文章目录

Radiometry
总览
辐射能量与辐射通量 Radiant Energy and Flux (Power)
- 重要的度量单位
- - Radiant Intensity （辐射强度）
  - - Angles and Solid Angles（角和立体角）
    - - Differential Solid Angles（立体角微分）
      - ω\omegaω as a direction vector（ω\omegaω是方向向量）
        
        Isotropic Point Source（各向同性点光源的辐射强度计算）
  - Irradiance
  - - Lambert’s Cosine Law
    - Correction: Irradiance Falloff
  - Radiance
  - - Incident Radiance
    - Exiting Radiance
    - Irradiance vs. Radiance
Luminance and Photometry
扩展
引用

辐射度量学

主要参考 https://sites.cs.ucsb.edu/~lingqi/teaching/resources/

Radiometry

Measurement system and units for illumination

Accurately measure the spatial properties of light

New terms: Radiant flux, intensity, irradiance, radiance

Perform lighting calculations in a physically correct manner

因为关于辐射亮度的很多单位在中文上都比较相似，很容易引起歧义，所以这里直接参考ppt中的内容

总览

辐射能量与辐射通量 Radiant Energy and Flux (Power)

Definition: 辐射能量是电磁辐射的能量，度量单位是焦耳，符号表示如下
Radiant energy is the energy of electromagnetic radiation. It is measured in units of joules, and denoted by the symbol:
Q[J=Joule ]Q[\mathrm{~J}=\text { Joule }] Q[ J= Joule ]

Definition: 辐射通量（功率）是单位时间放射、反射、传输或接收的能量。
Radiant flux (power) is the energy emitted, reflected, transmitted or received, per unit time:
Φ≡dQdt[W=Watt][lm=lumen ]⋆\Phi \equiv \frac{\mathrm{d} Q}{\mathrm{d} t}[\mathrm{~W}=\mathrm{Watt}][\mathrm{lm}=\text { lumen }]^{\star} Φ≡dtdQ[ W=Watt][lm= lumen ]⋆

Flux – #photons flowing through a sensor in unit time
通量 - 单位时间内通过传感器的光子数

重要的度量单位

从一个光源出射的光：“Radiant Intensity”（辐射强度）
落到一个表面点上的光：“Irradiance”
沿着射线传输的光：“Radiance”

Radiant Intensity （辐射强度）

Definition: 辐射（发光）强度是点光源发出的单位立体角的功率。
The radiant (luminous) intensity is the power per unit solid angle (立体角) emitted by a point light source.

Angles and Solid Angles（角和立体角）

平面角和立体角的定义以及计算

Differential Solid Angles（立体角微分）

立体角足够小的时候，球面可以看做是平面

ω\omegaω as a direction vector（ω\omegaω是方向向量）

Isotropic Point Source（各向同性点光源的辐射强度计算）

Irradiance

Definition: Irradiance 是入射到表面点上的单位面积的功率。The irradiance is the power per unit area incident on a surface point.

Lambert’s Cosine Law

表面上的Irradiance与光线与表面法线方向夹角的余弦成正比
Irradiance at surface is proportional to cosine of angle between light direction and surface normal.

Correction: Irradiance Falloff

均匀分布的光源朝任意方向的功率与半径 rrr 的平方 r2r^2r2 成反比，即以 r2r^2r2 衰减

Radiance

Radiance是描述环境中光分布的基础场度量
Radiance is the fundamental field quantity that describes the distribution of light in an environment

Radiance is the quantity associated with a ray
Rendering is all about computing radiance

Definition: radiance (luminance) 是单位立体角，单位投影面积，放射、反射、传输或接收的功率。The radiance (luminance) is the power emitted, reflected, transmitted or received by a surface, per unit solid angle, per projected unit area.

因为

Irradiance: power per projected unit area
Intensity: power per solid angle
所以，Radiance有两种解释方式
Radiance: Irradiance per solid angle
Radiance: Intensity per projected unit area

Incident Radiance

入射 radiance 是到达表面的单位立体角的 irradiance
Incident radiance is the irradiance per unit solid angle arriving at the surface.

i.e. it is the light arriving at the surface along a given ray (point on surface and incident direction).

Exiting Radiance

出射表面 radiance 是离开表面的单位投影面积的 intensity
Exiting surface radiance is the intensity per unit projected area leaving the surface.

e.g. for an area light it is the light emitted along a given ray (point on surface and exit direction).

Irradiance vs. Radiance

Irradiance: total power received by area dA
Radiance: power received by area dA from “direction” dω\mathrm{d} \omegadω

dE(p,ω)=Li(p,ω)cos⁡θdωE(p)=∫H2Li(p,ω)cos⁡θdω\begin{aligned} d E(\mathrm{p}, \omega) &=L_{i}(\mathrm{p}, \omega) \cos \theta \mathrm{d} \omega \\ E(\mathrm{p}) &=\int_{H^{2}} L_{i}(\mathrm{p}, \omega) \cos \theta \mathrm{d} \omega \end{aligned} dE(p,ω)E(p)=Li(p,ω)cosθdω=∫H2Li(p,ω)cosθdω

Luminance and Photometry

所有像flux、radiance等radiometric度量单位都有对应的photometric度量单位。

Photometry 是基于人眼视觉系统感知的可视电磁radiation。

***Luminance***表示人眼感知到的频谱能量分布的亮度。设其度量单位为 YYY，其对应的 spectral radiance 为 L(λ)L(\lambda)L(λ) 则
Y=∫λL(λ)V(λ)dλY=\int_{\lambda} L(\lambda) V(\lambda) \mathrm{d} \lambda Y=∫λL(λ)V(λ)dλ
其中 spectral response curve V(λ)V(\lambda)V(λ) 跟color的 XYZ 表示相关

Table 5.1: Representative Luminance Values for a Number of Lighting Conditions. ConditionLuminance(cd/m2,ornits)Sun at horizon 600,00060-watt lightbulb 120,000Clear sky 8,000Typical office 100−1,000Typical computer display 1−100Street lighting 1−10Cloudy moonlight 0.25\begin{aligned} &\text { Table 5.1: Representative Luminance Values for a Number of Lighting Conditions. }\\ &\begin{array}{ll} \hline \textbf{ Condition } & \textbf{ Luminance }\left(\mathbf{c d} / \mathbf{m}^{2}, \textbf{ or nits }\right) \\ \hline \text { Sun at horizon } & 600,000 \\ \hline \text { 60-watt lightbulb } & 120,000 \\ \hline \text { Clear sky } & 8,000 \\ \hline \text { Typical office } & 100-1,000 \\ \hline \text { Typical computer display } & 1-100 \\ \hline \text { Street lighting } & 1-10 \\ \hline \text { Cloudy moonlight } & 0.25 \end{array} \end{aligned} Table 5.1: Representative Luminance Values for a Number of Lighting Conditions. Condition Sun at horizon 60-watt lightbulb Clear sky Typical office Typical computer display Street lighting Cloudy moonlight Luminance (cd/m2, or nits )600,000120,0008,000100−1,0001−1001−100.25

所有其他的 radiometric quantities 如下表
Table 5.2: Radiometric Measurements and Their Photometric Analogs. RadiometricUnitPhotometricUnitRadiant energy joule(Q)Luminous energy talbot (T) Radiant flux watt(W)Luminous flux lumen (lm) Intensity W/srLuminous intensity lm/sr=candela (cd)Irradiance W/m2Illuminance lm⁡/m2=lux⁡(lx)Radiance W/(m2sr)Luminance lm⁡/(m2sr)=cd/m2=nit\begin{aligned} &\text { Table 5.2: Radiometric Measurements and Their Photometric Analogs. }\\ &\begin{array}{ll} \hline \textbf{ Radiometric} & \textbf{Unit} & \textbf{ Photometric}& \textbf{Unit} \\ \hline \text { Radiant energy } & \mathrm{ joule (Q) } & \text{ Luminous energy } & \text{ talbot (T) }\\ \hline \text { Radiant flux } & \mathrm{ watt (W) } & \text{ Luminous flux } & \text{ lumen (lm) }\\ \hline \text { Intensity } & \mathrm{W} / \mathrm{sr} & \text { Luminous intensity } & \mathrm{lm} / \mathrm{sr}=\text { candela }(\mathrm{cd}) \\ \hline \text { Irradiance } & \mathrm{W} / \mathrm{m}^{2} & \text { Illuminance } & \operatorname{lm} / \mathrm{m}^{2}=\operatorname{lux}(\mathrm{lx}) \\ \hline \text { Radiance } & \mathrm{W} /\left(\mathrm{m}^{2} \mathrm{sr}\right) & \text { Luminance } & \operatorname{lm} /\left(\mathrm{m}^{2} \mathrm{sr}\right)=\mathrm{cd} / \mathrm{m}^{2}=\mathrm{nit} \end{array} \end{aligned} Table 5.2: Radiometric Measurements and Their Photometric Analogs. Radiometric Radiant energy Radiant flux Intensity Irradiance Radiance Unitjoule(Q)watt(W)W/srW/m2W/(m2sr) Photometric Luminous energy Luminous flux Luminous intensity Illuminance Luminance Unit talbot (T) lumen (lm) lm/sr= candela (cd)lm/m2=lux(lx)lm/(m2sr)=cd/m2=nit

扩展

我们实现的球谐光照，在球谐系数中编码的就是，单位立体角单位面积上的功率，即 Radiance

引用

[1] https://sites.cs.ucsb.edu/~lingqi/teaching/resources/

[2]http://www.pbr-book.org/3ed-2018/Color_and_Radiometry/Radiometry.html

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文章目录

Radiometry

总览

辐射能量与辐射通量 Radiant Energy and Flux (Power)