 |
| Volume 5, Number 5, Article 5, Pages 444-454 |
doi:10.1167/5.5.5 |
http://journalofvision.org/5/5/5/ |
ISSN 1534-7362 |
Different sensations from cones with the same photopigment
Heidi Hofer |
Center for Visual Science, University of Rochester, Rochester, NY, USA |
|
Ben Singer |
Center for Visual Science, University of Rochester, Rochester, NY, USA, & Center for the Study of Brain, Mind, and Behavior, Princeton University, Princeton, NJ, USA |
|
David R. Williams |
Center for Visual Science, University of Rochester, Rochester, NY, USA |
|
Abstract
We used adaptive optics to study color fluctuation in the appearance of tiny flashes of light. For five subjects, near threshold, monochromatic stimuli with full widths at half maximum of 1/3 arcmin were delivered throughout a patch of retina near 1 deg in which we also determined the locations of L, M, and S cones. Subjects reported a wide variety of color sensations, even for long-wavelength stimuli, and all subjects reported blue or purple sensations at wavelengths for which S cones are insensitive. Subjects with more L cones reported more red sensations, and those with more M cones tended to report more green sensations. White responses increased linearly with the asymmetry in L to M cone ratio. The diversity in the color response could not be completely explained by combined L and M cone excitation, implying that photoreceptors within the same class can elicit more than one color sensation.
History
Received October 16, 2004; published May 19, 2005
Citation
Hofer, H., Singer, B., & Williams, D. R. (2005). Different sensations from cones with the same photopigment.
Journal of Vision, 5(5):5, 444-454,
http://journalofvision.org/5/5/5/,
doi:10.1167/5.5.5.
Keywords
cones, adaptive optics, color vision
for related articles by these authors
for papers that cite this paper |
Color vision depends on three classes of cones that are
interleaved spatially into a single layer of photosensitive cells. Therefore,
the reconstruction of spectral variations across the scene requires the
comparison of signals from cones with different pigments that are sampling
somewhat different portions of the retinal image. This sampling strategy
succeeds in normal scenes because it relies on the fact that the spectral
reflectance varies slowly on the spatial scale of the cones. However, for
extended stimuli of high spatial frequency, the grain of the trichromatic mosaic
can sometimes intrude in visual experience. For example, high frequency black
and white patterns appear to contain splotches of color (Brewster, 1832) caused by inability of the visual system to reconstruct color and brightness information from the undersampled or aliased retinal image (Williams and Collier, 1983; Williams, Sekiguchi, Haake, Brainard, & Packer, 1991; Sekiguchi, Williams, &
Brainard, 1993).
A similar kind of chromatic artifact occurs with
stimuli that are very small. Holmgren ( 1884) reported that tiny monochromatic flashes
of light appear to fluctuate in color, presumably as involuntary eye movements
cause each flash to stimulate different cones. Hartridge ( 1954) found more than three sensations under
these conditions and concluded erroneously that there must be more than three
kinds of receptors in the retina. Many investigators have subsequently studied
the detection and appearance of tiny flashes (Bouman & Walraven,
1957; Krauskopf, 1964; Krauskopf & Srebro, 1965;
Ingling , Scheibner, & Boynton, 1970;
Williams, MacLeod, &
Hayhoe , 1981; Cicerone & Nerger, 1989; Vimal ,
Pokorny, Smith, & Shevell, 1989;
Wesner , Pokorny, Shevell, & Smith,
1991; Otake ,
Gowdy, & Cicerone, 2000). Both the
chromatic aliasing with large stimuli and the fluctuation in color of small
flashes of light could provide insight into the fine scale topography of the
mechanisms responsible for color vision. While it has usually been assumed that
these phenomena reveal the granularity of the cone mosaic, they may also reveal
the discrete nature of the postreceptoral microcircuitry for color and spatial
vision.
An understanding of the role of the cone mosaic in the
fluctuations in color appearance of tiny flashes of light has been hampered for
at least two reasons. First, it has not been possible to determine the
topography of the three cone classes in the subject’s eye. Second, blur by
the eye’s optics has prevented imaging a spot of light on the fovea with
an area smaller than that of a dozen or more cones. We have overcome both these
problems by using an adaptive optics system (Hofer et al., 2001) that removes blur caused by
imperfections in the eye’s optics.
Adaptive optics combined with retinal densitometry
(Rushton, 1972; Roorda & Williams, 1999;
Roorda , Metha, Lennie, & Williams,
2001) allowed us to determine the
locations of L, M, and S cones in patches of retina near 1-deg retinal
eccentricity in five subjects with normal color vision
(Hofer , Carroll, Neitz, Neitz, & Williams, 2005) (see Figure 1).
Figure 1. The retinal mosaics of the five
subjects studied. Each figure shows the location of L (red), M (green), and S
(blue) cones in patches of retina at approximately 1-deg retinal eccentricity.
The ratio of L to M cones for these subjects is HS, 1:2.7; YY, 1.1:1; AP, 1.2:1;
MD, 1.9:1; and BS, 16.5:1. The scale bar represents 5 arcmin. All images are
shown to the same scale.
Brief (<4 ms), monochromatic (500 nm, 550 nm, and
600 nm) test flashes were presented at
~1-deg retinal eccentricity. The
subject viewed the stimulus through an adaptive optics system to minimize the
diameter of the test flash. The stimulus consisted of a 25-micron pinhole
backlit by a broad-band white light light-emitting diode (LED), which subtended
just less than 0.3 arcmin at the retina. Based on convolutions of the pinhole
with the point-spread functions calculated from wave aberration measurements for
each observer, the test flash full width at half maximum was approximately
one-third of an arcmin. This is less than half the diameter of an individual
cone inner segment near 1 deg, which ranged from 0.8 to 1.0 arcmin for the
subjects we used. Wavelength was controlled with narrow-band (10 or 25 nm)
interference filters, and a suitable focus correction was made for the chromatic
aberration of the eye at each wavelength. Stimuli were presented near threshold
on an otherwise dark field except for an 820-nm point source, which served as
the fixation target as well as the wave-front sensing beacon necessary to
measure the eye’s optical quality during adaptive correction. The
intensity of the beacon required for accurate wave-front sensing was higher than
that required for fixation alone. For this reason a control experiment was
performed on two subjects (YY and AP) to ensure that the brightness of the
beacon did not affect spot detection (see Figure
2). To suppress any contribution from rods, trials were performed in 7-min
blocks from 4-11 min after a white light bleach of both rod and cone pigment.
Figure 2. The
detection curve for one subject (AP) for a 550-nm small spot of light when using
a dim 820-nm fixation target (~0.25 μw incident on the eye’s pupil)
judged just bright enough for fixation (red dots, without wave-front sensing),
and when using the relatively bright 820-nm wave-front sensor beacon (~1.25
μw incident on the eye’s pupil) as the fixation target (blue dots,
with wave-front sensing). The brightness of the wave-front sensing beacon did
not affect the number of flashes seen. Results for another subject (YY) were
similar. Flashes were presented without aberration correction to a single
location at 1.25 deg retinal eccentricity through a 3-mm artificial
pupil.
We sought to distribute the test flashes fairly
uniformly throughout the retinal area that had been characterized in each
subject, so the results would not be biased by local variation in L and M cone
density. Flashes were presented to one of five retinal locations, four of which
lay at the corners of a square retinal region 14 arcmin on a side, and one of
which lay at the center of the square. Fixational eye movements further
dispersed the test flash location throughout the characterized region. The
average standard deviation in fixation measured under similar experimental
conditions in three of the subjects from the displacements between multiple
retinal images was about 3.5 arcmin. The position of the stimulus was controlled
manually with precision micrometers. The five locations were randomly permuted
between each 7-min block of stimulus trials.
The stimulus duration was chosen to minimize the motion
blur due to eye movements. The frequency of motion artifacts could be readily
estimated from the individual retinal images, which were acquired with a 4-ms
imaging flash, obtained in the same subjects while classifying cones. Roughly 5%
of imaging trials were subject to motion blur. The color-naming stimuli were
always briefer than 4 ms. On those few trials where motion blurred stimuli they
probably went undetected by the subject. This is because the motion would have
caused the tiny threshold stimulus to be spread over a large number of cones,
which makes it unlikely that enough quanta would be absorbed by those cones for
detection to occur. Control experiments indicated the main result of the study was obtained even when using stimuli as brief as 100 microseconds, which is an order of magnitude too brief to be affected by eye movements.
Adaptive correction and stimulus presentation were
self-initiated by subjects. On each trial subjects were asked to report whether
or not the test flash was seen, and if so its appearance using one of eight hue
categories (red, orange, yellow, yellow-green, green, blue, blue-green, blue,
and purple) or white. Two subjects (AP and YY) required an additional
“indescribable” category for when the flash was seen yet caused no
definable perceptual response. When analyzing the data, trials were kept only if
the adaptive correction had reached an acceptable level, chosen to be a residual
root-mean-square wave-front error over a 6-mm pupil of 0.11 microns or less. For
most subjects about 25% of trials were rejected because they did not meet these
criteria. This was important to ensure a relatively constant retinal stimulus
profile. Typically, stimuli were presented at 5-6 intensity levels spanning each
subject’s detection curve for each wavelength. Intensity was randomized
from trial to trial. Approximately 10% of trials contained no stimulus. These
trials were used to assess the subjects’ error rates, which were always
less than 1.5%. For two subjects, BS and AP, the experiment was repeated for one
wavelength (BS, 600 nm; AP, 550 nm) on a different occasion separated by
some months from the main experimental sessions. They did not show any
significant difference in their responses. The average number of stimulus trials
per wavelength for each subject was HS, 90; BS, 525; AP, 823; YY, 826; and MD,
1495.
All research on human subjects adhered to the tenets of
the Declaration of Helsinki and was approved by the Institutional Review Board
at the University of Rochester. Informed consent was obtained from all subjects
after explanation of the nature and possible consequences of the study. None of
the data reported here were obtained on the eyes of the authors; however, the
first author verified the main conclusions of the experiment on her own
eye.
Figure 3 illustrates
the benefit of using adaptive optics to observe the color fluctuations of tiny
spots. In preliminary experiments, sharpening the flash of light imaged on the
retina with adaptive optics increased two-fold the fraction of 560-nm flashes
that appeared a saturated
color.
Figure 3. The percentage of 560-nm flashes seen
that were judged saturated in color when aberrations were corrected with
adaptive optics (with AO) and when aberrations were uncorrected (without AO).
Twice as many flashes were judged saturated in color when adaptive optics was
used to sharpen the small spot stimulus. All stimuli with adaptive optics were
viewed through a 6-mm artificial pupil. Without adaptive optics, data are shown
for stimuli viewed through both 3-mm and 6-mm artificial pupils. Data are
averaged for three subjects and error bars represent ±1
SD.
A main result of this initial investigation of the
color fluctuations of tiny flashes of light is that subjects required a large
number of hue categories to describe their percepts, in disagreement with
previous work that has suggested that only two hue categories are needed to
describe tiny flashes in the long wavelength end of the spectrum
(Cicerone & Nerger, 1989;
Krauskopf, 1978). To facilitate a
comparison of the color-naming results across subjects, data were interpolated
at the 50% probability of seeing using a linear interpolation of the data
between 20% to 85% probability of seeing, where the percentage of flashes seen
in each hue category tended to be approximately constant or else vary in an
approximately linear way, given the uncertainty of the data, for each subject.
Subjects’ responses for 550-nm flashes of light at 50% probability of
seeing are shown in Figure 4. Subjects with
L-rich retinas report a larger fraction of flashes as red, and M-rich subjects
tend to report a larger fraction of flashes as green. However, the most striking
observation is that all subjects required five to seven of the eight hue
categories and all required white.
Figure 4. The
color sensations reported by subjects when viewing a small spot of 550-nm light.
At this wavelength only L and M cones participate in detection. Shown are the
percentages of white and colored responses that were placed in each response
category, interpolated at 50% frequency of
seeing. Percentages for BS are white,
56%; red, 42%; yellow-green, 0.7%; green, 0.7%; blue-green, 0.3%; and blue,
0.8%. In addition to white, each subject used at least five different hue
categories.
Table 1 lists the
percentage of spots each subject placed in each color category, interpolated at
50% probability of seeing, for each wavelength. The large variety of colors seen
and the general trend of increasing reds and decreasing greens with higher L to
M ratios are present at all three wavelengths tested. The difference we observed
in color-naming behavior across subjects is different from the results of
previous experiments performed without adaptive optics, where the statistics of
the color names given to small, dim stimuli presented to the fovea were found to
be constant across individuals (Bouman & Walraven, 1957; Ingling et al., 1970; Cicerone & Nerger, 1989; Krauskopf, 1978). The dependence of red and green
responses on L to M cone ratio is strikingly different from what is known about
the color appearance of macroscopic stimuli. In the latter case, color
appearance as assessed, for example, by unique yellow is completely independent
of L to M cone ratio (Brainard et al., 2000;
Neitz, Carroll, Yamauchi, Neitz, & Williams, 2002).
Table
1. The percentage of spots seen at 500, 550, and 600 nm that subjects placed in
the different color categories. Data were interpolated at 50% probability of
seeing.
Data in Figure 4 and Table 1 also reveal that subjects reported blue or
purple sensations for both 550-nm and 600-nm flashes of light. These stimuli
presented at threshold for the L and M cones are unlikely to stimulate S cones
because S cones are over a 100 times less sensitive than L or M cones at these
wavelengths. Moreover, S cones represent only about 5% of the cones at this
retinal location. This implies that only L or M cones can contribute to
detection for 550-nm and 600-nm flashes presented at threshold. That subjects
report blue and purple sensations at these wavelengths indicates that light
absorption in S cones is not essential for the sensation of these hues. If L and
M cones contribute to sensations of red and green, respectively, as predicted by
the standard model of color opponency, then blue and purple sensations would be
prohibited. Our data support previous suggestions that M cones may contribute to
sensations of blueness (Drum, 1989;
DeValois & DeValois, 1993; Schirillo
& Reeves, 2001). A possible explanation
for the bluish sensations is that they occur when the test flash excites M cones
much more strongly than L cones, which mimics the ratio of excitation that
would occur when actually viewing a bluish light. Another possibility is that
blue or purple sensations are the result of electrical coupling between L and M
cones and S cones. However, this seems unlikely because blue responses decreased
with wavelength in a manner suggestive of the relative excitation of M to L
cones, and recent work has also suggested that S cones are not electrically
coupled to L and M cones (Hornstein, Verweij, & Schnapf, 2004).
Jameson and Hurvich ( 1967) reported that the chromaticity of a
fixation target can significantly bias color-naming behavior. While control
experiments showed that dimming the 820-nm fixation point by a factor of 5 (see
Figure 2) did not affect the detection of test
flashes or color-naming (color-naming results not shown), it is still possible
that the hue of the fixation target biased subjects’ color responses.
However, we do not believe this accounts for the blue sensations because
subjects in our earlier experiments reported a significant fraction of blue
responses with foveally presented flashes (560 nm and 580 nm) and yellowish
fixation targets (560 nm and 580 nm) as well as no fixation target. (These
observations did not require the presence of a laser beacon because a static
aberration correction was used.) A possible systematic hue bias also does not
affect the wide variety of responses each subject used, nor the differences in
response across subjects with different L to M cone
ratios.
Model of small spot detection
We created a simple model of detection to gain insight
into why we observed such large variability in color responses to monochromatic
flashes. Previous models of small spot detection (Cicerone & Nerger, 1989; Vimal et al., 1989; Wesner et al., 1991) relied on the assumption that the stimulus
always illuminates an integral number of cones uniformly on each presentation.
In actuality of course, the retinal light distribution of the stimuli used in
these experiments is nonuniform and broadened by diffraction and aberrations,
and thus on any given presentation will illuminate some cones more strongly than
others. In addition, the number of cones expected to absorb enough quanta to
elicit a response will vary from flash to flash depending not only on quantal
fluctuations as previous investigators have assumed, but also on where the flash
lands, for example, near the center of a cone or in between cones. The model we
constructed incorporates the measured point-spread functions and the measured
cone mosaics of our subjects to estimate quantum catches in the cones resulting
from randomly distributed test flashes. All calculations were performed using
custom MatLab software.
Stimulus light distribution on the retina
Point-spread functions were calculated from the
residual aberration recorded by the adaptive optics system’s wave-front
sensor for each subject ( HSPSF500.txt, HSPSF550.txt, HSPSF600.txt; YYPSF500.txt, YYPSF550.txt, YYPSF600.txt; APPSF500.txt, APPSF550.txt, APPSF600.txt; MDPSF500.txt, MDPSF550.txt, MDPSF600.txt; BSPSF500.txt, BSPSF550.txt, BSPSF600.txt; these
files are 100 x 100 matrices written as tab delimited text files. The scale for
each point-spread function is the same as that specified in the cone location
file cones.txt.). These
point-spread functions included the effects of diffraction and the uncorrected
aberrations of both the optical system and the subject’s eye, but did not
include ocular scatter, which is not captured by wave-front sensors. The
point-spread function was then convolved with a 0.3-arcmin circular function,
representing the small spot stimulus, to generate the retinal profile of the
stimulus after diffraction and blur by residual aberrations.
Though our model does not include scattered light, we
believe its effects can be safely ignored. Scattered light forms a dim, diffuse
halo or skirt around the core of the point-spread function generated by
aberrations and diffraction. The contribution of the scatter is not well known
close to the peak of the point-spread function. However, Vos et al. ( 1976) estimated that for a 5.8-mm pupil, similar to
what we used, the amount of scattered light 5 arcmin from the peak is a thousand
times smaller than the height of the point-spread function. Our use of adaptive
optics increases the peak height by an additional factor of 10, implying that
scattered light is roughly 10,000 times dimmer than the point-spread function
peak.
The model incorporated the trichromatic cone mosaics of
each subject, obtained with adaptive optics retinal imaging (Hofer et al., 2005) ( cones.txt). One problem with this was that for some subjects, not every cone in the patch of retina could be characterized, which would have distorted the model due to locations of artificially low sensitivity. In the case where there were no large patches of contiguous cones that could be successfully characterized, as occurred for HS, cone locations from a patch of a different subject’s retina were used (scaled to reflect the cone spacing of the original subject), and cone identities were assigned randomly based on the observed proportion in the retina of the subject of interest. This is justified because foveal cone pigment assignment is generally random (Roorda & Williams, 1999; Roorda et al., 2001; Bowmaker et al., 2003; Hofer et al., 2005).
Figure 5 shows an
example of a stimulus light distribution and a retinal sensitivity map. Maps of
retinal sensitivity were constructed by convolving arrays of subjects’
cone locations with a Gaussian cone aperture function (MacLeod, Williams, &
Makous, 1992; Chen, Makous, & Williams,
1993; Qi, 1996; He
& MacLeod, 1998). The actual number used
in the model for the full width at half maximum of the Gaussian cone aperture
function was 0.615 times the inter-cone spacing. Each cone’s aperture
function was then weighted by the appropriate relative quantal
sensitivity for L, M, or S cones using the Smith and Pokorny cone fundamentals
(Smith & Pokorny, 1975). It was assumed
that the L, M, and S cones have equal quantal sensitivity at their respective
peak
wavelengths.
Figure 5. Example of a retinal sensitivity map
and retinal stimulus profile used to model the microstimulation of the mosaic. L
and M cones have been colored red and green to aid in their identification. The
full width at half maximum of the retinal profile of the spot imaged with
adaptive optics is smaller than the radius of individual cone inner segments
near 1 deg.
Generating cone quantum catches
Monte-Carlo simulations were performed in which the
computed stimulus light distribution was allowed to fall randomly throughout the
retinal patch. The stimulus was restricted from falling within a buffer zone
near the edge of the sensitivity map to ensure that the entirety of the stimulus
light distribution landed within the retinal area considered. On each
presentation the average number of photons absorbed by each cone was computed by
integrating the product of each cone’s sensitivity profile and the
stimulus light distribution. The actual number of photons absorbed by each cone
was computed from these averages by assuming that a random Poisson process
governs absorption. This process generated the number of photons absorbed for
each cone in the array for each trial.
The results of the model depend on the minimum number
of quanta required for detection to occur. In accordance with previous estimates
(Cicerone & Nerger, 1989; Wesner et al.,
1991; Marriot, 1963; Williams et al., 1981), a minimum number of quanta required
for detection in the range of 1-10 photons was considered. The results of the
model also depend on rules for pooling signals across cones prior to detection.
Detection was modeled under two different scenarios, independent cone detection
and spatial summation of all cone signals. In the case of independent cone
detection, detection occurred when any cone absorbed at least the requisite
number of photons for threshold, and all cones absorbing at least this number of
quanta participated in detection. In the case of spatial summation of all cone
signals, detection was assumed to occur if the sum of quanta received by all
cones exceeded the minimum number of quanta required for detection. All cones
receiving quanta in trials where detection occurred were assumed to participate
in the detection process. The minimum number of quanta required for detection
that provided the best match between the slopes of the model’s and
subjects' psychometric functions was 10 or more quanta if cones detect
independently, and 6-7 quanta if signals are summed over all cones.
Figure 6 shows the
model’s results for the percentage of flash detections at 550 nm that will
be mediated by individual cones at 50% probability of seeing for both spatial
pooling and independent cone detection. Results for the other wavelengths in the
study were similar. As can be seen, the detection rule dramatically influences
the number of cones participating in the psychophysical task. If cones are
independent detectors, the model predicts that more than 90% of test flash
detections will be due to excitation of individual cones at 50% probability of
seeing. However, if cones pool their signals across the entire retina, fewer
than 3% of test flash detections will be due to individual cone excitation, with
detection of most test flashes mediated by two or three cones. The curve
representing spatial pooling was generated under the assumption that there is
complete summation across the entire patch of retina. Psychophysical estimates
of spatial pooling in foveal vision are substantially smaller, not more than
three cones (Davila & Geisler, 1991;
Sekiguchi et al ., 1993). However, the size of the summation pool
assumed has very little effect on the spatial pooling curve in Figure 6. This is because if cones pool their
signals even modestly, it is unlikely that one cone alone will reach the
requisite number of quanta for threshold without the surrounding cones also
absorbing some quanta.
Figure 6. The model’s prediction of the
percentage of detections at 50% frequency of seeing that are mediated by a
single cone as a function of the minimum number of quanta that must be absorbed
for detection to occur. For independent cones, the
x-axis represents the number of quanta
each cone is required to absorb if it is to participate in detection. For
spatial summation of all cone signals, the
x-axis represents the number of quanta
that must be absorbed by the entire ensemble of cones if detection is to occur.
Each curve represents 2000 simulations at a wavelength of 550 nm. The best match
to subjects’ data is 10 or more photons if cones detect independently and
6-7 photons if signals from cones are summed across the retina.
If foveal cones act as independent detectors, then
detection of near-threshold tiny test flashes is almost always mediated by a
single cone. If this were true, then the rich diversity of color sensations
reported by our observers at threshold would immediately imply that stimulation
of two cones of the same class will not necessarily evoke the same color
sensation. This is because our observers required six-to-eight color categories
in circumstances when only two classes of cones (L and M) were capable of
participating in detection. On the other hand, there is little evidence that
cones are independent detectors, and several studies indicate that foveal cones
pool their signals to some extent (Davila & Geisler, 1991; Sekiguchi et al., 1993; Hsu, Buschbaum, & Sterling, 2000; DeVries, Qi, Smith, Makous, & Sterling, 2002). If cones pool their signals at detection
threshold, then multiple cones contribute to detection, even for the very tiny
stimuli we used.
Can excitation of multiple cones explain the diversity of subjects’ responses?
If multiple cones are involved in detection, then it
might be possible to explain the diversity of color sensations experienced by
subjects to variations in L and M cone quantum catches from flash to flash,
without having to conclude that excitation of one particular L(M) cone can
result in a different sensation than excitation of any other L(M) cone. For
example, white percepts might result from the combined excitation of L and M
cones (Krauskopf, 1978).
We do not believe that the diversity of color
experiences our subjects reported can be completely explained by combined
stimulation of both L and M cones. The fraction of white responses made by
subjects with different cone ratios is not consistent with the idea that all
white responses are due to excitation of mixtures of both L and M cones. This
theory predicts that subjects with more equal numbers of L and M cones will
report the most white responses, because these subjects have the largest
fraction of their retinal mosaics made up of neighboring L and M cones. Figure 7 shows this expectation is not bourn out by
the data. Subjects with very similar numbers of L and M cones report very few
white responses, whereas subjects with very different numbers of L and M cones
report a large number of white sensations, despite the fact that it is least
likely that both L and M cones will participate in flash detection for these
subjects.
Figure 7. White responses as a function of the
asymmetry in L to M cone ratio. Shown is the percentage of all spots seen that
each subject reported as white, averaged from 20% to 85% probability of seeing
and averaged over wavelength. Subjects with the most balanced numbers of L and M
cones report the fewest white responses, whereas subjects with the most extreme
ratios of L and M cones report the greatest number of white responses. The same
trend is evident at each of the three individual wavelengths tested. This is
contrary to expectation if all white responses could be explained by stimulation
of mixtures of L and M cones. Error bars represent ±1
SD. Horizontal error bars represent the
uncertainty in the determination of each subject’s L to M ratio.
Moreover, the fraction of white responses for subjects
with extreme ratios is too large to be explained by combined excitation of M and
L cones. With our detection model, we also calculated the expected fraction of
all flashes seen in which detection is mediated by both L and M cones. This is
the upper bound on the number of white responses that is consistent with the
mixture theory. Figure 8 shows this upper limit
for one subject, BS, at 550 nm. Because this subject has so few M cones in
his retinal mosaic, even if cone signals are summed across the entire retina,
both L and M cones will be excited on fewer than a quarter of all trials in
which the flash is seen. However, BS reported over 55% of all flashes seen as
white. This is significantly higher than the upper bound allowed if all white
responses are caused by combined excitation of L and M cones, and this
discrepancy increased for longer stimulus wavelengths. This result implies that
white sensations can result from excitation of cones of only one class.
Apparently, then, stimulation of cones containing the same photopigment can give
rise to different color
sensations.
Figure 8. Percentage of spots seen called white
by BS at 550 nm, 50% frequency of seeing, compared with the maximum
percentage of white responses allowed if white responses are caused only by
combined excitation of L and M cones. Predictions from the model are shown if
all cone signals are summed and if cones detect independently. Error bars for BS
are the 95% confidence limits. Error bars on the maximum percentage of white
responses allowed by excitation of both L and M cones represent the range for
quantal detection thresholds from 5-10 photons. The inset shows BS’s
retinal mosaic. Because there are so few M cones, even if cones’ signals
are summed across the entire retina, both L and M cones will be excited on fewer
than a quarter of all trials in which the flash is seen. However, BS reported
over 55% of all flashes seen as white, more than twice the maximum expected if
white responses are caused only by combined stimulation of L and M cones.
Other explanations for the white response
While equal and simultaneous excitation of both L and M
cones may very well cause a white percept, the actual behavior exhibited by
subjects with different cone ratios indicates that this cannot explain the
majority of white sensations experienced. We explored two alternative
explanations for the origin of the white response. One hypothesis is that the
circuitry responsible for carrying chromatic signals, whether it be the midget
system or some other pathway, is highly spatially localized in the retina. If
this is true, there will be some retinal regions, due to the generally random
arrangement of L and M cones, where only one cone type will be present, and it
will not be possible to form a spectrally opponent signal. Perhaps excitation of
cones in these regions does not evoke a chromatic response. In this case the
number of white responses is expected to be proportional to the fraction of
cones in each subject’s mosaic that are in clumps of like-type cones.
Because the number of clumps will increase with the asymmetry in cone ratio,
subjects with the most balanced ratios will exhibit the fewest white responses,
in line with our results.
Another hypothesis is that the white responses are a
consequence of the different neural weighting that must be given to signals
arising from individual L and M cones in subjects with different relative L and
M cone numerosity. For example, consider YY and BS. Both see a large stimulus of
580 nm as yellow, yet BS has about 16 times more L cones for each M cone
than YY. This implies that somewhere in the chromatic pathway a signal from an
individual M cone in BS’s retina must acquire a weight about 16 times
larger, relative to the weight given to an individual L cone signal, than is
given to the signal from an individual M cone in YY’s retina. It
would be expected that an L cone in both YY’s and BS’s retinas would
be required to absorb the same number of quanta for either of them to detect the
presence of a stimulus. However, depending on where in the chromatic pathways
signals from L or M cones are normalized, it could be that an L cone in
BS’s retina may have to absorb 16 times more quanta than an L cone in
YY’s retina before BS will say he saw the stimulus as colored. This
essentially results in separate thresholds for detecting a stimulus and seeing a
stimulus as colored, with the difference being largest in those subjects with
the least balanced ratio of L to M cones. This is similar to an idea put forth
by Massof ( 1977) to explain the variation in
appearance of near-threshold stimuli as a consequence of quantal fluctuations
and generalized opponent color mechanisms.
The percentage of flashes seen that should be called
white, given this hypothesis, was modeled under the simple assumption that the
most numerous cone type in the retina has a separate threshold for seeing color
that is related to the detection threshold by the ratio of the more numerous to
least numerous type of cone. This hypothesis was modeled at 550 nm, so only L
and M cones were considered. For example, with a minimum number of quanta
required for detection of n, we assumed, for a subject with a ratio of L to M
cones of 3 to 1, that a white response would occur when only L cones absorbed
quanta from the flash and the L cone excitation (either combined, in the case of
spatial pooling, or for each individual L cone, in the case of cone
independence) was at least as large as
n but less than 3
n (for less than
n quanta absorbed no detection occurs).
We did not consider additional white responses that may be due to mixtures of L
and M cone excitation, as the low numbers of white responses made by YY and AP,
who exhibit L to M ratios near 1 to 1, indicate that these should be responsible
for a very small number of white sensations. In both cases, for cone spatial
pooling and cone independence, the model’s prediction of the percentage of
spots seen that should be called white did not depend significantly on the
number chosen for minimum number of quanta required for detection.
Figure 9 replots the
percentage of spots seen that each subject called white as well as the
percentage of cones in each subject’s mosaic that were in clumps of
like-type cones (L or M cones that neighbored only other L or M cones), and the
model’s results for the percentage of spots seen that should be called
white if white responses are caused by the normalization hypothesis, as a
function of cone ratio asymmetry. For comparison, the percentage of cones in
each subject’s mosaic that border cones of another type, which would
predict white responses if they were only due to combined L and M cone
excitation, is also shown. It is quite clear that both the neural normalization
hypothesis with spatial pooling of cone signals and the hypothesis that cones
within clumps produce white sensations qualitatively predict subjects’
behavior. However, the hypothesis that cones within clumps produce achromatic
sensations comes closest to matching subjects’ data. Note that the neural
normalization hypothesis with cones acting as independent detectors does a poor
job of predicting subjects’ behavior.
Figure 9.
Comparison of the percentage of flashes seen that subjects called white (black
dots) with predictions based on the hypothesis that cones within clusters of
like-type cannot signal chromatic information (red curve) and the hypothesis
that white responses result from differences in neural weighting given to L and
M cone signals (blue and green curves). Also shown is the fraction of each
subject’s mosaic that contains L and M cone borders (purple curve);
subjects’ data should follow the shape of this curve if most white
responses were caused by combined stimulation of L and M cones. Subjects’
responses are best predicted by considering the fraction of cones in the mosaic
within clumps of like-type. Data for the neural normalization scenarios
represent 2000 simulations at each cone ratio with a 550-nm flash at 50%
probability of seeing; results were averaged for detection thresholds from 5-10
quanta.
If cones do pool their signals, then both of these
alternative explanations for the white response seem to qualitatively match the
behavior of subjects’ white responses with cone ratio asymmetry. However,
if white responses are due to differing thresholds for detecting and seeing
color as a result of a neural normalization, then the model also predicts, as
expected, that the number of spots that appeared colored should rise with
increasing probability of detection and the number of white responses should
decrease. For subjects in general this is not what occurred (data not shown). In
fact, only one subject, YY, generally showed an increase in colored responses as
the probability of seeing increased, and because this is the subject with the
most balanced cone ratio, this is the subject that would be least affected by
the type of neural normalization considered here. For all other subjects the
number of colored responses either decreased or remained constant as the
probability of seeing increased. This makes the hypothesis that the white
responses were mainly due to the effects of normalization in the chromatic
pathways (at least in the simple manner considered here) somewhat less plausible
than the alternative that white responses are linked to the spatial organization
of the cone
mosaic.
The spatial grain of the cone mosaic is remarkably
invisible in perceptual experience (Williams, 1990). For stimuli of large spatial extent,
color vision is independent of the relative numbers of cones, and color
circuitry organizes itself to produce constant perception despite variations in
the relative numbers of cones (Brainard et al., 2000; Neitz et al., 2002; Pokorny & Smith, 1987). But adaptive optics allows us to present
stimuli on a smaller spatial scale than arises in normal perceptual experience,
stimuli for which cortical circuitry had no opportunity to develop. Our
experiments firmly reject the idea that excitation of all cones within the same
class results in the same hue sensation. This idea has been implicit in nearly
all other experiments on the appearance of small spot stimuli (Hartridge, 1954; Krauskopf, 1964; Krauskopf & Srebro, 1965; Krauskopf, 1978; Otake et al., 2000). Our
results run counter to a commonly held view of the organization of color vision
throughout the history of its investigation, which we refer to as the elemental
sensation hypothesis. Helmholtz ( 1896)
endorsed this view when he stated that “The eye is provided with three
distinct sets of nervous fibers. Stimulation of the first excites the sensation
of red, stimulation of the second the sensation of green, and stimulation of the
third the sensation of violet.” Though Helmholtz’s view
has been superseded by modern color theory in which each cone class contributes
to the hue of a stimulus through two opponent mechanisms (Hurvich & Jameson,
1957), even opponent color theory explicitly
links the hues perceived with stimulation of particular cone classes.
One apparent challenge to elemental sensation theory
comes from a large body of literature demonstrating that excitation of cones at
a distant retinal location can influence perceived color (e.g.,
Chevreul, 1839). Another apparent challenge
is that color signals from cones can be strongly influenced by the excitation of
other cone classes in the same retinal location (Knoblauch &
Shevell, 2001). However, neither of these
phenomena actually rejects the elemental sensation theory because both can be
attributed to postreceptoral interactions among signals arising from cones with
different spatial locations or photopigment. The notion survives that excitation
of cones within the same class should result in the same hue sensations when
stimulation of adjacent locations is precluded. Here we show that each cone
class can signal multiple chromatic sensations even in the absence of changes in
stimulation elsewhere in the retina or in other classes of cones. Our data
indicate that even isolated stimulation of cones containing the same pigment can
result in different color sensations.
Why should the number of sensations produced by
excitation of individual cones exceed the number of cone classes? The visual
system uses signals from single cones to derive intensity as well as spectral
information, and ideally these attributes should be extractable at every retinal
point. However, the cone classes are intermingled in a single mosaic so
trichromatic vision is impossible on the spatial scale of a single cone.
Furthermore, the cone classes are randomly arranged in the mosaic, creating
clumps of cones of like type, which exacerbates the problem of collecting three
spectral samples at every point. Moreover, neural circuits, such as those
responsible for the receptive fields of ganglion cells, tend to draw their cone
inputs from localized retinal regions. Consequently, every cone of the same
class cannot possibly make the same contribution to cortical circuitry for
extracting hue and brightness.
Given these organizational constraints, it may be
inevitable that color sensations are not uniform within a single class of
photoreceptors and reflect instead the microcircuitry of postreceptoral color
mechanisms. For example, it may be that cones within clusters of cones of the
same class generate achromatic sensations because the localized circuitry they
serve cannot be spectrally opponent, and the task of conveying hue is left to
circuits that are able to draw signals from cones of different classes. It is
also conceivable that the white verses colored responses our observers
frequently reported correspond to the activity of different retinal circuits
that have already been identified. For example, white responses could be
mediated by the parasol ganglion cells, whereas colored responses could be
mediated by the midget pathway. Coupling between cones (Hsu et al., 2000; DeVries et al., 2002; Hornstein et al., 2004) could also play a role in generating the
observed diversity of color experiences.
In this first study, the use of adaptive optics allowed
us to probe visual microcircuitry with much smaller psychophysical stimuli than
has been possible before. It has also allowed us to characterize the optics of
the eye and the trichromatic cone mosaic in the same subjects. However, a
complete understanding of the topography of the functional microcircuits
underlying color vision will require the ability to record which cone(s) is
stimulated with each tiny probe. Our present experiments do not allow us to
distinguish with certainty whether different cones of the same class evoke
different sensations or whether different sensations can result from stimulating
the same cone multiple times. Putnam et al. ( 2005) have shown that it is possible to measure
the location of a stimulus on the cone mosaic with an accuracy of one-fifth of a
foveal cone diameter. It may ultimately be possible to use this method to assign
color experiences to specific cones in the cone
mosaic.
Thanks to Don MacLeod for suggesting a possible origin
for blue sensations without S cone stimulation and Joel Pokorny, Dave Brainard,
and Joe Carroll for helpful comments. Thanks to Jay and Maureen Neitz for
providing interesting subjects. This work has been supported in part by the
National Science Foundation Science and Technology Center for Adaptive Optics,
managed by the University of California at Santa Cruz under cooperative
agreement No. AST-987673, and National Institutes of Health Grants EY0436 and
EY0139. Commercial relationships:
none.
Corresponding author: David R. Williams.
Email: david@cvs.rochester.edu.
Address: 274 Meliora Hall, Center for Visual
Science, University of Rochester, Rochester, NY
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