Three components of an absorption image are denoted by:

, the input light distribution on the atom,

, the output light (after absorption),

, the background.

The formula for calculating the optical density (OD) is

,

where

,

is the intensity distribution of light on the atom,

is the pixel size of the camera,

is the real pixel size including the magnification of the image system,

is the wavelength of the probe light,

is the transmission rate of the image system,

is the camera quantum efficiency,

is the analog-to-digital conversion efficiency of the camera,

is the exposure time.

The noise can be written as

Then, the SNR is

.

References

[1] G. Reinaudi, T. Lahaye, Z. Wang and D. Guéry-Odelin, "Strong Saturation Absorption Imaging of Dense Clouds of Ultracold Atoms," Optics Letters, 32(21), 2007 pp. 3143–3145. doi:10.1364/ol.32.003143.