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==== Luminous Flux ====
**Definition**\\
Luminous flux is a physical quantity in photometry used to measure the perceived power of light by the human eye. It represents the total luminous energy emitted by a light source per unit time, providing an intuitive indication of "how bright overall" the light source is.
{{ :yanding:成像基础知识:光学:光度学:光通量6.png?200 |}}
(Image source: https://en.wikipedia.org/wiki/Radiant_flux#/media/File:Photometry_radiometry_units.svg)\\
Its calculation principle involves applying a "human eye sensitivity weighting" to the radiant flux of the light source using the "[[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 (V(λ))]]", thereby quantifying the rate of energy flow in visible light that is effective for human vision. The specific calculation formula is as follows:

 $$\Phi_{v}(\lambda)=K_{m}V(\lambda)\Phi_{e}(\lambda)$$

  * $\Phi_{v}(\lambda)$ is the luminous flux at wavelength λ (unit: lm);
  * $K_{m}$ is the [[yanding:成像基础知识:光学:辐射度学与光度学:发光效能|maximum luminous efficacy]], with a standard value of 683 lm/W (corresponding to the 555 nm yellow-green light to which the human eye is most sensitive);
  * $V(\lambda)$ is the [[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|spectral luminous efficiency function]];
  * When $\lambda=555nm $, V (λ)=1; as the wavelength deviates from this value, $V(\lambda)$ gradually decreases (e.g., V (λ) approaches 0 for red and violet light);
  * $\Phi_{e}(\lambda)$ is the [[yanding:成像基础知识:光学:辐射度学与光度学:辐射通量|radiant flux]] of the light source at wavelength λ (unit: W).

**Unit**\\
The SI unit of luminous flux is the lumen (lm). One lumen represents the luminous flux emitted by a uniform point source with a luminous intensity of one candela within a solid angle of one steradian. The expression is:
$$1  lm = 1 cd  \times 1 sr$$

**Measurement of Luminous Flux**\\
According to the GB/T 20178-2010 standard "Methods for Measurement of Luminous Flux", luminous flux can be measured using the following methods: //calculating luminous flux from luminous intensity distribution, calculating luminous flux from illuminance distribution, and measuring luminous flux using an integrating sphere.//

**1. Calculating Luminous Flux from Luminous Intensity Distribution**

The luminous flux $\Phi$ can be obtained from the spatial distribution of luminous intensity using the formula:
$$\Phi = \int_{(\Omega)} I \mathrm{d}\Omega$$

where $\Omega = 4\pi\ \text{sr}$ is the total solid angle. The luminous intensity distribution can be measured using a goniophotometer.


**2. Calculating Luminous Flux from Illuminance Distribution**

Given the illuminance distribution E on a closed surface A in the space surrounding the light source, the luminous flux $\Phi$ can be derived using the following formula:
$$\Phi = \int_{(\mathrm{A})} E \mathrm{d}A$$
The illuminance distribution can be measured on a spherical surface around the light source using a goniophotometer. The light source does not need to be placed exactly at the center of the virtual sphere, but it is recommended to position it as close to the center as possible.\\

**3. Measurement Using an Integrating Sphere**

The luminous flux of a light source can be obtained by comparative measurement with a standard lamp inside an integrating sphere. During the test, the light source and the standard lamp must be placed sequentially at the same position inside the integrating sphere. The indirect illuminance on the inner surface of the sphere is measured to determine the luminous flux.\\
{{ :yanding:成像基础知识:光学:光度学:积分球测量.png?400 |}}
where L is the light source; H is the auxiliary lamp with a baffle; S is the baffle; d is the diameter of the sphere; and F is the photometer probe section of the sphere.\\
Precautions:\\
1. The integrating sphere should have a sufficient diameter to accommodate the largest light source to be measured. There should be enough distance between the light source and the sphere wall to allow for multiple diffuse reflections without interference from the light source itself.\\
2. The coating on the inner surface of the sphere should exhibit non-selective diffuse reflection and should not be luminescent.\\
3. A baffle should be placed inside the integrating sphere to prevent direct light from the source from reaching the photometer probe.\\
4. All objects inside the sphere, such as baffles and lamp holders, will affect the test results and should therefore be kept as small as possible. The light source itself will also absorb radiation.\\
5. The receiving surface of the photometer probe should be made of a material with good diffuse reflection (or transmission) properties.\\
6. If the test lamp and the standard lamp share the following characteristics, the luminous flux measured in the spherical photometer using the substitution principle will be accurate: identical size and shape, identical spectral distribution, and identical spatial distribution. If the test lamp and the standard lamp differ in one or more of these characteristics, measurement errors will occur.\\

**See Also**\\
[[yanding:成像基础知识:光学:辐射度学与光度学:发光效能]], [[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]], [[yanding:成像基础知识:光学:辐射度学与光度学:照度]]