shimao hijack time

We can measure how much light we've been exposed to in units of steradian meter^2 seconds, where we multiply the time of our exposure (T), by the area of our sensor (A), by the solid angle of sky exposed to the sensor (S). Thus we can compute exposure as STA.

Typically in photography, you might also crop the image, resulting in a ratio of cropped image area to original image area of K. Since the crop affects both sensor area and sky angle by a multiplicative factor, thus we get STAK^2

The solid angle of sky can be related to the focal length (F) and the sensor area with a small angle approximation: S = A/F^2, so we prefer the formula T(AK/F)^2

Example: I made 14 exposures of 15 seconds each with my camera (366.6 mm^2 sensor), a crop ratio of roughly (3/8), and a focal length of 200mm. This comes out to 100 micro sr*m^2*s

If you're confused, here's some intuition: Screen brightness is often measured in nits, where something like 200 nits is a fairly average monitor brightness. It turns out that sr*m^2*s = joule/nit, so if you think of the sky as a really dim and faraway monitor (let's say 0.01 nits), then an exposure of 100 micro joule/nit * (1/100) nits means our sensor was exposed to a microjoule of light energy. If we knew the exact wavelength of light, we could even go further and compute the number of photons per pixel or something like that.

Anyway, since micro sr*m^2*s is annoying to write out, and joule/nit is more intuitive, I propose calling this "ujpn" for "micro joules per nit". This below photograph was taken at an exposure level of 100 ujpn.