1CIE– Commission Internationale de l’Eclairage or International Commission on Illumination; responsiblefor standards in this area. Now absorbed into the International Standard Organization, ISO.

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Luminous Efficiency Function, 2016James T. FultonNeural Concepts

https://neuronresearch.net/vision/ Memorialized @ DOI: 10.13140/RG.2.2.12060.95364

June 18, 2019

Abstract:

The Scientific, Medical and Engineering communities have lived with a Luminous Efficiency Function, LEF,previously the Visibility Function, V(λ), for human vision that has nothing to do with actual human vision.

In 1924, with a lack of a majority agreeing with regard to the available data on human vision, the CIE1 defined a, non-human, “Standard Observer.” Wright, one of the members of the Committee at that time, described the events invirtually comical terms in 1969. In the 1950's, Judd, also a member of the 1924 CIE Committee, formally objected tothe gross error in the 1924 Visibility Function. At the time, the CIE indicated it would be too disruptive to introducea new Standard. These failures to advance the state-of-the-art was over 65 and 40 years ago respectively. Nothingsubstantive has changed recently except the CIE has been integrated into the International Standards Organization.

The Theory of Biological Vision, including human vision, has greatly progressed since the middle of the 20th Century. It is now time to recognize a new LEF, R(λ) under both Photopic (daylight) and R’(λ) under Scotopic (after sunset)conditions. These functions bracket mesotopic conditions. Both a graphic and a set of mathematical equations forthis new LEF are presented. They compare the theoretical versus measured performance of four human eyes (using10 nm interference filters at intervals of 10 nm). The measured performance also identified a new Stiles-CrawfordEffect of the third kind.

The single mathematical equation describing the LEF also describes the Bezold-Brucke Effects and the PurkinjeEffects. This equation also introduces the Boltzmann-Helmholtz Equation of physical chemistry to the biologicalsciences. Because the measurements are functions of the photon flux/unit wavelength, it is mandatory that the protocol used in LEF measurements explicitly describe the spectrum of the stimulation, preferably 6500 Kelvin(Illuminant D65) and the state of spectral adaptation versus time for each subject examined. With a proper protocol,and data from a greater number of subjects, the average response will approach the theoretical model (labeled theIdeal Luminosity Function).

Keywords: Luminosity Efficiency Function, Photopic, Scotopic, Purkinje Effect, Bezold-Brucke Effect,Chromophores, Rhodonine, Boltzmann-Helmholtz Equation, Ideal Luminosity Function, visibility function.

Citations: In-text citations beginning with Section followed by a numeric string are to sections within Chapters (thefirst numeric value) in “Processes in Biological Vision,” PBV, by the author unless indicated otherwise. The work, of

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over twenty chapters, is available on the Internet in its entirety at http://neuronresearch.net/vision . Specific chaptersand sections can be located faster at http:/neuronresearch.net/vision/document.htm

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Table of Contents

Abstract: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.0 Introduction & Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.2 The Graphic of the Luminous Efficiency Function, 2016 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.2.1 Cautions in measuring the spectra of individual chromophores related to the LEF . . . . . . . . 61.3 The equations of the Luminous Efficiency Function, 2016 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

1.3.1 Cautions in implementing these equations of the LEF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91.3.2 Choices in increasing the peak of the LEF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.0 Background– Setting the stage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92.1 The Wright evaluation of the CIE 1924 Visibility Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92.2 Preview of the real versus imaginary (Standard) Photopic Luminous Efficiency Function . . . . . . . . . . 112.3 The need to employ narrow band spectrometry in order to identify visual phenomena successfully . . . 112.4 The need to employ statistically rigorous data collection and presentation standards . . . . . . . . . . . . . . 12

3.0 Exploring the biological mechanisms involved in the LEF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133.1 The signal processing within the retina & the brain leading to the LEF . . . . . . . . . . . . . . . . . . . . . . . . 133.2 All animals have retina with four chromatic sensory neurons (photoreceptors) . . . . . . . . . . . . . . . . . . 15

3.2.1 The theoretical spectra of the four chromophores of animal vision . . . . . . . . . . . . . . . . . . . 153.2.2 Examples of the measured tetrachromatic retina in humans . . . . . . . . . . . . . . . . . . . . . . . . . 20

3.3 All chromatic sensory neurons contain individual adaptation mechanisms . . . . . . . . . . . . . . . . . . . . . . 233.4 The lens as a limiting factor in spectral sensitivity of eyes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243.5 The impact of differential spectral adaptation on psychophysical measurements in chromaticity . . . . 24

3.5.1 Unusual precision is needed to evaluate Bezold-Brucke and Purkinje phenomena . . . . . . . 243.5.2 Unusual care in evaluating chromophore spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

4.0 Assembling the theoretical mechanisms important in defining the LEF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 254.1 An Ideal vs Measured human Luminous Efficiency Function, LEF . . . . . . . . . . . . . . . . . . . . . . . . . . . 254.2 The progression from photopic to scotopic vision in human LEF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

5.0 Proposed laboratory conformation program . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285.1 Protocol & laboratory measurement of the Luminous Efficiency Function, LEF . . . . . . . . . . . . . . . . . 285.2 A mosaic of potential outcomes of a measurement program . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295.3 Measurement of the individual spectral channels of the eye . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

2CIE (1978) Light as a true visual quantity: Principles of measurement. Publ. CIE No 41 (TC-1.4) Paris,FR: Bureau Central de la CIE

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1.0 Introduction & Results

1.1 Introduction

The Scientific, Medical and Engineering communities have lived with a Luminous Efficiency Function, LEF,previously the Visibility Function, V(λ), for human vision that has nothing to do with actual human vision. In 1924,with a lack of a majority agreeing with regard to the available data on human vision, the CIE defined a, non-human,“Standard Observer” and assigned the Committee’s best guess on the human spectral response to that Observer. Wright, one of the leaders of the Committee at that time, described the events in virtually comical terms in 1969.

The psychophysics community has for centuries attempted to define the luminous efficiency of the human eyewithout any regard for the physiology of the neural system. A multitude of superficial descriptions of the possibleorganization of that physiology have been put forth. Modern physiology, dating largely from the late 1950's provide adefinitive description of the neural system serving vision. As a result, a description of the luminous efficiency can beprovided that is both physiologicaly precise and compatible with the psychophysical data (when interpreted correctlybased on the physiology).

In the 1950's, Judd, also a member of the 1924 CIE, formally objected to the gross error in the 1924 VisibilityFunction. This resulted in the recognition of both the Judd data and the inadequacy of the 1924 function by the CIE,but not the issuance of a new standard. At the time, the CIE indicated it would be too disruptive to introduce a newStandard. In 1978, after further complaints that the 1924 Visibility Function was misleading, the CIE recommended afurther modification in the short wavelength region but refused to issue a new Standard2. These failures to advancethe state-of-the-art was over 65 and 40 years ago respectively. In 1976, the CIE largely abandoned any focus on theluminosity function in favor of a focus on the chromaticity function. It instituted a new empirical CIE LAB and CIELUV framework. Nothing has changed more recently except the CIE has been integrated into the InternationalStandards Organization.

The Theory of Biological Vision, including human vision, has greatly progressed since these early days. It is nowtime to recognize a new Luminous Efficiency Function under both Photopic (daylight) and Scotopic (after sunset)conditions.

The current Theory includes detailed values for all of the parameters associated with individual mechanisms relatingto the Luminous Efficiency Function as well as explicit mathematical relationships between these mechanisms. It isshown that a single equation remains correct for a wide range of illumination conditions bounded by the photopic andscotopic regimes. That single equation describing the Luminous Efficiency Function also describes the Bezold-Brucke Effects and the Purkinje Effects. It also introduces the Boltzmann-Helmholtz Equation of physical chemistryto the biological sciences. Because there are multiple laboratory protocols for measuring the LEF, and thesemathematical relationships are functions of the radiant stimulation of the individual photoreceptors of eachchrominance channel, it is mandatory that the individual protocol explicitly describe the spectrum of the stimulation,

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preferably 6500 Kelvin (Illuminant D65) and the state of spectral adaptation versus time for each subject examined.

It is now possible to define the theoretical response of the average human to visual stimulation to within limits of afew percent at 5 nanometer intervals across the visual spectrum. With a proper protocol, one or more subjects can becompared to the theoretical response. As the response of a greater number of subjects is averaged, the averageresponse will approach the theoretical model.

1.2 The Graphic of the Luminous Efficiency Function, 2016

Figure 1.2.1-1 presents the Luminous Efficiency Function, 2016, including its variants. It displays the photopicfunction, R(λ), using a solid line, the scotopic function, R’(λ) using a dashed line, and the mesopic regime betweenthese two conditionf for the complete human eye. It also shows the Aphakic (lens-less) human eye under photopicconditions using a dotted line. The Aphakic eye illustrates the actual sensitivity of the human retina. The BabuckeEye is the average data for four normal eyes obtained at 0.001 cd/m2 using a filter window of only 10 nm.

Figure 1.2.1-1 Ideal Luminosity Function with data overlays for both photopic and scotopic vision. The function islabeled “Ideal” because vision employs four chromophores chemically derived from retinol and employed in a specificconfiguration. The four normalized chromophores are shown at the bottom of the figure. The vertical scale does notrelate to these representations. The eyes of animal vision, as actually implemented may exhibit marginal differences(typically less than 1.5:1) from ideal performance. Only the photopic aphakic eye is shown. The long wavelength skirtof the aphakic scotopic eye follows the long wavelength skirt of the normal scotopic eye. The Babucke eye representsthe recent average response of four individuals.

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The data of Babucke, collected from four normal eyes using 10 nm FWHA interference type bandpass filters, isshown as an overlay on the Ideal Luminous Efficiency Function of the human eye. As noted in Section 2.2 of thispaper, the light source used by Babucke was unable to support truly photopic regime measurements. His datarepresents the average of four eyes operating in the mesotopic regime. In other respects, the data of Babucke exhibitsexcellent technique in capturing the actual characteristics of the human eye. The deviations from the Ideal LuminousEfficiency Function are described in the cited section.

The data from Tan, and Griswald & Stark, collected from aphakic human eyes is presented in Section 3.1.2 of thispaper. That data shows similar precision (but using wider filters of the time) and fits the Ideal Aphakic LuminousEfficiency Function quite well. The peak to mean variation in the amplitude of the measured aphakic data supportingthe LEF is less than 3:1 based on data collected in the 1980's.

1.2.1 Cautions in measuring the spectra of individual chromophores related to the LEF

There are multiple psychophysical methods of measuring the spectra of the complete visual spectrum as well as thespectra of individual chromophores. Wyzsecki & Stiles illustrated over a dozen methods in 1982 (Figure 1(5.2.5). These have converged to only three. The prominent methods are described as the direct method, the flicker methodand a step-by-step method. Even these can give very erroneous results unless all of the unstated parameters areaccounted for. Sperling (1958) compared the direct method and the flicker method and found major differences inthe results. There are two distinct schools within the psychophysical community. One school asserts the longwavelength channel peak is near 625 nm (Thornton et al). The other insists the long wavelength channel peak is near570 nm (Stockman et al.). Sharanjeet-Kaur et al. have shown that the results using the flicker method varies with thefrequency of the flicker. Figure 1.2.1-2 summarizes the discussion in Section 3.5 of this paper and the extensive datapresented in Section 17.2.5.3. As the flicker frequency approaches zero, the measured spectral peak in of the L-channel chromophore approaches asymptotically the true spectral absorption peak at 625 nm. At any flickerfrequency greater than three Hertz, the reported wavelength peak in the L-channel response decreases systematicallyuntil at 17 Hertz, it is equal to the wavelength claimed by the Stockman et al. school of 561 nm. At a flickerfrequency of about 30 Hertz, the two color samples fuse as expected due to the Critical Flicker Frequency, CFF,(Section 17.2.5.3.4) of the human eye; no difference between the two color samples can be perceived at any higherflicker frequency.

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1.3 The equations of the Luminous Efficiency Function, 2016

The generic equation describing the Luminous Efficiency Function can be assembled from the material in latersections of this paper. In its most general form, the equation employs two critical expressions relating to the stage 0optics of the eye; the first relates to the spectral transmission of the lens, L(λ), which is a variable dependent on theaxial thickness of the crystalline lens of the eye. In the equations below, the thickness can be assumed to be aconstant by restricting the discussion to mature eyes (nominally over 18 years of age). The second relates to thecumulative transmission of the optics after accounting for the Purkinje reflections at each optical surface of the eye.

Because all of the apertures of the outer segments of photoreceptor in the mammalian eyes share a common plane

Figure 1.2.1-2 CRUCIAL PROTOCOL ISSUE--Predicted long wavelength peak versus flicker frequency. The flickerfrequency plays a critical role in determining the perceived center wavelength of the long-wavelength chromophore whenusing the flicker method of spectral analysis. The perceived response of the L–channel is a function of two variables, thespectral wavelength and the flicker frequency, L(λ, freq).

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they necessarily only capture a fraction of the incident light. If the light was divided equally between the four typesof chromophores, the division would provide 25% of the light, Spat, to each photoreceptor type. There is no reliabledata on how the light is distributed between the photoreceptors at different locations within the retina. Therefore, it isexpedient to divide the light proportionally. This assumption defines the “Ideal” form of the Luminous EfficiencyFunction, LEF, defined here. If the distribution is not uniform, the values of the coefficients labeled, mX, can beadjusted to accommodate this distribution of light more appropriately.

Since the spatial distribution of individual types of photoreceptors may vary over the retina, it is expedient toconcentrate measurements on the 1.2 degree diameter of the foveola. This area is most likely to be the mostconsistent area between human retina. Expanding the area to even 2 degree diameter introduces a potentialerror due to “Maxwell’s spot,” a well documented variation in foveal uniformity (Section 17.3.1.8).

The mX coefficients for each spectral band are expected to be nearly the same for all properly dark adapted eyes whenexamined under threshold conditions. If they are not, the spectral performance of the eye will reflect this fact (as itappears to do in the average performance of four eyes reported by Brucke.

The most important terms are the voltages at the pedicles of each photoreceptor. These voltages represent the naturallogarithms of the cumulative photon flux captured by the outer segment of each individual photoreceptor.

Within the foveola of the retina, the individual voltages are processed separately in the signal processing of stage 2,and subsequently are encoded and propagated individually to the thalamus by the stage 3 ganglion neurons of theretina.

There is a critical feature of the Ideal LEF; that is shown in its simplest form for the long wavelengthphotoreceptors. Because of a minimum threshold energy requirement at the input to the Activa within eachphotoreceptor neuron, individual photons can stimulate the long wavelength chromophores quantum-mechanically, but the excitons so created within the liquid crystalline coating of all discs within a givenouter segment cannot stimulate the Activa. However, according to semiconductor physics, these individualexcitons can group in pair with sufficient energy to stimulate the Activa. In the LEF, this phenomenon isbest described by squaring the incident flux to represent both the initial stimulation forming excitons withinthe outer segments and then stimulating the Activa with these paired excitons to obtain the “effective”stimulus.

The mechanisms relating to the long wavelength channel are developed in detail in Section 12.5.2.4.

R(λ) = L(λ)CTransCSpatC [mUVCln(UV(λ)) + mSCln(S(λ)) + mMCln(M(λ)) + mLCln(L(λ)2)] Complete equation

RA(λ) = TransCSpatC [mUVCln(UV(λ)) + mSCln(S(λ)) + mMCln(M(λ)) + mLCln(L(λ)2)] Aphakic condition

RP(λ) =L(λ)CTrans.CSpatC [mUVCln(UV(λ)) + mSCln(S(λ)) + mMCln(M(λ)) + mLCln(L(λ)2)] Photopic regime

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RS(λ) =L(λ)CTransCSpatC [mUVCln(UV(λ)) + mSCln(S(λ)) + mMCln(M(λ))] Scotopic regime

The values of mX vary marginally with stimulus level (Section 17.3.4). The perceived shifts amount to ±5 nm ( lessthan ±1.0%) over 5 to 6 orders of magnitude in luminance (Section 17.3.4.4.1). The precision of ±1.0% is remarkablein a scientific field where ±20% or greater is a common criteria for a range of less than one order of magnitude.

1.3.1 Cautions in implementing these equations of the LEF

These equations can be implemented while recognizing that only positive values of the logarithms are appropriate andthe logarithms are implemented in the neural circuits of the photoreceptors. These neural circuits have only a limitedinstantaneous dynamic range of about 200:1. The dynamic range, associated with the actual liquid crystallinechromophores, is the key to the 107:1 dynamic range of the eye.

1.3.2 Choices in increasing the peak of the LEF

The technique of sharing spectrally distinct photoreceptors within the focal plane of the retina can be described as“chromatic diversity within the retina.” This technique is used in all animal eyes and all man-made electroniccameras. It requires additional signal processing, in some applications, to create a luminance channel from themultiple chrominance channels. There is an alternate called “chromatic diversity within the optical path.” Thistechnique was used in the now largely archaic photographic film of the 19th and 20th Centuries. It is currently used inbroadcast television cameras. However, signal processing of one type or another is still needed to create a luminancechannel. Only one 4-color television camera was ever developed with a separate luminance and three chrominancechannels; the RCA TK-45. It was a commercial failure and was abandoned. The commercial printing industryoccasionally uses a 4-color printing process, rather than the normal 3-color process, at extra cost. Electronic camerasusing chromatic diversity within the optical path, requiring a five surface pentaprism, can achieve an effective peakLEF in the 80% range across the visible spectrum compared to the 20% range in retinal diversity. The pentaprism ismade from two dichromic prisms with their individual separation lines at ~494 nm and ~570 nm .

2.0 Background– Setting the stage

There is a gross difference between the spectral response of the actual human eye and the CIE Visibility function,V(λ), Standard of 1924. This function was incorporated into The CIE imaginary “Standard Observer” promulgatedby the CIE in 1931 and still supported in 2016. This difference will be discussed in Section 2.2 after presenting theremarks of Wright and others in Section 2.1. The CIE did recognize and “recommend” modification of the function in1951 and 1978. These modifications were not incorporated into a new “Standard.” 2.1 The Wright evaluation of the CIE 1924 Visibility Function

In the 21st Century, the accuracy of the Luminous Efficiency Function is of great importance of future research andapplications of the LEF are to be fruitful. Wright, one of the original laboratory investigators, had some important

3Wright, W. (1969) The Origins of the 1931 CIE System Color Group Journal (G. Britain) As reproducedin Boynton, R. (1979) Color Vision NY: Holt, Rinehart Appendix, Part II

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remarks on this subject in 19693 when he suggested the accuracy of the values at a given wavelength for the visibilityfunction were probably in error by a factor of 10 and in fact no measurements were incorporated into the standard forwavelengths less than 400 nm (Section 17.2.3.6.5).

“The CIE Colorimetry Committee recently in their wisdom have been looking at the old 1931observer and have been smoothing the data to obtain more consistent calculations with computers. This has also involved some extrapolation and, in smoothing, they have added some additionaldecimal places. When I look at the revised table of the x (bar), y(bar), z(bar) functions, I am rathersurprised to say the least. You see, I know how inaccurate the actual measurements really were.(Laughter from audience) Guild did not take any observations below 400 nm and neither did I, andneither did Gibson and Tyndall on the V(8) curve, and yet at a wavelength of 362 nm, for example,we find a value y(bar) of 0.000004929604! This, in spite of the fact that at 400 nm the value ofy(bar) may be in error by a factor of 10 (Laughter).”

Clearly, interpolation, and extrapolation, of crude data gives grossly erroneous results.

Although not addressed significantly in the early literature, there has also been a problem related to the spectrum ofthe light used in vision experiments. The Planck Radiation Formula was only promulgated within the theoreticalphysics community in 1900. It appears that most of the experimenters working in vision up through at least the1930's lacked an adequate understanding of the importance of the spectral distribution of light in their experiments. They were primarily concerned with the total integrated energy, which might be called the photopic energy, enteringthe visual system and typically used lamps with a color temperature in the 2400-2800°K range. The specific problemrelates to the relationship between the amount of energy radiated by a source per unit spectral bandwidth versus thenumber of photons, the photon flux, radiated by that same source per unit bandwidth. As late as 1963, the Committeeon Colorimetry of the Optical Society of America (erroneously) defined an equal energy spectral distribution as onecharacterized by equal flux per unit wavelength interval. Wyszecki & Stiles gave a correct interpretation of thisrelationship on page 4 of their 1982 work. The term “equal-energy” source began appearing in the vision literature inthe 1950's. The term was frequently shown as above in quotation marks and was seldom if ever defined rigorously. In reading the articles of that period, the typical experimenter was using a nearly fixed spectral bandwidthspectrometer to filter the luminance of a commercial tungsten lamp. The goal was to control the total integratedenergy entering the eye in accordance with Stefan’s Law, rather than concern themselves with the uniformity of theflux entering the eye in accordance with the more detailed Planck Distribution Law. This lack of definition leads toconsiderable difficulty in correlating the early data to the real world and any theory.

As a result, the current CIE Standards represent the average values obtained from smoothed data collected withinadequate light sources and interpolated to a precision exceeding that of the original data by ten to one.

The problem is actually worse if Wyszecki & Stiles are correct on page 395. Quoting, “Thevalues adopted in 1924 were those suggested by Gibson and Tyndall (1923) who composed asmooth and symmetrical V(λ)-curve from the data cited above. The final result was not anaverage of the experimental data, but a weighted assembly of the different sets of data. From

4Babucke, H. (2007) private communications (See Section 17.3.7.2)

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400 to 490 nm, the V(λ)-curve represents roughly the results of Hartman (1918); from 490 to540 nm, those of Coblentz and Emerson (1918); from 540 to 650 nm, those of Gibson andTyndall; and above 650 nm, those of Coblentz and Emerson (1918).”

It is also noteworthy that there have been fundamental revisions (greater than 7%) in the relationship between theCandela and the Watt during the period 1920-1970.

Section 17.1.5.4 describes the problems that surfaced leading to the CIE Visibility Function being redefined in twoversions, the photopic (daylight) and scotopic (after sunset) functions. The new Scotopic LEF was defined in 1951 asthe function, V’(λ).

2.2 Preview of the real versus imaginary (Standard) Photopic Luminous Efficiency Function

The discrepancies between the recent measurements of the LEF and the CIE Standards are so large as to question theuse of the imaginary “Standard Observer” for even pedagogical purposes. The difference is shown in Figure 2.2.1-1. The CIE 1924 V(λ) is reproduced from Wyszecki & Stiles (1982, pg 395). The modern LEF was obtained byBabucke and colleagues in 20074 provided the most precise measurements of the LEF using the most demanding testprotocol and best available instrumentation of the time. After carefully eliminating all of the internal reflections in histest equipment, precise spectra were obtained for five eyes of five people using 10 nm FWHA interference filters. Inthe process, Babucke isolated a new third type of Stiles-Crawford Effect, SCEIII (Section 17.3.7.6).

Gunter Wyszecki has also provided his own LEF showing a short wavelength response significantly higher than theCIE 1924 V(λ) predicts (Wyszecki & Stiles, 1982).

This figure confirms Wright’s assertion, noted above, forall wavelengths shorter than 0.47 nm, the CIE 1924V(λ) function is in error by more than an order ofmagnitude.

Wyszecki, a Don of the visual sciences, was very criticalof much of the CIE framework in 1982 (Section 17.1.9).

2.3 The need to employ narrow bandspectrometry in order to identify visualphenomena successfully

A large number of the spectral measurements reported inthe literature were acquired with inadequatespectrometers. This can profoundly affect theexperimental results obtained as shown in Figure 2.3.1-1from Wolken. The caption was transcribed exactly. He

Figure 2.2.1-1 Comparison of measured human eye LEFand the CIE Standard Observer of 1931. The StandardObserver incorporated the CIE Visibility Function, V(λ) of1924. It does not incorporate the Judd modification of 1951.

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Figure 2.3.1-1 Examples of spectral recording precision.(a) Absorption spectrum of frog rhodopsin at unspecifiedspectral resolution. (b) Absorption spectrum at 5 mμintervals from 460 to 530 mμ. From Wolken (1966)

shows two spectra of a chromophore from a frog. The differences are startling. The two spectra taken withspectrometers of 30 nm and 5 nm resolution are hardly comparable. He gives little detail but it appears the twowaveforms have been scaled since (b) cannot be positioned correctly if it was to be represented by (a) when smoothedby a 30 nm. filter. There is virtually no detail in the 30 nm. recording. In the 5 nm recording, the central peak is thatof the M-channel chromophore and the adjoining peaks are both secondary perceptions related to the Bezold-Bruckephenomena (discussed below).

The CIE luminous efficiency function, CIE LEF, for both photopic and scotopic conditions are generallycompatible with smoothing by a 30 nm wide window (they show no detail at narrower intervals). The CIELEF, after approval as Standards, were then interpolated at 1 nm intervals. Neither the gross CIE LEFgraphical responses or the interpolated numerical values show any resemblance to the actual spectralsensitivity of the human eye.

A spectrometer with a bandwidth of less than or equalto 10 nm. is necessary for modern laboratory work invision. It must also be capable of reaching photopicintensity levels at a color temperature of D65 for humanvisual measurements and D70 for tetrachromaticmeasurements in aphakic humans and other smalleranimals.

2.4 The need to employ statisticallyrigorous data collection and presentationstandards

Research and applications related to vision have longignored the statistical requirements on the data used toquantify the accuracy of the data upon whichhypotheses are based and decisions on future directions to be taken in the field. These requirements have frequentlybeen depracated based on the limited group of cohorts available to the investigator. In this situation, it is even moreimportant to explicitly note the size of the cohort used in the final data collection along with an expression of theaccuracy of the data, frequently an R2 or p value that must be associated with a cohort size or other dimension.

Statistics, being primarily a specialty of mathematics, has a long history but only a superficial applications within thefield of psychophysics, and of physiology, related to vision. Pearson and colleagues were the first widely recognizedinvestigators into the statistical parameters of data sets (ca. 1880). Their work was not integrated into biophysicalexperiments until much later.

While statistical precision has long been a cornerstone of physics, and it is now a required element of anyexperimental program in the behavioral sciences, it has yet to enter the field of psycophysics to an appropriate degree. Section 1.3.2.3.1 reviews this subject, and the progress made within the behavioral and educational fields. A criticalportion of that review is the introduction of a more precise “effect-size” parameter that is now part of the academicbehavioral science literature. It allows an analyst to relate the data associated with various cohort sizes used bydifferent investigators more precisely than previously.

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“Classes of effect-sizes include standardized differences (e.g., the experimental group mean minus the controlgroup mean, divided by the estimated population standard deviation). Alternatively, because all analyses arecorrelational (cf. Knapp, 1978; Thompson, 1991), variance-accounted-for effect-sizes can be computed in allstudies.”

In terms of the Luminous Efficiency Function, there is no available “control group mean” or “population standarddeviation” of adequate spectral precision. The alternative is a detailed and precise theoretical model that can betreated as the control group mean with a population standard deviation of zero. The model would contain detailedresponses that include expected deviations from the ideal case that would prevent investigators from making patentlyfalse hypotheses based on their data from their small experimental group. Such a model is presented below.

3.0 Exploring the biological mechanisms involved in the LEF

To develop a theory-based Luminous Efficiency Function, it is necessary to understand the operation of allphysiological elements of the visual modality that are involved. Fortunately, the visual modality like all sensorymodalities operate in a constant amplitude signal processing mode after the stage 1 signal detection process.

There are a few parallel signal paths associated with the Alarm Mode found incorporated in many sensorymodalities. These paths are not of concern here.

This mode of operations simplifies the still complex mechanisms required to develop a theoretical LEF. Section 3.1describes the functional elements of stage 1 that are critical to developing the LEF, specifically the elements involvedin the formation of the synthetic brightness signal, R( λ) used within the visual modality. The term brightness is usedto differentiate the perceived signal within the neural system from the luminance signal associated with the externalstimuli of vision. The perceived signal is largely independent of the intensity of the luminance signal as illustrated inSection 2.1.1.1, Figure 2.1.1-2.

3.1 The signal processing within the retina & the brain leading to the LEF

An investigator must have a well grounded understanding of the physiology he plans to investigate as well as a clearunderstanding of the limitations of his test equipment before preparing a test protocol and proceeding to thelaboratory. Otherwise, his experiments can only be described as exploratory science. With adequate preparation, theinvestigator will be able to interpret his data better, and define the controlled parameters along with his results.

The interface between Stage 1 and Stage 2 circuitry in Chordata is shown in Figure 3.1.1-1 along with the lens of thephysiological optics, Stage B. [17.2-17.4]. This figure is developed in greater detail in Section 11.6.4.4. Threecrucial situations are illustrated. First, the formation of multiple signaling channels at the output of the photoreceptorcells is described. Three chrominance channels, one luminance channel, and one appearance channel are described. The calculations performed in and the resulting performance of the appearance channel are unique. They will bedescribed in Section 3.2. Second, the subdivision of the photoreceptor cells into their functional elements is shown. Finally, a graphic representation of the signals carried by the individual channels at the location of the S-plane of theretina is presented. This figure shows that the theory presented here is an extension of the earlier zone theory. Itexpands the old Young-Helmholtz theory by adding the ultraviolet channel (ultraviolet light was unknown in Young’stime and largely a curiosity in Helmholtz’s time). It also introduces a series of color difference channels reminiscent

14

Figure 3.1.1-1 (Color) The luminance, chrominance and appearance channels of the eye of tetrachromats and aphakichumans. The spectral response in the O-, P- and Q- channels are shown as sinusoidal for illustration. The UVphotoreceptor cells are known to be functional in humans of all ages. Research is ongoing to determine if the signal inthe O-channel of the aphakic human is typical of tetrachromats. If it is, an aphakic human will be able to tell us what“color” other animals perceive in the ultraviolet.

of Hering. However, the difference channels are derived from the spectral channels and are defined in terms of theUV–, S–, M– and L–channel peak wavelengths rather than some other arbitrary colors. The differencing results inthree “opponent channels” rather than the two of the Hering school. They are labeled the O–, P– and Q–channels asshown. These are the chrominance channels of chordate vision.

There is also a summing channel, labeled the R–channel. This is the luminance channel of chordate vision. Notecarefully, there is no achromatic (or rod) sensor channel in this configuration. All of the necessary information isacquired from the spectrally selective sensor channels. This figure shows a familial resemblance to many otherfigures in the literature (except for the addition of the ultraviolet channel). The functional difference will be discussedafter discussing the elements of the photoreceptor cell.

3.2 All animals have retina with four chromatic sensory neurons (photoreceptors)

For largely historical reasons, dating from before the discovery of ultraviolet light, the human eye has been assumed

5Fulton, J. (1968) The structure and mechanisms of vision CBS Laboratories, Inc. (Unpublished)

6Fulton, J. (1985) The perception of luminance under various states of adaptation, Hughes Aircraft Co.(unpublished)

7Mees, C. & James, T. (1966) The theory of the photographic process, 3rd ed. New York: Macmillan, pg 205

15

and widely taught, that it employs only three types of chromatic sensory neurons. This is in spite of the currentknowledge that a wide variety of mammals, as well as fish and birds exhibit four distinct types of chromatic sensoryneurons. It is also well documented that aphakic (lens-less) human eyes also exhibit four distinct types of chromaticsensory neurons.

3.2.1 The theoretical spectra of the four chromophores of animal vision

Until Platt developed the theory of theory of light absorption by polyenes and porphyrins in 1956, there was onlyspeculation concerning how the retinoids absorbed light in the configuration of the photoreceptors of biologicalvision. His theory, when combined with the broad experience of the chemists at Eastman Kodak in creatingchromophores for photographic film provided the answer to the question. The combination showed that the retinoidscontaining two oxygen atoms, the Rhodonines formed a series of four chromophores with unique spectral absorptionproperties along their molecular axis when present in a liquid crystalline state. These retinoids readily formed amonolayer on a wide variety of substrates. The absorption along their molecular axes were well described by theBoltzmann–Helmholtz Equation of physics. Section 5.5 provides a complete review of both the chemistry andmechanism of interest here.

The equations and their parameters for the spectra predicted by this work for a body temperature of 310 Kelvin aregiven in the following Table 3.1.1-1 (modified from the earlier Table 5.5.10-1 in PBV). The precise values wereobtained by comparing a large amount of data in the literature as well as the ability of these values to accuratelypredict the precise parameters of the Ideal human luminosity functions under a range of spectral adaptations. Theequations do not exhibit a term describing a “peak wavelength” for each chromophore. The peak values shown arethe geometric mean, the square root of the product of the half-amplitude wavelengths.

The resulting equation for the absorption peaks of each Rhodonine in the series is then given by the equation8p=0.095n + 0.152 microns5 ,6, where n is the number of conjugated isoprene units incorporated between the polaratoms of the chain. The bands are separated by 0.095 +/-0.005 microns which is a typical spacing for thesehomologs7. These values are believed to be accurate to three digits based on the flat spectral response across theentire spectrum of the human retina graphed as the Ideal Luminous Efficiency Function, LEF. The ultravioletspectrum is only observed in aphakic human subjects.

16

TABLE 3.1.1-1Tables of Parameters based on the goal of a uniform sensitivity across the spectra of the retina

for humans in-vivo at 310 degrees Kelvin (37 degrees Celsius) Updated to May 29, 2019

The Helmholtz-Boltzmann Equation (based on Fermi-Dirac Statistics)

a

KT KT

x x

x xs xl x

( )

exp exp

λ

λ λ λ λ

=

+ −⎛⎝⎜

⎞⎠⎟

⎡

⎣⎢

⎤

⎦⎥

⎡

⎣⎢⎢

⎤

⎦⎥⎥

⋅ + −⎛⎝⎜

⎞⎠⎟

⎡

⎣⎢

⎤

⎦⎥

⎡

⎣⎢⎢

⎤

⎦⎥⎥

1

11 1 1

11 1 1

where x can be replaced with u, s, m, or l to indicate the spectral band of interest. The values of λxs and λxl are takenfrom the appropriate row of the following table to define the short and long wavelength half-amplitude wavelengthsfor that band.

Receptor Spectrum Res. chain λXS Mean λXL ResonanceLabel length nm. Wavelength nm. Factor Q

Rhodonine(11) au(8) 2 305 342 383 4.4

Rhodonine(9) as(8) 3 405 437 474 6.3

Rhodonine(7) am(8) 4 508 532 554* 11.3

Rhodonine(5) al(8) 5 599* 625 653 11.5

The difference between the long wavelength half-amplitude point of one chromophore and the short wavelength half-amplitude point of the next longer wavelength chromophore varies between 22 and 54 nm in this table. A differenceof 30 nm between λML and λLS is mentioned in Kraft, et. al. (1990) based on Loppnow et. al. (1989), but withoutfurther substantiation. Their work was not comprehensive, focused on Opsin rather than the chromophores, and isnow archaic.

K = Boltzman’s constant/(Planck’s constant x Speed of light)K = 0.0000862 electron volts/degree Kelvin, T = 310 temperature in degrees Kelvin, ˆ KT = 0.0267

From file in MathCad; a_four_ln_sum_spectraZ_flat.mcd

The resonance factor, Q, can be used as a guide to compare the laboratory results of various experimenters. It iscalculated as the quotient of the “peak wavelength” divided by the difference between the wavelengths of the twohalf-amplitude points for the spectrum of each chromophore. When computing the precise spectral characteristics ofthe chromophores of vision as found in laboratory experiments (that occurs in Chapter 16 & 17) the appropriate Qwas determined.

The absolute value of the long-wavelength parameter for Rhodonine(5) is known precisely from the work of Sliney,

8Sliney, D. Wangemann, R. Franks, J. & Wolbarsht, M. (1976) Visual sensitivity of the eye to infrared laserradiation. J. Opt. Soc. Am. vol. 66, no. 4

9Wald, G. (1964) The receptors of human color vision. Science, vol. 145, pg. 1009

10Wolbarsht, M. (1976) The function of intraocular color filters. Fed. Proc. vol. 35, no. 1, pp 44-50(caption to figure 3)

17

et. al.8 in defining the human eye response in the infrared spectra. They showed that the long wavelength half-amplitude point for Rhodonine(5) matches the human visual data over a range of 13 orders of magnitude, aremarkable result of their test accuracy and this theory. There is a slight deviation between the measured andpredicted sensitivity in the region beyond 650 nm that will be accounted for in Section 17.2.2.2. It has been exploredby Brindley. It is explained by the change in chrominance in this wavelength region unrelated to the actualluminance.

The difference in wavelength between the short wave parameter of Rhodonine(5) and the long wavelength parameterof Rhodonine(7) is known precisely because of the sensitivity of the Purkinje Shift to this difference. Similarly, thedifference between the short wave parameter of Rhodonine(7) and the long wavelength parameter of Rhodonine(9) isknown precisely because of its effect on the visual spectrum in the region of 495 nm, the Bezold-Brucke phenomena. These dependencies will be discussed in Section 15.5. The short and long wavelength parameters for Rhodonine(9),as well as the very flat top of the spectrum, are known quite precisely from the work of Wald9. The short and longwavelength parameters of Rhodonine(11) have been confirmed from the composite spectrum of aphakic humans. SeeSection 17.3.3. The half-amplitude full width of these absorptions are in good agreement with the estimates ofWolbarsht when the broader peaks of Fermi-Dirac statistics compared to Gaussian statistics are recognized10.

Figure 3.2.1-1 illustrates the spectra for the Rhodonines as presented in the above table.

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A particularly important parameter is given by the half-amplitude for the two skirts of each of these waveformsbecause of the way these chromophores are employed in vision. If the adjacent skirts cross at their half-amplitudevalues, the overall spectral response of the eye is as shown in Frame C; It is flat across the spectra and truncated bythe absorption of the lens as documented below. If the crossings occur below the half-amplitude level, the overallresponse will show dips in the region of the crossings. Conversely, if the crossings occur above the half-amplitudevalues, the overall response will show rises in the response at these locations. The effect of differential spectraladaptation in the chrominance channels can have additional effects discussed below. The reason for the aboveassertions is the manner in which the spectral stimulation is processed by photoreceptors of that type. Thephotoreceptor neurons act as a logarithmic converter between the photon flux stimulation and the voltage at thepedicle of the neural axon.

Figure 3.2.1-2 shows the overall spectral sensitivity for the Ideal Luminous Efficiency Function, LEF, defined by thetable above. Changing any of the half-amplitude wavelengths by even one nm introduces a significant Bezold-Brucke

Figure 3.2.1-1 The theoretical spectra of biological, including human, vision. The spectra are shown on both alogarithmic, A, and linear, B, vertical axes for convenience. Although the linear axis is more familiar to most, thelogarithmic axis is more relevant to the theoretical characteristics of the chromophores. The absorption of the human lensis shown by the dashed blue lens on the left of each frame. The absorption is negligible at these scales for wavelengthslonger than 0.4 microns. The horizontal line at 0.5 is particularly relevant. Frame C characterizes where the skirts ofadjacent spectra cross. See text.

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or Purkinje Effect. This suggests the first three digits of the values given are correct for the Ideal LEF To achieve theequal number of photons per unit wavelength, within 10 percent across the spectal band, a thermal source of 7,000Kelvin, D70, is required. To confirm only the normal (phakic) human eye, a thermal source at a color temperature of6500 Kelvin, D65, is required to achieve this uniformity of stimulation across the spectrum.

The broadband spectral signal passed to the brain over the R-channel provides the basis of the photopic and scotopicspectral response. The R–channel signal is created by combining the logarithmic signals from the individualphotoreceptors according to the equation,

R(λ) =L(λ)CTransCSpatC [mUVCln(UV(λ)) + mSCln(S(λ)) + mMCln(M(λ)) + mLCln(L(λ)2)]

The value of the terms, mUV, mS, mM & mL are functions of the state of adaptation of the photoreceptors of a givenspectral sensitivity, and are sensitive to the integral of the product of the prior stimulus and time (Section 7.2). Thespectral transmission coefficient, L(λ), of the lens of the eye varies with species and may vary with the age of aspecific species (Section 2.4.7).

As the values of the mX coefficients, vary individually, the relative amplitudes of the spectral responses in Frames A& B of the above figure vary. That change causes further complication in the spectral responses caricaturized inFrame C.

Figure 3.2.1-2 Ideal Luminous Efficiency Functions, LEF at the human retina, assuming equal area for each spectralchannel on the surface of the retina and equal aperture area for all types of photoreceptors. Obtained by summing thenatural logarithms of the individual chromophores using the wavelengths in the accompanying table. The skirts arestraight lines in semilog coordinates. The LEF is quantum-based and not thermal energy-based. In order to confirm thiscurve in the laboratory, the stimulus must maintain equal photons per unit wavelength across the spectrum.

20

The equation between the brackets corresponds to the spectral response of the biological retina, and isequivalent to the tetrachromatic visibility function of the aphakic human eye shown in Figure 3.2.1-2 abovewhen appropriate values for the coefficients are used.

The cumulative reflectance within the optics of the eye, Refl, amounts to about 5%, resulting in a transmissionefficiency, Trans, of about 95%. These reflections, known as Purkinje reflections in ophthalmology, are the majorlimitation on the overall performance of the biological eye within a specific spectral band. The outer segments of thephotoreceptors consist of a waveguide filled with “spaced” chromophoric absorbers; the result is an essentially 100%photon absorption of the spectrally selected light.

A unique problem is encountered when using interference filters within the optical test equipment. Interference filters can introduce out-of-passband transmission/reflectances that are sensitive to the tiltbetween the filter and the optical axis of the test set. Bruck encountered these early in his test program. Thesharp notch at 0.54 microns, shared in the data from all of his subjects, may be due to this anomaly. Its narrowcharacter cannot be explained by any other theoretical consideration.

The biological eye also suffers from a loss in efficiency, Spat, due to the spatial distribution of the chromaticallysensitive photoreceptors. This loss is not well understood because of the variation in chromatic types ofphotoreceptors with position in the retina. Lacking more specific information, it can be estimated at 25% to 30%efficiency for each chromatic channel.

Note the presence of the square term associated with the long wavelength term in the above equation. This term isrequired to account for several crucial factors related to the physical chemistry of the long wavelength photoreceptorneurons. Because of the minimum threshold energy (between 2.0 and not more than 2.34 electron volts) of theActiva, the transistor like amplifier present in each photoreceptor neuron, to achieve spectral sensitivity beyond awavelength of between 570–610 nm, it is necessary to sum the energy from two photons in order to stimulate theL–channel photoreceptor neurons. This requirement is expressed mathematically by the square term in the equation. In the performance of the photoreceptors of the biological eye, this requirement accounts for the conversion fromphotopic to scotopic vision as the photon flux is reduced in intensity in the spectral region beyond a wavelength of570–610 nm.

As the stimulus level in the L–channel is reduced, the amplitude of the L-channel response falls faster than the otherspectral channels and becomes negligible at Scotopic light levels. The result can be clearly seen in Frame C of theprevious figure. The long wave spectral limit of the composite spectrum becomes defined by the long wavelengthskirt of the M-channel instead of the long wavelength skirt of the L-channel.

3.2.2 Examples of the measured tetrachromatic retina in humans

Surgery to remove the lens of the human eye has frequently been necessary in the past. It has been found that thehuman eye exhibits significant ultraviolet sensitivity after such an operation (in the absence of a prosthetic that mayitself absorb in the ultraviolet). Griswold & Stark have provided excellent spectral data on such eyes down to a

11Griswold, M. & Stark, W. (1992) Scotopic spectral sensitivity of phakic and aphakic observers extendinginto the near ultraviolet. Vision Res. vol. 32, no. 9, pp 1739-1743

12Tan, K. (1971) Vision in the ultraviolet. Ph. D. thesis. Utrecht, Holland: Rijksuniversiteit te Utrecht, alsoUniversity of Missouri (Columbia) Library, call no. QP481.T16. Also available in a review by Stark, W. & Tan, K.(1982), Photochem. Photobiol. vol. 36, pp 371-380

13Boettner, E. & Wolter, J. (1962) Transmission of the ocular media. Invest. Ophthal. Vis. Sci. Vol. 1, pp776-783

14Van den Berg, T. & Tan, K. (1994) Light transmittance of the human cornea from 320 to 700 nm fordifferent ages. Vision Res. vol. 34, no. 11, pp 1453-1456

21

wavelength of 315 nm11. Figure 3.2.2-1 presents their data, and that of Tan12, in the context of this work. Alsoshown are the set of theoretical absorption spectra defined in Table 3.1.1 of this paper. This Table updates an earliertable in Section 5.5.10.

The one data set is labeled as “with B & W.” This notation refers to the studies by Boettner & Wolter of theabsorption of the other elements of the physiological optical system, except for the lens13. The Tan data is also “withB & W.” A recent paper by Van den Berg & Tan provide additional data relative to the Boettner & Wolter paper. While published in 1994, it reports on the mining of data collected in 1967-6814. It is unknown whether Boettner &Wolter included the absorption and scattering within the neural layer of the retina (the field lens of the physiologicaloptics, and potentially the source of macular absorption).

22

Figure 3.2.2-1 Comparison of aphakic vision and the theoretical scotopic model. The data curves were normalized withrespect to each other by Griswold & Stark. The Ideal Scotopic LEF overlays the data at an arbitrary relative response.The data points were acquired under Scotopic illumination levels (no long wavelength sensitivity). The four chromophoreabsorption curves are shown normalized separately as a reference. The skirt cross-over points are an order of magnitudelower than the peak amplitudes. B & W; Boettner & Wolter. See text. Data points from Griswold & Stark, 1992.

Griswold & Stark made considerable effort to perfect and calibrate their test instrumentation. However, there are anumber of theoretical problems with their analytical procedure. First, they discuss their work in terms of scotopicsensitivity measurements. However, they use a stimulus that is only 38 minutes in diameter. This differs from theCIE suggested diameter. The CIE has adopted a stimulus diameter of two degrees for photopic measurements and tendegrees for scotopic measurements. Their figure 1 shows the nominal CIE scotopic luminosity function overlaid onsome of their data. As shown in [Figure 17.2.2-9], the difference between using the CIE scotopic and photopiccharacteristics would be small at this wavelength relative to their ordinate. Their figure 3 shows the net absorption ofthe lens based on their experiments. This data will be discussed in the next section. It shows a maximum absorptionof slightly over 4 log units (a transmission of only 0.01% at 360 nm). This peak wavelength is consistent with otherliterature.

Second, they attempt to relate the absorption in the region of 350 nm to the cis-peak in the dilute isotropic absorptionpeak of the retinoids (not actually limited to the cis-peak of rhodopsin) in their results section. In their discussionsection, they back off from this position and posit the possibility of a separate UV sensitivity mechanism (based onother work within their group). As seen from the above figure, the anisotropic UV absorption of Rhodonine(11) whenconfigured as a liquid crystal within the Outer Segment of the photoreceptor cells is a much better match to the datathan an isotropic cis-peak. Furthermore, the literature does not explicitly define a cis-peak for the retinoids associatedwith vision (See Chapter 6).

15 Hecht, S. Haig, C. & Chase, A. (1937) The influence of light adaptation on subsequent dark adaptation ofthe eye. J Gen Physiol Vol. 20, pp. 831-850

23

The graphic insets for the chromophores of vision portray the precise values in Table 3.1.1 of this paper.

The small zebrafish, Danio rerio, a small freshwater fish (<6 cm.), exhibits excellent vision in the ultraviolet (Section1.7.2.3.2) because of its small crystalline lens. The scotopic LEF of the zebrafish overlays both the Ideal scotopicLEF (dashed line) and the aphakic human eye data points in this figure very well.

3.3 All chromatic sensory neurons contain individual adaptation mechanisms

The phenomenon of adaptation to stimulus level in order to preserve a near constant signaling level within the neuralsystem is critically important in biological vision. It is accomplished within the outer segments of the photoreceptorneurons. It is colloquially known as bleaching and is a physical chemistry phenomenon. It involves the fact that,when the individual chromophores are stimulated by photon absorption, they become transparent to furtherstimulation until they are returned to their ground state electronically. This occurs at the junction between the liquid-crystalline chromophores covering the discs of the outer segment and the dendrites of the photoreceptor neuron(frequently labeled microtubules by cytologists). See Section 4.3.2 for information on the internal structure of thephotoreceptor neurons.

The mechanism of adaptation is a consequence of the Excitation/De-excitation mechanisms used in all sensoryneurons (with slight variations in time constants). The mechanism is defined by the E/D Equation (previously the P/DEquation when limited to the vision modality) of Section 7.2.4. The transient performance of this equation, itsadaptation performance is described in Section 17.6 It is important to note there is a “light adaptation” as well as a“dark adaptation” process. The light adaptation phenomenon is very fast compared to the dark adaptationphenomenon and is seldom of major interest, except for the loss of dark adaptation within one second. Crawfordcaptured the complete character of adaptation in 1947 (Section 17.6.1). However the dark adaptation portion of thisphenomenon was mis caricaturized shortly thereafter as a two-step mechanism involving exponential functions,which it is not! The mechanism is a characteristic of the mathematically continuous third order differential E/DEquation. The temporal solution of a third order differential equation involves the product of an exponential ana sinefunction, an “exposine” (Section 17.6.2). It is similar to a damped sinusoid, but in this case the pitch of the sinusoidis longer than the time constant of the exponential.

The data points shown in Figure 3.3.1-1 are reproduced from one of the most widely published graphs of Hecht, et.al15. Solving the E/D Equation in the temporal domain results in the two smooth curves shown. The solid curverepresents only the exponential component of the solution to the third order differential equation. It clearly shows theunique shape of the reciprocal of an exponential function with a time constant of thirty minutes. The dashed curveshows the complete solution to the differential equation. It shows the product of the damped sinusoid and theexponential, called hereafter the exposine function. By selecting the time constant and period of the waveforms, thedata points can be matched very well. The precision of the model is sufficient to highlight the unexpected decrease insensitivity (upward excursion of the data points) in the recorded data near 35 minutes. For the conditions Hechtdefined, the time constant of the exponential function is 30minutes. The period of the sinusoidal function is 12minutes. The modulation of the exponential by the sinusoid is approximately 25%.

16Sharanjeet-Kaur, (no initial). Kulikowski, J. & Walsh, V. (1997) The detection and discrimination ofcategorical yellow Ophtha Physiol Opt vol 17(1), pp 32-37

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Figure 3.3.1-1 Dark adaptation curve of a human observer,following a 2 minute exposure to an adapting light of 4 x 105

td. The solid and dashed lines are from this theory. Thedotted line indicates the value of the time constant of anexposine plotted as a reciprocal. The multiples of πindicate phase angles of the sine component. The datapoints are from Hecht, et. al, 1937. The test spot was violet,had a diameter of 3 degrees, a duration of 200 ms, and fell30 degrees from the fovea.

Spillmann & Conlon captured the true character of thedark adaptation mechanism in 1972 but did notdocument it mathematically in the absence of the E/DEquation (Section 17.6.1.1.4).

3.3.1 The performance of the adaptationmechanism prior to spectral measurements

When attempting to measure the spectral response of thebiological eye, it is important that its state of adaptationbe carefully controlled. The eye should preferably bedark adapted for at least 30 minutes, with no exposureto a direct light source–a bare light bulb, a pilot light ona piece of test equipment, the screen of a cellphone oreven an LED as part of a display. The dark adaptationstate can be destroyed with stimulation from a directsource for less than one second.

3.4 The lens as a limiting factor in spectralsensitivity of eyes

Section 2.4.7 discusses the lenses of a variety of speciesand how it limits the short wavelength performance of their eyes.

3.5 The impact of differential spectral adaptation on psychophysical measurements inchromaticity

Sharanjeet-Kaur et al. have also explored the spectral responses of vision at slow (1 Hz) and 25 Hz flicker rates16. Their work shows additional subtleties of the visual process and bridges the chasm between the “fundamental spectra”of the Stockman school and the “spectral sensitivity curves” of Foster & Snelgar and Thornton (and Stiles) and thiswork. Their graphic is shown above, in Section 1.2.1 of this paper. Further discussion of how the flicker frequencyaffects the results when the flicker-method of spectral analysis is used in vision (Section 17.1.9 and Section 17.1.10). The data collected by Stockman et al. using the flicker method is addressed in Section 17.2.3.5.4

3.5.1 Unusual precision is needed to evaluate Bezold-Brucke and Purkinje phenomena

Preparation of Table 3.1.1 surfaced the fact that spectral measurements of individual chromophores require precisionmeasurements to an accuracy of at least 0.1 nm (one part in 5,000) if they are to address the Bezold-Brucke andPurkinke phenomena in detail. This is an unusual precision within the psychophysical community.

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3.5.2 Unusual care in evaluating chromophore spectra

The evaluation of chromophore spectra in-vivo are relatively simple because the orientation of all elements in theoptical system, including the photoreceptors, is necessarily appropriate.

When attempting to make measurements on individual chromophores of vision in-vitro, these same orientations andconditions must be achieved. The requirements are critical;

1. The chromophoric material (Rhodonine(x) ) must be present in a liquid-crystalline form.2. The chromophoric material must be present in a monolayer, or a known number of layers.

For maximum accuracy, there may be a requirement that the chromophore be in 2 micron diameter islandsdue to Pauli’s (not Pauling) Exclusion Principle (see Section 5.4.3.1 for this and other considerations).

3. The material must be maintained at 310 Kelvin (37 Centigrade) if the measurements are to apply to humans.4. The stimulation must by along an axis perpendicular to the monolayer.

When in non-liquid-crystalline form, all of the chromophores of vision exhibit an omnidirectional spectracharacteristic of the retinoid family and peaking with near 500 nm (Section 5.5.10.3.3).

4.0 Assembling the theoretical mechanisms important in defining the LEF

4.1 An Ideal vs Measured human Luminous Efficiency Function, LEF

Figure 4.1.1-1 provides a comparison between the ideal (theoretical) spectrum of human vision, potentialperturbations to the biological spectrum and the most recent precision measurements of human vision.

The ideal response is based on the equation derived earlier with the short wavelength skirt defined by the absorptionof light by the lens. The long wavelength skirt is defined by the response of the long wavelength chromophore,Rhodonine(5). The in-band absorption of the lens and the Purkinje reflections within the eye are negligible at thescale of this figure. Their sum would lower the ideal curve to about 0.95 on the vertical scale.

The ideal response is often perturbed by two additional mechanism as indicated by the dashed blue lines. Thepositive going peaks, known as the Bezold-Brucke peaks in the literature (Section 17.2.6). The short wavelengthpeak (1) occurs near 380 nm and is largely inconsequential. The mid wavelength peak (2)occurs near 494 nm andcan easily perturb precision measurements. Tthe long wavelength peak (3) occurs near 572 nm. The Bezold-BruckeEffect is not transient in character. It is liable to disturb any precision measurements regardless of the stimulationlevel. Similar Purkinje Effects, usually observed as a dip (5) near a wavelength of 572 nm and an accentuatedresponse (4) near 625 nm at sunset (Figure 17.2.6-12), However, the Purkinje Effect is generally considered atransient effect frequently appearing near sunset. The potential negative perturbation (6) near 380 nm has not beendocumented.

It is interesting that the Bezold-Brucke effect appears to be important in the tropical rainforest. Where thereis an excess of material in the scene that reflects in the “green” portion of the spectrum, the absorptionfunction of the human eye is suppressed (M-channel adaptation) and the relative sensitivity of the eye toyellows and aquas (Bezold-Brucke Effects (2 & 3) is increased disproportionately.

26

The measured data is the average of four subjects using a custom designed test set and employing 10 nm FWHAinterference filters. Care was taken to insure the subjects were sufficiently dark adapted in order to avoid differentialspectral adaptation. To the extent they were properly and adequately adapted, the figure provides considerableinformation. The measured data was normalized to the ideal response in the region of 0.53 to 0.56 microns, thecentral region of sensitivity of the M-channel chromophore, Rhodonine (7). Based on this normalization, the averageS-channel response at 0.437 microns, Rhodonine(9) was at about 70% of the nominal M-channel response. Theaverage L-channel spectral response, Rhodonine(11), at 0.625 microns was at about 40% of the nominal M-channelresponse. These are commonly observed values (Section 17.2).

Brucke asserted that his data (curving blue line) was collected at a light level of 10–3 cd/m2. This is too low forthe photopic (color constancy) range and a loss in L-channel sensitivity is to be expected relative to the M-channel sensitivity as noted earlier. Ideal photopic measurements would be made at light levels in the 3x10+3

cd/m2 range.

Brucke indicated that his light source was limiting in his experiments with the narrowband interference filters(that rejected a vast majority of the light from his source). As a result, his data of Sept 16, 2008 was obtainedin the Mesotopic illumination range. The perturbation in his spectral response at about 0.650 microns (7) isalso found in the following figure for what is labeled Mesotopic #2. Note the potential Bezold-Brucke peak inthe mesotopic response near 480 nm. Note also the potential Purkinje dip near 570 nm causing a dip belowboth the photopic and scotopic theoretical curves.

The skirt crossings near 0.494 microns occurred slightly above the 50% response level, resulting is a slightly highercomposite response than for the ideal case. In the case of the skirt crossings near 0.572 microns, the opposite casewas observed. A dip is observed of about the same amplitude as the peak near 0.494 microns. This dip may becaused by the reduced sensitivity of the L-channel photoreceptors.

The long wavelength skirt would be very close to the ideal case if the peak sensitivity of the L-channel response wasraised from 40% to 100% of the sensitivity of the M–channel.

17Fulton, J. (1985) The perception of luminance under various states of adaptation (unpublished butavailable on request)

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The relative amplitudes of the S-channel and the L-channel relative to the M-channel may be related to how they aredistributed within the foveola of the retina. As discussed in Section 3.2.2, the photoreceptors are formed into apattern similar to the segments on a spherical surface (such as a basketball). The array of photoreceptors cannot bebased exclusively on a hexagonal grid and yet form a spherical surface. It must contain one pentagon surrounded byfive hexagonal segments.

4.2 The progression from photopic to scotopic vision in human LEF

Figure 4.2.1-1 builds on the baseline developed in Section 17.2 to illustrate the spectral response of the eye undermesotopic conditions (conditions where the pupil size is fixed)17. It uses the equations of that chapter and Chapter16. The loss in sensitivity in the long wavelength region of the spectrum is obvious as the stimulus level is decreased. The curve mesotopic #1 represents a loss in sensitivity of 10:1 relative to the sensitivity normally observed at thelower limit of the photopic region. Mesotopic #2 represents a loss of 100:1 compared to the lower limit of thephotopic region. If the eye is chromatically adapted at the top of the mesotopic region by suppressing the M-channel

Figure 4.1.1-1 Ideal (theoretical) photopic vs the measured human spectrum at 0.001 cd/m2. The ideal spectral responseis based on the same spectral sensitivity, on a quantum (photon) flux basis, for each spectral channel of human vision andwith the skirts of the spectral responses crossing at precisely 50% of the peak response. The dashed lines are not to scalebut suggest where anomalies might occur. 1, 2 & 3; Bezold-Brucke Effects (named in 1931). 4, 5 & 6; Potential PurkinjeEffects. 7; kink in Brucke data found also in theoretical model at Mesotopic stimulus levels. The solid blue linerepresents the mean response of four subjects as reported by Brucke in September, 2008 under mesotopic conditions. Seetext for additional analyzes.

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Figure 4.2.1-1 Caricature of human luminance thresholdresponse under mesotopic conditions (pupil size fixed).Mesotopic levels #1 & #2 are one and two orders lower inthreshold than for the lower edge of the photopic condition(lower limit of color constancy). The slight dip to the left ofthe Purkinje peak is part of the Purkinje Effect. See text.

sensitivity, or if the spectrum of the stimulus is deficient in the M-channel region, the regions labeled the Bezold(Bezold-Brucke) Effect and the Purkinje Effect can be observed. See Section 17.2.3.4. The Purkinje Effect isultimately lost as the sensitivity of the L–channel is lost.

5.0 Proposed laboratory conformationprogramThis section will define two laboratory programs. Thefirst is to confirm the potentially complex spectralresponse of the human eye in about five nanometerintervals from 400 nm to at least 650 nm at D65 undercarefully controlled dark adapted conditions. Theprogram will quantify the Luminous EfficiencyFunction, LEF, of the human eye under photopic andscotopic conditions in-vivo. In a minor extension, theprogram will explore the mesotopic regime conditions(with a focus on the L–channel performance) betweenthe photopic and scotopic regimes.

The fact that the photoreceptors of vision arequantum-mechanical devices rather than energysensors cannot be overemphasized. Allmeasurements should be in terms of the quantum-catch at a given wavelength, and not in watts(Section 2.1.1.7.2).

The second program will use the same testconfiguration to determine the specific spectrum of theS–, M – & L–channels individually under in-vivoconditions.

5.1 Protocol & laboratory measurement of the Luminous Efficiency Function, LEF

The theoretical human spectrum and its possible perturbations suggest that a protocol for measuring the LuminousEfficiency Function should be broken into two operational sections; the first is to measure the relative sensitivities ofthe S–, M – & L– spectral channels, and the second to measure the perturbations from the portions of the spectra dueto potential Bezold-Brucke and Purkinje Effects.

As noted above, the level of adaptation of the individual spectral channels of the eye are difficult to control. Itis suggested that the following operational sections be accomplished on eyes that have been dark adapted for aminimum of one hour (with no opportunity to be stimulated by any light source for even a moment). Lightadaptation requires seconds to undo dark adaptation that has require tens of minutes. This suggests the chanceof light adaptation be rigidly controlled by the technical staff.

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The goal in the first step is to determine the spectral sensitivities of the channels without perturbation due to theEffects defined above. This can be accomplished by making measurements at the center wavelengths of thechromophores, typically at 437, 532 & 625 nm. If the standard deviation in the data collected at 625 nm issignificantly greater than that collected at 437 & 532 nm, it is likely that the stimulus level was not within thephotopic illumination regime, and steps should be taken to confirm the precise stimulation range. Once the data issuccessfully collected from at least 20 cohorts, the second operational section can commence.

The goal in the second step is to determine the spectral locations and/or deviation magnitude within the overallspectra due to the crossover locations described above. These are recognized as the Bezold-Brucke Effect and thePurkinje Effect. The wavelength of the optimal spectral points is difficult to predict based on only theoreticalevidence and the very limited information in the literature. However, the regions of interest are near 572 nm, 494 nm& 395 nm (if of interest). It is suggested that measurements be made very close to these wavelengths and possibly 5to 10 nm each side of these values. The data points may deserve a cluster analysis since it is possible some of thecohort may show peaks above the levels measured in the first step and others may show dips near the samewavelengths due to the different known Effects and their causes.

If desired, the experiments can be continued, in a third step, to explore the change in the spectral sensitivity of the L-channel compared to the S– & M–channel values as the stimulation level is reduced through the mesotopic regimeand into the scotopic regime (where the L–channel sensitivity will approach negligible).

The results of the measurements in the first step should provide enough evidence to create a real and documentedhuman photopic Luminous Efficiency Function for comparison with the ideal spectrum above. The data from thesecond step should provide information about the perturbation in the real human photopic LEF, if any, due to theBezold-Brucke and Purkinje Effects.

If extended to the third step, the collected data should establish the loss in L-channel sensitivity with reductions instimulus compared to the other channels, and also demonstrate the performance of the eye represents a continuuminvolving the same group of chromophores (and photoreceptor neurons) between the photopic and scotopic regime.

5.2 A mosaic of potential outcomes of a measurement program

The null hypotheses associated with these tests can be illustrated in Figure 5.2.1-1. This mosaic summarizes a largevolume of material cited above regarding the various operating modes of human vision. The normalized spectralresponse of the chromophores fully configured within the outer segments of the photoreceptor neurons are shown forreference. Their amplitude is unrelated to the vertical scale. It should be noted that the long wavelength skirt of theUV-channel chromophore extends beyond the short wavelength skirt of the overall photopic and scotopic LEF,resulting in a number of observable phenomena in human vision attributable to the UV-channel in human vision.

The first three frames, A, B & C describe the theoretical and measured performance of human eyes. Frames D & Eillustrate the theoretical and measured performance of human eyes lacking a crystalline lens, so-called aphakic eyes. All of the theoretical responses in frames A through E represent neutrally adaptaed eyes (typically neutrally adaptedto a light source at D65 for the normal eyes and adapted to a light source at D70 for aphakic eyes. These light sourcesprovide maximally equal photon flux per unit spectral interval as possible using black body sources. Finally, framesF & G illustrate the poorly documented but frequently encountered results of differential spectral adaptation. These

30

are usually attributed to phenomena resulting in the observation of the Bezold-Brucke and the Purkinje Effects.

Frame A illustrates the theoretical “Ideal Photopic Luminous Efficiency Function,” R( λ), acquired at a sourceintensity of 3 x 10+4 Cd/M2. This is a high intensity not usually achieved in the psychophysical laboratory. D65 hasalso been infrequently used in the laboratory. The use of sources with color temperatures below 2800 Kelvin havegenerally been used to obtain spectra in both photopic and scotopic regimes.

The Candela/M2 is not defined, even remotely adequately, for use in precision photometry and colorimetry ofanimal vision. In the middle years of the 20th Century, it was defined at a color temperature of only 2045Kelvin (the color temperature of a dim incandescent lamp). The Candela can only be used as a relative unitwhen teamed with the color temperature of a source optimally at 6500 Kelvin, D65. This pairing is clearlyincompatible with the definition of the Candela at 2045 Kelvin (Section 2.1.1).

A second problem has been the frequent use of gelatin bandpass filters or spectrometers with passbands on the orderof 30 nm prior to the turn of the 21st Century. The result of these two situation is most spectral responses in theliterature are seriously deficient in the short wavelength region. The dashed line in frame A shows the grosslydeficient spectral response of the CIE Standard Observer of 1925 incorporating the CIE 1924 visibility function, V(λ). At long wavelengths, the CIE data suffers from the smoothing related to using wide bandpass filters in data gathering.

Frame B shows the theoretical “Ideal Scotopic Luminous Efficiency Function,” R’(λ), acquired at a source intensityof 3 x 10–4 Cd/M2 following neutral spectral adaptation at D65. Also shown is the CIE 1951 V’(λ). The CIE Standardwas acquired 25 years later using more modern equipment and is much closer to the theoretical R’(λ). However, itstill suffers from the use of filters wider than appropriate and suffers from data smoothing.

The wavy line in Frame C is the averaged spectral response of only a few individuals obtained under more modernconditions, maximally equal photon flux per unit spectral width and 10 nm FWHA bandpass filters. The intensity ofthe available source was not adequate to satisfy the photopic requirement, but it exceeded the scotopic requirement. Therefore, these measurements represent the mesotopic operating regime and the long wavelength skirt of thesemeasurements fall between the photopic and scotopic asymptotes of normal human vision. Both the theoreticalphotopic, R( λ), and scotopic, R’( λ), are also shown.

The data in frame C was acquired based on the quantum-mechanical character of the actual photo-transductionprocess. It was also based on measurements within a two degree diameter circle centered on the point of fixation. The data clearly shows the average spectra of the cohort remaining near a relative response of 1.0 down to 410 nm, amuch more robust response than predicted by either CIE Standards.

Frames D & E explore the tetrachromatic character of the human retina. Frame D provides the theoretical “IdealAphakic Luminous Efficiency Function” of the aphakic eye under both photopic and scotopic conditions in theabsence of the crystalline lens, Aphakic R( λ), and Aphakic R’( λ), respectively. The data is drawn from Section17.2.3.1. Frame E shows multiple cases of aphakic eyes collected in the 1980's. The curves were displaced verticallyto aid interpretation. However, the trends are quite clear. The data was collected under scotopic conditions andapproaches the the Aphakic R’(λ) in the manner expected. The sensitivity of the human retina at wavelengths shorterthan 400 nm was substantial. The UV-channel frequently exceeds the sensitivity of the nearby S-channel. In the caseof the data displayed using open circles, the UV-channel sensitivity is equal to or rivals the M-channel sensitivity.

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This high sensitivity suggests, as theory predicts, the presence of a distinctly separate UV-channel receptor. The UVsensitivity is significant down to wavelengths of less than 330 nm.

Frames F & G are presented to address the proposed theoretical character of the frequently discussed, but poorlydocumented at the detailed mechanism level, Bezold-Brucke and Purkinje Effects. The Bezold-Brucke and PurkinjeEffects are transient phenomena frequently observable over a period of minutes. They are closely related to the stateof differential adaptation. Both the character of the surround and the size of the sample field affect the observedresults. The literature provides a wide variation in the specific spectral locations of these Effects. See Section 17.2.6and Section 17.3.4.4 for additional justifications and citations. For consistency with the chromophores defined in thiswork, wavelengths of 395, 480 and 571 will be used in describing these Effects. Most of the data in the literature wasgathered without specifying the spectral bandwidth of the filters or spectrometer used.

There are at least two effects labeled the Bezold-Brucke Effect. One has to do with shifts along the spectralregime, based on psychophysical testing, as a function of stimulus intensity (using the CIE StandardObserver). This usually refers to Bezold-Brucke hue-shifts (Section 17.3.4.4). This effect is not explored here! The second Bezold-Brucke Effect involves small intensity perturbations when obtaining full spectrum datasupporting the photopic and scotopic Luminous Efficiency Functions. This is the effect discussed here.

Frame F presents a conceptual explanation of the Bezold-Brucke Effect. It is generally associated with one or morepositive excursions near 395, 480 or 571 nm. Based on the spectra of the individual chromophores of vision and themathematical equation for the LEF, it appears this Effect is the result of anomalies in the summation of pairs ofspectra due to the individual chromophore spectra being wider than normal.

Frame G presents a conceptual explanation of the Purkinje Effect. It is usually associated with clear evidence ofdifferential spectral adaptation. It is usually described as one or more notches of low sensitivity adjacent to broadspectral areas. They generally occur near the same spectral locations as the Bezold-Brucke peaks.

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Figure 5.2.1-1 Caricatures of the Null hypotheses associated with the LEF experiments outlined earlier. A; the idealspectral response of the human eye under photopic conditions, R( λ). The dashed line shows the deviation of the CIE1924V(λ) from the achievable response. B; the ideal scotopic spectral response of the human eye under scotopic conditions,R’(λ). The dashed line shows the improved match of the CIE 1951 V’( λ) to the ideal response due to an improvedprotocol and better instrumentation. C; actual measured human average response under mesotopic conditions, slightlybelow the photopic level. D; the ideal responses of the aphakic human eye under both photopic and scotopic conditions.E; actual measured data for individuals under scotopic conditions showing significant UV sensitivity obtained in the1980's. F; concepts of the generally transient Bezold-Brucke Effects under differential spectral adaptation—one or morepeaks of limited amplitude. G; concepts of the Purkinje Effects shown as two low sensitivity areas bordering one areaof high sensitivity due to differential spectral adaptation. Both F & G are shown against the ideal photopic LEF. TheBezold-Bruck and Purkinje Effects are difficult to observe at 395 nm due to the presence of the absorption due to thecrystalline lens.

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5.3 Measurement of the individual spectral channels of the eye

Using the same test set as in the LEF determination, the spectral response of the individual spectral channels of thehuman eye can also be determined with unprecedented precision. The technique is a well documented one, thesuppression of the other spectral channels through narrowband stimulation to achieve the reduction in their sensitivitywhile precisely measuring the spectral response of the target channel.

The goal is to measure the spectrum of one or more spectral channels at intervals of five to ten nm using a set of fivenm interference filters or an equivalent performance spectrometer in-vivo. A cohort of at least 20 subjects is the targetfor statistical purposes. The purpose is to determine the coefficients of the Boltzmann-Helmholtz Equation describingone or more spectral channels at a precision greater than can be achieved by curve fitting. To achieve this accuracy, itis expected the skirts of each spectral channel would need to be measured over a stimulus range on the order of 100:1.

The results would be presented in a table similar to that for the Boltzmann-Helmholtz Equation given above.

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Luminous Efficiency Function Figures June 18, 2019

Figure 1.2.1-1 Ideal Luminosity Function with data overlays for both photopic and scotopic vision . . . . . . . . . . . . . 5Figure 1.2.1-2 CRUCIAL PROTOCOL ISSUE--Predicted long wavelength peak versus flicker frequency . . . . . . . 7Figure 2.2.1-1 Comparison of measured human eye LEF and the CIE Standard Observer . . . . . . . . . . . . . . . . . . . . 11Figure 2.3.1-1 Examples of spectral recording precision. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12Figure 3.1.1-1 (Color) The luminance, chrominance and appearance channels of the eye of tetrachromats . . . . . . . 14Figure 3.2.1-1 The theoretical spectra of biological, including human, vision . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18Figure 3.2.1-2 Ideal Luminous Efficiency Functions, LEF at the human retina . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19Figure 3.2.2-1 Comparison of aphakic vision and the theoretical scotopic model . . . . . . . . . . . . . . . . . . . . . . . . . . 22Figure 3.3.1-1 Dark adaptation curve of a human observer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24Figure 4.1.1-1 Ideal (theoretical) photopic vs the measured human spectrum at 0.001 cd/m2 . . . . . . . . . . . . . . . . . . 27Figure 4.2.1-1 Caricature of human luminance threshold response under mesotopic conditions . . . . . . . . . . . . . . . 28Figure 5.2.1-1 Caricatures of the Null hypotheses associated with the LEF experiments outlined earlier . . . . . . . . 32

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SUBJECT INDEX

50% . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26, 2795% . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20Activa . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8, 20adaptation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1, 5, 15, 18, 19, 23, 24, 26-28, 30-32alarm mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13anisotropic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22Bezold-Brucke . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1, 4, 12, 17, 18, 24-32Black Body . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29bleaching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23broadband . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19CFF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6CIE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1, 4, 9-12, 22, 30-32cis- . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22continuum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29critical flicker frequency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6dark adaptation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23, 24, 28dynamic range . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9E/D . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23, 24effect-size . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12exposine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23, 24field lens . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21flicker frequency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6, 7, 24Gaussian . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17half-amplitude . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15-18homologs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15in-vitro . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25in-vivo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16, 25, 28, 33light adaptation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23, 28liquid-crystalline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23, 25Maxwell’s Spot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8mesotopic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1, 6, 26-30, 32modulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23narrow band . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11P/D equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23protocol . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1, 5, 7, 11, 13, 28, 32Purkinje Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1, 19, 25, 28, 29, 31quantum-mechanical . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28, 30reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10resonance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16SCEIII . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11stage 0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

36

stage 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13stage 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8, 13stage 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8stage B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13Standard Observer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1, 4, 9, 11, 30, 31Stiles-Crawford . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1, 11thalamus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8threshold . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8, 20, 28transduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30waveguide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20