Jayoung Nam

Impact of contact lens zone geometry and ocular optics on bifocal retinal image quality

To examine the separate and combined influences of zone geometry, pupil size, diffraction, apodisation and spherical aberration on the optical performance of concentric zonal bifocals.

Scale and spatial distribution of aberrations associated with tear breakup.

Purpose We examined the spatial correlation between tear breakup (TBU) and the associated optical anomalies on multiple spatial scales. Methods Five subjects refrained from blinking while the time course and patterns of TBU were sequentially observed using fluorescein, retroillumination, and Shack-Hartmann (SH) aberrometry. Wavefront error maps were developed using Zernike polynomials, as well as local zonal analysis of measured wavefront slopes. The difference between these maps reveals the presence of very high-order aberrations missed by standard modal fitting methods. Size of SH spots was also quantified to estimate optical perturbations on a microscopic scale. The spatial correlation between TBU and optical aberrations was also computed. Results Degradation of the tear film increased wavefront aberrations over all spatial scales measured. Consistent with tear thinning, blink suppression induced an irregular pattern of phase advances in regions of TBU. SH spot size also increased in regions of TBU, which indicates the presence of optical aberrations on a scale smaller than individual lenslets. Conclusions The optical signature of TBU caused by blink suppression is a combination of wavefront aberrations on macroscopic and microscopic scales due to non-uniform tear film thinning and possible exposure of a rough epithelial surface. Localized optical defects correspond temporally and spatially with TBU revealed by fluorescein and retroillumination. In addition to gross wavefront aberrations, scatter develops in areas of TBU that will further contribute to image degradation and visual disturbances after TBU.

Forward light scatter analysis of the eye in a spatially-resolved double-pass optical system

An optical analysis is developed to separate forward light scatter of the human eye from the conventional wavefront aberrations in a double pass optical system. To quantify the separate contributions made by these micro- and macro-aberrations, respectively, to the spot image blur in the Shark-Hartmann aberrometer, we develop a metric called radial variance for spot blur. We prove an additivity property for radial variance that allows us to distinguish between spot blurs from macro-aberrations and micro-aberrations. When the method is applied to tear break-up in the human eye, we find that micro-aberrations in the second pass accounts for about 87% of the double pass image blur in the Shack-Hartmann wavefront aberrometer under our experimental conditions.

Wavelength adjustment using an eye model from aberrometry data

We developed a method to convert aberrometry data obtained in one wavelength to the corresponding data in another wavelength using an eye model. A single map of aberrometry data is used to construct a free-form one-surface eye model. A general algorithm for the surface construction is described and implemented for real aberrometry data. Our method can handle varying conjugate distances of the measurement plane of the aberrometer and can also manage the chief ray prism that may be present. The algorithm is validated with the aid of an artificial plastic eye. The wavefronts in different wavelengths are compared through the Zernike analysis not only for lower-order aberrations, but also for higher-order aberrations. The results show that the changes of the Zernike aberration coefficients due to wavelengths are non-uniform. The defocus term has the highest effect from wavelength changes, which is consistent with the previous literature. Our method is compared with two approximate semi-analytical algorithms. The wavelength adjustments from a multi-surface eye model are contrasted with our method. We prove analytically that the conventional method of wavelength adjustment is based on paraxial analysis. In addition, we provide a method of finding the chief ray using back-projection in some cases and discuss different meanings of prism.

Describing ocular aberrations with wavefront vergence maps

A common optometric problem is to specify the eyes ocular aberrations in terms of Zernike coefficients and to reduce that specification to a prescription for the optimum sphero‐cylindrical correcting lens. The typical approach is first to reconstruct wavefront phase errors from measurements of wavefront slopes obtained by a wavefront aberrometer. This paper applies a new method to this clinical problem that does not require wavefront reconstruction. Instead, we base our analysis of axial wavefront vergence as inferred directly from wavefront slopes. The result is a wavefront vergence map that is similar to the axial power maps in corneal topography and hence has a potential to be favoured by clinicians. We use our new set of orthogonal Zernike slope polynomials to systematically analyse details of the vergence map analogous to Zernike analysis of wavefront maps. The result is a vector of slope coefficients that describe fundamental aberration components. Three different methods for reducing slope coefficients to a spherocylindrical prescription in power vector forms are compared and contrasted. When the original wavefront contains only second order aberrations, the vergence map is a function of meridian only and the power vectors from all three methods are identical. The differences in the methods begin to appear as we include higher order aberrations, in which case the wavefront vergence map is more complicated. Finally, we discuss the advantages and limitations of vergence map representation of ocular aberrations.

Numerical reconstruction of optical surfaces

There are several problems in optics that involve the reconstruction of surfaces such as wavefronts, reflectors, and lenses. The reconstruction problem often leads to a system of first-order differential equations for the unknown surface. We compare several numerical methods for integrating differential equations of this kind. One class of methods involves a direct integration. It is shown that such a technique often fails in practice. We thus consider one method that provides an approximate direct integration; we show that it is always converging and that it provides a stable, accurate solution even in the presence of measurement noise. In addition, we consider a number of methods that are based on converting the original equation into a minimization problem.

Weighted Zernike expansion with applications to the optical aberration of the human eye

We propose to use weighted Zernike functions to represent the aberrations of an eye. Methods for computing the phase of an aberrated ophthalmic wavefront in terms of weighted Zernike functions are discussed. In particular, we consider several options for integrating the phase out of its measured slopes. The weighted functions involve a free parameter. Clinical data on subjective refraction and aberration maps of individual subjects are used to determine an estimate for this parameter.

The statistics of refractive error maps: managing wavefront aberration analysis without Zernike polynomials

The refractive error of a human eye varies across the pupil and therefore may be treated as a random variable. The probability distribution of this random variable provides a means for assessing the main refractive properties of the eye without the necessity of traditional functional representation of wavefront aberrations. To demonstrate this approach, the statistical properties of refractive error maps are investigated. Closed‐form expressions are derived for the probability density function (PDF) and its statistical moments for the general case of rotationally‐symmetric aberrations. A closed‐form expression for a PDF for a general non‐rotationally symmetric wavefront aberration is difficult to derive. However, for specific cases, such as astigmatism, a closed‐form expression of the PDF can be obtained. Further, interpretation of the distribution of the refractive error map as well as its moments is provided for a range of wavefront aberrations measured in real eyes. These are evaluated using a kernel density and sample moments estimators. It is concluded that the refractive error domain allows non‐functional analysis of wavefront aberrations based on simple statistics in the form of its sample moments. Clinicians may find this approach to wavefront analysis easier to interpret due to the clinical familiarity and intuitive appeal of refractive error maps.

Price Discovery in the Stock, OTC Corporate Bond, and NYSE Corporate Bond Markets

This paper examines intraday price discovery in three closely-related U.S. markets: stocks, Over-The-Counter (OTC) corporate bonds, and New York Stock Exchange (NYSE) electronically-traded corporate bonds. We calculate the Hasbrouck (1995) information shares of these three markets over five years. We find that OTC corporate bond trades have a 5.7% information share, despite zero pre-trade transparency in the OTC market. Further, NYSE corporate bonds have a 45.8% information share, despite having a tiny market share, because of publicly-displayed, frequently-updated bid-ask quotes that can be traded at any time. OTC corporate bond information shares are inversely related to credit quality and are relatively constant over time. This is consistent with multi-security informed trading theory and the Merton (1974) corporate bond model. NYSE corporate bond information shares are positively related to their update frequency. Thus, the subset of NYSE bonds that are updated more frequently are more informative.

Testing the LCAPM vs. Generalized Liquidity-Adjusted Asset Pricing: New Evidence and New Perspectives

The Liquidity-adjusted Capital Asset Pricing Model (LCAPM) includes two specific testable predictions: (1) the coefficient on expected liquidity cost equals average turnover and (2) the coefficient on market beta equals the coefficient on net liquidity risk beta. By contrast, generalized liquidity-adjusted asset pricing models allow liquidity characteristics and/or liquidity risk factors without such parameter restrictions. We empirically test these alternative theories. In doing so, we expand the range of evidence in multiple ways. First, we extend forward and backwards in time to cover 80 years. Second, we analyze NASDAQ-listed stocks as well as NYSE/AMEX-listed stocks. Third, we analyze four alternative liquidity measures: (1) the Corwin and Schultz proxy, (2) closing percent quoted spread, (3) the Amihud proxy, and (4) zeros. Fourth, we analyze the impact of adding Fama and French/Carhart risk factors to the model. Our main finding is that both of these specific predictions of LCAPM are robustly rejected. This outcome supports generalized liquidity-adjusted asset pricing. Finally, we ask can the original LCAPM results be replicated? We qualitatively replicate most tables, but obtain mixed results for two tables. We make publicly available our SAS code and the resulting data files for both our new empirical tests and our replication.First, we replicate the Liquidity-adjusted Capital Asset Pricing Model (LCAPM) tests of Acharya and Pedersen (2005) using their original methodology and covering both their original time period and a more recent period. We successfully qualitatively replicate the descriptive and the first-stage tables and figures, but are not successful in replicating the second-stage tables that perform cross-sectional tests. In the large majority of cases, our replication evidence fails to support that the main LCAPM predictions all hold simultaneously. Next, we extend tests of the LCAPM following the Lee (2011) methodology and expanding to: (1) three different time periods spanning 90 years, (2) add NASDAQ stocks, (3) use four alternative liquidity measures, and (4) add risk or characteristic factors. Our extension evidence always fails to support that the main predictions of the Lee two-beta LCAPM and of the four-beta LCAPM hold at the same time. Overall, we fail to support that liquidity risk matters in the specific functional form predicted by the LCAPM. However, we are silent on the more general question of whether liquidity risk matters in some different functional form. We make publicly available our SAS code.