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450 J. Opt. Soc. Am. A /Vol. 12, No. 3/March 1995 Aggarwala et al.
Spectral bandwidth and ocular accommodation
Karan R. Aggarwala, Ekaterina S. Kruger, Steven Mathews, and Philip B. Kruger
Schnurmacher Institute for Vision Research, State College of Optometry,
State University of New York, 100 East 24th Street, New York, New York 10010
Received April 13, 1994; revised manuscript received October 4, 1994; accepted October 4, 1994
Previous studies have suggested that targets illuminated by monochromatic (narrow-band) light are less
effective in stimulating the eye to change its focus than are black –white (broadband) targets. The present
study investigates the influence of target spectral bandwidth on the dynamic accommodation response in
eight subjects. The fixation target was a 3.5-cycleydeg square-wave grating illuminated by midspectral light
of various bandwidths [10, 40, and 80 nm and white (CIE Illuminant B)]. The target was moved sinusoidally
toward and away from the eye, and accommodation responses were recorded and Fourier analyzed. Ac-
commodative gain increases, and phase lag decreases, with increasing spectral bandwidth. Thus the eye
focuses more accurately on targets of wider spectral bandwidth. The visual system appears to have the
ability to analyze polychromatic blur to determine the state of focus of the eye for the purpose of guiding the
accommodation response.
Key words: Aberration, accommodation, bandwidth, blur, chromatic, focus, retinal image, spectral,
wavelength
1. INTRODUCTION
Accommodation is the process by which the eye focuses
objects in response to changes in viewing distance. Al-
though studies have shown that perceived distance,1,2 cog-
nitive demand,3and voluntary effort4,5 contribute to the
accommodation response, the eye accommodates with re-
markable accuracy even when these cues are eliminated.6
This implies that optical (dioptric) stimuli for accommo-
dation (e.g., blur produced by defocus) are important for
driving accommodation.
Blur has been regarded by several investigators as
the primary optical stimulus for accommodation.7–10 Yet
blur of a monochromatic (narrow-band) target is not an
effective stimulus for accommodation.11–14 This implies
that the visual system obtains certain information about
the state of focus of the eye from the blurred image of a
polychromatic target and that such information is absent
in monochromatic light. Crane15 proposed that, in the
presence of chromatic aberration, the three photoreceptor
mechanisms of the eye, with their individual spectral sen-
sitivity functions, sample the polychromatic retinal image
at three levels of focus. As a natural consequence of lon-
gitudinal chromatic aberration, contrast of the retinal im-
age is maximum for the wavelength in focus such that if
long-wave light is in focus, image contrast is maximum
at long wavelengths and is reduced for short-wavelength
light.16 It seems plausible that a comparison of image
contrast between two wavebands could yield information
(encoded as neural signals) that represents the state of
focus of the eye. In a computational model, Flitcroft17
suggests that spatially antagonistic, color-opponent cells
might form a substrate for comparing contrast in different
wavebands to monitor the focus of targets of intermediate
spatial frequency [2–8 cycles per degree (cycydeg)].
In the present study we illuminated a grating target
by light of four nominal spectral bandwidths [10, 40,
and 80 nm and broadband white (CIE Illuminant B)] to
determine whether targets of progressively wider spec-
tral bandwidth encourage more-accurate accommodation.
We analyzed the nature of the blur spread function for
targets of increasing spectral bandwidth after consider-
ing the effects of the photopic spectral sensitivity of the
eye and longitudinal chromatic aberration.18,19
2. METHODS
The eight subjects were young adults with normal color
vision (Nagel anomaloscope) and 20y20 corrected Snellen
acuity. A 3.5-cycydeg square-wave grating target was
presented to the subject’s eye in a Badal optical system20
so that changes in target distance altered focus without
affecting the size or illumination of the target.21 The
grating was a Ronchi ruling, illuminated by broadband
white light (4874-K CIE Illuminant B) or by bandpassed
light produced by the introduction of interference fil-
ters (10, 40, and 80 nm) in front of a tungsten– halogen
source. Target luminance was equalized by a neutral-
density wedge. An aerial image of the target moved
sinusoidally toward and away from the Badal lens to
stimulate the eye to change its focus. Accommoda-
tion of the eye was monitored by a high-speed infrared
optometer,22 and the data were analyzed by a fast Fourier
transform (FFT). Gain and phase lag of the response at
the temporal frequency of target motion (0.2 Hz) served
as an index of accommodative performance to the various
spectral targets.
A. Optical System
The optical system used for presenting targets and stimu-
lating accommodation is described in Fig. 1. The re-
cording optometer was described previously22 and is
represented in Fig. 1 as a rectangle (IR OPT).
1. Illumination Optics (Dashed Lines)
Light from a tungsten–halogen source (3200 K) was
filtered by a Kodak (80 B) color-compensating filter to
produce light of a higher color temperature (CIE Illumi-
0740-3232/95/030450-06$06.00 1995 Optical Society of America
Aggarwala et al. Vol. 12, No. 3/March 1995/J. Opt. Soc. Am. A 451
Fig. 1. Schematic of the Badal optical system for stimulating
accommodation of the eye (E). Dashed lines show the optical
path from the source of illumination, and solid lines represent
target optics. Interference filters of three bandwidths (10, 40,
and 80 nm) could be introduced at F to alter the spectral composi-
tion of a square-wave grating target (T). The sinusoidal motion
of prism P2 moved an aerial image of target T0toward and away
from the Badal lens (L4) through a range of 1.0 D.
nant B, 4874 K),23 and the light source was imaged onto
an opal diffuser (D). Light from a circular patch on the
diffuser was collimated by lens L1, and interference fil-
ters of various half-peak bandwidths (10, 40, and 80 nm)
were introduced to alter the spectral bandwidth of the
source. The collimated beam was deflected by a mirror
(M) and illuminated a grating target (T) from behind.
Lens L2 formed an image of the source in the plane of a
12-mm aperture (A). Lenses L3 and L4 together imaged
the source in the plane of the subject’s pupil (Maxwellian
view). Aperture A was imaged by these lenses (L3 and
L4) as a 3-mm artificial pupil. Light rays of the illumi-
nation system remained collimated as they reflected off
the mirrored surfaces of prisms P1 and P2.
2. Target Optics (Solid Lines)
The target was a Ronchi ruling oriented vertically, pre-
sented in a 6-deg circular field with blurred margins.
Rays from target T (Fig. 1) were collimated by lens L2
and focused by lens L3 to form an aerial image at T0af-
ter reflection off mirrored prisms P1 and P2. The po-
sition of the aerial image (with regard to Badal lens L4)
could be altered by movement of prism P2 toward or away
from prism P1, as shown by the arrows. Prism motion
was controlled by computer and synchronized with the
data acquisition. The subject’s eye was positioned with
the pupil plane at the second principal focus of the Badal
lens sf10 cmdby viewing of the first Purkinje image of
the target in a telescope (not shown). Each centimeter
of target motion sT0dgenerated a 1.0-D change in optical
vergence at the eye.
B. Spectral Bandwidths
Two definitions of spectral bandwidth have been em-
ployed in the present study. For the interference filters
used, the manufacturer’s specifications were used, and
these are defined as the wavelength interval at half-peak
transmittance. For the analysis presented in the dis-
cussion (Section 4 below), bandwidth is defined as wave-
length interval at 1yeof peak normalized luminance.
Four bands of light were used for illuminating the tar-
get. Light from the source (4874 K) was passed through
interference filters (peak transmittance at 550 nm) to cre-
ate the spectral bands depicted in Fig. 2. Luminance of
the targets was measured through the Maxwellian-view
system21 by a Pritchard photometer and maintained at
80 cdym2by a neutral-density wedge.
C. Procedures
Subjects were positioned on a bite plate assembly to sta-
bilize the head and to facilitate alignment. The target
moved sinusoidally toward and away from the subject’s
eye at a temporal frequency of 0.2 Hz with a peak-to-peak
amplitude of 1.0 D, around a mean level of 2 D. Subjects
were instructed to look at the center of the grating and
to pay undivided attention to the target. A temporal fre-
quency of 0.2 Hz was used because at higher temporal fre-
quencies gain declines substantially,6,13 thereby reducing
the signal-to-noise ratio, whereas at lower temporal fre-
quencies voluntary accommodation is more likely to have
some influence on the response.
Each accommodation trial lasted 40.96 s, yielding an
array of 4096 (212) data points at a sampling rate of 100ys.
We chose 40.96 s (as opposed to 40 s) because of con-
straints posed by the FFT procedure, which required an
array size that is an integer power of 2. During each
trial eight sinusoidal cycles of target focus were presented
monocularly. Subjects were allowed to blink but were in-
structed not to use blinks in an attempt to improve the
perceptual clarity of the target. Most subjects did not
blink more than three or four times, and data with ex-
cessive blinks (e.g., produced by tearing) were rejected.
Blinks produced high-amplitude transient artifacts in the
data that were eliminated by filtering if their velocity ex-
ceeded 12 Dys. The four spectral conditions (10, 40, and
80 nm and white) were presented five times to each sub-
ject in random order. Gain and phase lag of accommoda-
tion for each trial were obtained by Fourier analysis (FFT)
and were vector averaged for each condition. Analysis-
of-variance and post hoc multiple comparison procedures
were applied to the mean gain and phase data sn8dfor
a within-subject experimental design.
Fig. 2. Spectral distributions of the four test conditions (10,
40, and 80 nm and white) normalized to their individual peaks.
The bandwidths specified here are nominal in that they refer to
the filter manufacturer’s specifications of bandwidth at half-peak
transmittance.
452 J. Opt. Soc. Am. A /Vol. 12, No. 3/March 1995 Aggarwala et al.
Fig. 3. Accommodation responses to the four target conditions
for two subjects. The uppermost trace (stimulus) shows sinu-
soidal target motion (0.2 Hz, 1-D amplitude) toward and away
from the Badal lens. The response traces represent accommo-
dation to a 3.5-cycydeg square-wave grating target illuminated
by light of a specified spectral distribution (Fig. 2). The two
subjects shown here are not typical but rather depict extremes
of the range of accommodative behaviors observed in the present
study.
3. RESULTS
Accommodation responses to the four target conditions
(10, 40, and 80 nm and white) are plotted for two
subjects (S1 and S2) in Fig. 3. These two subjects rep-
resent the extremes of the range of accommodative be-
haviors exhibited by the sample (eight subjects in all).
Notice that the high-frequency oscillations of accommo-
dation are more pronounced for subject S2 than for sub-
ject S1 for all conditions. Another notable difference is
that the response of subject S1 to the 10-nm condition
shows some time periods during which little or no accom-
modative tracking is evident, whereas subject S2 exhibits
reasonable tracking ability in this condition (10 nm), al-
beit of reduced amplitude and longer phase lag than for
the white target. For both subjects the amplitude of
the response increases progressively as the bandwidth of
light illuminating the target is increased, suggesting that
accommodation is facilitated for targets of wider spectral
bandwidth. It is apparent from these raw data (Fig. 3)
that the natural high-frequency oscillations of accommo-
dation make it somewhat difficult to judge the accuracy
of the accommodation response. To make a quantitative
assessment of the data, gain and phase lag of the re-
sponse at the temporal frequency of the stimulus (0.2 Hz)
were computed (FFT) and were vector averaged for the
five trials from each subject.
Gain and phase lag for two typical subjects are plotted
in Fig. 4. Error bars represent one standard error on ei-
ther side of the mean for five data trials per condition.
It is clear from these data that, despite individual differ-
ences, the gain of accommodation increases and the phase
lag decreases as the spectral bandwidth of the illumina-
tion is changed from narrow-band (10 nm) to broadband
(white).
Average gain and phase lag (Fig. 5) demonstrate the ef-
fect of spectral bandwidth on accommodative function in a
group of eight subjects. Univariate analysis of variance
shows that the gain of accommodation differs significantly
across spectral bandwidth fFs3, 21d42.3, p,0.001g,
as does the phase lag fFs3, 21d17.9, p,0.001g.A
conservative multiple comparison test (Tukey HSD) be-
tween means illustrates that gain increases significantly
between successive progressive increases in bandwidth
sp,0.05d, except for the 40- and 80-nm pair of condi-
tions. However, mean phase lags of accommodation for
Fig. 4. Gain and phase lag of accommodation as a function of
the spectral bandwidth of the target for two typical subjects,
determined by a vector average of five trials per condition. The
gain is an amplitude ratio (responseystimulus), and the phase lag
is a time lag of the response with regard to the stimulus. As
the target’s spectral bandwidth increases, accommodative gain
improves and phase lag declines.
Fig. 5. Average gain and phase data for eight subjects to each
of the four spectral conditions (10, 40, and 80 nm and white).
Accommodative gain increases and phase lag decreases with
increasing spectral bandwidth.
Aggarwala et al. Vol. 12, No. 3/March 1995 / J. Opt. Soc. Am. A 453
Fig. 6. Effective spectral distribution of the test conditions
computed by multiplication of the photopic spectral sensitivity
function of the eye by the functions depicted in Fig. 2. The
horizontal line is 1yeheight for these effective wavebands.
The points of intersection of the 1yeline with the wavebands
in the short-wave region (below 550 nm) are designated lS, and
those in the long-wave region are represented by lL. Numerical
values for lSand lLare given in Table 1.
these two conditions are significantly different sp,0.05d.
Average phase data also differ at the 0.05 level for all
pairs of conditions, excluding the 10- and 40-nm bands,
to which the gain data were significantly different.
4. DISCUSSION
Taken together, the present results indicate that a wider
spectral bandwidth of illumination allows the visual
system to focus more accurately. From an ecological
standpoint this does not come as a surprise because natu-
ral objects possess broad spectral reflectance functions,24
and the eye is seldom confronted with narrow-band light.
Even the spectral distributions of colorful objects can be
relatively broadband.24 When sunlight reflects diffusely
from these objects, the retinal image is composed of light
of a spectrum of wavelengths. Thus it seems reasonable
to speculate that the visual system might have evolved
focusing mechanisms that operate best in the presence of
broadband illumination.
Spectrally broadband targets, when imaged by the op-
tics of the eye, produce a complex retinal image that can
be thought to consist of a series of image planes, one image
plane for each wavelength of light. These image planes
are displaced axially by an amount that depends on the
longitudinal chromatic aberration of the eye and on the
particular wavelengths in question. In addition, the ef-
fects of chromatic aberration are altered by the spectral
sensitivity of the eye,23,25 which declines substantially at
the extremes of the visible spectrum. To help to illus-
trate the effects of chromatic aberration, we multiplied
the spectral luminous efficiency function of the eye (CIE:
193125) by the normalized spectral radiance of the four
targets used in the experiment. As a result, the band-
widths of the stimuli are reduced, most notably for the
white target, which now appears as a bandpass function
(see Fig. 6).
Two extreme wavelengths (lSand lL) were chosen for
each of the four wavebands, based on the 1yeheight
of the functions shown in Fig. 6. Dioptric vergence at
the retina was computed for each wavelength17 and is
presented in Table 1. For the present experiment the
chromatic difference in focus between lSand lLcan be
regarded as the ocular longitudinal chromatic aberration
(LCA) present in each of the four targets. Figure 7 illus-
trates the effects of chromatic aberration on the retinal
image of a luminance border (edge) for each of the four
wavebands of light when the longer wavelength slLdis in
focus. Nominal values for bandwidth (10, 40, and 80 nm
and white) have been retained in the figure. Real values
Fig. 7. Effect of increasing spectral bandwidth on the blur-
spread function (of a luminance edge) for an eye with a 4-mm
pupil. The longer wavelength slLdof each spectral condition
is in focus (dotted curves), and the shorter wavelength slSdis
out of focus (dashed curves) by an amount dependent on the
longitudinal chromatic aberration produced by light of these two
wavelengths.
Table 1. Optical Vergence and LCA for Each of the Four Spectral Wavebands at Two Extreme
Wavelengths, lL
lL
lLand lS
lS
lS
lLlSlL2l
S
Bandwidth Wavelength Vergence Wavelength Vergence Wavelength LCA
(nominal) (nm) (D) (nm) (D) (nm) (D)
10 nm 556 20.123 544 20.199 12 0.076
40 nm 576 20.010 531 20.288 45 0.278
80 nm 594 10.081 526 20.324 68 0.405
White 619 10.191 505 20.490 114 0.681
454 J. Opt. Soc. Am. A /Vol. 12, No. 3/March 1995 Aggarwala et al.
for lSand lLand for 1yebandwidth slL2l
S
dare tabu-
lated (Table 1) along with the dioptric vergence and the
amount of chromatic aberration.
The dashed curves in Fig. 7 show the luminance distri-
bution of lSwhen lL(dotted curves) is in focus on the
retina. The defocus of lSwith regard to lL(Table 1,
rightmost column) was used to find the standard deviation
(in minutes of arc) of a Gaussian point-spread function,
by the methods of Fry,26 for a schematic eye with a 4-mm
pupil. The edge-spread functions of Fig. 7 represent the
definite integral of the point-spread function for the tabu-
lated amounts of LCA. The type of blur depicted in Fig. 7
is a natural consequence of longitudinal chromatic aber-
ration in an eye with a pupil of 4-mm diameter. All sub-
jects in the study had pupils larger than 3 mm, and the
choice of a 4-mm pupil (for Fig. 7) is arbitrary. Larger
pupils result in wider edge-spread functions, and smaller
pupils (e.g., 2 mm) reduce the blur produced by LCA.
Although the difference in ocular focus between the
ends of the visible spectrum is substantial18,19 (2D or
more), even the relatively small amounts of chromatic
aberration used for the present analysis produce a sig-
nificant decline in the slope (contrast) of the edge-spread
function. The width of the effective edge-spread function
(including Vl) for the 40-nm band of light is ,4arcmin,
and for white light it is approximately 10 arcmin. It is
important to note that Fig. 7 has been generated strictly
for the purpose of illustrating the fact that, even after
the severely band-limiting effects of Vlare included, the
chromatic aberration of the eye has a notable effect on the
blur profile of a luminance edge.
Results of the present experiment are in agreement
with studies indicating that the visual system has the ca-
pacity to detect blur produced by chromatic aberration at
luminance edges.11 – 14 The three cone types of the retina,
with their individual spectral sensitivity functions, effec-
tively sample the retinal image at three different levels
of defocus, corresponding to their wavelengths of peak
sensitivity15 or perhaps to a weighted average includ-
ing the radiance distribution of the image.17 It seems
plausible that a comparison of retinal image quality be-
tween cone types, possibly through spatially bandpass,
color-opponent pathways, could generate a neural signal
that varies in proportion to ocular defocus and that could
be used to direct accommodation. However, further re-
search is necessary to confirm the involvement of color-
opponent mechanisms in the control of accommodation to
defocus of polychromatic targets.
In the present investigation the accuracy of dynamic
accommodation was influenced significantly by incre-
mental changes in target spectral bandwidth. Our
findings agree with the results of studies done concur-
rently by other investigators who used different stimulus
parameters.12 Previous investigators10 seem to disagree
with the view that spectrally bandpass light (and thereby
reduced ocular LCA) impairs accommodation, and the
reasons for this discrepancy are not entirely clear. One
possible explanation is that previous investigators tested
this issue by using stationary targets (stimulus–response
function), and they may have trained their observers to
accommodate voluntarily. Those authors reported on
one na¨
ıve subject (aged 20 years) who showed poor ac-
commodation to spectrally bandpass (red or blue) targets
(Ref. 10, Fig. 2f, p. 462); however, they disregarded these
data as an artifact of inadequate training. They noted
that “Training and motivation undoubtedly also play an
important role, as is illustrated by subject (f ), a secretary
chosen to typify effects found with untrained observers.
She evidently failed to respond at all to the lens-induced,
higher target vergences.” After reinstructing this subject
(“careful explanation of the nature of the experiment”),
the authors reported that she too could focus in monochro-
matic light. They reported a similar initial inaccuracy
of accommodation for other na¨
ıve subjects to red or blue
targets,10 but their conclusions were based on the results
obtained from trained observers. In the present experi-
ment two of the authors served as subjects, while the re-
maining six were na¨
ıve to the purpose of the experiment.
We find that trained observers respond in the same way
as na¨
ıve subjects to moving targets, and we have used
moving targets in our experiments to minimize the influ-
ence of voluntary accommodation. A systematic study of
the effect of training is in order, but it must be conducted
by use of both stationary and moving targets.
The effects of ocular chromatic aberration are usually
dismissed as being small and not significant enough to
influence visual mechanisms.27,28 It is generally argued
that, if a midspectral wavelength (say, 555 nm) is in fo-
cus, the spectral sensitivity of the eye reduces the effective
chromatic aberration to very small amounts (0.15 D),28
which may lie within the depth of focus of the eye. How-
ever, the oscillations of accommodation29,30 are constantly
changing the wavelength in focus, and, when a target
moves toward or away from the eye, once again a new
wavelength comes into focus. In fact the natural lag of
accommodation to near targets and the lead of accommo-
dation to far targets31 also change the wavelength in fo-
cus. In the present study the 40-nm condition produced
only 0.278 D of LCA; however, even such small amounts
of LCA produce substantial facilitation of dynamic accom-
modation (see Section 3).
The data (Figs. 3 –5) and the statistical analysis (Tukey
HSD test) indicate that successively wider bands of target
illumination produce an incremental improvement in ac-
commodative performance. The bandwidth at which ac-
commodative performance is the same as that for white
is difficult to identify from these data mainly because the
response to a white target (CIE Illuminant B) is signifi-
cantly better than accommodation to the 80-nm bandpass
target. The improvement in gain (and reduction in phase
lag) from the 80-nm to the broadband white condition
indicates the involvement of short-wavelength-sensitive
cones in the analysis of the blur-spread function. Al-
though the notion of accommodative control by individual
cone types15 (or by comparisons of image quality between
cone types mediated by color-opponent cells17) is attrac-
tive, more experimental evidence is required.
The present investigation supports the view that the
visual system has mechanisms for utilizing chromatic
aberration as a source of information about the state of
focus of the eye, and it uses this information to guide
the accommodation response. These mechanisms could
operate at levels close to the thresholds for chromaticity
discrimination32 – 34 and contrast-decrement sensitivity.35
Further research is needed to uncover the neural sub-
strate for the observed sensitivity of the eye–brain system
Aggarwala et al. Vol. 12, No. 3/March 1995 / J. Opt. Soc. Am. A 455
to blur produced by polychromatic targets in the presence
of ocular longitudinal chromatic aberration.
ACKNOWLEDGMENTS
This research was supported by grants from the National
Eye Institute (EYO7494, EYO8953, EYO5901) and by a
postdoctoral fellowship (F 32 EYO6403-02) awarded to
K. R. Aggarwala. We thank Dean Yager, Milton Katz,
and Jordan Pola for their helpful suggestions, John
Orzuchowski and Mathew Polasky for technical assis-
tance, and Jong Park for assistance with data collection.
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