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
Now that we know how to determine how many photons impinge on a sensor we can estimate its Effective Quantum Efficiency, that is the efficiency with which it turns such a photon flux (
) into photoelectrons (
), which will then be converted to raw data to be stored in the capture’s raw file:
(1) 
I call it ‘Effective’, as opposed to ‘Absolute’, because it represents the probability that a photon arriving on the sensing plane from the scene will be converted to a photoelectron by a given pixel in a digital camera sensor. It therefore includes the effect of microlenses, fill factor, CFA and other filters on top of silicon in the pixel. Whether Effective or Absolute, QE is usually expressed as a percentage, as seen below in the specification sheet of the KAF-8300 by On Semiconductor, without IR/UV filters:
For instance if an average of 100 photons per pixel were incident on a uniformly lit spot on the sensor and on average each pixel produced a signal of 20 photoelectrons we would say that the Effective Quantum Efficiency of the sensor is 20%. Clearly the higher the EQE the better for Image Quality parameters such as SNR. Continue reading What is the Effective Quantum Efficiency of my Sensor?
How many photons impinge on a pixel illuminated by a known light source during exposure? To answer this question in a photographic context under daylight we need to know the effective area of the pixel, the Spectral Power Distribution of the illuminant and the relative Exposure.
We can typically estimate the pixel’s effective area and the Spectral Power Distribution of the illuminant – so all we need to determine is what Exposure the relative irradiance corresponds to in order to obtain the answer.
Continue reading How Many Photons on a Pixel at a Given Exposure
How many photons are emitted by a light source? To answer this question we need to evaluate the following simple formula at every wavelength in the spectral range of interest and add the values up:
(1) 
The Power of Light emitted in 
is called Spectral Exitance, with the symbol 
when referred to units of energy. The energy of one photon at a given wavelength is
(2) 
with 
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:
(3) 
I measured the Spectral Photon Distribution of the three CFA filters of a Nikon D610 in ‘Daylight’ conditions with a cheap spectrometer. Taking a cue from this post I pointed it at light from the sun reflected off a gray card and took a raw capture of the spectrum it produced.
An ImageJ plot did the rest. I took a dozen captures at slightly different angles to catch the picture of the clearest spectrum. Shown are the three spectral curves averaged over the two best opposing captures, each proportional to the number of photons let through by the respective Color Filter. The units on the vertical axis are raw black-subtracted values from the raw file (DN), therefore the units on the vertical axis are proportional to the number of incident photons in each case. The Photopic Eye Luminous Efficiency Function (2 degree, Sharpe et al 2005) is also shown for reference, scaled to the same maximum as the green curve (although in energy units, my bad). Continue reading Nikon CFA Spectral Power Distribution