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 ($dA$).

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 ($\mathrm{W/m^2}$).