Luminance is a physical quantity that describes the brightness of a light-emitting body (or a reflecting/transmitting surface) in a specified direction. It is defined as the ratio of the luminous intensity in that direction to the projected area of the emitting surface perpendicular to that direction. It directly determines the human eye's perception of the “brightness” of an object and is closely related to the luminous efficacy of the emitter and the surface reflection/transmission characteristics. (Image source: https://en.wikipedia.org/wiki/Radiant_flux#/media/File:Photometry_radiometry_units.svg)
Unit: The SI unit is candela per square meter (cd/m², also known as “nit”). Since 1 candela (cd) = 1 lumen per steradian (lm/sr), it follows that $1\ \text{cd/m}^2 = 1\ \text{lm/(sr·m}^2\text{)}$

Mathematical expression: $L = \frac{I_\theta}{S \cdot \cos\theta}$

• $L$ is the luminance in the specified direction (unit: cd/m²);
• ${I_\theta}$ is the luminous intensity of the emitting surface in the specified direction (unit: cd);
• $S$ is the actual area of the emitting surface (unit: m²);
• $ \theta$ is the angle between the specified direction and the normal to the emitting surface (unit: rad or °), and ${S \cdot \cos\theta}$ is the projected area in that direction.

If the luminous intensity in a given direction is greater while the apparent emitting area in that direction is smaller, the perceived brightness is higher, meaning the luminance is greater. The emitting surface here can be a directly radiating area light source, or a reflecting or transmitting surface illuminated by light. Luminance can be directly measured using a luminance meter.

Practical scenario:
Question: Why does the book area appear brighter to the human eye than the edge of the desk?
The desk lamp uses a lampshade to direct light, concentrating the projection onto the book, which makes the reflected luminous intensity per unit area much higher than that at the edge of the desk. The human eye observes the book directly without directional loss, whereas the edge of the desk not only has a weaker reflected luminous intensity per unit area but also suffers a further reduction in luminance due to the viewing angle. Therefore, the human eye perceives the book area as brighter.

FAQ:
Q: Under what conditions can a light source achieve high luminance?
A: A light source achieves high luminance when it produces a high luminous flux from a small emitting area and emits it within a small solid angle (e.g., flashlights, laser pointers).

Q: What is the relationship between luminance and the perceived brightness of an object?
A: For objects resolvable by the human eye, luminance determines their perceived brightness. When an observer moves away from a light source, the light entering the pupil decreases, but the image of the light source on the retina also shrinks proportionally. As long as the angular resolution of the eye is sufficient, the effects of luminous flux attenuation and image shrinkage compensate for each other, keeping the apparent brightness constant; thus, luminance is independent of observation distance. However, at greater observation distances where the eye's angular resolution is insufficient, the apparent brightness decreases even though the luminance remains constant.

Q: Why does adding a lampshade make the observer perceive the light as brighter when the luminous flux of the light source remains unchanged?
A: With the total luminous flux of the light source unchanged, the light-concentrating design of the lampshade restricts the solid angle of light emission, projecting the dispersed light onto a smaller illuminated area. This focuses the reflected light onto a smaller area of the retina, significantly increasing the areal density of light and thereby creating a brighter visual perception.