conservation of energy | Strolls with my Dog

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.

Continue reading The Physical Units of Raw Data →

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*}$

Continue reading Photons Emitted by Light Source →

Musings about Photography