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A magnitude zero point fixes the reference measurement $I_0$ in a specified photometric passband. Relative to a zero-magnitude reference, the apparent magnitude is $m=-2.5{\log }_{10}(I/I_0)$. Both measurements must use the same passband and calibration convention.

An optical spectrum describes the distribution of optical radiation over wavelength or frequency. A spectrograph records it by separating wavelengths, while a photometric passband integrates a chosen part.

The traditional infrared photometric bands extending the optical photometric system into this range are approximatelyTheir photometric passbands lie mainly in atmospheric windows between strong molecular absorption bands. This makes ground-based observations practical. The exact centers depend on the system: $L^{\prime }$ is near $3.8\mu \mathrm{m}$, and shortened $K_s$ and $M^{\prime }$ bands reduce unwanted background or absorption. At the longest wavelengths, atmospheric and instrumental thermal radiation make sky brightness especially important. A modern $Y$ band near $1.0\mu \mathrm{m}$ is an additional choice, rather than one of the traditional $JHKLM$ extensions.

The magnitude zero point is defined by the reference response $I_0$. With zero magnitude assigned to that reference, the apparent magnitude isThe two responses must use the same photometric passband and instrumental weighting. If the reference has assigned magnitude $m_0$ instead, add $m_0$ to the right-hand side.

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

Spectral flux density is radiant power received per unit area and per unit wavelength or frequency. The two conventions satisfy $F_{\lambda }d\lambda =-F_{\nu }d\nu$ under $\nu =c/\lambda$, hence $F_{\lambda }=(c/{\lambda }^2)F_{\nu }$ when the arguments refer to the same photons. Integrating over a photometric passband gives its measured flux.