450J. Opt. Soc. Am. A/Vol. 12, No. 3/March 1995Aggarwala 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.
study investigates the influence of target spectral bandwidth on the dynamic accommodation response in
eight subjects.The fixation target was a 3.5-cycle?deg square-wave grating illuminated by midspectral light
of various bandwidths [10, 40, and 80 nm and white (CIE Illuminant B)].
toward and away from the eye, and accommodation responses were recorded and Fourier analyzed.
commodative gain increases, and phase lag decreases, with increasing spectral bandwidth.
focuses more accurately on targets of wider spectral bandwidth.
ability to analyze polychromatic blur to determine the state of focus of the eye for the purpose of guiding the
Aberration, accommodation, bandwidth, blur, chromatic, focus, retinal image, spectral,
The target was moved sinusoidally
Thus the eye
The visual system appears to have the
Accommodation is the process by which the eye focuses
objects in response to changes in viewing distance.
though studies have shown that perceived distance,1,2cog-
nitive demand,3and voluntary effort4,5contribute 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
Blur has been regarded by several investigators as
the primary optical stimulus for accommodation.7–10
blur of a monochromatic (narrow-band) target is not an
effective stimulus for accommodation.11–14
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.Crane15proposed 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
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 (cyc?deg)].
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
The eight subjects were young adults with normal color
vision (Nagel anomaloscope) and 20?20 corrected Snellen
acuity.A 3.5-cyc?deg 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
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.
tion of the eye was monitored by a high-speed infrared
optometer,22and 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
The optical system used for presenting targets and stimu-
lating accommodation is described in Fig. 1.
cording optometer was described previously22and is
represented in Fig. 1 as a rectangle (IR OPT).
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-
Illumination Optics (Dashed Lines)
1995 Optical Society of America
Aggarwala et al.Vol. 12, No. 3/March 1995/J. Opt. Soc. Am. A 451
accommodation of the eye (E).
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).
of prism P2 moved an aerial image of target T0toward and away
from the Badal lens (L4) through a range of 1.0 D.
Schematic of the Badal optical system for stimulating
Dashed lines show the optical
The sinusoidal motion
nant B, 4874 K),23and 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.
nation system remained collimated as they reflected off
the mirrored surfaces of prisms P1 and P2.
Light rays of the illumi-
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.
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.
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 ?f ? 10 cm? by viewing of the first Purkinje image of
the target in a telescope (not shown).
of target motion ?T0? generated a 1.0-D change in optical
vergence at the eye.
Target Optics (Solid Lines)
Two definitions of spectral bandwidth have been em-
ployed in the present study.
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 1?e of 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.
For the interference filters
the targets was measured through the Maxwellian-view
system21by a Pritchard photometer and maintained at
80 cd?m2by a neutral-density wedge.
Subjects were positioned on a bite plate assembly to sta-
bilize the head and to facilitate alignment.
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.
were instructed to look at the center of the grating and
to pay undivided attention to the target.
quency of 0.2 Hz was used because at higher temporal fre-
quencies gain declines substantially,6,13thereby 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 100?s.
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.
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.
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 D?s.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.
of-variance and post hoc multiple comparison procedures
were applied to the mean gain and phase data ?n ? 8? for
a within-subject experimental design.
A temporal fre-
Most subjects did not
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
Spectral distributions of the four test conditions (10,
452J. Opt. Soc. Am. A/Vol. 12, No. 3/March 1995 Aggarwala et al.
for two subjects.
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-cyc?deg square-wave grating target illuminated
by light of a specified spectral distribution (Fig. 2).
subjects shown here are not typical but rather depict extremes
of the range of accommodative behaviors observed in the present
Accommodation responses to the four target conditions
The uppermost trace (stimulus) shows sinu-
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.
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.
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
Average gain and phase lag (Fig. 5) demonstrate the ef-
fect of spectral bandwidth on accommodative function in a
These two subjects rep-
To make a quantitative
group of eight subjects.
shows that the gain of accommodation differs significantly
across spectral bandwidth ?F?3, 21? ? 42.3, p , 0.001?,
as does the phase lag ?F?3, 21? ? 17.9, p , 0.001?.
conservative multiple comparison test (Tukey HSD) be-
tween means illustrates that gain increases significantly
between successive progressive increases in bandwidth
?p , 0.05?, except for the 40- and 80-nm pair of condi-
tions. However, mean phase lags of accommodation for
Univariate analysis of variance
the spectral bandwidth of the target for two typical subjects,
determined by a vector average of five trials per condition.
gain is an amplitude ratio (response?stimulus), and the phase lag
is a time lag of the response with regard to the stimulus.
the target’s spectral bandwidth increases, accommodative gain
improves and phase lag declines.
Gain and phase lag of accommodation as a function of
of the four spectral conditions (10, 40, and 80 nm and white).
Accommodative gain increases and phase lag decreases with
increasing spectral bandwidth.
Average gain and phase data for eight subjects to each
Aggarwala et al.Vol. 12, No. 3/March 1995/J. Opt. Soc. Am. A 453
computed by multiplication of the photopic spectral sensitivity
function of the eye by the functions depicted in Fig. 2.
horizontal line is 1?e height for these effective wavebands.
The points of intersection of the 1?e line 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.
values for lS and lLare given in Table 1.
Effective spectral distribution of the test conditions
these two conditions are significantly different ?p , 0.05?.
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.
Taken together, the present results indicate that a wider
spectral bandwidth of illumination allows the visual
system to focus more accurately.
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
When sunlight reflects diffusely
from these objects, the retinal image is composed of light
of a spectrum of wavelengths.
to speculate that the visual system might have evolved
focusing mechanisms that operate best in the presence of
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.
are displaced axially by an amount that depends on the
From an ecological
Thus it seems reasonable
These image planes
longitudinal chromatic aberration of the eye and on the
particular wavelengths in question.
fects of chromatic aberration are altered by the spectral
sensitivity of the eye,23,25which declines substantially at
the extremes of the visible spectrum.
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.
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 (lS and lL) were chosen for
each of the four wavebands, based on the 1?e height
of the functions shown in Fig. 6.
the retina was computed for each wavelength17and is
presented in Table 1.For the present experiment the
chromatic difference in focus between lS and lL can be
regarded as the ocular longitudinal chromatic aberration
(LCA) present in each of the four targets.
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 ?lL? is in
focus. Nominal values for bandwidth (10, 40, and 80 nm
and white) have been retained in the figure.
In addition, the ef-
To help to illus-
As a result, the band-
Dioptric vergence at
Figure 7 illus-
spread function (of a luminance edge) for an eye with a 4-mm
pupil. The longer wavelength ?lL? of each spectral condition
is in focus (dotted curves), and the shorter wavelength ?lS? is
out of focus (dashed curves) by an amount dependent on the
longitudinal chromatic aberration produced by light of these two
Effect of increasing spectral bandwidth on the blur-
Table 1. Optical Vergence and LCA for Each of the Four Spectral Wavebands at Two Extreme
lL and lS
454 J. Opt. Soc. Am. A/Vol. 12, No. 3/March 1995Aggarwala et al.
for lSand lLand for 1?e bandwidth ?lL2 lS? are 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 lS when lL (dotted curves) is in focus on the
retina. The defocus of lS with 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,26for 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.
jects in the study had pupils larger than 3 mm, and the
choice of a 4-mm pupil (for Fig. 7) is arbitrary.
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 ?4 arcmin,
and for white light it is approximately 10 arcmin.
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
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
sensitivity15or perhaps to a weighted average includ-
ing the radiance distribution of the image.17
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.
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.
findings agree with the results of studies done concur-
rently by other investigators who used different stimulus
Previous investigators10seem 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.
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
However, further re-
(Ref. 10, Fig. 2f, p. 462); however, they disregarded these
data as an artifact of inadequate training.
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,10but their conclusions were based on the results
obtained from trained observers.
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.
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
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.
ever, the oscillations of accommodation29,30are 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.
accommodation to near targets and the lead of accommo-
dation to far targets31also 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 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.
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.
operate at levels close to the thresholds for chromaticity
discrimination32–34and contrast-decrement sensitivity.35
Further research is needed to uncover the neural sub-
strate for the observed sensitivity of the eye–brain system
In the present experi-
A systematic study of
It is generally argued
In fact the natural lag of
The bandwidth at which ac-
These mechanisms could
Aggarwala et al. Vol. 12, No. 3/March 1995/J. Opt. Soc. Am. A 455 Download full-text
to blur produced by polychromatic targets in the presence
of ocular longitudinal chromatic aberration.
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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