==== 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** to visible light of different wavelengths under specific photometric conditions.\\ **Strict Definition：**Under specific photometric conditions, if radiant flux $\Phi_{e,\lambda}$ at wavelength $\lambda$ and radiant flux $\Phi_{e,\lambda_m}$ at the peak sensitivity wavelength $\lambda_m$ produce an identical visual sensation of brightness, the ratio of these two fluxes, $\Phi_{e,\lambda_m}/\Phi_{e,\lambda}$, defines the spectral luminous efficiency $V(\lambda)$. **II. Unit**\\ Spectral luminous efficiency is a dimensionless quantity with a unit of 1. It represents only the relative ratio of radiant flux and has no physical dimension. \\ **III. Luminous Efficiency Functions**\\ Human spectral sensitivity depends on visual adaptation, field of view (FOV), and the angle of incidence. The CIE defines several standard functions for different photometric conditions:\\ ---- **Photopic Vision \(V(\lambda)\)**\\ * **Operating Conditions:**: $L > 5 cd·m⁻²$(e.g., daylight or bright artificial lighting).\\ * **Physiological Mechanism**: Mediated by cone cells (3 types, containing photopigments corresponding to red/green/blue perception). They have low light sensitivity and high noise in dark environments, functioning only in bright environments, and are responsible for color vision and detail resolution.\\ {{ :yanding:成像基础知识:光学:辐射度学与光度学:锥状细胞.png?240|}} **Figure 1: Schematic Diagram of Cone Cells**\\ **Source:** https://en.wikipedia.org/wiki/Cone_cell#media/File:Cone_cell_eng.svg\\ * **Relevant Standards**: ISO 23539:2005 (E) / CIE S 010; * **On the visual axis:**\\ * $V(\lambda)$: CIE 1924 photopic spectral luminous efficiency (corresponds to the fovea of the retina); * $CIE 1988 (CIE 086-1990)$: Corrected the shortcomings of CIE 1924 at short wavelengths * **Off the visual axis:**\\ * Below $4^\circ$ viewing angle: \(V(\lambda)\) (CIE 1924, peak at 555 nm, green light band); * Above $4^\circ$ viewing angle: \(V_{10}(\lambda)\) (CIE 1964, CIE 165:2005), adapted for large field of view and off-axis visual tasks. * **Practical Applications**: In LED lighting design, matching the 555 nm peak improves luminous efficacy of luminaires; automobile headlights use the photopic curve to optimize white light spectrum and enhance road visibility.\\ ---- **Scotopic Vision \(V'(\lambda)\)**\\ * **Applicable Scenarios**: $L < 0.005\ \mathrm{cd\cdot m^{-2}}$(e.g., darkrooms, unlit night).\\ * **Physiological Mechanism**: Mediated by rod cells (rhodopsin). High sensitivity; achromatic perception; no color vision.\\ {{ :yanding:成像基础知识:光学:辐射度学与光度学:杆状细胞.png?240|}} **Figure 2:Schematic Diagram of Rod Cells**\\ **Source:** https://en.wikipedia.org/wiki/Rod_cell#/media/File:Rod_Cell.svg\\ * **Relevant Standards**: ISO 23539:2005 (E) / CIE S 010\\ * **Core Characteristics**: The CIE 1951 scotopic spectral luminous efficiency function $V'(\lambda)$ peaks at 507 nm (blue-green spectrum).\\ * **Applications**: Night-vision and astronomical equipment (optimized for 507 nm); blue-green reflective materials in nighttime road signage to enhance low-light visibility.\\ ---- **Mesopic Vision \(V_{\text{mes},m}(\lambda)\)**\\ * **Operating Conditions:**: $0.005\ \mathrm{cd\cdot m^{-2}} < L < 5\ \mathrm{cd\cdot m^{-2}}$(e.g., twilight, parking garages).\\ * **Physiological Mechanism**: Co-mediated by rods and cones. Sensitivity and color perception shift dynamically with luminance.\\ * **Relevant Standards**: CIE 191:2010\\ * **Core Characteristics**: A weighted combination of photopic and scotopic functions, defined by the adaptation coefficient $m$.\\ * **Applications**: Urban night lighting and smart streetlamps (balancing visibility and energy efficiency).\\ ---- **Comparison of Spectral Luminous Efficiency Functions**\\ {{ :en:yanding:imaging_basics:optics:radiometry_photometry:cie_standard_luminous_efficiency_function.png?500 |}} (Image source: https://commons.wikimedia.org/wiki/File:LuminosityCurve1.svg)\\ The figure clearly shows the spectral sensitivity differences between photopic and scotopic vision. Scotopic vision is more sensitive to blue - green light (507 nm), while photopic vision is most sensitive to green light (555 nm). The horizontal axis represents wavelength, with units of nanometers (nm).\\ **IV. Photometric calculations based on the luminous efficiency function**\\ The primary application of the luminous efficiency function is to convert radiometric quantities into photometric quantities. The general calculation model is:\\ $$\varPhi_{\text{v}} = K_{\text{m}} \int_{0}^{\infty} \varPhi_{\text{e},\lambda}(\lambda) \cdot V(\lambda) \, d\lambda$$\\ where:\\ * \(\varPhi_{\text{v}}\) is the [[en:yanding:imaging_basics:optics:radiometry_photometry:luminous_flux|luminous flux]] (unit: lm), representing the total light output perceived by the human visual system from the visible radiation emitted by a light source; * \(\varPhi_{\text{e},\lambda}(\lambda)\) is the spectral radiant flux (unit: $\mathrm{W\cdot nm^{-1}}$), describing the radiant power distribution of the source per unit wavelength interval; * $K_\mathrm{m}$ is [[en:yanding:imaging_basics:optics:radiometry_photometry:luminous_efficacy|the maximum luminous efficacy]] (unit: $\mathrm{lm\cdot W^{-1}}$), with a standard value of $683\ \mathrm{lm/W}$, corresponding to the upper limit of energy conversion efficiency at the peak wavelength of photopic vision ($555\ \mathrm{nm}$); * $V(\lambda)$ is the spectral luminous efficiency function for photopic vision; for scotopic or mesopic conditions, it is replaced by $V'(\lambda)$ or $V_\mathrm{mes}(\lambda)$, respectively. As an example, under photopic conditions, the spectral luminous efficiency of the human eye at $480\ \mathrm{nm}$ is approximately $20\%$ of that at $555\ \mathrm{nm}$. Therefore, a monochromatic source at $480\ \mathrm{nm}$ with five times the radiant power of a $555\ \mathrm{nm}$ source would yield identical luminous flux. Under identical viewing conditions (same emitting area, field of view and observation distance), the two sources produce the same perceived brightness.