Standards for Reporting the Optical Aberrations of Eyes

Larry N. Thibos,1 Raymond A. Applegate,2 James T. Schwiegerling,3 Robert Webb4, and VSIA Standards Taskforce Members

1School of Optometry, Indiana University, Bloomington, IN 47405, 2Department of Ophthalmology, University of Texas Health Science Center at San Antonio, San Antonio, TX 78284, 3Department of Ophthalmology, University of Arizona, Tucson, AZ 85721, 4Schepens Research Institute, Boston, MA 02114

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Background

Reference Axis Selection

Methods for aligning the eye during measurement

Page 2

Description of Zernike Polynomials

Indexing Scheme

Coordinate System

Page 3

A standard aberrator for calibration

Plans for Phase II

Acknowledgements
References

Abstract: In response to a perceived need in the vision community, an OSA taskforce was formed at the 1999 topical meeting on vision science and its applications (VSIA-99) and charged with developing consensus recommendations on definitions, conventions, and standards for reporting of optical aberrations of human eyes. Progress reports were presented at the 1999 OSA annual meeting and at VSIA-2000 by the chairs of three taskforce subcommittees on (1) reference axes, (2) describing functions, and (3) model eyes.

The following summary of the committee’s recommendations is available also in portable document format (PDF) at the Schepens Eye Research Institute at Harvard University.
ftp://color.eri.harvard.edu/standardization/Standards_TOPS4.pdf.
OCIS codes:
(330.0330) Vision and color; (330.5370) Physiological optics


Background

The recent resurgence of activity in visual optics research and related clinical disciplines (e.g. refractive surgery, ophthalmic lens design, ametropia diagnosis) demands that the vision community establish common metrics, terminology, and other reporting standards for the specification of optical imperfections of eyes. Currently there exists a plethora of methods for analyzing and representing the aberration structure of the eye but no agreement exists within the vision community on a common, universal method for reporting results. In theory, the various methods currently in use by different groups of investigators all describe the same underlying phenomena and therefore it should be possible to reliably convert results from one representational scheme to another. However, the practical implementation of these conversion methods is computationally challenging, is subject to error, and reliable computer software is not widely available. All of these problems suggest the need for operational standards for reporting aberration data and to specify test procedures for evaluating the accuracy of data collection and data analysis methods.

Following a call for participation [1], approximately 20 people met at VSIA-99 to discuss the proposal to form a taskforce that would recommend standards for reporting optical aberrations of eyes. The group agreed to form three working parties that would take responsibility for developing consensus recommendations on definitions, conventions and standards for the following three topics: (1) reference axes, (2) describing functions, and (3) model eyes. It was decided that the strategy for Phase I of this project would be to concentrate on articulating definitions, conventions, and standards for those issues which are not empirical in nature. For example, several schemes for enumerating the Zernike polynomials have been proposed in the literature. Selecting one to be the standard is a matter of choice, not empirical investigation, and therefore was included in the charge to the taskforce. On the other hand, issues such as the maximum number of Zernike orders needed to describe ocular aberrations adequately is an empirical question which was avoided for the present, although the taskforce may choose to formulate recommendations on such issues at a later time. Phase I concluded at the VSIA-2000 meeting.

 


Reference Axis Selection

Summary

It is the committee’s recommendation that the ophthalmic community use the line-of-sight as the reference axis for the purposes of calculating and measuring the optical aberrations of the eye. The rationale is that the line-of-sight in the normal eye is the path of the chief ray from the fixation point to the retinal fovea. Therefore, aberrations measured with respect to this axis will have the pupil center as the origin of a Cartesian reference frame. Secondary lines-of-sight may be similarly constructed for object points in the peripheral visual field. Because the exit pupil is not readily accessible in the living eye whereas the entrance pupil is, the committee recommends that calculations for specifying the optical aberration of the eye be referenced to the plane of the entrance pupil.

Background

Optical aberration measurements of the eye from various laboratories or within the same laboratory are not comparable unless they are calculated with respect to the same reference axis and expressed in the same manner. This requirement is complicated by the fact that, unlike a camera, the eye is a decentered optical system with non-rotationally symmetric components (Fig. 1). The principle elements of the eye’s optical system are the cornea, pupil, and the crystalline lens. Each can be decentered and tilted with respect to other components, thus rendering an optical system that is typically dominated by coma at the foveola.


(Click on Image for full-size version.)

Fig. 1. The cornea, pupil, and crystalline lens are decentered and tilted with respect to each other, rendering the eye a decentered optical system that is different between individuals and eyes within the same individual.

The optics discipline has a long tradition of specifying the aberration of optical systems with respect to the center of the exit pupil. In a centered optical system (e.g., a camera, or telescope) using the center of the exit pupil as a reference for measurement of on-axis aberration is the same as measuring the optical aberrations with respect to the chief ray from an axial object point. However, because the exit pupil is not readily accessible in the living eye, it is more practical to reference aberrations to the entrance pupil. This is the natural choice for objective aberrometers which analyze light reflected from the eye.

Like a camera, the eye is an imaging device designed to form an in-focus inverted image on a screen. In the case of the eye, the imaging screen is the retina. However, unlike film, the "grain" of the retina is not uniform over its extent. Instead, the grain is finest at the foveola and falls off quickly as the distance from the foveola increases. Consequently, when viewing fine detail, we rotate our eye such that the object of regard falls on the foveola (Fig. 2). Thus, aberrations at the foveola have the greatest impact on an individual’s ability to see fine details.

Fig. 2. An anatomical view of the macular region as viewed from the front and in cross section (below). a: foveola, b: fovea, c: parafoveal area, d: perifoveal area. From Histology of the Human Eye by Hogan. Alvarado Weddell, W.B. Sauders Company publishers, 1971, page 491.

Two traditional axes of the eye are centered on the foveola, the visual axis and the line-of-sight, but only the latter passes through the pupil center. In object space, the visual axis is typically defined as the line connecting the fixation object point to the eye’s first nodal point. In image space, the visual axis is the parallel line connecting the second nodal point to the center of the foveola (Fig. 3, left). In contrast, the line-of-sight is defined as the (broken) line passing through the center of the eye’s entrance and exit pupils connecting the object of regard to the foveola (Fig. 3, right). The line-of-sight is equivalent to the path of the foveal chief ray and therefore is the axis which conforms to optical standards. The visual axis and the line of sight are not the same and in some eyes the difference can have a large impact on retinal image quality [2]. For a review of the axes of the eye see [3]. (To avoid confusion, we note that Bennett and Rabbetts [4] re-define the visual axis to match the traditional definition of the line of sight. The Bennett and Rabbetts definition is counter to the majority of the literature and is not used here.)

When measuring the optical properties of the eye for objects which fall on the peripheral retina outside the central fovea, a secondary line-of-sight may be constructed as the broken line from object point to center of the entrance pupil and from the center of the exit pupil to the retinal location of the image. This axis represents the path of the chief ray from the object of interest and therefore is the appropriate reference for describing aberrations of the peripheral visual field.

 


Methods for aligning the eye during measurement.

Summary

The committee recommends that instruments designed to measure the optical properties of the eye and its aberrations be aligned co-axially with the eye's line-of-sight.

  

Fig. 3. Left panel illustrates the visual axis and panel right illustrates the line of sight.
(Click on Image for full-size version.)

Background

There are numerous ways to align the line of sight to the optical axis of the measuring instrument. Here we present simple examples of an objective method and a subjective method to achieve proper alignment.

Objective method

In the objective alignment method schematically diagramed in Fig. 4, the experimenter aligns the subject’s eye (which is fixating a small distant target on the optical axis of the measurement system) to the measurement system. Alignment is achieved by centering the subject’s pupil (by adjusting a bite bar) on an alignment ring (e.g., an adjustable diameter circle) which is co-axial with the optical axis of the measurement system. This strategy forces the optical axis of the measurement device to pass through the center of the entrance pupil. Since the fixation target is on the optical axis of the measurement device, once the entrance pupil is centered with respect to the alignment ring, the line-of-sight is co-axial with the optical axis of the measurement system.

Fig. 4. Schematic of a generic objective alignment system designed to place the line of sight on the optical axis of the measurement system. BS: beam splitter, FP: on axis fixation point.

Subjective method

In the subjective alignment method schematically diagramed in Figure 5, the subject adjusts the position of their own pupil (using a bite bar) until two alignment fixation points at different optical distances along and co-axial to the optical axis of the measurement device are superimposed (similar to aligning the sights on rifle to a target). Note that one or both of the alignment targets will be defocused on the retina. Thus the subject’s task is to align the centers of the blur circles. Assuming the chief ray defines the centers of the blur circles for each fixation point, this strategy forces the line of sight to be co-axial with the optical axis of the measurement system. In a system with significant amounts of asymmetric aberration (e.g., coma), the chief ray may not define the center of the blur circle. In practice, it can be useful to use the subjective strategy for preliminary alignment and the objective method for final alignment.

Fig. 5. Schematic of a generic subjective alignment system designed to place the line of sight on the optical axis of the measurement system. BS: beam splitter, FP: fixation point source.

Conversion between reference axes

If optical aberration measurements are made with respect to some other reference axis, the data must be converted to the standard reference axis (see the tools developed by Susana Marcos at our temporary web site: http://color.eri.harvard.edu/standardization/ ). However, since such conversions involve measurement and/or estimation errors for two reference axes (the alignment error of the measurement and the error in estimating the new reference axis), it is preferable to have the measurement axis be the same as the line-of-sight.


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