Imagine a bucolic scene on a clear sunny day at the equator, sand warmed by the tropical sun with a typical irradiance (
) of about 1000 watts per square meter. As discussed earlier we could express this quantity as illuminance in lumens per square meter (
) – or as a certain number of photons per second (
) over an area of interest (
).
(1) 
How many 
per unit area can we expect on the camera’s image plane (irradiance 
)?
In answering this question we will discover the Camera Equation as a function of opening angles – and set the stage for the next article on lens pupils. By the way, all quantities in this article depend on wavelength and position in the Field of View, which will be assumed in the formulas to make them readable, see Appendix I for a more formally correct version of Equation (1).
color space, obtained by multiplying wavelength-by-wavelength its SPD (the blue curve below) by the Color Matching Functions of a Standard Observer (
)
value to normalize it to 1.
= [0.9593 1.0000 0.8833] 
, 
, 
for short.
triplet representing a point within it. The system is bounded in the raw data by the extent of the Analog to Digital Converter, with all three channels spanning the same range, from Black Level with no light to clipping with maximum recordable light. Therefore it can be thought to represent a space in the form of a cube – or better, a parallelepiped – with the origin at [0,0,0] and the opposite vertex at the clipping value in Data Numbers, expressed as [1,1,1] if we normalize all data by it.
color space designed for viewing. Such spaces have names like 
, 
or 
. The output space can also be shown in 3D as a parallelepiped with the origin at [0,0,0] with no light and the opposite vertex at [1,1,1] with maximum displayable light. 
, 
, 
displayed in Figure 1 are an exact linear transform of Stockman & Sharpe (2000) 2 deg Cone Fundamentals 
, 
, 
displayed in Figure 2![\begin{equation*} \left[ \begin{array}{c} \bar{x}} \\ \bar{y} \\ \bar{z} \end{array} \right] = M_{lx} * \left[ \begin{array} {c}\bar{\rho} \\ \bar{\gamma} \\ \bar{\beta} \end{array} \right] \end{equation*}](https://i0.wp.com/www.strollswithmydog.com/wordpress/wp-content/ql-cache/quicklatex.com-641037cf449c1fce6e76d66b53f1d297_l3.png?resize=161%2C64&ssl=1 "Rendered by QuickLaTeX.com")
a 3×3 matrix and 
matrix multiplication. Et voilà:
values recorded in the raw data in the center of the image plane in units of Data Numbers per pixel – by a digital camera and lens as a function of absolute spectral radiance 
at the lens – can be estimated as follows:
indicating absolute-referred units and 
the three system Spectral Sensitivity Functions. In this series of articles 
is wavelength by wavelength multiplication (what happens to the spectrum of light as it progresses through the imaging system) and the integral just means the area under each of the three resulting curves (integration is what the pixels do during exposure). Together they represent an inner or dot product. All variables in front of the integral were previously described and can be considered constant for a given photographic setup. 
) that reflects the performance of the hardware only; and an output-referred one (
is called Spectral Exitance, with the symbol 
when referred to units of energy. The energy of one photon at a given wavelength is
the wavelength of light in meters and 
and 
Planck’s constant and the speed of light in the chosen medium respectively. Since Watts are joules per second the units of (1) are therefore 
. Writing it more formally:
