Luminous exitance (symbol: $M_v$, $M$) is a core physical quantity in photometry that characterizes the luminous properties of an area light source. It is used to quantify the ability of a surface to emit visible light outward, describing the total light output per unit area without considering the directional distribution of the emitted light.

1. Definition
According to the International Commission on Illumination (CIE) standards, luminous exitance is defined as: at a given point on the surface of an area light source, the total luminous flux emitted per unit area into the outward hemispherical space ($2\pi$ solid angle).
Mathematically, it is the ratio of the luminous flux $d\Phi_v$ leaving the surface element at that point to the area $dA$ of the surface element.

Figure 1: Physical model of the total luminous flux $d\Phi_v$ emitted by a surface element $dA$ into the hemispherical space

2. Mathematical Expression
$$M_v = \frac{d\Phi_v}{dA}$$ Parameter description:

• $d\Phi_v$: Total luminous flux emitted by the surface element $dA$ into the outward hemispherical space (unit: lumen, lm);
• $dA$: Infinitesimal area element of the light source surface at that point (unit: square meter, $m^2$).

3. Unit:
The International System of Units (SI) unit is lumens per square meter ($\text{lm/m}^2$).

Distinction:
The dimensional unit of luminous exitance is numerically completely equivalent to the unit of illuminance ($E$), the lux ($\mathrm{lx}$) ($1\ \mathrm{lm/m^2} = 1\ \mathrm{lx}$), but their physical natures are entirely different:

• Luminous exitance ($M_v$): Describes the luminous flux “leaving” a surface (emitted/reflected), characterizing the luminous capability of a light source or reflecting surface;
• Illuminance ($E$): Describes the luminous flux “incident” on a surface, characterizing the illumination condition of the environment.

4. Derivation and Relationships
1. Spectral Conversion:
Luminous exitance can be derived from the spectral radiant exitance:
$$M_v = K_m \int_{0}^{\infty} M_{e,\lambda}(\lambda) V(\lambda) d\lambda$$ where:

• $K_m = 683\ \text{lm/W}$ is the maximum spectral luminous efficacy for photopic vision;
• $M_{e,\lambda}(\lambda)$ is the spectral radiant exitance at wavelength $\lambda$;
• $V(\lambda)$ is the CIE standard luminous efficiency function for photopic vision;
• The integration range $[0, \infty)$ covers the entire spectrum, but in practical calculations, the visible light band from $380\ \text{nm}$ to $780\ \text{nm}$ is typically used.

2. Lambertian Surface Characteristics:
For an ideal diffuse emitting surface (Lambertian surface), the luminous exitance and the luminance $L_v$ at that point satisfy a simple proportional relationship:
$$ M_v = \pi L_v $$

3. Radiometric Equivalent:
Radiometric equivalent: Radiant Exitance ($M_e$), with the unit $\mathrm{W/m^2}$.

See Also
Luminous Flux, Radiant Exitance, CIE Luminous Efficiency Function