Tag Archives: energy

Connecting Photographic Raw Data to Tristimulus Color Science

Absolute Raw Data

In the previous article we determined that the three r_{_L}g_{_L}b_{_L} 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 L(\lambda) at the lens – can be estimated as follows:

(1)   \begin{equation*} r_{_L}g_{_L}b_{_L} =\frac{\pi p^2 t}{4N^2} \int\limits_{380}^{780}L(\lambda) \odot SSF_{rgb}(\lambda)  d\lambda \end{equation*}

with subscript _L indicating absolute-referred units and SSF_{rgb} the three system Spectral Sensitivity Functions.   In this series of articles \odot 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.

Figure 1. The journey of light from source to sensor.  Cone Ω will play a starring role in the narrative that follows.

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.

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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 such a spectrum from the scene: we will dissect what is sometimes referred to as the system’s Spectral Response or Sensitivity.

Figure 1. Spectral Sensitivity Functions of an arbitrary imaging system, resulting from combining the responses of the various components described in the article.

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Photons Emitted by Light Source

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)   \begin{equation*} \frac{\text{Power of Light in }W/m^2}{\text{Energy of Average Photon in }J/photon} \end{equation*}

The Power of Light emitted in W/m^2 is called Spectral Exitance, with the symbol M_e(\lambda) when referred to  units of energy.  The energy of one photon at a given wavelength is

(2)   \begin{equation*} e_{ph}(\lambda) = \frac{hc}{\lambda}\text{    joules/photon} \end{equation*}

with \lambda the wavelength of light in meters and h and c 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 photons/m^2/s.  Writing it more formally:

(3)   \begin{equation*} M_{ph} = \int\limits_{\lambda_1}^{\lambda_2} \frac{M_e(\lambda)\cdot \lambda \cdot d\lambda}{hc} \text{  $\frac{photons}{m^2\cdot s}$} \end{equation*}

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Converting Radiometric to Photometric Units

When first approaching photographic science a photographer is often confused by the unfamiliar units used.  In high school we were taught energy and power in radiometric units like watts ($W$) – while in photography the same concepts are dealt with in photometric units like lumens ($lm$).

Once one realizes that both sets of units refer to the exact same physical process – energy transfer – but they are fine tuned for two slightly different purposes it becomes a lot easier to interpret the science behind photography through the theory one already knows.

It all boils down to one simple notion: lumens are watts as perceived by the Human Visual System.

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What Is Exposure

When capturing a typical photograph, light from one or more sources is reflected from the scene, reaches the lens, goes through it and eventually hits the sensing plane.

In photography Exposure is the quantity of visible light per unit area incident on the image plane during the time that it is exposed to the scene.  Exposure is intuitively proportional to Luminance from the scene $L$ and exposure time $t$.  It is inversely proportional to lens f-number $N$ squared because it determines the relative size of the cone of light captured from the scene.  You can read more about the theory in the article on angles and the Camera Equation.

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