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The authors' reply.


An objective of the work discussed in the above letter was to test the proposal by Dr. Berman and his colleagues that the perception of spatial brightness is related to the S/P ratio--they have promoted the expression P x [(S/P).sup.0.5] as a correlate for brightness perception. The results of our study suggested that this expression does not work. In their letter, Drs. Berman and Clear highlight what they believe to be errors in our statistical analyses and misunderstandings in our application of trichromacy.

In recent years, following Dr. Berman's suggestions, we have carried out new experiments to test his assertions about the visual field (for example: flat neutral surface, neutral interior space) [Fotios and Cheal, in press] and evaluation mode (for example: rapid-sequential, side-by-side) [Houser, Fotios and Royer, 2009; Fotios and Cheal, 2010]. In both cases, we did not find statistically significant effects. This demonstrates our willingness to consider and test alternative ideas even though this is done at the expense of a delay to our focus, which is to understand the spectral determinants of brightness and color perceptions in natural viewing conditions. This work is important because light sources with spectra more closely aligned with human vision have the potential to reduce energy use while simultaneously enhancing color and brightness perceptions.


The brightness discrimination trial was developed and designed with the express intent of analyzing the results using Variance Stable Rank Sums (VSRS) [Dunn-Rankin and others, 2004]. We chose this statistical test because it was previously applied to discrimination data in the Quellman and Boyce study of preferred skin appearance [Quellman and Boyce, 2002] and because the type of data matches that described for use with VSRS [Dunn-Rankin and others, 2004]. We reviewed this decision in response to the comments from Drs. Berman and Clear, who state: "the viability of this test is based on the assumption of a fixed estimate of the rank variance. This assumption is grossly violated if some or all of the comparisons have zero or little variance, which turns out to be the case for the data of Houser and others," Comments from Dunn-Rankin and King [Dunn-Rankin and King, 1969] do not support this assertion:

* "Where ... (other) ... procedures yield scales based on a normalizing transformation, the rank scale is a variance-stable scale....This is immediately apparent from the fact that any given rank-sum difference has the same significance no matter where the rank totals may be located on the scale. Thus the variances for all scale values are equal, a feature that other methods assume but do not guarantee." [Dunn-Rankin and King, 1969]

* "It is insensitive to extreme frequencies. Sometimes a sample preference proportion will be 1 or 0, for which the normal deviates are plus or minus infinity. Compensating for such problems is avoided in the Rank Method." [Dunn-Rankin and King, 1969]

Following this review, we remain confident that VSRS was an appropriate analysis method.

Drs. Berman and Clear re-analyzed our data using an alternative statistical method, the binomial test, which employs multiple paired-comparisons rather than treating the data as a complete set. The binomial test requires correction (they employed a Bonferroni correction) when multiple comparisons are made to avoid capitalizing on chance, whereas the VSRS test is intrinsically designed for data from a collection of multiple paired-comparisons. The rank order data of the VSRS use data from all comparisons to decipher the rank of an individual stimulus, whereas the binomial test relies only on data from the direct comparison of two stimuli.

Using the binomial test, Drs. Berman and Clear found two comparisons, in one of the two methods, where the conclusions drawn were different than as found using the VSRS method. When only one of these two were significantly different when a multiple comparison adjustment was added, they then looked at the probability of both events occurring together. This has the appearance of fishing for the right statistic, where just the right amount of information was included so that the data confirm a preconceived idea.

McNemar's test was used to investigate whether the side-by-side and rapid-sequential evaluations produced similar results. There were ten lamp pairs and hence ten separate comparisons. In two cases McNemar's test suggested differences to be significant (p < 0.05) and in eight cases it did not suggest a difference (p > 0.05). Our approach to interpretation was to look for the overall trend suggested by the results, and in this case the majority of the data do not suggest a difference, hence our conclusion that side-by-side and rapid-sequential evaluations lead to similar results. As part of our review the data were further modeled using Generalized Estimating Equations (GEE) [Agresti 2002, 2007]. In this analysis, we included method (that is, side-by-side and rapid-sequential evaluations) as a factor for predicting the choice of the subject. In essence, the GEE method allows individual McNemar tests to be considered simultaneously, and a statistical conclusion to be drawn. Method was not found to be significant, supporting our conclusion that the side-by-side and rapid sequential methods led to similar brightness judgments.

Drs. Berman and Clear suggest that some of the results are nearly opposite. For example, in pair AC the expert subject vote was 56-44 and the naive subject vote was 33-67. Where the collective vote approaches 50-50, it is not unexpected to find that, in some cases, results from two different subject groups split in opposite directions. A similar situation was apparent in the results of the brightness judgments reported by Berman and others, [Berman and others, 1990]. In those tests, twelve observers each repeated a brightness assessment ten times for the same lamp pair. Ten subjects reported the same stimulus to be brighter on at least eight of the ten presentations (Results of test comparing WWG lamp at 40 cd/[m.sup.2] with R213 lamp at 30 cd/[m.sup.2]) while two subjects reported the alternative stimulus to be brighter on all ten trials, and these opposite results did not appear to warrant comment.


Drs. Berman and Clear imply that the conditions we examined were artificial. The conditions we employed were similar to that of Dr. Berman and his colleagues [Berman and others, 1990] except that our subjects viewed a real interior space rather than a flat surface. Fotios and Cheal carried out brightness matching with four different types of field, including a flat neutral surface and a neutral interior space, and these results did not suggest any significant differences [Fotios and Cheal, in press].

Drs. Berman and Clear imply that we were erroneous not to match the stimuli for equal chromaticity. While our stimuli were different from those used by Berman and his colleagues, this does not imply that our stimuli were erroneous. Quite the contrary, varying CCT was intentional; we wished to address the fact that some people are advocating the use of high CCT light sources at lower illuminance levels as an energy saving strategy. Berman and others, [Berman and others, 1990] chose to compare lamps of equal chromaticity, but with unequal S/P ratios. In later articles, however, Dr. Berman and his colleagues have generalized this result, asserting that lamps with a higher S/P ratio can be substituted for those with a lower S/P ratio at a reduced illuminance, without the caveat that this is only valid if the lamps in question have equal chromaticity [Berman and Liebel, 1996]. With most common light sources a change in the S/P ratio is accompanied by a change in chromaticity.

Berman questions the side-by-side method of presenting stimuli, also referred to as simultaneous evaluation. This method has been widely employed by others [Boyce, 1977; Alman 1977; Rea, Redetsky and Bullough, in press] and is both natural and common in everyday viewing. For example, simultaneous evaluations are performed when people look at adjacent storefronts illuminated by different types of light sources, or when a person views a perimeter daylight office adjacent to an interior office that is illuminated with fluorescent lamps. Recent work at mesopic levels [Fotios and Cheal, 2010] compared sequential and simultaneous modes of evaluation and did not find any significant differences. Uchikawa and Ikeda [Uchikawa and Ikeda, 1986] concluded that simultaneous evaluations of brightness tend to result in more stable results than sequential evaluations and this has lead at least one research group to adopt simultaneous evaluation rather than sequential for their brightness judgments [Bullough, Yuan and Rea, 2007].


Drs. Berman and Clear state "In a series of articles from 1990 on, Berman and others, showed, at typical interior light levels, that brightness perception and pupil size could not be predicted from photopic luminance alone in two scenes that were identical in color". While many others had previously demonstrated that photopic luminance does not correlate with brightness when comparing lamps of different SPD [Alman 1977; Boyce 1977; Chapanis and Halsey, 1955; Harrington, 1954; Thornton and others, 1980] their evidence also suggested that pupil size did not correlate with photopic luminance. It was initially proposed by Dr. Berman and his colleagues that the rod and cone responses together mediated pupil size at photopic levels and hence a brightness model was constructed using the S/P ratio. Others have suggested that the P x [(S/P).sup.n] brightness model is physiologically implausible [Rea, Radetskyand Bullough, in press]. The rod contribution was strongly asserted by Berman and his colleagues at all possible opportunities. However, since the discovery of the ipRGC, Drs. Berman and Clear now ascribe the presumed brightness effect of short wavelength optical radiation to the participation of the ipRGCs, rather than to rods. While it appears to be established that ipRGCs contribute to pupil function, we are unaware of any direct evidence that ipRGCs contribute to photopic brightness.

Despite our reservations about the P x [(S/P).sup.0.5] model we chose to directly test it by experiment [Houser, Fotios & Royer, 2009]. The results did not provide support. In their review Drs. Berman and Clear suggest that neither a rod nor an ipRGC model should be expected to be accurate for narrow band sources. Given the widespread use of triphosphor fluorescent lamps, and the emergence of tri-band LED light sources, we question the practical utility of a model that cannot be used for narrow-band spectra.


Drs. Berman and Clear suggest that lighting of higher CCT will appear brighter at photopic light levels. CCT is a one-dimensional simplification of an illuminant's spectral power distribution (SPD). While few studies report a positive correlation between CCT and brightness [Harington,1954], many other studies have not [Boyce 1977; Boyce and Cuttle 1990, Davis and Ginthner,1990; Houser and others, 2004; Hu and others, 2006]. Spatial brightness perception at photopic light levels may not be not related to CCT or to the S/P ratio. These measures have been shown to be too simplistic to encapsulate brightness perception at photopic light levels [Hu and others, 2006], which is driven by the complex interaction between the spectrum of optical radiation entering the eyes and the response of the human visual system.


We think that Drs. Berman and Clear have misunderstood Thornton's description of trichromacy, and have incorrectly characterized our use of the term and concept. Thornton makes it clear that the trichromacy he speaks of is a system-based trichromacy that resides in the rear of the visual system (cortex), not in the front (retina). In the introduction to Thornton's 6-part work on colorimetry, he states: "A ... troublesome basic question is: What are the three spectral sensitivities of the normal human visual system as a whole? Since an accurate colorimetry must be based on psychophysical experiment, we are speaking here of system sensitivity as seen from the rear end of the visual system, not of retinal processes" [Thornton, 1992a]. Elsewhere, Thornton writes: "The essence of psychophysics is synoptic response, and pronouncement. Such pronouncements are far removed from retinal processing. In my view, they must relate most closely to the output end of the human visual system, and therefore these indicated visual sensitivities must lie so deep in that system as to make direct relation to retinal processes a matter for the future-probably the far future" [Thornton, 1992b]. It can also be seen in the trichromatic peaks of 450, 530, and 610 nm that we referenced in our article [Houser, Fotios and Royer, 2009] based on Thornton's work [Thornton, 1992a], which do not coincide with the peaks of the cone photoreceptors.

In Part III of his work, Thornton [Thornton, 1992c] summarizes his prime-color concepts in the following list, stating:

"a. That psychophysical data, representative of change of spectral power distribution of the input light to the pupil ... indicate directly the functioning of (three) spectral visual-system sensitivities;

b. That these three spectral sensitivities are characteristic of the output interface of the visual system (the retina being the input interface);"

c. That a useful colorimetry must and can be structured only around these "output" spectral system sensitivities;

d. That these spectral system sensitivities are too far removed from the retina--down the chain of visual processing--for assignment of one or another of them to one or another rod or cone absorption; that is, that any spectral curve (like absorption) characteristic of a certain photoreceptor in the retina should be expected to be masked by further signal processing on the way to the output of the visual system;

e. that it is more reasonable to relate [Thornton 1982] "scotopic response" and "photopic response" to the same three spectral system responses, and to ascribe the difference [Ikeda and Shimozono 1980] between scotopic and photopic to strong reduction in the redmost system response when input levels fall to those labeled "scotopic" [the envelopes [Ikeda and Shimozono 1980] of photopic response and that of scotopic response both show indications of being composed of the same three broad components near 450 nm, 530 nm, and 610 nm];

f. That the view of item (e) is not necessarily inconsistent with important and increased 'rod contribution' at lower input levels, but that, as seen at the output interface of the visual system, such increased rod contribution at the retina must simply change the triple ratio of the three spectral system responses in favor of blue and green."

Our article was designed to be consistent with Thornton's conceptualization of trichromacy and his prime color theory.


Drs. Berman and Clear suggest that we are mistaken to expect constant brightness when two light sources have unequal chromaticity, citing chromatic contributions to brightness. We fully agree that chromatic contributions (likely from the opponent channels) have the potential to lead to different perceptions of brightness at different locations in the chromaticity diagram, even along the blackbody locus. This phenomenon, the Helmholtz-Kohlrausch effect, occurs when different illuminants are dominated by very different wavelengths of optical radiation. The Helmholtz-Kohlrausch effect is not incompatible with what we have postulated.

The article postulated that, at equal luminance, brightness will remain constant along the region of the blackbody locus that is approximately white when the primary set is held constant, and the primary set selected is similar to the fundamental spectral sensitivities of the normal human visual system. That is, those regions near 450, 530, and 610 nm, and given the name "prime-color" by Thornton. When tri-band illuminants are created using a prime-color primary set, movement along the blackbody locus is achieved by adjusting the relative proportion of the same three spectral primaries, rather than by adjusting the peak wavelengths of one or more of the primaries in the set. The results of our experiment suggest that under these conditions, brightness perception is unaffected by the S/P ratio or by CCT.

We manipulated the SPDs experienced by the subjects in a very purposeful way to remove confounding variables associated with previous work. Specifically, we held the primary set constant, whereas earlier work by others has not. The change of wavelengths (in order to move to a different position on the chromaticity diagram) is a possible cause of the brightness effects found by earlier researchers.

Drs. Berman and Clear refer to the three channels of vision as a brightness channel and two chromatic channels. We suggest this is an unintentional error as the opponent color model is usually considered to comprise a luminance channel and two chromatic channels, brightness having contributions from all three channels.

Drs. Berman and Clear claim that we are confused over prime colors because of our statement: "if the primary components had been changed, brightness perception can be expected to be different even at equal chromaticity and luminance". Drs. Berman and Clear dismiss this statement based on an article that we did not reference, but that they incorrectly referenced. The paper referenced by Drs. Berman and Clear is about CCT and brightness perception by Hu, Houser, and Tiller [Hu and others, 2006]. We supported our statement with a reference to the Houser and Hu study where daylight fluorescent lamplight was visually matched with two primary sets [Houser and Hu, 2004]. The 2004 Houser and Hu paper provides support for our original statement, as does work by Thornton [Thornton 1992a, 1992b, 1992c], who first introduced this phenomenon to one of us (Houser).

Please note that when Drs. Berman and Clear assert that the 2006 Hu and others, study "was based on a side-by-side comparison of a chromatically complex scene" they are perhaps referring to Houser, Tiller, and Hu 2004 [Houser and others, 2004]. The 2006 Hu and others, paper [Hu and others, 2006] summarizes analytical results from three linear brightness models, two nonlinear color appearance models, and two psychophysical experiments. The five models are based on uniform fields and have neither chromatic nor spatial complexity. Of the two experiments, one was carried out in a chromatically complex scene; the other was carried out in a spectrally neutral environment.


Drs. Berman and Clear suggest the S/P model is tetrachromatic. However, the S/P model uses only two functions, V(X) and V'(X), and is therefore bichromatic. Tetrachromatic models have been proposed in the past [Trezona 1973; Trezona 1974; Clarke and Trezona 1976], and have been shown to have more explanatory power than trichromatic models. A pentachromatic model would have more power still. This is related to the additional degrees of freedom as much as it is to the underlying mechanisms of vision. A practical goal, however, is to find a model with the least number of degrees of freedom that provides the most explanatory power, while still having a basis that is reasonably rooted in vision science. Trichromacy, while imperfect at explaining all visual phenomena, explains a great deal of visual phenomena in applied lighting. Evidence from Thornton's work, as well as ours, suggests that this is true.


The letter written by Drs. Berman and Clear to Leukos as a nonrefereed letter-to-the-editor and thus has not had the benefit of the checks-and-balances associated with a peer review. Our response also has not been subjected to peer-review.

How much weight should be placed in an item that has not been subject to peer review? When two publications that were not refereed (that is, a PhD thesis and a CIE conference paper) were referenced in a discussion to counter a proposed effect of lamp spectrum on visual acuity, Berman and his colleagues stated that these articles "have not had the benefit of peer review in archival publications" [Berman and others, 2006]. Dr. Berman and his colleagues employed this tactic as a means of denigrating the evidence, rather than evaluating the work for its merit and offering a balanced response to claims that do not support their work. It is therefore inconsistent for Drs. Berman and Clear to cite an item that has not been peer reviewed [Berman, 2008] in their correspondence without noting it to be nonrefereed in their reference list. Readers without the benefit of this background may place more weight in the citation than Dr. Berman and his colleagues would give it themselves.


The paper that initiated these letters was about an experiment that we performed to: 1) test the hypothesis that the ratio P x [(S/P).sup.0.5] can be used to predict the perception of spatial brightness, and 2) directly compare the rapid-sequential and side-by-side evaluation modes for assessing spatial brightness. Red, green, and blue light emitting diodes (LEDs) were employed to create four light settings that were permutations of two S/P ratios (1.7 and 2.6) and two luminance levels (24 and 30 cd/[m.sup.2]). The S/P ratios corresponded to the practical extremities of CCT (2900 and 7200 K) and were structured to have their chromaticity on the blackbody locus. At equal luminance there was no difference in the perception of brightness, irrespective of CCT. At unequal luminance, but when the ratio of P x [(S/P).sup.0.5] was set to 1:1, brightness perception was predicted by luminance. The two evaluation modes produced comparable results. These data suggest that spatial brightness perceptions at photopic light levels are unrelated to the S/P ratio of the illumination and provide indirect support for Thornton's prime-color theory of vision.

We remain confident about the design and analysis of the reported experiment. However, we have high regard for Drs. Berman and Clear and in consideration of their concerns we will continue to study experimental design and analysis methodologies. Fotios and Houser are members of CIE technical committee TC1-80, which has the aim of evaluating experimental methods for measuring brightness and comprises specialists in lighting, vision and psychology.



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Author:Houser, K.W.; Fotios, S.A.; Royer, M.P.
Article Type:Report
Geographic Code:1USA
Date:Jul 1, 2010
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