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==== Luminous Exitance ====
**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.
|  {{ :yanding:成像基础知识:光学:辐射度学与光度学:光出射度.png?500 |}}  |
^  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: **[[yanding:成像基础知识:光学:辐射度学与光度学:辐射出射度|Radiant Exitance]]** ($M_e$), with the unit $\mathrm{W/m^2}$.

**See Also**\\
[[yanding:成像基础知识:光学:辐射度学与光度学:光通量|Luminous Flux]], [[yanding:成像基础知识:光学:辐射度学与光度学:辐射出射度|Radiant Exitance]], [[yanding:成像基础知识:光学:辐射度学与光度学:cie标准光视效率函数|CIE Luminous Efficiency Function]]