In the last article we showed how a digital camera’s captured raw data is related to Color Science. In my next trick I will show that CIE 2012 2 deg XYZ Color Matching Functions 
, 
, 
displayed in Figure 1 are an exact linear transform of Stockman & Sharpe (2000) 2 deg Cone Fundamentals 
, 
, 
displayed in Figure 2
(1) ![\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")
with CMFs and CFs in 3xN format, 
a 3×3 matrix and 
matrix multiplication. Et voilà:[1]
We’ve seen how humans perceive color in daylight as a result of three types of photoreceptors in the retina called cones that absorb wavelengths of light from the scene with different sensitivities to the arriving spectrum.
A photographic digital imager attempts to mimic the workings of cones in the retina by usually having different color filters arranged in an array (CFA) on top of its photoreceptors, which we normally call pixels. In a Bayer CFA configuration there are three filters named for the predominant wavelengths that each lets through (red, green and blue) arranged in quartets such as shown below:
A CFA is just one way to copy the action of cones: Foveon for instance lets the sensing material itself perform the spectral separation. It is the quality of the combined spectral filtering part of the imaging system (lenses, UV/IR, CFA, sensing material etc.) that determines how accurately a digital camera is able to capture color information from the scene. So what are the characteristics of better systems and can perfection be achieved? In this article I will pick up the discussion where it was last left off and, ignoring noise for now, attempt to answer this question using CIE conventions, in the process gaining insight in the role of the compromise color matrix and developing a method to visualize its effects.[1] Continue reading The Perfect Color Filter Array
Now that we know how to create a 3×3 linear matrix to convert white balanced and demosaiced raw data into 
connection space – and where to obtain the 3×3 linear matrix to then convert it to a standard output color space like sRGB – we can take a closer look at the matrices and apply them to a real world capture chosen for its wide range of chromaticities.
We understand from the previous article that rendering color with Adobe DNG raw conversion essentially means mapping raw data in the form of 
triplets into a standard color space via a Profile Connection Space in a two step process
![\[ Raw Data \rightarrow XYZ_{D50} \rightarrow RGB_{standard} \]](https://i0.wp.com/www.strollswithmydog.com/wordpress/wp-content/ql-cache/quicklatex.com-062c1798a46be7f6f42a79b450d40bde_l3.png?resize=298%2C15&ssl=1 "Rendered by QuickLaTeX.com")
The first step white balances and demosaics the raw data, which at that stage we will refer to as , followed by converting it to Profile Connection Space through linear projection by an unknown ‘Forward Matrix’ (as DNG calls it) of the form
(1) ![\begin{equation*} \left[ \begin{array}{c} X_{D50} \\ Y_{D50} \\ Z_{D50} \end{array} \right] = \begin{bmatrix} a_{11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23} \\ a_{31} & a_{32} & a_{33} \end{bmatrix} \left[ \begin{array}{c} r \\ g \\ b \end{array} \right] \end{equation*}](https://i0.wp.com/www.strollswithmydog.com/wordpress/wp-content/ql-cache/quicklatex.com-b9f4277814179e1fbcf64e1a69a53818_l3.png?resize=273%2C64&ssl=1 "Rendered by QuickLaTeX.com")
with data as column-vectors in a 3xN array. Determining the nine 
coefficients of this matrix 
is the main subject of this article[1]. Continue reading Color: Determining a Forward Matrix for Your Camera
How do we translate captured image information into a stimulus that will produce the appropriate perception of color? It’s actually not that complicated[1].
Recall from the introductory article that a photon absorbed by a cone type (
, 
or 
) in the fovea produces the same stimulus to the brain regardless of its wavelength[2]. Take the example of the eye of an observer which focuses on the retina the image of a uniform object with a spectral photon distribution of 1000 photons/nm in the 400 to 720nm wavelength range and no photons outside of it.
Because the system is linear, cones in the foveola will weigh the incoming photons by their relative sensitivity (probability) functions and add the result up to produce a stimulus proportional to the area under the curves. For instance a cone may see about 321,000 photons arrive and produce a relative stimulus of about 94,700, the weighted area under the curve:
This article will set the stage for a discussion on how pleasing color is produced during raw conversion. The easiest way to understand how a camera captures and processes ‘color’ is to start with an example of how the human visual system does it.
Light from the sun strikes leaves on a tree. The foliage of the tree absorbs some of the light and reflects the rest diffusely towards the eye of a human observer. The eye focuses the image of the foliage onto the retina at its back. Near the center of the retina there is a small circular area called fovea centralis which is dense with light receptors of well defined spectral sensitivities called cones. Information from the cones is pre-processed by neurons and carried by nerve fibers via the optic nerve to the brain where, after some additional psychovisual processing, we recognize the color of the foliage as green[1].
Continue reading An Introduction to Color in Digital Cameras
We now know how to calculate the two dimensional Modulation Transfer Function of a perfect lens affected by diffraction, defocus and third order Spherical Aberration – under monochromatic light at the given wavelength and f-number. In digital photography however we almost never deal with light of a single wavelength. So what effect does an illuminant with a wide spectral power distribution, going through the color filter of a typical digital camera CFA before the sensor have on the spatial frequency responses discussed thus far?
Not much, it turns out. Continue reading A Simple Model for Sharpness in Digital Cameras – Polychromatic Light