In this article we confirm quantitatively that getting the White Point, hence the White Balance, right is essential to obtaining natural tones out of our captures. How quickly do colors degrade if the estimated Correlated Color Temperature is off?
Tag Archives: spectral response
A Question of Balance
In this article I bring together qualitatively the main concepts discussed in the series and argue that in many (most) cases a photographer’s job in order to obtain natural looking tones in their work during raw conversion is to get the illuminant and relative white balance right – and to step away from any slider found in menus with the word ‘color’ in them.
If you are an outdoor photographer trying to get balanced greens under an overcast sky – or a portrait photographer after good skin tones – dialing in the appropriate scene, illuminant and white balance puts the camera/converter manufacturer’s color science to work and gets you most of the way there safely. Of course the judicious photographer always knew to do that – hopefully now with a better appreciation as for why.
White Point, CCT and Tint
As we have seen in the previous post, knowing the characteristics of light at the scene is critical to be able to determine the color transform that will allow captured raw data to be naturally displayed from an output color space like ubiquitous sRGB.
White Point
The light source Spectral Power Distribution (SPD) corresponds to a unique White Point, namely a set of coordinates in the 
color space, obtained by multiplying wavelength-by-wavelength its SPD (the blue curve below) by the Color Matching Functions of a Standard Observer (
)
Adding (integrating) the three resulting curves up we get three values that represent the illuminant’s coordinates in the color space. The White Point is then obtained by dividing these coordinates by the 
value to normalize it to 1.
The White Point is then seen to be independent of the intensity of the arriving light, as represents Luminance from the scene. For instance a Standard Daylight Illuminant with a Correlated Color Temperature of 5300k has a White Point of[1]
= [0.9593 1.0000 0.8833] Continue reading White Point, CCT and Tint
Linear Color Transforms
Building on a preceeding article of this series, once demosaiced raw data from a Bayer Color Filter Array sensor represents the captured image as a set of triplets, corresponding to the estimated light intensity at a given pixel under each of the three spectral filters part of the CFA. The filters are band-pass and named for the representative peak wavelength that they let through, typically red, green, blue or 
, 
, 
for short.
Since the resulting intensities are linearly independent they can form the basis of a 3D coordinate system, with each 
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.
The job of the color transform is to project demosaiced raw data to a standard output 
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. Continue reading Linear Color Transforms
Cone Fundamentals & the LMS Color Space
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]
Connecting Photographic Raw Data to Tristimulus Color Science
Absolute Raw Data
In the previous article we determined that the three 
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:
(1) 
with subscript 
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. Continue reading Connecting Photographic Raw Data to Tristimulus Color Science
The Physical Units of Raw Data
In the previous article we (I) learned that the Spectral Sensitivity Functions of a given digital camera and lens are the result of the interaction of light from the scene with all of the spectrally varied components that make up the imaging system: mainly the lens, ultraviolet/infrared hot mirror, Color Filter Array and other filters, finally the photoelectric layer of the sensor, which is normally silicon in consumer kit.
In this one we will put the process on a more formal theoretical footing, setting the stage for the next few on the role of white balance.
The Spectral Response of Digital Cameras
Photography works because visible light from one or more sources reaches the scene and is reflected in the direction of the camera, which then captures a signal proportional to it. The journey of light can be described in integrated units of power all the way to the sensor, for instance so many watts per square meter. However ever since Newton we have known that such total power is in fact the result of the weighted sum of contributions by every frequency that makes up the light, what he called its spectrum.
Our ability to see and record color depends on knowing the distribution of the power contained within a subset of these frequencies and how it interacts with the various objects in its path. This article is about how a typical digital camera for photographers interacts with the spectrum arriving from the scene: we will dissect what is sometimes referred to as the system’s Spectral Response or Sensitivity.
How Many Photons on a Pixel at a Given Exposure
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
Nikon CFA Spectral Power Distribution
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