Background

Intensity and Optical Density

To characterize the scanners, a measure of both light and darkness is needed. In this case, the easiest way to characterize the darkness of an object is to shine a light on the object and compare the original light with the amount of light that passes through the object. This is done by taking the ratio of the intensity of the light which passes through the object to the intensity of the light wave incident upon it.

Because this ratio varies through a wide range of values, it is useful to express it in terms of logarithms, and because there is always less light emerging from the object than was incident upon it, the negative of the logarithm is commonly used. Therefore, the darkness of an object is related to the ratio of the intensities of the light waves entering and leaving it by the following formula.

The measure of darkness is known as optical density, which is represented by OD in the formula above. Also in the formula above, I₀ is the intensity of the light incident upon the object, I is the intensity of the light transmitted through the object, and all logarithms are to the base 10.

The intensity of light is the amount of light energy that passes through a unit amount of area in a unit amount of time. Intensity (I) is related to the amplitude of the electric field (E) of a light wave by the equation

where c = 3.0 x 10⁸ m/s, and e ₀ = 8.85 x 10^-12 C²N^-1m^-2.

Gamma Correction

Sometimes when a picture is scanned, the image produced has very low contrast between its lightest and darkest regions. To improve image quality, the dynamic range of pixel values can be increased at the expense of some loss in image quality of the bright regions. An image correction of this kind is known as gamma correction and is represented by the formula

where v is the original pixel value displayed on the screen, v' is the gamma-corrected pixel value, and the greek letter "gamma" is a constant called gamma.

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