MEASUREMENT UNITS
The intensity of light is commonly quantified as radiance, which represents the power (measured in Watts, W) emitted, reflected, transmitted, or received by a surface per unit solid angle (measured in steradians, sr) and per unit projected area (measured in square meters, m²). Therefore, the unit of radiance is W/sr/m².
Alternatively, radiance can be normalised to the wavelength unit (measured in micrometers, µm; nanometers, nm; or angstroms, Å), resulting in spectral radiance. Spectral radiance allows comparison of light intensity across different wavelength ranges, which is the case when measuring light intensity with different instruments.
Instead, when speaking about light as perceived by the human eye, the appropriate term is luminance. The corresponding unit for luminance is lumen / m² sr (lumen per square metre per steradian) or more commonly cd / m² (candela per square metre).
Measurements from ground-based instruments are often reported as sky brightness at zenith, that is at the point in the sky directly overhead. This is typically expressed in units of mag/arcsec² (magnitudes per square arcsecond), which quantifies the apparent magnitude of light emitted from a very small square portion of the sky, where 1 square arcsecond equals 1/3600 × 1/3600 of a square degree. For comparison, the Moon has an angular diameter of about 30 arcminutes and covers an area of approximately 700,000 arcsec². The darkest skies on Earth have a brightness of around 22 mag/arcsec².
Magnitude is a logarithmic scale used by astronomers to quantify the brightness of astronomical objects. By definition, larger magnitudes correspond to fainter objects. Because it is a logarithmic scale, changes in magnitude are not linear in intensity: a difference of 5 magnitudes corresponds to a brightness ratio of 100, meaning that the dimmer celestial object of two is 100 times fainter than the other one.
For example, Vega is a very bright star with a magnitude of 0, while the fainter Polaris has a magnitude of about +2. The faintest stars visible to the trained naked eye are around magnitude +7. Venus, at its brightest, reaches a magnitude of -4.6, nearly 100 times brighter than Vega. The full Moon can reach a magnitude of -12.6, making it nearly 1,000,000 times brighter than Polaris.
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