==== Luminous Exitance ====
**Luminous exitance** (symbol: $M_v$, $M$)is a fundamental physical quantity in photometry used to characterize the emission properties of a surface light source. It quantifies the capability of a surface to emit visible light outwards, describing the total luminous flux output per unit area, regardless of the directional distribution of the emitted light.\\

**Definition**\\
According to the International Commission on Illumination (CIE) standards, luminous exitance is defined as the luminous flux density leaving a point on a real or imaginary surface.Specifically, it is the total luminous flux ($d\Phi_v$）emitted into the outer hemispherical space ($2\pi$ steradians) per unit area ($dA$).\\

|  {{ :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: $d\Phi_v$  emitted from $dA$ into hemispherical space.    ^

The mathematical expression is given by:\\
$$M_v = \frac{d\Phi_v}{dA}$$
where:\\
  * $d\Phi_v$ is the total luminous flux emitted by the surface element $dA$ into the outer hemispherical space(Unit: lumen,$lm$ );
  * $dA$ is the infinitesimal surface area element at the point on the source surface(Unit:square meter, $m^2$).

** Unit:**\\
The SI unit of luminous exitance is the lumen per square meter ($\text{lm/m}^2$).\\

While luminous exitance $(M_v)$ and illuminance $(E)$ share the same unit dimension—the lux ($lx$), where $1\ \mathrm{lm/m^2} = 1\ lx$—their physical natures are fundamentally distinct:\\
  * **Luminous Exitance $(M_v)$**: Describes the luminous flux "leaving" a surface (via emission or reflection). It characterizes the luminous capacity of a light source or a reflective surface.
  * **Illuminance $(E)$**: Describes the luminous flux  "incident upon'' a surface. It characterizes the lighting conditions received by the environment or an object.


**Relationships**\\
**1. Spectral Conversion**\\
Luminous exitance can be derived from the spectral radiant exitance using the following integral:\\
$$M_v = K_m \int_{0}^{\infty} M_{e,\lambda}(\lambda) V(\lambda) d\lambda$$
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 Surfaces**\\
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 Counterpart**\\
The corresponding quantity in the field of radiometry is Radiant Exitance ($M_e$), which is measured in watts per square metre ($\mathrm{W/m^2}$).