The following figure is presented here at reduced scale (resolution)to accommodate a browser. A version offering greater precision is available in Chapter 17 in the Download Files area reached from the Site navigation bar.
Spectral Response of the Human Visual System under scotopic conditions
[from Section 17.2.2]
The theoretical perceived (as reported) spectral response of the visual system is given by the luminance channel signal as received at the cortex. This signal is defined by the weighted logarithmic summation of the signals from the individual spectrally selective photoreceptor channels of vision. It should be noted that a logarithmic summation is significantly different from a linear summation under large signal conditions.
The above figure includes the spectral response of the two spectral channels of human (long wavelength trichromatic) vision active under scotopic conditions. These responses are shown by the left two waveforms in the lower portion of the figure, on a relative amplitude scale. Also shown is a horizontal line representing the one-half amplitude ordinate for these spectra. Whereas these individual spectrums show only limited overlap when displayed on a relative amplitude basis, this is not the way they are used in vision. In vision, the M-channel signal is given an emphasis of between ten and sixteen to one over the S- and L-channels (depending at least on location within the retina). In the case shown the ratio is 16 to one between the M- and S-channels. When summed under this condition, the theoretical scotopic luminous efficiency function appears as shown by the (dotted line).
Note the theoretical scotopic luminous efficiency function exhibits three individual relative peaks. Two of these peaks occur at nearly the same wavelength as for the individual spectral responses. However, there is an additional peak, near 490 nm, due to the logarithmic summation process.
All three of the theoretical peaks in the scotopic luminous efficiency function are easily observed with adequate instrumentation. However, the historical measurements leading to the current CIE (1951) Scotopic Luminous Efficiency Standard (solid line) were acquired using instrumentation of the 1930's and 1940's. These instruments had an instantaneous spectral half-amplitude bandwidth of not less than 20 nm. Due to the signal to noise considerations, it was also necessary to use large size test images, 10 x 10 degrees, which caused a significant averaging of the performance of the retina. When the results from various experiments were averaged, the result exhibited an average spectral bandwidth for the instrumentation alone of between 20 and 30 nm. Such instrumentation is completely inadequate for observing spectrums exhibiting spectral variations over intervals of 5-10 nm.
An additional problem has to do with the sampling plan used by these experimenters. Being unaware of the detailed structure of the waveform they were attempting to measure, they invariably centered their measurements at wavelengths that were multiples of 10 nm. This binning convention had the effect of further suppressing details of the spectrum occurring over intervals of 5-10 nm.
The importance of controlling the color temperature of the source illumination was still not well understood during the above time period. Most of the measurements used to define the scotopic response were made using incandescent light sources with color temperatures in the 2000-3000 Kelvin range. This had the effect of suppressing the measured spectral response of the eye in the blue region of the spectrum. Theoretical discussion occasionally addressed this insufficiency under the assumption that the visual process used "energy detectors." In fact the photosensitive mechanisms of animal vision employ "photon detectors." The theoretical and observed performance differences between these two cases are significant .
If the above instrumentation problems are taken into account, filtered (smoothed) versions of the theoretical function are found to approximate the CIE Standard. However, the number of uncontrolled variables in the test data was high. The difference between the smoothed theoretical curve and the CIE curve also surfaces the use of sodium glass lamp bulbs in the early experiments. These bulbs exhibit higher absorption in the blue region of the spectrum than anticipated, or documented, by the experimenters.
Both the smoothed theoretical scotopic response and the CIE Standard exhibit peaks near 505 nm. These peaks are totally unrelated to the peak absorption of the retinoid family of chromophores that occurs near 493 nm when plotted on an equal flux basis.
The above features are discussed in detail in Chapter 17.
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