https://wiki.yanding.com/ 2026-10-09T12:28:33+00:00 https://wiki.yanding.com/ https://wiki.yanding.com/lib/tpl/myconfluence/images/favicon.ico text/html 2026-08-07T07:58:52+00:00 Anonymous (anonymous@undisclosed.example.com) https://wiki.yanding.com/doku.php?id=en:yanding:imaging_basics:optics:radiometry_photometry:cie_luminous_efficiency_function&rev=1786089532&do=diff CIE Standard Luminous Efficiency Function I. Definition The CIE luminous efficiency function $V(\lambda)$ is a standard response function established by the International Commission on Illumination (CIE) to describe the relative visual sensitivity of the standard observer$\Phi_{e,\lambda}$$\lambda$$\Phi_{e,\lambda_m}$$\lambda_m$$\Phi_{e,\lambda_m}/\Phi_{e,\lambda}$$V(\lambda)$$L > 5 cd·m⁻²$$V(\lambda)$$CIE 1988 (CIE 086-1990)$$4^\circ$\(V(\lambda)\)$4^\circ$\(V_{10}(\lambda)\)$L < 0.005\ \math… text/html 2026-08-31T02:53:19+00:00 Anonymous (anonymous@undisclosed.example.com) https://wiki.yanding.com/doku.php?id=en:yanding:imaging_basics:optics:radiometry_photometry:illuminance&rev=1788144799&do=diff Illuminance In photometry, illuminance (symbol:E)is the total luminous flux incident on a surface per unit area. It serves as a measure of how intensely a surface is illuminated. Figure 1: Definition of Illuminance ( Source: <https://en.wikipedia.org/wiki/Illuminance> ) The mathematical relationship is expressed as:$$E = \frac{\Phi}{S}$$$E$$\Phi$$S$$m^2$$$1\ \mathrm{lx} = 1\ \mathrm{lm/m^2}$$$V(\lambda)$ text/html 2026-07-23T06:02:30+00:00 Anonymous (anonymous@undisclosed.example.com) https://wiki.yanding.com/doku.php?id=en:yanding:imaging_basics:optics:radiometry_photometry:irradiance&rev=1784786550&do=diff Irradiance I.Definition Irradiance (denoted by $E$) is the radiant flux incident on a surface per unit area. Its SI unit is $W\cdot m^{-2}$ Mathematical Expression: $$E = \frac{d\Phi}{d$}$$ where $\Phi$ is the radiant flux and $A$ is the surface area. II.Irradiance from a point source For an isotropic point source, the radiant intensity in a given direction is denoted by $I$$W\cdot sr^{-1}$$dA$$dA$$$d\Omega = \frac{dA}{r^2}$$$$d\Phi = I \cdot d\Omega = I \cdot \frac{dA}{r^2}$$$$E = \fra… text/html 2026-07-22T07:40:20+00:00 Anonymous (anonymous@undisclosed.example.com) https://wiki.yanding.com/doku.php?id=en:yanding:imaging_basics:optics:radiometry_photometry:luminance&rev=1784706020&do=diff Luminance Luminance (symbol:$L$) is a photometric measure of the luminous intensity per unit area of light travelling in a given direction. It describes the amount of light that passes through, is emitted from, or is reflected off a particular surface. Luminance characterizes the human visual perception of $$L = \frac{I_\theta}{S \cdot \cos\theta}$$$L$$\mathrm{cd/m^2}$$I_\theta$$\mathrm{cd}$$S$$\mathrm{m^2}$$\theta$$\mathrm{rad}$$^\circ$$S \cdot \cos\theta$$\mathrm{cd/m^2}$ text/html 2026-08-31T08:11:26+00:00 Anonymous (anonymous@undisclosed.example.com) https://wiki.yanding.com/doku.php?id=en:yanding:imaging_basics:optics:radiometry_photometry:luminous_efficacy&rev=1788163886&do=diff Luminous Efficacy 1. Definition Luminous efficacy is the ratio of luminous flux $\Phi_\mathrm{V}$ to power, expressed in lumens per watt (lm·W⁻¹). $$K = \frac{\Phi_V}{\Phi_e} = \frac{\int_{380,\mathrm{nm}}^{780,\mathrm{nm}} K(\lambda),\Phi_{e,\lambda},\mathrm{d}\lambda}{\int_{0}^{\infty} \Phi_{e,\lambda},\mathrm{d}\lambda}$$ where $\Phi_{\mathrm{e},\lambda}$ is the spectral radiant flux and $V(\lambda)$ is the luminous efficiency function for photopic vision. * Radiant flux $\Phi_{\mathrm… text/html 2026-07-22T08:42:07+00:00 Anonymous (anonymous@undisclosed.example.com) https://wiki.yanding.com/doku.php?id=en:yanding:imaging_basics:optics:radiometry_photometry:luminous_exitance&rev=1784709727&do=diff Luminous Exitance Luminous exitance (symbol: $M_v$, $M$)is a fundamental physical quantity in photometry used to characterize the emission properties of a surface light source. It quantifies the capability of a surface to emit visible light outwards, describing the total luminous flux output per unit area, regardless of the directional distribution of the emitted light.$d\Phi_v$$2\pi$$dA$$d\Phi_v$$dA$$$M_v = \frac{d\Phi_v}{dA}$$$d\Phi_v$$dA$$lm$$dA$$m^2$$\text{lm/m}^2$$(M_v)$$(E)$$lx$$1\ \mathr… text/html 2026-07-21T12:02:37+00:00 Anonymous (anonymous@undisclosed.example.com) https://wiki.yanding.com/doku.php?id=en:yanding:imaging_basics:optics:radiometry_photometry:luminous_flux&rev=1784635357&do=diff Luminous Flux Definition Luminous flux (symbol:$\Phi_v$ ) is a photometric quantity that measures the light power perceived by the human eye. It represents the total luminous energy emitted by a light source per unit time, and directly reflects the overall brightness of the source.$$1\ \text{lm} = 1\ \text{cd} \times 1\ \text{sr}$$$lm$$$\Phi_{v}(\lambda)=K_{m}V(\lambda)\Phi_{e}(\lambda)$$$K_{m}$$\Phi_{v}(\lambda)$$V(\lambda)$$\lambda$$\Phi_v$$$ \Phi_v = \int_{(\Omega)} I_v \, d\Omega$$$\Omega… text/html 2026-07-21T13:06:56+00:00 Anonymous (anonymous@undisclosed.example.com) https://wiki.yanding.com/doku.php?id=en:yanding:imaging_basics:optics:radiometry_photometry:luminous_intensity&rev=1784639216&do=diff Luminous Intensity Definition Luminous intensity (symbol:$I_v$ ) describes the intensity of a light source in a given direction, defined as the luminous flux emitted per unit solid angle. It is an inherent property of the light source, independent of the source area and observation distance.$$ I_v = \frac{\mathrm{d}\Phi_v}{\mathrm{d}\Omega} $$$I_v$$\Phi_v$$\Omega$\(\mathrm{cd}\)\(540\times 10^{12}\ \mathrm{Hz}\)\(K_{\mathrm{cd}}\)\[ K_{\mathrm{cd}} = 683\ \mathrm{lm\,W^{-1}}. \]\(\Phi_v\)\(I_v… text/html 2026-08-31T05:31:38+00:00 Anonymous (anonymous@undisclosed.example.com) https://wiki.yanding.com/doku.php?id=en:yanding:imaging_basics:optics:radiometry_photometry:lv_luminance_exitance_conversion&rev=1788154298&do=diff Conversion between Lv, Luminance, and Luminous Exitance Background: Expressing Film Speed on a Logarithmic Scale In 1960, the ASA (American Standards Association, renamed the American National Standards Institute, or ANSI, in 1969) published a standard:$$S_v = \log_2 (N S_x) \tag{1}$$$S_x$$S_v$$S_x = 100, \quad S_v = \log_2(0.3 \times 100) = 4.9 \approx 5 $$\mathrm{ASA}\ 100 = \mathrm{ASA}\ 5^\circ$$$E_v = A_v + T_v = B_v + S_v \tag{2}$$$A_v = \log_2(A^2)$$A$$T_v = \log_2(1 / T)$$T$$B_v = \log… text/html 2026-07-23T03:24:16+00:00 Anonymous (anonymous@undisclosed.example.com) https://wiki.yanding.com/doku.php?id=en:yanding:imaging_basics:optics:radiometry_photometry:radiance&rev=1784777056&do=diff Radiance Definition Radiance(symbol: $L$) is the radiant flux emitted, reflected, transmitted, or received by a surface, per unit solid angle per unit projected area in a specified direction.As the fundamental property of extended sources, it characterizes the radiant intensity per unit projected area of a surface element along a given line of sight. \(\mathrm{W \cdot sr^{-1} \cdot m^{-2}}\)$L$$$L = \frac{dI}{dA \cos\theta} = \frac{d^2 \Phi}{dA \cos\theta \, d\Omega}$$$L$$I$$\Phi$$A$$\theta$$\… text/html 2026-08-31T11:18:37+00:00 Anonymous (anonymous@undisclosed.example.com) https://wiki.yanding.com/doku.php?id=en:yanding:imaging_basics:optics:radiometry_photometry:radiant_energy&rev=1788175117&do=diff Radiant Energy Definition Radiant Energy is the energy carried by electromagnetic radiation during its emission, propagation, or absorption. It is a fundamental energy quantity in radiometry, used to characterize the total energy transferred by radiation, and is denoted by the symbol: $Q_e$$$Q_e = \int_{t_1}^{t_2} \Phi_e(t) dt$$$\Phi_\mathrm{e}(t)$$[t_1,t_2]$$c$$$E = h\nu$$$h$$\nu$$$\alpha + \rho = 1$$$\alpha$$\rho$$\tau$$$\alpha + \rho + \tau = 1$$ text/html 2026-07-10T08:02:54+00:00 Anonymous (anonymous@undisclosed.example.com) https://wiki.yanding.com/doku.php?id=en:yanding:imaging_basics:optics:radiometry_photometry:radiant_energy_density&rev=1783670574&do=diff FIXME This page is not fully translated, yet. Please help completing the translation. (remove this paragraph once the translation is finished) Radiant Energy Density I. Definition Radiant energy density is defined as the electromagnetic radiant energy stored per unit volume of space\(w\)\(u\)\(J/m^3\)\([M L^{-1} T^{-2}]\)$$w = \frac{dQ}{dV}$$\(dQ\)\(dV\)$Q = 8000 J$$V= 23 L= 0.023 {m}^3$$w \approx 347\,826.09 {J/m}^3$\(E\)\(B\)$$w = \frac{1}{2}\left(\varepsilon E^2 + \frac{1}{\mu} B^2\righ… text/html 2026-09-01T05:46:55+00:00 Anonymous (anonymous@undisclosed.example.com) https://wiki.yanding.com/doku.php?id=en:yanding:imaging_basics:optics:radiometry_photometry:radiant_exitance&rev=1788241615&do=diff Radiant Exitance Radiant exitance, denoted as $M$, refers to the radiant flux emitted per unit time from a unit area of a surface into the outward hemispherical space, with the unit being $W/m^2$. Its mathematical expression is: $$M = \frac{d\Phi}{dA}$$ Relationship with Radiance $$M = \int_{\Omega} L(\omega) \cos\theta \, d\omega$$$L(\omega)$$\omega$$\theta$$\Omega$$$M = \rho E$$$\rho$$E$$\mathrm{W/m^2}$$$M = \pi L$$$lm/m^2$ text/html 2026-07-23T06:27:50+00:00 Anonymous (anonymous@undisclosed.example.com) https://wiki.yanding.com/doku.php?id=en:yanding:imaging_basics:optics:radiometry_photometry:radiant_flux&rev=1784788070&do=diff Radiant Flux I.Definition Radiant flux ($\Phi_e$), also known as radiant power, is the time rate of change of radiant energy. It represents the total radiant energy emitted, transferred, or received per unit time. The quantity is denoted by $\Phi_e$ or $P$ and is defined as:$$\Phi_\text{e} = \frac{\mathrm{d}Q_\text{e}}{\mathrm{d}t}$$$Q_\text{e}$$t$$\Phi_e$$\Phi_e$$$\Phi_e = K \cdot S$$$S$$K$$$\Phi_e = \int_{\lambda_1}^{\lambda_2} \Phi_{e,\lambda}(\lambda) d\lambda$$$I(\theta,\varphi)$$$ \Phi … text/html 2026-07-10T08:02:52+00:00 Anonymous (anonymous@undisclosed.example.com) https://wiki.yanding.com/doku.php?id=en:yanding:imaging_basics:optics:radiometry_photometry:radiant_intensity&rev=1783670572&do=diff FIXME This page is not fully translated, yet. Please help completing the translation. (remove this paragraph once the translation is finished) Radiant Intensity Definition: The radiant flux emitted by a radiation source in a specific direction per unit solid angle, denoted by the symbol $I$$$I = \frac{d\Phi}{d\Omega}$$$\Omega$$A$$r$$\Omega = \frac{A}{r^2}$$\Phi $$\Omega$$ I = \frac{d\Phi}{d\Omega}$$D$$ I = \frac{d\Phi}{d\Omega}$ text/html 2026-07-22T09:45:23+00:00 Anonymous (anonymous@undisclosed.example.com) https://wiki.yanding.com/doku.php?id=en:yanding:imaging_basics:optics:radiometry_photometry:solid_angle&rev=1784713523&do=diff Solid Angle Definition: In geometry and radiometry, a solid angle is a measure of the amount of the field of view from some particular point that a given object covers. For an arbitrary surface that subtends a region at a point (the vertex), the solid angle $\Omega$$A$$r$$$\Omega = \frac{A}{r^2}$$$\Omega$$A$$r$$r$$sr$$4\pi$