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Eye And Color

The eye form a “optical image” on the light sensitive cell of the retina.  It is very often compared to a camera in it so workings.  However it is like a camera in its focusing properties but is very different after the light has hit the retina.  The camera just prints a point to point representation of the image on film, where as the is much more complex and interesting.  The visible light is only a very small portion of the electromagnetic spectrum and various wavelength in this visible spectrum of light represent different colors.  Short wavelength light is reddish, medium wavelength light is greenish and long wavelength light is bluish.  This make apparent in the a schematic of electromagnetic radiation below.  The various structures of the eye refract the light entering the eye to focus is on the photosensitive retina.  This structure are like the lenses we studied in class.

Path The light takes

Rods Vs. Cones

Rods

Cones

Cone and Color

If the retina has receptors for only three colors receptors how are we able to see all the other colors?

The cones do not just only absorb red, green or blue light.  The cones absorb light of wavelengths in a given neighborhood, with peak absorbency occurring at 580nm, 540nm, and 450nm respectively for L, M, S receptors.  This statement is represented in the relative sensitivity vs. wavelength graph below.  It is important not to get hung  up on the color names for the cones.  These are just given names and do not reflect the complete nature of cones, so I think L, M, S are better names. There are various experimental ways of measuring cone absorbency.  For example scientist isolate, then suspend in glass and then measuring the light absorbency of a cone by shining lights of different wavelengths on it.  Now a distinction has to be made between color absorbency and colors sensitivity of a cone.  Color sensitivity is directly related to color absorbency of a cone. Color sensitivity is rate of absorption (color absorbency) of a cone inside the eye where it subject to effects by the macular and lens pigments, where as color absorbency is measured outside without the influence of the pigments.  In coming light of a particular color wavelength is absorbed by the different cones at a different rate (0 to maximum).  This essentially breaks down the incoming color information into different values of the three primaries of the cones and assembled in the brain again to get what the perceived color is.  How can three colors account for all the colors we see? This is explained by the trichromatic theory and for details refer the trichomatic theory section bellow.

Spectral Sensitivity Vs. Wavelength

The graphs bellow show how cone sentivity differs with wavelenght in the three cones.  The graph on the left plots the fractional light abosrbance against wavelenght, where as the graph on the right plots the cone sensticity. The three curves on the right side can also be reffered to as l(lambda), m(lambda), and s(lambda) or color matching fuctions for the three cones.

Color Perception In the human Eye.

The perception of the color by the human is not a purely physical mechanism, but also depends on physiological and psychological characteristics.  This has been evident in many famous experiments in regards to vision over the decades.  Stated differently your eye observes the physical aspects it can and  from the retinal neurons onward you brain fills in the blanks to make a 'best fit" picture.  But the brain is some times tricked by the information being presented to it by out physical surroundings and gets its fill in the blank answers wrong.  To see how this is done refer to the images bellow. To get the volume of information we get from our visual sense if it were a completely physical mechanism system would require a unproportionaly large amounts of bodies energy reserves  and brains computational power.  Further, neural tissue and blood vessels above the photoreceptores would cast a shadow on the visual image if it were just a physical process.  The image on the retina is also formed upside down and backwards due to refraction of light rays, this has to be corrected by the brain aswell. So, the eye combines physical mechanism with memory and memory is necessary for sight.

Focus your eye's at the black dot in the middle of the pattern of colors for at least 30 seconds,  then keep a white paper between you and the screen and look at the white area and see a negative afterimage of the pattern in complementary hues.

As we already now that the color can be distinguished by its wavelength and this in fine at most basic level but visible color is more than just the wavelength.  It can be described in term of hue, saturation and luminance (intensity for physiologist).  Our eyes are sensitive to this hue, saturation and luminance which allows us to differentiate between colors with similar wavelengths. The photoreceptors in our eyes absorb colors with different hue, saturation and luminance at different rates, breaking up the information to be reassembled in the brain.  This is evident in color matching experiments.  Note that the terminology for these parameters differs form text to text.

Hue-perceptually distinguishes between colors and relates to dominant wavelength

Saturation-purity of light of particular color, essentially how far for gray the color is, for example red is more saturated than pink.

Note: Some colors are perceived to be more saturated by the human eye even though this not the case.

Brightness/Luminance/Intensity-measure of perceived intensity, is essentially the number of protons present.  Brightness of the light reaching the eye from the object in question. This parameter does not relate color information, rather only its brightness. 

Note: Some colors are perceived to be brighter than others even at equal luminance, this is due to inherent physiology of the eye.

Trichromatic Theory

Based on the premises that the color vision of the human eye is based on there classes of cone cells which with their selective absorbance of specific wavelengths of light allow us to perceive all the colors. This observation is reinforced by color matching experiments. (see bellow)

Primary Colors RGB

The theory simply states that all colors in the spectrum can be produced by a certain mixture of Red, Green, and Blue light. Before we go further let us define some terms and clarify this point.

Achromatic light- light consisting of equal numbers of photons for each primal wavelength in the visible ray. In other words equal amount of red, green and blue. This light is perceived as grey light. But you ask what about white light, it has equal number of photons for each primal wave length? Yes with light is achromatic light at maximum luminance (luminance as defined above).

Monochromatic light- light with photons of only one wavelength.  Never truly exits but with lasers we can come close, i.e. pure red light would be monochromatic light but we never get absolutely pure red light.

Chromatic light - Light with different numbers of photon of different primal wavelengths. The heart of the theory which states a spectral color can be contracted by mixture (adding or subtracting) of RGB.

Metamers-lights which are perceptually the same but have different spectral distributive curves (i.e.. look the same but the numbers do not match exactly.)

Color Matching Experiments:

When an individual is shown a monochromatic light or a chromatic light on one side of a divider and is asked to match it to a chromatic light on the side which changed through a series of colors.

This color matching is perceptual and the test light does not have to me match exactly as long as the eye perceives that it is a match.  However the Luminance values of the reference (test) light has to equal the luminance of the matched light

But why go through all this trouble to check how a given color (hue or dominant wavelength, saturation, and luminance) is perceived and what mixtures on the primaries results in this color?

The answer to this complex question is simply to get color matching functions. These color matching functions are plotted against wavelength. These functions allow us to display how colors (wavelengths) can be made from mixture of primary colors.  But if you look at the curve you see for certain wavelengths we would require negative values on red.  Physically this is hard to do, take away red light from a ray without red light.  This is precisely the reason a CRT monitor which uses the RGB primaries can not display the colors with these wavelengths accurately.

What is this business with 2 degree and 10 degree matching functions?

Historically color matching function were obtained with 2 degree field of view to avoid stimulating the rods outside the fovea centralis.  However this field was too small for many practical purposes so l0 degree field was adopted.  But for the measurements for the 10 degree field have to be done at a very high luminance to reduce any effect from stimulation of the rods.

Tristimulus Values R, G, B

These r(Lambda), g(lambda), and b(lambda) functions can be used to calculate RGB values or Tristimulus values. These values are the amount of the color primaries that are needed to match a test color.

What is the Formulae for R, G, B?

Where P(lambda) is "the irradiance per unit wavelength interval" and RGB are obviously red, green, and blue.

Chromaticity Coordinates r, g, b

The values r, g, b are normalized tristimuli values and define the hue and saturation of colors that fall with in the RGB field. Further, r + g + b = 1 so a two dimensional representation called chromaticity diagram for two of the coordinates is sufficient to display all the information. Another way to describe the color curves of the trichromatic theory is the Maxwell triangle shown below. The nature of the chromatic coordinate does not allow for the luminance to be accounted for in the 2 dimensional representation. So a better representation is needed.

CIE (Comission Internationale de l'Eclairage) Standard

The RGB description has it's short comings, mainly negative values in color matching functions, does not account form luminance specification, and does not cover all the colors perceived by the human eye.  

The Chromaticity Diagram and Tristimulus Values

Just line RGB primaries color matching function can be calculated in the lab and are plotted against wavelength, as mentioned above the functions have all positive values.  From these color matching functions a tristimulus values X, Y, Z can be calculated.  Normalized values for the tristimulus values are called chromaticity coordinates x, y, z.  Where x + y + z = 1 so given any two of these the third can be calculated so we are able to represent this standard in 2D chromaticity diagram (colorful figure above) with would losing information.

Properties of the Chromaticity Diagram

Converting Spaces

Now we know that all visual colors can be represented by xyz values we can switch back and forth between rgb values (if we want) using matrix multiplication.  But our ultimate goal is go from the xyz space to the lms space of our retinal cones and this can also be accomplished by matrix multiplication.  As for where do these matrices come from?  The weights in the matrices can not be directly measured but are derived form experimental research like color matching experiments ( color matching is done through the macula and lens so the "macular and eye lens pigments have to be taken into account").  We make this conversion form xyz (imaginary components of light) to lms with matrix multiplication and photoreceptors do this through chemical reactions and convert component of light into electrical signals.  As long we are converting spaces we might as well re iterate that rgb space is limited in the colors it can show and can not represent all visual colors as graphically presented below by inserting the rgb color range (gamut) and another popular color standard used by the press diagram into the xyz chromatic diagram.

Now we have come full circle and can now say that the three cones in the retina can represent all the colors we perceive.  But the trichromatic theory does not account for all the visual phenomenon, remember the trick with the four colorful squares towards the beginning of the section.  That phenomenon and many other like can not be explained with tricromatic theory alone, so a combination  of tricromatic theory and opposition theory are used to explain vision.  But the trichromatic system works at the retinal level where as the opposition is at the cerebral level.

Rerferences Used For Information and Images