San José State University

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Thayer Watkins
Silicon Valley
USA

 The Perceptive Efficiencyof the Human Eyeas a Function ofWavelength

Human beings are so used to observing the physical world visually that we equate visual observation with reality. But this is not necessarily correct. The human eye has operating characteristics that limit the accuracy of visual observations. For example, everyone knows that we can only see light over the limited range from red to blue but we presume that there is no distortion of perception over this visual range. But this is definitely not true. Shown below is a curve that indicates the efficiency of perception as a function of the wave length of the light.

Thus our perception of red light compared to our perception of yellow light of the same radiological intensity makes the red light seem much less bright than the yellow even though they are equally intense. The same diminished perception of blue light applies at the other end of the spectrum.

The above curve is for the human accustomed to daytime light, so called photopic vision. The maximum efficiency is for light at a wavelength of 0.555 μm. For the human eye adapted for night vision, so called scotopic vision, the maximum efficiency is for light at a wavelength of 0.510 μm. Under scotopic conditions perception of color is extremely weak.

The varying efficiency of the human eye as a function of the wavelength of light has led to a distinction between photometry and radiometry. Radiometry refers to physical measurement of light whereas photometry refers to the human perception of radiation. There are two sets of units for radiation measurement, one for objective physical reality and the other for human perception of that physical reality.

energyJoules=Watt-secondstalbots=lumens-seconds
fluxWattslumens
exitanceWatts/m2lux=lumens/m2
luminance

Photometric measurement is related to radiometric measurement by the following relationship:

#### L(λ) = 685E(λ)R(λ)

where E(λ) is the efficiency as given by the CIE luminous efficiency curve shown above. R(λ) is the intensity of the radiation in radiometric units whereas L(λ) is the photometric intensity.

Here is an illustration. Suppose a viewer is one meter from a 60W light bulb. The area of a sphere r meters in diameter is equal to 4πr2. Thus a one meter sphere has an area of 12.566 square meters and hence the intensity of the light from a 60W bulb is 60/12.566 or 4.775 Watts per square meter. The photometric intensity in lumens per square meter depends upon the wavelength of the light. If the bulb radiated pure yellow green light of wavelength 0.555 μm then the luminous intensity would be L = 685*1*4.775 = 3271 lumens per square meter. The same power bulb radiating pure green light at 0.510 μm where the efficiency of the eye is 50 percent would have a luminous intensity of L = 685*(0.5)*4.775 = 1635 lumens per square meter. For a bulb radiating red light at 0.48 μm, where the eye has an efficiency of about 10 percent the luminous intensity would only be 327.1 lumens per square meter.

The optical efficiency curve can be extended to color vision. Colors are perceived by the cones in the eye. Below shows the effectiveness of the three types of cones as a function of wavelength.

The efficiency curves for the red and green cones cross (i.e., are exactly equal) for radiation of wavelength about 0.56 μm. When the eye sees 0.56 μm radiation it stimulates the red and green cones about equally. The visual perception of near equal stimulation of the red and green cones is yellowness. The radiation of wavelength 0.56 μm is not yellow itself anymore than microwave radiation or radio waves have a color. Yellowness comes from equal stimulation of the red and green cones. Light including radiation of equal intensity at the 0.58 μm and 0.54 μm wavelength, the wavelengths of maximum efficiency for the red and green cones, would also be perceived as yellow light. There would be some stimulation of the blue cones by the 0.54 μm radiation which would lighten the yellowness of the perception.

The efficiency curves for the cone receptors are shown in the above diagram as going to zero, but they likely taper off asymptotically to zero like a Gaussian curve. The reason for saying this is that very high intensity light from a laser emitting infrared light is perceived as being deep ruby red. The infrared does not have a color but its intensity is so great that it stimulates the red cones in the tail of the efficiency curve where the efficiency of the perception is small but nonzero.

The deep ruby red color stimulated by the infrared light from a laser shows what the output of the red cones is. What we see when the eye perceives light in the red region of the spectrum is a mixture of the output of the red cone with some stimulation of the green cones. The deep ruby red of the output of the red cones is still thought of as red. The situation is different at the other end of the spectrum.

When the eye perceives light of wavelength of about 0.35 μm the color observed is violet. This is the output of the so-called blue cones unmixed with the output of the green cones. The so-called blue cones should be called the violet cones. They were labeled blue because they are most sensitive to light in the region of the spectrum where the eye observes blue color. But that blue color comes from the combined stimulus of the so-called blue cones and the green cones, with some tiny stimulus of the red cones.

For years art students have been taught that violet is not a primary color but instead a mixture of red and blue. In fact blue is a mixed color and it is violet which is the primary color.

It is a fact that a mixture of red and blue light or red and blue pigment looks violet. This is because when the three cones are stimulated the level of stimulation of the cones receiving the lowest stimulation combines with equal levels of the stimulation of the other two cones to produce a shade of gray. This gray tone serves to lighten the perceived color resulting from the residual levels of stimulation of the other two cones. Thus if a low level of red is combined with blue the stimulation of the green cones from the blue light combines with red to create a level of gray which then lightens the stimulus of the violet cones from the blue light. The result is the perception of a lightened violet.

It is not possible to stimulate the green cones without also stimulating the red cones and/or the violet cones. But a wavelength of light that equally stimulates the red cones and the violet cones would produce a gray tone that would merely lighten the perception of the green. This would give an approximation of what the color stimulus the green cones would give if they alone were stimulated.

More on violet as a primary color.