A Macintosh Quadra 950 computer and 4 National Instruments (Austin, TX) interface boards (MIO-16, AO-6, and 2 DMA 2800) controlled an 8-channel colorimeter (Figure 1). The colorimeter presented a 6° circular center and a 16° annular surround. The center and surround each consisted of 4 channels. The optics of the center and surround channels were identical prior to combination. Light from each light-emitting diode (LED) (L1-L8) was first spatially homogenized by 2 spaced holographic diffusers (Physical Optics, Torrance, CA; 20° angle of diffusion), and then collimated by a lens (76-mm focal length; 29-mm diameter). Collimated light from each LED passed through a 3-cavity interference filter. The 4 lights within the center or surround pathway were merged using dichroic mirrors, then focused on a 2-mm artificial pupil by a field lens (60-mm focal length; 29-mm diameter). The center-surround field configuration was formed by a photometric cube with a mirrored ellipse on the hypotenuse. The photometric cube was placed 1 focal length away from the field lens; hence, the image of the center-surround field was focused at optical infinity. The optical pathlengths from each of the 8 LEDs to the field lens were identical. The head of the observer was held stable by a chin-rest, with the superciliary ridge of the viewing eye resting against the eyepiece. Each observer's eye was 8 mm from the artificial pupil. The size of the surround LED beam at this location, measured with an optical comparator, was 2.2 mm in diameter. This size is consistent with the calculated beam half-height width. A fixation point allowed the field to be viewed at 10° in the temporal retina. Inconel neutral density filters, calibrated for each primary, were inserted in the final common path to control the average light level. The LED/interference filter combinations determined the spectra of the primaries. The peak wavelengths of the 4 primaries for both center and surround were 459, 516, 561, and 664 nm with half-height bandwidths of 8-10 nm. LEDtronics (Torrance, CA) manufactured the LEDs for the 459- and 664-nm primaries; the 516- and 561-nm primaries originated from Nichia LEDs (San Jose, CA). The LED luminance output was controlled by a train of 2 microsec constant-amplitude pulses with varying density provided by the LED drivers. Twelve-bit digital/analog (D/A) converters fed the LED drivers. A potentiometer scaled the input voltage to the LED driver and, therefore, allowed adjustment of the maximum luminance output of each LED. To maximize the bit resolution of the primaries, gelatin neutral density filters were added to 459-nm (0.9 log unit), 516-nm (0.6 log unit), and 664-nm (0.3 log unit) primaries, so that the DA output voltage for each LED was near 50% of its maximum for a stimulus of illuminance 100 photopic td and a chromaticity metameric to the equal energy spectrum.

Figure 1. Eight-channel colorimeter diagram. L1 to L4 are center light-emitting diodes (LEDs); L5 to L8 are surround LEDs. Light from each LED passed through plastic diffusers (DF) before being collimated by a lens (L), and passing through an interference filter (IF). The LED/filter combinations produced primaries with dominant wavelengths of 459, 516, 561, and 664 nm. Lights within the center and the surround pathways were combined using dichroic mirrors (D). A photometric cube (PC) with a mirrored ellipse on the hypotenuse formed the center-surround field configuration. A field lens (FL) focused the LED images on the 2-mm artificial pupil (AP), and produced an image of the field at optical infinity.

Calibration

The spectral distributions and the radiant outputs of the primaries were measured at the eyepiece. The spectral output of each channel was measured at the maximum LED output with an Optronics (Orlando, FL) OL754 spectroradiometer at 2-nm intervals. Although the pulse-frequency modulation technique offers high LED output linearity over a 3-log unit range for modulation around a mean level (Swanson, Ueno, Smith, & Pokorny, 1987), we observed small but systematic deviations from linearity with variation in steady light level. These deviations are presumably caused by thermal effects associated with changes of current in the diode junction (Watanabe, Mori, & Nakamura, 1992). Linearization of each LED output was attained with 3 linear equations for the ranges of 0.1-1, 0.01-0.1, and 0.001-0.01 of the maximum LED output. The maximum photopic illuminance output of the center 561-nm LED was measured with an EG&G (Gaithersburg, MD) 550 radiometer/photometer and used as a reference to calculate the illuminances of other LEDs.

Observers

Two observers, H.S. (author) and S.S. (naïve to the purpose and design of the experiments), were normal trichromats as assessed with Ishihara pseudoisochromatic plates and the Neitz OT anomaloscope. H.S. had a Farnsworth-Munsell 100-hue error score of 4, and S.S. had an error score of 20. H.S. was myopic (-5.5) and wore nontinted contact lenses during the experiment. S.S. was emmetropic.

Use of the 4 Primary Colorimetric System

Shapiro, Pokorny, and Smith (1996) gave a theoretical introduction to a 4 primary colorimetric system. To implement a 4 primary colorimetric system, it is necessary to have accurate estimates of an individual observer's receptoral spectral sensitivities and prereceptoral filtering. First, we developed a technique to evaluate whether an individual observer's receptoral sensitivities could be characterized as linear transforms of standard observer data after correcting for prereceptoral filtering differences between the individual and the standard observer.

The CIE scotopic luminosity function V'(l) can be decomposed into 2 components: the spectral sensitivity of the photoreceptor at the retina, and the spectral transmittance of the prereceptoral filters:

where W'(l) represents the CIE V'(l) expressed at the retinal level and F_s(l) represents transmittance of the prereceptoral filter associated with the standard observer for scotopic photometry. The physiological basis of the W'(l) distribution is the rhodopsin-absorption spectrum. We assume W'(l) is invariant across observers because no rhodopsin polymorphisms have been reported for human observers with normal visual function (Sung et al, 1991). Prereceptoral filter transmittances F(l) are known to vary among observers. For a scotopic luminance match between 2 narrow band lights, reference light P_ref and a test light P_test, the standard observer match is given by:

(2)

where a_s is calculated based on V'(l). For a scotopic match made by an individual observer

(3)

where F_o(l) is the prereceptoral filter transmittance for the individual observer, and a_o is set by the individual observer. Ratio a_s/a_o represents the ratio of the prereceptoral filtering for the standard observer and an individual observer. Scotopic-luminance matching can be used to assess the prereceptoral difference between an individual observer and the standard observer for wavelengths where the scotopic sensitivity is higher than the photopic sensitivity. In particular, this method is appropriate for primaries 459, 516, and 561 nm.

At long wavelengths, the cones and the rods have similar sensitivities, preventing the use of a scotopic luminance match to calibrate individual prereceptoral filtering of the 664-nm primary. For this primary, we used a photopic colorimetric match. The CIE 10° standard observer for colorimetry has a unique match for the mixture of 459 and 561 nm matched to the mixture of 516 and 664 nm (Figure 2):

where b₁, b₂, and b₃ are the tristimulus values calculated from CIE 10° color-matching functions. For an individual observer, the values of the 459-, 516-, and 561-nm primaries are first corrected for the individual prereceptoral filtering differences measured by the scotopic luminance matches, and then they are fixed at the matching values b₁, b₂, and 1.0. If the observer can make a color match by adjusting only the radiance of the 664-nm primary (b₃), his or her receptoral spectral sensitivities at the 4 primary wavelengths can be approximated by linear transforms of the standard observer data. The difference between the 664-nm setting for the individual observer and the standard observer corrects for the individual prereceptoral transmittance at 664 nm.

Figure 2. The equation (4) color match represented on the CIE 10� chromaticity diagram. The radiance of the 664-nm primary was adjustable; the radiances of the 459, 516, and 561 were set at the expected match for the CIE 10� standard observer, after correction for the differences in prereceptoral filtering between the individual and the standard observer.

Heterochromatic Modulation Photometry

It is necessary to have accurate scotopic retinal illuminance matches to ensure good isolation of the rod and cone receptors. Heterochromatic modulation photometry (HMP) is a precise method for obtaining equiluminance for a pair of heterochromatic standard/test lights presented in temporal alternation (Pokorny, Smith, & Lutze, 1989). The average illuminance of the standard light is fixed, and the average illuminance of the test light is set at a series of prechosen values. On a given trial, the contrasts of the standard and test lights are adjusted in tandem to determine the contrast threshold. The contrast sensitivity, plotted as a function of the average illuminance of the test light, appears V shaped. If we fit the data with a V-shaped template, the equiluminant point between the test and standard lights can be estimated from the lowest sensitivity point of the template.

The HMP and color-matching experiments were performed separately for the 6° center or 16° annular surround. For the HMP measurements, the stimulus consisted of 2 primaries, a standard 561-nm primary, and a test primary that was either 459 or 516 nm. The standard and test primaries were square-wave modulated in counterphase at 6 Hz. The time-average illuminance of the standard primary was fixed at 0.08 photopic td, corresponding to 0.07 scotopic td. The time-average illuminance of the test primary varied from 0.04 scotopic td to 0.14 scotopic td. Four sets of HMP curves were obtained: center 561 and 459 nm, center 561 and 516 nm, surround 561 and 459 nm, and surround 561 and 516 nm. The method of adjustment was used to obtain the modulation thresholds. The observer dark-adapted for 30 minutes prior to testing. Test illuminance was randomized from trial to trial in each session. Modulation thresholds and standard deviations were calculated from 10 threshold settings.

Each HMP data set was fitted with 2 templates (Pokorny et al, 1989), an illuminance-independent contrast template and an illuminance-dependent amplitude template. For a pair of temporally alternated standard and test lights, the psychophysical response amplitude, A, can be calculated as:
contrast template,

or amplitude template,

where L is the time-average illuminance, C is the illuminance contrast of a pair of temporally alternated standard and test lights, L₀ is a normalizing constant, and M_t is the optimal modulation threshold for human observer determined by the Weber fraction. The contrast template is appropriate if the time-average illuminance is constant, or if the temporal sensitivity is independent of illuminance level (Weber's law). The amplitude template is appropriate if the time-average illuminance is varied, or if the temporal sensitivity is dependent on illuminance level. The assumption that temporal sensitivity is independent of illuminance level is true at lower temporal frequencies, but not at higher temporal frequencies where the threshold is dependent on modulation amplitude (Kelly, 1961). Pokorny et al (1989) used the amplitude template to fit data collected at a frequency of 15 Hz. In our experiment, the average illuminance of the standard primary 561 nm was kept constant, but the average illuminance of the test light was varied. The frequency of the square-wave temporal modulation was 6 Hz. The results of fitting were compared with both templates.

HMP results for center primaries are shown in Figure 3. The equiluminant points obtained with the 2 templates differed by 0.02 to 0.08 log unit. For both observers, the contrast template fits were accepted because the root mean square residuals for the fits were lower than for the amplitude template for most of the data sets. For both observers, the prereceptoral filter corrections from center and surround HMP agreed within 5%. At 459 nm, the prereceptoral filtering for observer H.S. was 20% higher (.079 log unit) than that for observer S.S.

Figure 3. Heterochromatic modulation photometry (HMP) results of center primaries for 2 observers. The left panel shows data for observer H.S., and the right panel shows data for observer S.S. The circles represent HMP for 561 and 459 nm, and the triangles represent HMP for 561 and 516 nm. The lines represent the contrast template fits.

Colorimetric Match

The observer was asked to make a successive color match between the mixture of center (or surround) 459 + 561 nm and the mixture of center (or surround) 516 + 664 nm at about 390 photopic td. The 459-, 516-, and 561-nm primaries were fixed at the expected match values calculated from the standard observer with correction for individual prereceptoral filtering determined by HMP. Only the radiance of 664 nm was adjustable. The observer pressed a button to switch between the 2 epochs, and adjusted the amount of 664 nm until a satisfactory color match was made (ie, the observer could not identify the direction of color difference between the 2 center epochs). The difference in 664-nm settings between the individual and the standard observer was used to correct for prereceptoral filter variation at 664 nm.

Both observers could make satisfactory color matches: When center 459 + 561 nm was matched to center 516 + 664 nm, the observers could not tell the direction of the chromatic difference between the 2 stimuli. Therefore, the 2 observers, though differing slightly in prereceptoral filtering, both had receptoral spectral sensitivities at the colorimeter primaries that could be approximated by linear transforms of CIE 10° standard observer data.

To transform from the CIE 10° color matching into cone-based chromaticity, we used the Smith-Pokorny transformation (Smith & Pokorny, 1975) applied to the 1964 10° color-matching functions (Shapiro et al):

(7)

Rod Induction

The nulling technique that we used is similar to that employed by Krauskopf et al (1986) and Zaidi et al (1991). Figure 4 shows a schematic diagram of the method. When an observer perceives an annular surround change from bright to dark, a center field of the time-average luminance of the surround will appear to change from dark to bright. By adding luminance modulation to the center, the induced brightness change can be nulled, and the center may appear steady again. In our experiments, the rod activity in an annular surround was modulated. If there was a perceptual change in the center, the observer attempted to null or minimize the change by adding modulation to the center.

Figure 4. Schematic diagram of the nulling method. The surround is temporally modulated. The induced modulation (dashed line) in the center is nulled by the nulling modulation (solid line).

The surround-inducing modulation was a rod-temporal modulation. The center-nulling modulation was either rod or cone (S+M+L) modulation. For the (S+M+L) cone nulling, the nulling modulation amplitudes of all 3 cone types were varied together, maintaining a constant chromaticity. We ran 3 additional conditions. (1) In one condition, we varied the phase offset between the surround (inducing) and center (nulling) modulations by fixing the surround at the maximal inducing contrast and the center at the best nulling contrast measured without phase offset. The observer adjusted the phase offset between center and surround modulation to obtain minimal perceptual modulation of the center. (2) Because the observers noted a small change in hue at the best cone- (S+M+L) nulling modulation, we evaluated whether variation in chromaticity could reduce the residual center modulation. The observer could vary the magnitude of S-cone modulation (kS), with the M- and L-cone modulations fixed at the same contrast as the best (S+M+L) cone-nulling contrast. In this procedure, variation in k altered the chromaticity of the modulated component of the nulling stimulus. (3) We also ran a condition in which the surround-inducing modulation was a cone-temporal modulation. We used a rod-nulling modulation of the central test field to cancel the induced cone modulation.

The temporal profile of the modulation was either square-wave, an on-pulse train, or an off-pulse train (Figure 5). The modulation frequency was 1 Hz. The time-average chromaticity of both center and surround was metameric to the equal energy spectrum (s = 1, l = 0.67). For the square-wave condition, the time-average illuminance of center and surround was the same, either 0.1, 1, 10, or 100 photopic td (0.052, 0.52, 4.83, 48.26 scotopic td). The scotopic values do not scale exactly the photopic values because the time-average scotopic troland was varied to get maximum rod contrast at 0.1 and 1 td. For the on-pulse or off-pulse condition, the minimum or maximum center or surround illuminance was fixed at the average illuminance levels of the square-wave condition, and time-average illuminance changed with modulation contrast.

Figure 5. Temporal configurations of the stimuli for induction. There were 3 temporal profiles: square-wave, on-pulse train, and off-pulse train. In the square-wave condition, the surround was modulated around the steady center illuminance level. In the on-pulse condition, the surround had only incremental changes. In off-pulse condition, the surround had only decremental changes.

Table 1. Fitting equations for the induction conditions. All fits except one have an R value between 0.95 and 0.99.

Figure 6. Rod induction with rod or cone nulling and cone induction with rod nulling at 1 td. The left panels show data for observer H.S., and the right panels show data for observer S.S. Upper panels show square-wave modulation data, middle panels show on-pulse modulation data, and lower panels show off-pulse modulation data. Circles represent rod induction with rod nulling data, solid squares represent rod induction with cone nulling data, and open squares represent cone induction with rod nulling data. The solid and dashed lines represent linear or polynomial fits.

Figure 7 shows the results of rod induction with rod nulling at 0.1 td. These data were fitted with linear functions with slope close to unity. There was little difference in rod nulling of rod induction for data obtained at 1 td and 0.1 td.

Figure 7. Rod induction with rod nulling at 0.1 td. The left panel shows data for observer H.S., and the right panel shows data for observer S.S. Circles represent square-wave data, erected-triangles represent the on-pulse data, and inverted-triangles represent the off-pulse data.

Figure 8 shows rod induction with (kS+M+L) cone nulling. For both observers, kS cone-nulling slope was about 1.5, higher than the slope of (S+M+L) cone nulling.

Figure 8. Rod induction with (kS+M+L) or (S+M+L) cone nulling. Squares represent (S+M+L) cone-nulling data, and circles represent (kS+M+L) cone-nulling data. For the (kS+M+L) cone-nulling condition, the center M- and L-cone contrasts were set to the nulling contrast for the (S+M+L) cone-nulling condition. For both observers, kS cone-nulling slope was about 1.5.