Accommodation responses to stimuli in cone contrast space · Accommodation responses to stimuli in cone contrast space Frances J. Rucker *, Philip B. Kruger Schnurmacher Institute

www.elsevier.com/locate/visres

Vision Research 44 (2004) 2931–2944

Accommodation responses to stimuli in cone contrast space

Frances J. Rucker *, Philip B. Kruger

Schnurmacher Institute for Vision Research, State University of New York, State College of Optometry, 33 West 42nd Street, NY 10036-8003, USA

Received 29 April 2003; received in revised form 6 November 2003

Abstract

The aim was to identify the cone contributions and pathways for reflex accommodation. Twelve illumination conditions were

used to test specified locations in cone-contrast space. Accommodation was monitored continuously in a Badal optometer while

the grating stimulus (2.2 c/d sine-wave; 0.27 modulation) moved sinusoidally (0.195 Hz) towards and away from the eye from a

mean position of 2.00 D (±1.00 D). Mean accommodation level and dynamic gain and phase at 0.195 Hz were calculated. Mean

accommodation level varied significantly when the long- and middle-wavelength cone contrast ratio was altered in both the lumi-

nance and chromatic quadrants of cone-contrast space. This experiment indicates that L- and M-cones contribute to luminance and

chromatic signals that produce the accommodation response, most likely through magno-cellular and parvo-cellular pathways,

respectively. The L:M cone weighting to the luminance pathway that mediates accommodation is 1.63:1. The amplitude and direc-

tion of the response depends on changes in chromatic contrast and luminance contrast signals that result from longitudinal chro-

matic aberration and defocus of the image.

� 2004 Elsevier Ltd. All rights reserved.

Keywords: Accommodation; Longitudinal chromatic aberration; Long- and middle-wavelength sensitive cones; Neural pathways

1. Introduction

The standard view of accommodation control is thatthe stimulus arises from change in luminance contrast

of the retinal image. Accurate focus with an even-error

stimulus like luminance contrast relies on negative feed-

back, as the optical system searches for the point of

maximal luminance contrast and smallest blur-circle

diameter (Bobier, Campbell, & Hinch, 1992; Charman

& Tucker, 1978; Heath, 1956; Phillips & Stark, 1977;

Stark & Takahashi, 1965; Troelstra, Zuber, Miller, &Stark, 1964; Wolfe & Owens, 1981). However, the abil-

ity of subjects to accommodate in monochromatic light

without feedback (Kruger, Mathews, Katz, Aggarwala,

& Nowbotsing, 1997) indicates that the even-error signal

from changes in luminance contrast is not the sole signal

for reflex accommodation. This is supported by experi-

0042-6989/$ - see front matter � 2004 Elsevier Ltd. All rights reserved.

doi:10.1016/j.visres.2004.07.005

* Corresponding author. Tel.: +1 212 780 5122.

E-mail address: [email protected] (F.J. Rucker).

ments that elicit accommodation responses from short-

wavelength sensitive cones (Rucker & Kruger, 2001,

2004) that are typically considered to be insensitive tochanges in luminance contrast (Cavanagh, MacLeod,

& Anstis, 1987; Eisner & MacLeod, 1980; Tansley &

Boynton, 1978; Whittle, 1974).

The counter argument to the standard view, proposed

by Fincham (1951) is that odd-error signals drive

accommodation. Fincham suggested that odd-error

stimuli are derived from the effect of longitudinal chro-

matic aberration (LCA) on defocus blur at luminanceborders. Since 1951, several studies have supported the

idea that chromatic aberration provides a direction sig-

nal to reflex accommodation in humans (Aggarwala,

Mathews, Kruger, & Kruger, 1995; Aggarwala, Now-

botsing, & Kruger, 1995; Campbell & Westheimer,

1959; Crane, 1966; Flitcroft, 1990; Kotulak, Morse, &

Billock, 1995; Kruger, Aggarwala, Bean, & Mathews,

1997; Kruger, Mathews, Aggarwala, Yager, & Kruger,1995; Kruger, Mathews, Aggarwala, & Sanchez, 1993;

mailto:[email protected]

2932 F.J. Rucker, P.B. Kruger / Vision Research 44 (2004) 2931–2944

Kruger & Pola, 1986; Smithline, 1974; Toates, 1972) and

in Rhesus monkeys (Flitcroft & Judge, 1988). It has

been suggested that the signal from LCA is derived from

a comparison of cone contrasts (Flitcroft, 1990; Kruger

et al., 1995), and there is agreement that long-wave-

length sensitive cones (L-cones) and middle-wavelengthsensitive cones (M-cones) mediate this signal (Aggar-

wala, Mathews, et al., 1995; Aggarwala, Nowbotsing,

et al., 1995; Crane, 1966; Kotulak et al., 1995). Indeed

simulations based on a comparison of normalized L-

and M-cone contrasts drive accommodation in the pre-

dicted direction (Kruger et al., 1995; Lee et al., 1999;

Stark et al., 2002). On the other hand, when the pupil

is large and monochromatic aberrations are prominent,there is very little variation in retinal image quality

across the visible spectrum (McLellan, Marcos, Prieto,

& Burns, 2002). This makes it less likely that a chro-

matic signal from LCA provides an effective signed stim-

ulus. The ability of some subjects to accommodate in

monochromatic light (Fincham, 1951) also indicates

that LCA is not the sole signal for accommodation.

It has also been suggested that an odd-error signalmay originate from light vergence 1, perhaps via direc-

tionally sensitive cones (Fincham, 1951; Kruger, Math-

ews, Katz, et al., 1997). Fincham (1951) suggested that

small eye movements combined with the wave-guide

properties of cones produce a ‘‘difference of brightness’’

across the blur circle with a change in focus. A similar

effect occurs without eye movements if the Stiles-Craw-

ford effect is de-centered (Kruger, Aggarwala, Bean,et al., 1997; Kruger, Mathews, Katz, et al., 1997). An-

other possibility is that monochromatic aberrations pro-

vide the sign of defocus (Campbell & Westheimer, 1959;

Charman & Tucker, 1978; Chen, Kruger, & Williams,

2002; Fernandez & Artal, 2002; Fincham, 1951; Walsh

& Charman, 1989; Wilson, Decker, & Roorda, 2002).

However, the ability of some subjects to accommodate

in the absence of monochromatic aberrations (Chenet al., 2002), suggests that aberrations are also not the

sole source of the signal.

1.1. Neural pathways for defocus signals

Information on defocus is transmitted via cone sig-

nals, bipolar cells and retinal ganglion cells to the

LGN, and potentially to the pretectal nucleus and supe-rior colliculus. For retinal input to the cortex via the

LGN, signals are divided into three discrete pathways:

a luminance pathway, and two chromatic pathways;

1 The vergence of light is defined by

V ¼ nL;

where n is the index of refraction of the medium and L is the distance

in accordance with the Cartesian sign convention.

long- and middle-wavelength sensitive (Kelly & van

Norren, 1977), and short-wavelength sensitive (Hendry

& Reid, 2000). There is no known pathway for a single

retinal cell type to carry a vergence signal. However,

many different ganglion cell types exist and non-cortical

pathways to the superior colliculus and pretectal nucleusmay provide an alternative neural pathway for accom-

modation stimulus information.

1.2. Luminance pathway

The standard model of accommodation involves opti-

mization of the luminance contrast of the image through

negative feedback. The luminance pathway responds lin-early to changes in luminance contrast (Lee, Martin, &

Valberg, 1988) and sensitivity is described by the Vk

function (Smith & Pokorny, 1975). This function is a

weighted sum of L- and M-cone contributions with L-

cone weight up to twice as large as the M-cone weight

(Smith & Pokorny, 1975). However, the weighting var-

ies and is dependent on the color of the background

adapting field, spatial, and temporal frequency (Eisner& MacLeod, 1981; Stromeyer, Chaparro, Tolias, &

Kronauer, 1997; Stromeyer, Cole, & Kronauer, 1987;

Swanson, Pokorny, & Smith, 1988). This pathway is

often referred to as the magno-cellular pathway since

in the lateral geniculate nucleus cell types associated

with this pathway are referred to as magno-cellular cells.

1.3. Long- and middle-wavelength sensitive chromatic

pathway

Following suggestions that longitudinal chromatic

aberration provides a direction signal for accommoda-

tion, Flitcroft (1990) suggested that chromatic or oppo-

nent pathways could provide a signed accommodation

response. Flitcroft (1990) calculated the effect of defocus

on the red/green and blue/yellow opponent mechanisms,allowing for the effects of longitudinal chromatic aberra-

tion (LCA), spectral sensitivity of the cones, and modu-

lation transfer function. Calculations for an equal

energy white stimulus indicate that defocus could be

specified by the response of the opponent mechanisms.

The long- and middle-wavelength sensitive chromatic

pathway is sensitive to the difference between L-and

M-cone excitation (Derrington, Krauskopf, & Lennie,1984). The relative weighting of the L- and M-cone con-

trast signal to the chromatic pathway is equal and oppo-

site (Eisner & MacLeod, 1981; Stromeyer et al., 1987;

Stromeyer et al., 1997). This pathway is often called

the parvo-cellular pathway, since in the lateral genicu-

late nucleus cell types associated with this pathway are

referred to as parvo-cellular cells. Parvo-cells respond

non-linearly to changes in luminance contrast (Lee, Pok-orny, Smith, Martin, & Valberg, 1990; Yeh, Lee, & Kre-

mers, 1996).

F.J. Rucker, P.B. Kruger / Vision Research 44 (2004) 2931–2944 2933

The aim of this experiment is to quantify the cone

contributions to luminance and chromatic signals for

reflex accommodation. This experiment will explore the

range of reflex accommodation responses to changes in

the L- andM-cone contrast ratio of the stimulus, demon-

strating the effects of a signal from LCA at both lumi-nance and chromatic borders. In addition, the L- and

M-cone weighting to the luminance and chromatic path-

ways that mediate the signal for dynamic accommoda-

tion will be calculated, and the weighting of the

luminance and chromatic components of the accommo-

dation signal to the static response will be determined.

This experiment will determine the effect of changes

in the L- and M-cone contrast ratio of the stimulus onmean accommodation level. Kruger et al. (1995) indi-

cated that small changes in cone contrast drive accom-

modation in a pre-determined direction. Kruger et al.

(1995) measured the accommodation response to stimuli

with higher contrast for long-wavelengths and lower

contrast for short wavelengths, and vice versa. The

L/M-cone contrast ratio varied from 0.65/0.72 for

�1.00 D defocus, to 0.73/0.70 for +1.00 D defocus.The current experiment will measure a much greater

L/M cone contrast range from 0.27/0 to 0/0.27 with

several intermediate values included.

The effect of a chromatic signal from LCA at lumi-

nance and chromatic borders will be simulated by com-

parison of the responses to these stimuli. A previous

experiment (Kruger et al., 1993) demonstrated the effect

of LCA at luminance borders. This experiment will ex-tend these findings and demonstrate the effect of LCA

at both luminance and chromatic borders.

The weighting of the luminance and chromatic com-

ponents of the stimuli to the static response will be

determined. When both luminance and chromatic com-

ponents of the stimulus are available, as in white light in

the presence of LCA, the relative weight of each compo-

nent to the neural stimulus is unknown. The currentexperiment explores the relative importance of the lumi-

nance and chromatic components of the stimulus.

Finally, the L- and M-cone weighting to the lumi-

nance and chromatic pathways will be calculated. The

cone weighting to the luminance component of the reflex

accommodation signal will be derived from an iso-gain

response contour. Smith and Pokorny (1975) demon-

strated a 1.62:1 cone weighting of the L- and M-conesto V(k), and a 1:1 cone weighting for the chromatic

pathway. This experiment will explore the cone weight-

ing of the L- and M-cones to the luminance and chro-

matic pathways for reflex accommodation.

2. Methods

The target conditions isolated positions in cone con-

trast space in an effort to determine the cone contribu-

tions and mechanisms that stimulate accommodation.

The subject fixated a computer generated vertical sine

wave grating of 2.2 cycles per degree (c/d), 0.27 modula-

tion, which moved in sinusoidal motion toward and

away from the eye in a Badal stimulus system.

2.1. Infrared optometer and Badal stimulus system

An infrared recording optometer (Kruger, 1979), and

Badal optical system (Ogle, 1968) were used to measure

accommodation responses and present stimuli. The

apparatus has been described in detail (Lee, Stark,

Cohen, & Kruger, 1999). The advantage of the Badal

stimulus system is that a dioptric change in target dis-tance (vergence) occurs without a change in target lumi-

nance or visual angle subtended by the target (Ogle,

1968). Target position was modulated by a computer

program that controlled a motorized prism that moved

along the optical axis of the Badal system. The program

corrected for vertex distance of the trial lens (subject�sRx) and produced the correct accommodation stimulus

with an accuracy of ±0.12 D. A reference wavelength of550 nm was used for calibrating target vergence.

A field stop with blurred edges (5.20 D beyond the

emmetropic far point) subtended 7.2� at the eye, and

an artificial pupil (3 mm) was imaged in the real pupil

plane. Monochromatic aberrations have a minimal

effect on image quality at 2.2 c/d when viewed through

a 3 mm pupil (Liang & Williams, 1997; Walsh & Char-

man, 1985).

2.2. Calibration of accommodation responses

Calibration of the accommodative response involved

a method to relate subjective focus for a target at differ-

ent accommodation levels with optometer output (Lee

et al., 1999). This provided a measurement of subjective

focus while a simultaneous measurement of optometervoltage output was recorded. Principle axis regression

(Sokal & Rohlf, 1981) was then used to obtain a linear

equation relating accommodation response to infrared

optometer output. This method provides an absolute

calibration of the accommodation response.

2.3. Stimuli

Stimuli were generated by a video controller (Cam-

bridge Research Systems VSG2/5) and displayed on a

color monitor (Sony Trinitron color graphic display

GDM-F500R). Dual 8-bit video DAC provided 15-bit

output resolution per color (red, green, blue). Monitor

resolution was 640 · 480 pixels and frame rate was

150 Hz. A Cambridge Research systems Opti-Cal was

used to apply a Gamma correction to the computer dis-play (Sony Trinitron) and to monitor the (x,y) co-ordi-

nates of the stimuli throughout the experimental period.


Photometry was performed through the Badal stimulus

system using the method of Westheimer (1966). Meas-

urements were made using a Pritchard spectral-radiom-

eter (Spectra-Scan PR704, Photo Research). All gratings

were measured through the stimulus system and adjust-

ments were made for the small contribution of visiblelight from the optometer. All stimuli had a retinal illu-

minance of 140 tds.

Cone excitation was calculated from the spectral radi-

ation of each phosphor using Smith and Pokorny cone

fundamentals (Smith & Pokorny, 1975) based on trans-

formations from Judd (1951) color matching functions.

Relative intensity levels for each gun were calculated

based on the required Michelson cone-contrasts usingthe formula: contrast = (Emax � Emin)/(Emax + Emin),

where Emax is the maximum cone excitation for the grat-

ing and Emin is the minimum cone excitation for the

grating. Cone contrasts of the stimuli were maintained

in the eye by neutralization of LCA using a specially de-

signed achromatizing lens positioned in the stimulus sys-

tem (Kruger et al., 1993).

The grating stimuli can be represented graphically onorthogonal axes that represent. DL/L and DM/M cone

contrast. DL and DM represent the change in cone exci-

tation for the L- and M-cones above the mean excitation

level, and L and M represent the mean excitation of L-

and M-cones (Fig. 1). Fig. 1 describes the location of the

grating stimuli between 0� and 180�. This graphical rep-resentation, which is referred to as cone contrast space,

was first described by Noorlander and Koenderink(1983) and its use has become widespread (Gowdy,

L-cone contrast

-0.4 -0.2 0.0 0.2 0.4

M-cone contrast

0.0

0.2

0.4

vector length 0.27 (luminance)45 deg axis120 deg axisvector length 0.27 (chromatic)

Fig. 1. Stimuli represented in cone contrast space. Targets can be

represented graphically on orthogonal axes that represent DL/L and

DM/M cone contrast, where DL and DM represent the change in cone

excitation for the L- and M-cones above the mean excitation level, and

L and M represent the mean excitation of L- and M-cones.

Stromeyer, & Kronauer, 1999; Lee et al., 1990; Stro-

meyer et al., 1987; Tsujimura, Wolffsohn, & Gilmartin,

2001). The advantage of using cone contrast space is

that the DL/L and DM/M values do not change with dif-

ferent backgrounds in the way that cone excitation val-

ues change. In cone contrast space the origin alwaysrepresents the adapting field. A comparison of cone exci-

tation and cone contrast space can be found in Eskew,

McLellan, and Giulianini (1999).

The spatial frequency of the grating was chosen to en-

hance the contribution of the L- and M-cone contrast

signals to luminance and chromatic signals, yet still pro-

vide a stimulus for accommodation. The chromatic sen-

sitive neural pathway has greater contrast sensitivitythan the luminance sensitive neural pathway, at low spa-

tial (1–7 c/d) and temporal frequencies (Noorlander,

Heuts, & Koenderink, 1981; Stromeyer et al., 1987).

By selecting a grating of 2.2 c/d the accommodation re-

sponse of both the luminance and the chromatic mech-

anisms were optimized, while maintaining a spatial

frequency that provided a stimulus for accommodation.

2.4. Static stimulus

Twelve conditions tested the origin and seven L/M-

cone contrast ratios in cone contrast space (0�, 22.5�,45�, 67.5�, 90�, 120�, 145�). Stimuli located in the first

quadrant (Fig. 1) have L- and M-cone contrast in the

same spatial phase providing stimuli with pre-domi-

nantly luminance contrast. At 45� the amplitude ofL- and M-cone contrast is equal and in phase. Stimuli

rotated above or below this point have an imbalance

in the amplitude of L- and M-cone contrast, which adds

a small chromatic component to the stimulus. The chro-

matic contribution increases until at 90� and 0� there is

an equal amount of luminance and chromatic contrast

in the stimulus. Stimuli located in the second quadrant

have L- and M-cone contrast with 180� spatial phasedifference (spatial counter-phase), providing stimuli with

pre-dominantly chromatic contrast. The iso-luminant

axis (112�) corresponds to the direction of tan�1 (�x),

where x is the L/M cone excitation ratio of the adapting

field. The accommodation threshold for a sinusoidally

moving luminance grating is approximately 0.05 (Math-

ews & Kruger, 1989), so that isolation of an individuals

iso-luminant point was unnecessary.Seven of the twelve conditions tested loci that form a

circle with equal vector length (0.27) at 0�, 22.5�, 45�,67.5�, 90�, 120�, and 145� in cone contrast space. These

seven conditions test the effect of different ratios of L-

and M-cone contrast on the accommodation response.

Stimuli at 0�, 22.5�, 67.5� and 90� represent luminance

stimuli; L- and M-cone contrasts are in phase in this

quadrant and simulate the retinal image in the presenceof LCA and defocus at luminance borders. Stimuli

at 120 and 145� represent chromatic stimuli; L- and


M-cone contrasts are in spatial counterphase in this

quadrant. At 120� M-cone contrast is greater than L-

cone contrast, at 145� L-cone contrast is greater than

M-cone contrast. This imbalance in L- and M-cone con-

trasts introduces a small luminance component into the

chromatic stimulus and simulates the retinal images inthe presence of LCA and defocus at chromatic borders.

If the amplitude of LCA were large enough, a point

would be reached where the cone contrast of one cone

type would be reduced to zero, while the contrast of

the other cone type would be maximal. This is achieved

in the 90� and 0� stimulus position. However, this would

only happen in the human eye, with large pupils and at

high spatial frequencies. For a 2.2 c/d sine-wave gratingthe effect of LCA on contrast is small compared to the

effects at high spatial frequencies, and the 90� and 0�stimulus positions can only be achieved with low con-

trast in one cone type under normal circumstances.

Four additional conditions tested the effect of a

change in contrast (vector length) on the accommoda-

tion response. Modulations of 0, 0.13, 0.18, 0.27, and

0.42 were tested along the 45� axis, and modulationsof 0, 0.11 and 0.27 were tested along the 120� axis

(including the empty field described below and stimuli

with 0.27 vector length described above). These stimuli

varied in either luminance contrast or chromatic con-

trast with a constant L/M-cone ratio (45� or 120�) andconstant mean dioptric vergence (2.00 D).

The twelfth condition was an empty field stimulus

that was also the adapting field (CIE (x,y) co-ordinates(0.4554,0.3835)). The adapting field is represented at the

origin in cone contrast space and has zero contrast. The

empty field stimulus was included as a control condi-

tion, to determine if the static and dynamic accommoda-

tion responses were real under the different stimulus

conditions.

2.5. Dynamic stimulus

Each of the twelve stimuli moved at 0.195 Hz sinusoi-

dally towards and away from the eye between 1.00 D

and 3.00 D, while the effects of LCA were neutralized

with an achromatizing lens. As the stimulus moved sin-

usoidally towards and away from the eye, the dynamic

stimulus included changes in dioptric vergence and lumi-

nance contrast that were the same for all conditions. Thedynamic modulations tested for the optimal L/M-cone

contrast ratio in the stimulus for driving dynamic

accommodation in the absence of LCA.

It is important to recognize that the stimuli in this

experiment comprised both open-loop and closed-loop

components. First, LCA of the subject�s eye was neutral-ized by an achromatizing lens throughout the experi-

ment, and since LCA from the eye was absent, it canbe considered an open-loop stimulus. Second, the chro-

matic stimulus that was produced by altering the ratio of

L/M-cone contrast was also open loop. The ratio of L/

M-cone contrasts was fixed during each trial, and

changes in accommodation could not change the ratio

of L/M-cone contrasts. The ratio of L/M-cone-contrasts

was altered from trial to trial to simulate the effects of

LCA, and the effects of simulated LCA can be deter-mined by comparison of the ‘‘static’’ and ‘‘dynamic’’ re-

sponses to the individual stimuli. Finally, the luminance

stimulus was a closed-loop stimulus, because changes in

accommodation could alter defocus and thus change the

luminance contrast of the stimulus. In summary, LCA

of the eye and chromatic contrast provided an open-

loop stimulus, while luminance contrast of the target

provided a normal closed-loop stimulus foraccommodation.

The exceptions to this rule are the stimuli at 120� andthe empty field stimulus. Luminance contrast was small

(0.02) for the stimulus at 120� (0.27 vector length), so

this stimulus was effectively open loop (Mathews & Kru-

ger, 1989) for luminance contrast. The empty field stim-

ulus was open loop for all three types of stimulus.

2.6. Procedure

During preliminary examinations case histories were

recorded, and color vision (anomaloscope), subjective

refraction, visual acuity and amplitude of accommoda-

tion were measured. To begin experimental trials, trial

lenses were inserted in front of the left eye to correct

for ametropia and the right eye was patched. Subjectswere positioned on a chin and headrest mounted on a

three-way stage. Eye position was monitored by video

and the first Purkinje image was used to align the achro-

matic axis of the eye (Thibos, Bradley, Still, Zhang, &

Howarth, 1990) with the optical axis of the system

(Lee et al., 1999). Subjects were dark adapted for 10

min prior to the trials and then adapted to the back-

ground field for 2 min prior to measurement, and alsobetween conditions. The subject fixated on the stimulus

grating while being re-aligned before the start of

each trial. Each trial lasted 40.96 s with 8 cycles of sinu-

soidal motion towards and away from the subject (1.00–

3.00 D) per trial. There were eight trials of each condi-

tion performed in eight separate blocks (Subjects 9

and 3 had six trials of each condition). The conditions

were randomized without replacement within a block.

2.7. Instructions

The subject was instructed to ‘‘Keep the grating clear

with as much effort as if you were reading a book’’ and

to ‘‘Pay attention to the grating’’. The room was dark-

ened and the subject was unable to see the surrounding

apparatus while viewing the grating. There were noexternal cues to guide the direction of the subject�saccommodation.


2.8. Subjects

Subjects were excluded from the study for significant

ocular injury or disease, history of amblyopia, defective

color vision, excessive blinks, or low gain in monochro-

matic light. Since subjects demonstrate variability inresponse to monochromatic targets (Fincham, 1951;

Kruger et al., 1993; Lee et al., 1999) subjects with

accommodation dynamic gain of less than 0.2 in mono-

chromatic light to a high contrast maltese cross target,

were excluded. Hence, only those subjects that re-

sponded very poorly in monochromatic light were ex-

cluded. Only three out of nine subjects were excluded

for low gain in monochromatic light. Exclusion was nec-essary to distinguish between a weak response in mono-

chromatic light and a lack of response to the stimuli in

cone-contrast space. Exclusion reduces the probability

of demonstrating a difference in accommodation re-

sponse between trials, and decreases noise in the analysis

of gain. Trials with excessive blinks (>20%) or artifacts

were excluded. Six subjects were included in the

experiment.Subjects gave informed consent, the experiment was

approved by the Institutional Review Board of the col-

lege, and followed the tenets of the Declaration of Hel-

sinki. Subjects ranged from 23 to 29 years old and were

paid for participation. Refractive errors were corrected

either by contact lenses or trial lenses.

2.9. Analysis

The effects of blinks were removed from the data

using standard signal processing before analysis. Gain

and temporal phase lag were used as measures of the

sensitivity of the dynamic accommodation system to

changes in L/M-cone contrast ratios. Dynamic gain

and phase lag were calculated after Fourier analysis of

the data from each trial, as the ratio of response ampli-tude to stimulus amplitude at the stimulus frequency

(0.195 Hz). Mean gain and phase lag were calculated

for each condition using vector averaging. Mean gain

was plotted against stimulus vector angle in Cartesian

co-ordinates. In addition, predicted gain for a luminance

controlled mechanism was plotted from physical meas-

urements of the luminance contrast of each of the sti-

muli. For this plot the maximum predicted gain wasset equal to the maximum measured gain and predicted

gain values for all the other stimulus conditions were

scaled according to the relative change in luminance

contrast of the stimulus from the stimulus at 45�. Con-cordance is judged by the orientation and shape of the

responses and not by the amplitude of the responses.

For the stimuli along the 120� axis, a procedure using

principal axis regression was used to test for individualvariation in the dynamic accommodation response.

The procedure gives a quantitative measure of the size

of the response in the ‘‘120�’’ condition in terms of

standard deviations (Sokal & Rohlf, 1981). The results

of each individual�s six trials were plotted in Cartesian

co-ordinates; then the distance of the mean from zero

(or noise) was calculated in standard deviations, to give

an estimate of the size of the response above noise.Mean accommodation level was used as a measure of

the sensitivity of the accommodation system to the L/M-

cone contrast ratios of the image for a stimulus that

oscillates between 1.00 and 3.00 D. Mean accommoda-

tion level was calculated as the mean accommodation re-

sponse (D) over the duration of the trial. The measure of

‘‘mean accommodation level’’ describes the amplitude of

the accommodation response to the near target (mean2.00 D), and hence the direction of the response for an

image with a particular cone contrast ratio.

Mean accommodation level was plotted against sti-

mulus vector angle in Cartesian co-ordinates. Predicted

mean accommodation levels for a mechanism sensitive

to luminance contrast were plotted as described above

for gain. Conditions were compared using a single factor

Anova and t-tests for paired samples. t-tests were onlyperformed if the F value was significant at the a = 0.05

level.

2.10. Iso-response contours

The iso-response contour indicates the amount of L-

or M-cone contrast producing a constant response at

different locations in cone contrast space (Stromeyer,Kronauer, Ryu, Chaparro, & Eskew, 1995; Tsujimura

et al., 2001). One advantage of finding iso-response con-

tours is that the mechanism mediating the response can

be found from a vector orthogonal to the contour. The

contour forms a quadrilateral unless phase delays be-

tween the L- and M-cone responses change the stimulus

properties (Stromeyer et al., 1987). If this is the case then

the contour forms an elliptical shape as the phase delaybetween cone types introduces a small, additional, lumi-

nance or chromatic component. The length of the vector

orthogonal to the contour indicates the sensitivity of the

detection mechanism: the shorter the vector the greater

the sensitivity.

Iso-response calculations assume a linear relationship

between gain or mean accommodation level and change

in L- and M-cone contrast. Therefore linearity of themean accommodation level and gain responses with

increasing luminance and chromatic contrast was tested

by linear regression along the 120� and 45� axes.

2.11. Calculation of the iso-response contour

The signal to the chromatic mechanism depends on

the difference in cone contrast for L- and M-cones suchthat chromatic response amplitude (Dchrom):


Dchrom ¼ jaL0 � bM0j ð1Þwhere a and b represent weighting factors for the contri-

bution of L 0- and M 0-cone contrast to the chromaticmechanism.

The signal to the luminance mechanism depends on

the total amount of cone contrast; the sum of L- and

M-cone contrasts such that luminance response ampli-

tude (DLum):

DLum ¼ jcL0 þ dM0j ð2Þwhere c and d represent weighting factors for the contri-

bution of L 0- and M 0-cone contrast to the luminance

mechanism.

The iso-response contour for gain and mean accom-

modation level is calculated by scaling the L 0- and M 0-

cone contrasts for each stimulus by the ratio of DR:D,

where DR is the required constant accommodation re-sponse and D is the measured gain or mean accommo-

dation response such that:

ðDR=DLumÞ � ðL0 þM0Þ¼ DRLum for the luminance mechanism ð3Þ

and

ðDR=DchromÞ � ðL0 �M0Þ¼ DRchrom for the chromatic mechanism ð4Þ

Gain and Phase Pol

0.00.0

0.1

0.2

0.00.10.20.0

0.1

0.2

90

120

150

180

210

240

270

Stimulus Conditions (Deg)Empty Field

-90

-120

-150

0

22.5

45

90145

120

Degree

67.5

Fig. 2. Gain and temporal phase of responses. Radial axes represent gain, a

degrees in an anti-clockwise direction, phase lag as degrees in a clockwise dire

their location in degrees in cone contrast space as shown in Fig. 1. Gain incre

This stimulus has equal amounts of L- and M-cone contrast in the same spatia

M-cone contrast, gain decreased and phase-lag increased.

3. Results

3.1. Dynamic gain and phase at 0.2 Hz

Analysis of variance confirmed that changes in the

L/M-cone contrast ratio produced significant changesin dynamic gain at 0.195 Hz (F = 2.95; p = 0.004). Gain

and temporal phase lag of responses are plotted in Fig.

2. Gain was maximal and phase lag was smallest for the

stimulus at 45�. This stimulus has equal amounts of L-

and M-cone contrast in the same spatial phase. As the

stimulus shifted away from 45�, luminance contrast de-

creased with a corresponding decrease in gain and in-

crease in phase lag. The gain and phase lead in theempty field condition most likely arose from noise,

since gains were very small in this condition (0.01–

0.09), with large variations in phase angle (79 to

�152�).Subjects were selected based on their ability to pro-

duce gains of greater than 0.2 to a high contrast maltese

cross that contains a large range of spatial frequencies

and orientations. Gains varied widely from 0.2 to 0.6.As expected gains were further reduced when the stimu-

lus was changed to a medium contrast (0.27 modula-

tion), spatially restricted (2.2 c/d) sine wave grating.

The maximum mean gain was reduced to 0.39, and the

ar Plot

0.1 0.20

30

60

300

330-30

-60

Phase lead

Phase lagGain

s

nd angular axes describe temporal phase. Phase lead is represented as

ction. The length of the vector represents gain. Stimuli are described by

ased to a maximum for the stimulus at 45� and phase lag was smallest.

l phase. As the stimulus shifted away from a stimulus with equal L- and

Contrast (Vector length)0.0 0.1 0.2 0.3 0.4 0.5

Gai

n

0.0

0.1

0.2

0.3

0.4

0.5

Luminance contrast (45 deg)Chromatic contrast (120 deg)

Fig. 3. The effect of luminance contrast and chromatic contrast on

dynamic gain (in the absence of LCA) is examined by plotting gain

responses against vector length (contrast) for stimuli along the 45� and120� axis. Standard error of the mean is plotted for each data point.

Gain increased with increasing luminance contrast while increasing

chromatic contrast had little effect.


minimum to 0.03, for the stimulus at 45� in cone-con-

trast space. These results confirm previous reports that

accommodation gain responses vary widely among the

population (see Section 4) and decrease with reduced

contrast (Mathews & Kruger, 1989).

The effect of grating contrast on dynamic gain is illus-trated in Fig. 3. Gains are plotted for stimuli along the

45� axis (luminance contrast) and 120� axis (chromatic

contrast). Gain increases linearly (r = 0.99; r2 = 0.99)

with increasing luminance contrast, while increasing

chromatic contrast has little effect on gain.

In Fig. 4 measured gains are plotted together with

predicted gains modeled from a luminance controlled

mechanism. Fig. 4 shows gain for each stimulus loca-tion in degrees as a radial plot. Measured gain values

follow predicted values reasonably closely. Corre-

spondence between the measured and predicted values

should be judged by the orientation of the responses,

not by the amplitude, because the maximum predicted

amplitude was set equal to the maximum measured

response.

To determine whether the responses in the chromaticquadrant were real or noise, mean gain for six subjects

to the chromatic stimulus (at 120� in cone contrast

space) were compared with the empty field gains. Indi-

vidual response size ranged from 0.25 to 3.19 standard

Predicted v

0.00.00

0.05

0.10

0.15

0.20

0.25

0.00.050.100.150.200.250.00

0.05

0.10

0.15

0.20

0.25

Angl

e in

con

e co

ntra

st s

pace

(Deg

)

9

120

150

180

210

240

27ActualPredicted

Fig. 4. Gain for each stimulus location on a radial plot. Predicted gain was

stimuli. Predicted mean responses for a luminance-controlled mechanism are

responses. Measured gain responses follow predicted responses reasonably cl

the mean is plotted for each data point (dashed line). Alignment should be ju

predicted amplitude was normalized.

deviations times noise, but the difference was not signif-

icant (p = 0.124) when grouped together.

s Actual Gain

Gain0 0.05 0.10 0.15 0.20 0.250

0

30

60

0

0

300

330

plotted from measurements of the luminance contrast of each of the

represented by the dotted lines, while the solid line represents ‘‘actual’’

osely, with a greater than predicted response at 45�. Standard error of

dged by the orientation of the responses not by amplitude, because the


3.2. Mean accommodation level

Analysis of variance also confirmed that changes

in the L/M-cone contrast ratio produced significant

changes in the mean accommodation level (F = 2.29;

p = 0.02). To determine if the luminance and chromaticresponses were simply noise, mean response level for

stimuli at 45� and 120� were tested for significance when

compared with the mean accommodation level for the

empty field condition (�0.49 D). For the mean of six

subjects, mean accommodation level for a 45� and a

120� stimulus were significantly different from empty

field responses (p = 0.012; SD 1.18 D) and (p = 0.004;

SD 0.76 D) respectively.A polar graph representing mean accommodation

level is shown in Fig. 5. There are large changes in the

mean accommodation level that correspond to changes

in the ratio of L- and M-cone contrast. The mean

accommodation level is higher when M-cone contrast

is high and L-cone contrast is low, and lower when L-

cone contrast is high and M-cone contrast is low. The

effect of a difference in L- and M-cone contrast on themean accommodation level is similar for a luminance

grating (0–90�) and for a chromatic grating (90–180�).The actual mean accommodation level plot (solid line)

is at 60� to the predicted mean accommodation level

(dotted line) for a luminance sensitive mechanism, indi-

Predicted vs Actual Mean

0.00.0

0.5

1.0

1.5

2.0

0.00.51.01.52.0

Angl

e in

con

e-co

ntra

st s

pace

(Deg

)

90

120

150

180

210

240

270ActualPredicted

Fig. 5. A polar plot representing mean accommodation level. Stimuli are rep

levels for a luminance-sensitive mechanism are represented by the dotted line

mean is plotted for each data point (dashed line). ‘‘Actual’’ mean accommo

responses, indicating that there is an increased M-cone and chromatic co

luminance sensitive mechanism.

cating that there are both luminance and chromatic con-

tributions to the response.

Since both luminance and chromatic mechanisms

contribute to the mean accommodation level, the meas-

ured mean accommodation levels were plotted along

with predicted mean accommodation levels from a com-bined luminance and chromatic model. The weighted

sum of the luminance and chromatic components was

found empirically by minimizing the residuals between

the measured and predicted responses. The predicted

mean accommodation level was calculated from the

weighted sum of the luminance (0.8) and chromatic con-

trast (1.2) in the stimulus. As can be seen in Fig. 6, a

combination of luminance and chromatic contrast pro-vides a good fit to the measured response in both orien-

tation and shape.

3.3. The effect of contrast on mean accommodation level

in the absence of LCA

The effect of contrast on mean accommodation level

is shown in Fig. 7. Above some minimum threshold levelof contrast, changes in luminance or chromatic contrast

alone do not significantly change the mean accommoda-

tion level. Luminance contrast (45�) and chromatic con-

trast (120�) alone produce similar mean accommodation

Accommodation Level

Mean Accommodation Level (D)

0.5 1.0 1.5 2.00.0

0.5

1.0

1.5

2.0

0

30

60

300

330

resented in the same way as in Fig. 4. Predicted mean accommodation

s while the solid line represents actual responses. Standard error of the

dation levels are rotated 60� counter-clockwise to the predicted mean

ntribution to the mean accommodation level than is predicted by a

Mean Response (D)0.0 0.5 1.0 1.5 2.0 2.5

0.0

0.5

1.0

1.5

2.0

2.5

0.00.51.01.52.02.50.0

0.5

1.0

1.5

2.0

2.5

Angl

e in

Con

e C

ontra

st S

pace

(Deg

)

0

30

60

90

120

150

180

210

240

270

300

330

ActualPredicted

Mean accommodation level predicted from weighted luminance and chromatic contributions

Fig. 6. Mean accommodation level is plotted together with the predicted mean accommodation level calculated from the weighted sum of the

luminance (0.8) and chromatic contrast (1.2) in the stimulus, normalized to the peak mean response (2.08 D). A combination of luminance and

chromatic contrast provides a good fit to the measured response since the orientations of the predicted and measured responses overlap.

Contrast (Vector Length)0.0 0.1 0.2 0.3 0.4 0.5

Mea

n Ac

com

mod

atio

n Le

vel (

D)

0.0

0.5

1.0

1.5

2.0

2.5

Luminance contrast (45 deg) Chromatic contrast (120 deg)

Fig. 7. The effect of luminance contrast and chromatic contrast on

mean accommodation level in the absence of LCA. Standard error of

the mean is plotted for each data point (dashed line). The mean

accommodation level is at the resting position when target contrast is

below threshold. Amplitude of luminance or chromatic contrast alone

does not affect the mean accommodation level.


responses. Mean accommodation level falls to the tonicaccommodation level when contrast is below threshold.

As luminance modulation increased from 0.12 to 0.42

(vector length) there was no significant change in mean

accommodation response (0.34 D; p = 0.28). As chro-

matic modulation was increased from 0.13 and 0.27

(vector length) the increase in mean accommodation

level was small but approached significance ( p = 0.052).

3.4. Iso-response contour for gain

Fig. 8 shows the iso-response contour for dynamic

gain (0.2 Hz) calculated as described in Eqs. (3) and

(4), and assuming a linear change in gain with change

in contrast (r = 0.99). The iso-response contour for dy-

namic gain forms a straight line with a negative gradient

(gradient �1.63) indicating control by a luminancemechanism with an L-cone weighting 1.63 times as large

as the M-cone weighting. A vector at 31� (length 0.45) is

orthogonal to the contour in the luminance quadrant.

Contour points in the chromatic quadrant may not be

real responses, since the dynamic gain responses at

120� were not significantly different to the dynamic gain

response to the empty field. A vector at 174� (length

0.417) is orthogonal to the contour in the chromaticquadrant. There is no evidence of bowing of the contour

to form an ellipse, indicating that phase delays between

cone types do not contribute to the response (Stromeyer

et al., 1987).

L-cone contrast-1.0 -0.5 0.0 0.5 1.0

M-cone contrast

-1.0

-0.5

0.0

0.5

1.0

Fig. 8. Iso-response contour for dynamic gain (0.2 Hz) forms a

quadrilateral with straight lines perpendicular to a vector at 31� (length0.45; gradient �1.63) and 120� (length 0.81). The gain responses for

chromatic stimuli are not significantly different from noise. Gain is

determined by a mechanism sensitive to luminance contrast.


3.5. Iso-response contour for mean accommodation level

Data from Fig. 7 were examined to determine

whether iso-response contours might be used to identify

the mechanisms that control mean accommodationlevel. Mean accommodation level increases non-linearly

with increase in luminance contrast (r = 0.79; r2 = 0.63).

A comparison between responses to luminance stimuli

of 0.12 and 0.42 modulation (SEM 0.42 and 0.46 D)

indicates that the change in mean accommodation level

is small and not statistically significant (p = 0.28). The

function for chromatic contrast shows that mean

accommodation level increased almost linearly with in-crease in chromatic contrast (r = 0.94; r2 = 0.88). Again,

the increase in mean accommodation level is small but

approaches significance (p = 0.052) when stimuli of

0.13 and 0.27 vector length (SEM 0.31 and 0.36 D) are

compared. However, at higher levels of chromatic con-

trast (above 0.27) the response probably plateaus in

the same manner as the function for luminance contrast.

Non-linearity makes the use of iso-response contoursinappropriate for identifying the mechanisms that medi-

ate mean level of accommodation.

4. Discussion

The results support previous findings that both chro-

matic and luminance components are a necessary part ofthe signed stimulus for accommodation (Kruger et al.,

1995; Kruger, Mathews, Katz, et al., 1997; Rucker &

Kruger, 2004). The experiment confirms that defocus

and LCA at luminance borders produces a pronounced

direction signal for accommodation, and supports previ-

ous findings that signals from L- and M-cones contrib-

ute to the response and are compared to determine the

sign of defocus (Aggarwala, Nowbotsing, et al., 1995;

Flitcroft, 1990; Kotulak et al., 1995; Kruger et al.,1995; Lee et al., 1999; Stark, Lee, Kruger, Rucker, &

Ying, 2002).

In addition, this experiment demonstrates a large

range in response (1.46 D) to change in the L/M-cone

contrast ratio from 0/0.27 to 0.27/0, respectively. The ef-

fects of a change in cone contrast on the mean accom-

modation level were observed at both luminance and

chromatic borders. The ratio of the weighting of theluminance and chromatic components to the ‘‘static’’ re-

sponse was in the region of 2:3.

4.1. L- and M-cone contributions to accommodation

The results show that L-cones alone and M-cones

alone can mediate both static and dynamic accommoda-

tion. L-cone-contrast alone reduces the mean accommo-dation level for near, while M-cone-contrast alone

increases the mean accommodation level (Fig. 4).

Changes in the L-/M-cone contrast ratio between tri-

als alters the mean accommodation level significantly,

despite the constant ‘‘vergence’’ stimulus and negative

feedback signal. Mean accommodation level decreased

when L-cone contrast was higher than M-cone contrast,

and increased when M-cone contrast was higher thanL-cone contrast. These results confirm that the ratio of

L/M cone contrasts produces a pronounced direction

signal for accommodation (Kruger et al., 1995; Lee

et al., 1999; Stark et al., 2002) and extend the previous

results by using the full range of the chromatic signal

to drive accommodation.

4.2. Accommodation and luminance contrast

Dynamic accommodation to the moving grating

(0.195 Hz) increased when the amount of luminance

contrast in the stimulus increased (Fig. 3). This agrees

with the results of Mathews and Kruger (1989) who

found that gain increases as an exponential function of

luminance contrast.

On the other hand, mean accommodation level didnot increase when luminance contrast increased on its

own (Fig. 7). When luminance contrast was below

threshold (empty field condition) accommodation re-

turned to the tonic accommodation level (Leibowitz &

Owens, 1975), which was close to optical infinity (0 D)

for the present subjects. However, once luminance con-

trast was above a threshold level (0.12 and above) mean

accommodation level was unaffected by the amount ofcontrast. These findings with respect to mean accommo-

dation level and tonic accommodation level also agree


with previous findings (Bour, 1981; Ciuffreda & Rumpf,

1985; Tucker, Charman, & Ward, 1986; Ward, 1987).

Thus the amount of luminance contrast on its own has

a large effect on dynamic gain, but almost no effect on

mean accommodation level.

This experiment indicates (Fig. 8) that detection ofthe dynamic stimulus was mediated by a mechanism sen-

sitive to luminance contrast. In addition, since the iso-

response contour approximated a straight line it can

be deduced that a chromatic signal for accommodation

does not arise from a phase delay between cone signals.

Further, since the L/M cone weighting ratio for gain was

similar to that found by Smith and Pokorny (1975), it

can be assumed that the variations in optical densityof the photopigment, cone length, and lens density that

can affect photon absorption were within normal limits.

The wide variation in gain found in this experiment is

typical in accommodation experiments of this type, and

confirms previous results that show wide variation in dy-

namic gain to monochromatic stimuli (e.g. Aggarwala,

Mathews, et al., 1995; Aggarwala, Nowbotsing, et al.,

1995; Campbell & Westheimer, 1959; Charman &Tucker, 1978; Fincham, 1951; Kruger, Aggarwala,

Bean, et al., 1997; Kruger, Mathews, Katz, et al.,

1997; Kruger et al., 1993). The wide variation in re-

sponse to the stimuli also confirms previous findings of

wide variation in response to the effects of LCA (Fin-

cham, 1951; Kruger, Aggarwala, Bean, et al., 1997; Kru-

ger et al., 1995; Kruger, Mathews, Katz, et al., 1997;

Kruger et al., 1993; Lee et al., 1999; Stark et al., 2002;Troelstra et al., 1964). Again, the wide variation in

accommodative response is a hallmark of accommoda-

tion and has been found in many previous experiments.

4.3. Accommodation and chromatic contrast

While dynamic gain was relatively high in the lumi-

nance quadrant (0–90�) of cone-contrast space, gainwas low in the chromatic quadrant (90–180�) and phase

lags were very large. These results were anticipated and

agree with previous reports of poor accommodation to

chromatic stimuli (Rucker & Kruger, 2001; Stark

et al., 2002; Switkes et al., 1990; Wolfe & Owens,

1981). Wolfe and Owens (1981) found that isoluminant

red–green static edges produce responses that are only

15% of the response to a high luminance contrast targeteven in the presence of LCA. Wolfe and Owens (1981)

suggested that the small response may have been from

a small luminance component in the chromatic stimulus.

Subjects in the present experiment (LCA open-loop,

chromatic contrast open-loop) also may have responded

to the small amount of luminance contrast (0.02 at 120�)in the chromatic stimuli. Some subjects gave responses

that were up to 3.19 standard deviations times noiseindicating unusual sensitivity to the small amount of

luminance contrast. The iso-response contour in the

chromatic quadrant indicates that these stimuli were de-

tected by the chromatic pathway that demonstrates a

non-linear response to luminance contrast (Lee et al.,

1990; Yeh et al., 1996).

Mean accommodation level responded to changes in

the ratio of L/M cone contrasts in both luminance andchromatic quadrants of cone-contrast space, but was

unaffected by changes in amplitude of luminance or

chromatic contrast on its own (Fig. 7). Thus even when

L- and M-cone contrasts are in spatial counter-phase the

ratio of L/M cone contrasts drives accommodation for

near or far. For a fixed L/M cone contrast ratio, once

chromatic contrast was above a threshold level (0.12

or higher), an increase in the amplitude of chromaticcontrast had little effect on the mean accommodation

level. In fact the changes in mean accommodation level

were approximated best by a model that responds to

change in both the luminance and chromatic contrast

of the stimulus (Fig. 6). This experiment shows that both

luminance contrast and chromatic contrast are required

in a 2:3 ratio to model the effects of LCA at luminance

and chromatic borders.

4.4. Conclusions

Both L- and M-cones contribute to luminance

(L + M) and chromatic (L�M) signals that control

accommodation, most likely through magno-cellular

and parvo-cellular pathways. The amplitude of the

mean response depends on changes in luminance andchromatic contrast signals that arise as a result of

LCA and defocus of the image, at luminance and chro-

matic borders. In the absence of LCA the detection of

dynamic stimuli is mediated predominantly by a mecha-

nism sensitive to luminance contrast (L + M). It is

widely accepted that this mechanism utilizes negative

feedback to maintain focus, but it also may use an un-

known ‘‘vergence’’ signal.

Acknowledgments

We thank H. Wyatt, W. Swanson, B.B. Lee and S.

Tsujimura for their help with this experiment. This work

was supported by NEI K23 EY00394 to FR and RO1

EYO5901 to PK.

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Documents

Accommodation responses to stimuli in cone contrast space · Accommodation responses to stimuli in cone contrast space Frances J. Rucker *, Philip B. Kruger Schnurmacher Institute