberrations as the IQM to estimate the DOF. The results allowed comparison of the subjective DOF with the estimated DOF and determination of a threshold level for DOF estimation. Significant correlation was found between the subject.s estimated threshold level for the estimated DOF and HOA RMS (Pearson.s r=0.88, p<0.001). The linear correlation can be used to estimate the threshold level for each individual subject, subsequently leading to a method for estimating individual.s DOF from a single measurement of their wavefront aberrations. A subsequent study was conducted to investigate the DOF of keratoconic subjects. Significant increases of the level of HOAs, including spherical aberration, coma and trefoil, can be observed in keratoconic eyes. This population of subjects provides an opportunity to study the influence of these HOAs on DOF. It was also expected that the asymmetric aberrations (coma and trefoil) in the keratoconic eye could interact with defocus to cause regional blur of the target. A dual-Badal-channel optical system with a star-pattern target was used to measure the subjective DOF in 10 keratoconic eyes and compared to those from a group of 10 normal subjects. The DOF measured in keratoconic eyes was significantly larger than that in normal eyes. However there was not a strong correlation between the large amount of HOA RMS and DOF in keratoconic eyes. Among all HOA terms, spherical aberration was found to be the only HOA that helped to significantly increase the DOF in the studied keratoconic subjects. Through the first three studies, a comprehensive understanding of DOF and its association to the HOAs in the human eye had been achieved. An adaptive optics system was then designed and constructed. The system was capable of measuring and altering the wavefront aberrations in the subject.s eye and measuring the resulting DOF under the influence of different combination of HOAs. Using the AO system, we investigated the concept of extending the DOF through optimized combinations of 0 4 Z and 0 6 Z . Systematic introduction of a targeted amount of both 0 4 Z and 0 6 Z was found to significantly improve the DOF of healthy subjects. The use of wavefront combinations of 0 4 Z and 0 6 Z with opposite signs can further expand the DOF, rather than using 0 4 Z or 0 6 Z alone. The optimal wavefront combinations to expand the DOF were estimated using the ratio of increase in DOF and loss of retinal image quality defined by VSOTF. In the experiment, the optimal combinations of 0 4 Z and 0 6 Z were found to provide a better balance of DOF expansion and relatively smaller decreases in VA. Therefore, the optimal combinations of 0 4 Z and 0 6 Z provides a more efficient method to expand the DOF rather than 0 4 Z or 0 6 Z alone. This PhD research has shown that there is a positive correlation between the DOF and the eye.s wavefront aberrations. More aberrated eyes generally have a larger DOF. The association of DOF and the natural HOAs in normal subjects can be quantified, which allows the estimation of DOF directly from the ocular wavefront aberration. Among the Zernike HOA terms, spherical aberrations ( 0 4 Z and 0 6 Z ) were found to improve the DOF. Certain combinations of 0 4 Z and 0 6 Z provide a more effective method to expand DOF than using 0 4 Z or 0 6 Z alone, and this could be useful in the optimal design of presbyopic optical corrections such as multifocal contact lenses, intraocular lenses and laser corneal surgeries.

Depth of focus and visual acuity with primary and secondary spherical aberration

It is known that the depth of focus (DOF) of the human eye can be affected by the higher order aberrations. We estimated the optimal combinations of primary and secondary Zernike spherical aberration to expand the DOF and evaluated their efficiency in real eyes using an adaptive optics system. The ratio between increased DOF and loss of visual acuity was used as the performance indicator. The results indicate that primary or secondary spherical aberration alone shows similar effectiveness in extending the DOF. However, combinations of primary and secondary spherical aberration with different signs provide better efficiency for expanding the DOF. This finding suggests that the optimal combinations of primary and secondary spherical aberration may be useful in the design of optical presbyopic corrections. © 2011 Elsevier Ltd. All rights reserved.

Depth of focus of the human eye

In general optical systems, the range of distances over which the detector cannot detect any change in focus is called the depth-of-field. This may be specified by movement of the object or image planes, with the former being referred to as depth-of-field and the latter as depth-of-focus (DOF). Either term can be used in vision science, where we refer to changes in vergence which have the same value in both object and image space.

Depth of anaesthesia monitoring during procedural sedation and analgesia: A systematic review protocol

Background Procedural sedation and analgesia (PSA) is used to attenuate the pain and distress that may otherwise be experienced during diagnostic and interventional medical or dental procedures. As the risk of adverse events increases with the depth of sedation induced, frequent monitoring of level of consciousness is recommended. Level of consciousness is usually monitored during PSA with clinical observation. Processed electroencephalogram-based depth of anaesthesia (DoA) monitoring devices provide an alternative method to monitor level of consciousness that can be used in addition to clinical observation. However, there is uncertainty as to whether their routine use in PSA would be justified. Rigorous evaluation of the clinical benefits of DoA monitors during PSA, including comprehensive syntheses of the available evidence, is therefore required. One potential clinical benefit of using DoA monitoring during PSA is that the technology could improve patient safety by reducing sedation-related adverse events, such as death or permanent neurological disability. We hypothesise that earlier identification of lapses into deeper than intended levels of sedation using DoA monitoring leads to more effective titration of sedative and analgesic medications, and results in a reduction in the risk of adverse events caused by the consequences of over-sedation, such as hypoxaemia. The primary objective of this review is to determine whether using DoA monitoring during PSA in the hospital setting improves patient safety by reducing the risk of hypoxaemia (defined as an arterial partial pressure of oxygen below 60 mmHg or percentage of haemoglobin that is saturated with oxygen [SpO2] less than 90 %). Other potential clinical benefits of using DoA monitoring devices during sedation will be assessed as secondary outcomes. Methods/design Electronic databases will be systematically searched for randomized controlled trials comparing the use of depth of anaesthesia monitoring devices with clinical observation of level of consciousness during PSA. Language restrictions will not be imposed. Screening, study selection and data extraction will be performed by two independent reviewers. Disagreements will be resolved by discussion. Meta-analyses will be performed if suitable. Discussion This review will synthesise the evidence on an important potential clinical benefit of DoA monitoring during PSA within hospital settings.

Spatial Variability of the Depth of Weathered and Engineering Bedrock using Multichannel Analysis of Surface Wave Method

In this paper an attempt has been made to evaluate the spatial variability of the depth of weathered and engineering bedrock in Bangalore, south India using Multichannel Analysis of Surface Wave (MASW) survey. One-dimensional MASW survey has been carried out at 58 locations and shear-wave velocities are measured. Using velocity profiles, the depth of weathered rock and engineering rock surface levels has been determined. Based on the literature, shear-wave velocity of 330 ± 30 m/s for weathered rock or soft rock and 760 ± 60 m/s for engineering rock or hard rock has been considered. Depths corresponding to these velocity ranges are evaluated with respect to ground contour levels and top surface levels have been mapped with an interpolation technique using natural neighborhood. The depth of weathered rock varies from 1 m to about 21 m. In 58 testing locations, only 42 locations reached the depths which have a shear-wave velocity of more than 760 ± 60 m/s. The depth of engineering rock is evaluated from these data and it varies from 1 m to about 50 m. Further, these rock depths have been compared with a subsurface profile obtained from a two-dimensional (2-D) MASW survey at 20 locations and a few selected available bore logs from the deep geotechnical boreholes.

Investigation on Depth of Heat Affected Zone of Discharge Spot by High Repetitive Rate YAG Laser-Induced Discharge Texturing

It is known that the press formability and the elongation of laser textured sheet are improved, and the service life of textured roll is longer than that of the un-textured roll due to hardening of the treated surface. One of the goals to develop high repetitive rate YAG laser-induced discharge texturing (LIDT) is to get deeper hardening zone. By observing and measuring cross-section of LIDT spots in different discharge conditions, it is found that the single-crater, which is formed by the discharge conditions of anode, which is covered by an oil film and with rectangular current waveform, has the most depth of heat affected zone (HAZ) comparing with other crater shapes when discharge energy is the same. The depth of HAZ is mainly depends on pulse duration when the discharge spot is single-crater. The results are analyzed.

Determination of source finiteness and depth of large earthquakes

In this thesis, a method to retrieve the source finiteness, depth of faulting, and the mechanisms of large earthquakes from long-period surface waves is developed and applied to several recent large events.

In Chapter 1, source finiteness parameters of eleven large earthquakes were determined from long-period Rayleigh waves recorded at IDA and GDSN stations. The basic data set is the seismic spectra of periods from 150 to 300 sec. Two simple models of source finiteness are studied. The first model is a point source with finite duration. In the determination of the duration or source-process times, we used Furumoto's phase method and a linear inversion method, in which we simultaneously inverted the spectra and determined the source-process time that minimizes the error in the inversion. These two methods yielded consistent results. The second model is the finite fault model. Source finiteness of large shallow earthquakes with rupture on a fault plane with a large aspect ratio was modeled with the source-finiteness function introduced by Ben-Menahem. The spectra were inverted to find the extent and direction of the rupture of the earthquake that minimize the error in the inversion. This method is applied to the 1977 Sumbawa, Indonesia, 1979 Colombia-Ecuador, 1983 Akita-Oki, Japan, 1985 Valparaiso, Chile, and 1985 Michoacan, Mexico earthquakes. The method yielded results consistent with the rupture extent inferred from the aftershock area of these earthquakes.

In Chapter 2, the depths and source mechanisms of nine large shallow earthquakes were determined. We inverted the data set of complex source spectra for a moment tensor (linear) or a double couple (nonlinear). By solving a least-squares problem, we obtained the centroid depth or the extent of the distributed source for each earthquake. The depths and source mechanisms of large shallow earthquakes determined from long-period Rayleigh waves depend on the models of source finiteness, wave propagation, and the excitation. We tested various models of the source finiteness, Q, the group velocity, and the excitation in the determination of earthquake depths.

The depth estimates obtained using the Q model of Dziewonski and Steim (1982) and the excitation functions computed for the average ocean model of Regan and Anderson (1984) are considered most reasonable. Dziewonski and Steim's Q model represents a good global average of Q determined over a period range of the Rayleigh waves used in this study. Since most of the earthquakes studied here occurred in subduction zones Regan and Anderson's average ocean model is considered most appropriate.

Our depth estimates are in general consistent with the Harvard CMT solutions. The centroid depths and their 90 % confidence intervals (numbers in the parentheses) determined by the Student's t test are: Colombia-Ecuador earthquake (12 December 1979), d = 11 km, (9, 24) km; Santa Cruz Is. earthquake (17 July 1980), d = 36 km, (18, 46) km; Samoa earthquake (1 September 1981), d = 15 km, (9, 26) km; Playa Azul, Mexico earthquake (25 October 1981), d = 41 km, (28, 49) km; El Salvador earthquake (19 June 1982), d = 49 km, (41, 55) km; New Ireland earthquake (18 March 1983), d = 75 km, (72, 79) km; Chagos Bank earthquake (30 November 1983), d = 31 km, (16, 41) km; Valparaiso, Chile earthquake (3 March 1985), d = 44 km, (15, 54) km; Michoacan, Mexico earthquake (19 September 1985), d = 24 km, (12, 34) km.

In Chapter 3, the vertical extent of faulting of the 1983 Akita-Oki, and 1977 Sumbawa, Indonesia earthquakes are determined from fundamental and overtone Rayleigh waves. Using fundamental Rayleigh waves, the depths are determined from the moment tensor inversion and fault inversion. The observed overtone Rayleigh waves are compared to the synthetic overtone seismograms to estimate the depth of faulting of these earthquakes. The depths obtained from overtone Rayleigh waves are consistent with the depths determined from fundamental Rayleigh waves for the two earthquakes. Appendix B gives the observed seismograms of fundamental and overtone Rayleigh waves for eleven large earthquakes.

Enlarging the depth of focus by filtering in the phase-space domain

The ambiguity function was employed as a merit function to design an optical system with a high depth of focus. The ambiguity function with the desired enlarged-depth-of-focus characteristics was obtained by using a properly designed joint filter to modify the ambiguity function of the original pupil in the phase-space domain. From the viewpoint of the filter theory, we roughly propose that the constraints of the spatial filters that are used to enlarge the focal depth must be satisfied. These constraints coincide with those that appeared in the previous literature on this topic. Following our design procedure, several sets of apodizers were synthesized, and their performances in the defocused imagery were compared with each other and with other previous designs. (c) 2005 Optical Society of America.

Analysis of optical systems with extended depth of field using the Wigner distribution function

We describe the use of a Wigner distribution function approach for exploring the problem of extending the depth of field in a hybrid imaging system. The Wigner distribution function, in connection with the phase-space curve that formulates a joint phase-space description of an optical field, is employed as a tool to display and characterize the evolving behavior of the amplitude point spread function as a wave propagating along the optical axis. It provides a comprehensive exhibition of the characteristics for the hybrid imaging system in extending the depth of field from both wave optics and geometrical optics. We use it to analyze several well-known optical designs in extending the depth of field from a new viewpoint. The relationships between this approach and the earlier ambiguity function approach are also briefly investigated. (c) 2006 Optical Society of America.

Aspects of the washout of salmonid eggs. 6. Information on gravel composition , redd sites, the dimensions of redds and the depth of egg burial

Sampling was concentrated on the North Moor region and the series of ditches which drained this area to the Bristol Channel. Although most ditches were not deep the mud substratum precluded sampling from within the habitat. All samples were taken with a pond net from the banks. Efforts were made to sample each part of the habitat although in some ditches the macrophyte growth was so intense as to make sampling difficult particularly of the sediments. Organisms were identified on the 10 sampling sites.

Tunable focal depth of an apodized focusing optical system

The axial intensity distribution and focal depth of an apoclized focusing optical system are theoretically investigated with two kinds of incident light fields: a uniform-intensity-distribution beam and a Gaussian beam. Both a low-numerical-aperture and a high-numerical-aperture optical system are considered. Numerical results show that the depth of focus can be adjusted by changing the geometrical parameters and transmissivity of the apodizer in the focusing optical system. When a Gaussian beam is employed as the incident beam, the waist width also affects the depth of focus. The tunable range of the focal depth is very considerable. (c) 2005 Society of Photo-Optical Instrumentation Engineers.