Improving visual function diagnostic metrics Charles Campbell
Metrics - What are they? What are they used for? A metric assigns a numerical value or a set of values to characterize some chosen phenomenon Metrics are the measure of things Metrics are used to quantify change and difference
Metrics - What qualities do good ones have? Good metrics are linear with respect to variation in the phenomenon they characterize linear means that a change in the value of the metric means a proportional change has occurred in the phenomenon Good metrics have the same multiplicity as the phenomenon they measure For instance, if we consider a phenomenon such as acuity to be a single thing, then its metric should be a single value Good metrics are expressed in small, simple numbers
What visual function metrics do we have and use now? Visual acuity Standardized Sloan or British letter charts with high or low contrast Reported in logmar units or Snellen fraction Refractive error Sphere, cylinder and axis error measured at best attainable visual acuity at specified object distance Comparisons made to a target refractive state or to the refractive state found at some other time Contrast sensitivity Standardized grating targets at several spatial frequencies (typically 3,6,12 and 18 cpd) Set orientation, discrete contrast levels, controlled background illumination level
What do these measures tell us about visual function? Visual acuity A measure of the ability of the visual system to resolve medium to high spatial frequencies,i.e fine detail An idea of a person s perception of sharpness or clarity of their vision A measure of the amount of residual aberration in the visual system METRIC: logmar value or Snellen fraction
What do these measures tell us about visual function? Refractive error A measure of the amount of corrective treatment needed to remove lower-order aberrations A measure of the amount of blur experienced so giving some idea amount of fine detail or acuity loss expected METRICS: MRSE RMS blur, RMS cylinder blur,
What do these measures tell us about visual function? Contrast sensitivity A measure of ability of the visual system to resolve low to medium spatial frequencies at specific orientations under the tested illumination conditions A measure of the effect of residual aberrations on vision in the tested range of spatial frequencies An indication of the level of performance for visual tasks under non optimal conditions such as low illumination METRIC: Contrast sensitivity threshold values a selected spatial frequencies
What is lacking in these measures of visual function? Visual acuity Letter targets are orientation and spatial frequency content specific so they are perceived differently are different combinations of aberration If neutral targets, such as Landolt rings, are used communication with the person tested becomes difficult Correlation of acuity performance with aberrations of the eye is not tight Letter targets are not particularly good correlates of the visual scene detail experienced in normal life
What is lacking in these measures of visual function? Refractive error Only lower-order aberrations are measured In the presence of a moderate to large amount of higher-order aberration (aberrations that can t be corrected with sphero-cylindrical lenses) correction of the refractive error as commonly found gives poor indication of subsequent visual performance
What is lacking in these measures of visual function? Contrast sensitivity The testing is typically done with target sets that essentially have a single orientation. This means that the spatial frequency space tested is essentially one-dimensional whereas the human spatial frequency space is twodimensional Threshold testing is done with a fairly coarse contrast target grading so threshold detection is not too precise Information density is low so predictions of visual performance under specified conditions are difficult
What characteristics should any new visual function diagnostic metrics have? The clinical methods used to collect information should be simple and quick to administer Use should be made, if possible, of information that is already being collected in the clinic The new metrics should add to the knowledge gained from the tests already in use The new metrics should give direct guidance to the administration of treatment and diagnosis of reported visual difficulties
Information that is already available in the clinic Refractive error as measured using subjective methods (manifest refraction) Visual acuity Contrast sensitivity Corneal topography Wavefront error (becoming more common)
New metrics will come from the use of new information Wavefront error measurements are the primary source of new available information Wavefront error information comes primarily from aberrometers but can also come from corneal topography
What Metrics are commonly used today to utilize wavefront information? RMS (root mean square) error Either the RMS error of the wavefront is calculated directly or it is found by squaring, adding the squares and taking the square root of a set of Zernike coefficients Often only the portion of the RMS error associated with the higher-order aberrations is used as a metric Comparison or presentation of individual Zernike coefficient values
What these commonly used new metrics lack RMS error lumps the effect of what can be a complex error - hence a complex visual effect - into a single value Equal amounts of RMS error, over threshold,coming from different aberration combinations do not degrade vision by equal amounts Best used only as a threshold indication to tell when the aberrations will start to degrade vision - from the principles of physical optics RMS error of less than 1/13.5 wave has no significant effect of image formation ONLY OF VALUE AS A THRESHOLD INDICATOR
What these commonly used new metrics lack Zernike coefficient analysis Zernike decomposition is a useful method to represent a wavefront error when the entire set of available coefficients is used - but the individual terms are only loosely connected to visual function Because Zernike coefficient sets represent the wavefront, they do not directly describe image formation - they are in the wrong plane DO NOT REPRESENT A GOOD VISUAL METRIC IN THEMSELVES - BEST CONSIDERED AS THE SOURCE OF INFORMATION NEEDED TO CREATE USEFUL METRICS
Better metrics using wavefront data Measures based on the modulation transfer function (MTF) Describe the total effect of the wavefront in the image plane Closely related to the contrast sensitivity response Measures based on the point spread function (PSF) Describe phenomena such a multiple images, ghosts, flare and glare Describe the effect of local aberrations better than the MTF which is a more global measure
The Strehl ratio- a widely used metric of imaging quality Strehl ratio Definition 1 (original)- ratio of point spread function peak value to the diffraction limited PSF peak value Definition 2 - ratio of the volume under the MTF surface to the volume under the diffraction limited MTF surface The two definitions are mathematically equivalent
Modified band width limited Visual Strehl ratio in the sense of the second definition Using wavefront error values calculate the MTF of the eye Calculate the diffraction limited MTF for the same pupil diameter Reduce both MTFs by the neural threshold values - modified MTFs Calculate the volume under the modified MTFs in chosen spatial frequency band Form the ratio of the two volumes
Metrics based on the MTF Mean measured MTF value in an annular band covering medium to high spatial frequencies compared the diffraction limited MTF in the band - a bandwidth limited Visual Strehl ratio A correlate to visual acuity as visual acuity measures the response of the visual system to this band of spatial frequencies A metric related to the perception of clarity or sharpness in that it is an average of the spatial frequency response for detail at all orientations in the high frequencies range
Metrics based on the MTF Mean measured MTF value in an annular band covering low to medium spatial frequencies compared the diffraction limited MTF in the band - a bandwidth limited Visual Strehl ratio A metric related to the perception of overall visual quality in that it is an average of the spatial frequency response at all orientations in the spatial frequency range that composes most scenes A correlate to contrast sensitivity as contrast sensitivity measures the response of the visual system to this band of spatial frequencies
But there is seldom anything completely new 1972- E.M.Granger of Kodak proposes a Subjective Qualify Factor (SQF) for photographic systems - it is a type of band width limited Strehl ratio! Granger used the band 10 to 40 cycles/mm on the retina (3 to 12 cycles/degree) To give the measure a logarithmic character, the each MTF threshold value was divided by its spatial frequency value prior to the volume calculation SQF = K 12 Ú 3 df 2p Ú 0 MTF( f,q) f dq
A Visual Quality Factor for the eye (VQF) To create a metric covering the spatial frequencies measured by Contrast Sensitivity testing use the frequency range of the SQF test (3 to 12 cpd) with the normalization factor K being the 1/SQF(diffraction limited) and a modified MTF VQF = 12 Ú 3 12 Ú 3 df df 2p Ú 0 2p Ú 0 MTF ( eye f,q) - NTF( f) f MTF ( diff.lim. f) - NTF( f) f dq dq
A Subjective Sharpness Factor for the eye (SSF) To create a metric measuring the effect of higher spatial frequencies on perceived sharpness of images use that same formulation as that for the VQF but use the spatial frequency band from 15 to 40 cpd. SSF = 40 Ú 15 40 Ú 15 df df 2p Ú 0 2p Ú 0 MTF ( eye f,q) - NTF( f) f MTF ( diff.lim. f) - NTF( f) f dq dq
But there are many times when MTF related quality factors are not too helpful in explaining the clinical situation RMS = 1.150 m VQF =32.8% SSF =1.5%
The point spread, however, tells the story
Metrics based on the PSF Strehl ratio (original definition) Encircled energy Traditional encircled energy calculation - the fraction of the total energy in the point spread found within a specified subtended angle space Point spread quality (PSQ) A measure to give of the compactness of the PSF - Point spread quality - the concentration fo the point spread within a specified subtended angle space Multiplicity factor (MF) A measure to highlight multiple image and ghost formation
Point spread quality Imagine a cylinder the height of the point spread function peak - normalized to a height of one unit - with a diameter the size of a 20/25 letter in which the point spread function resides (6.5 arc min) Take away the point spread function and measure how much volume is left A compact point spread function - one that allow object to be well resolved - takes little volume away. A more spread out point spread function- one that makes resolution more difficult - takes away more. So a bigger value is found for the better case.
Point spread quality
Multiplicity factor A type of peak detector with the ability set the spacing between peaks a way to rule out bunched peaks An initial maximum peak is found and a local area around it is used to create a surface kernel The kernel is moved over the PSF and subtracted from it at each location similar to convolution but using subtraction instead of multiplication
Multiplicity factor When the kernel is positioned over a peak, the residual found is small this identifies the peaks Peaks are identified as areas where the residual is under a set threshold A spacing parameter limits the space between visible images The number of qualifying peaks is the Multiplicity Factor (MF)
New visual function diagnostic metrics Visual Quality Factor the ratio of the volume under the MTF to the diffraction limited MTF volume in an annular band from 3 to 12 cpd an analog of Contrast Sensitivity Subjective Sharpness factor - the ratio of the volume under the MTF to the diffraction limited MTF volume in an annular band from 15 to 40 cpd Point Spread Quality a measure of the compactness of a peak of the point spread function Multiplicity Factor a measure to aberrations to create ghosts or multiple images