Photometric system

A photometric system specifies photometric passbands and magnitude zero points, allowing calibrated brightness comparisons.

A colour index is the difference of an object's measured apparent magnitudes in two photometric passbands, such as $B-V$. Since magnitude is logarithmic, this difference measures a flux ratio after the respective magnitude zero points are accounted for. It describes spectral shape rather than the object's overall brightness, and changes with both intrinsic radiation properties and interstellar extinction.

The UBV photometric system measures stellar brightness in three broad photometric passbands: ultraviolet $U$, blue $B$ and visual $V$. Each measurement is an apparent magnitude defined relative to its calibration. Each of $U-B$ and $B-V$ is a color index: a difference in magnitudes that constrains spectral shape.

The measurement includes the filter, detector response and calibration convention, not merely a nominal wavelength. Effective temperature, composition, surface gravity and interstellar extinction can all affect the colours. Combining both indices with spectral classification therefore provides more information than interpreting one colour as a unique thermometer.

A photometric passband is the wavelength-dependent response used for a brightness measurement. An energy-weighted measurement is $I=\int {\eta }_{\lambda }{F}_{\lambda }d\lambda$, with spectral flux density $F_{\lambda }$. Photon-counting conventions can instead include a factor $\lambda /(hc)$; the calibration must use the same convention as the measurement.

The traditional near- and thermal-infrared photometric bands in the 1–5 micrometre region are $J,H,K,L,M$, with approximate centers $1.25,1.65,2.2,3.5,4.8$ micrometres. Variants such as $K_s$, $L^{\prime }$ and $M^{\prime }$ have different detailed responses. They largely follow atmospheric windows; transmission, sky brightness, and detector response determine practical band edges. The ISAAC filter documentation records instrument-specific variants, including an $L$ filter closer to $L^{\prime }$ near 3.8 micrometres.