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Exposure, imaging system, irradiance, luminance, radiance, Radiometry, reflectance, Uncategorized

Angles and the Camera Equation

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Imagine a bucolic scene on a clear sunny day at the equator, sand warmed by the tropical sun with a typical irradiance (E) of about 1000 watts per square meter.  As discussed earlier we could express this quantity as illuminance in lumens per square meter (lx) – or as a certain number of photons per second (\Phi) over an area of interest (\mathcal{A}).

(1)   \begin{equation*} E = \frac{\Phi}{\mathcal{A}} \; (W, lm, photons/s) / m^2 \end{equation*}

How many photons/s per unit area can we expect on the camera’s image plane (irradiance E_i )?

Figure 1.  Irradiation transfer from scene to sensor.

In answering this question we will discover the Camera Equation as a function of opening angles – and set the stage for the next article on lens pupils.  By the way, all quantities in this article depend on wavelength, which will be assumed in the formulas to make them more readable.

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Exposure

What Is Exposure

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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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