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ASME Y10.18-1967 — Letter Symbols for Illuminating Engineering
💡 USAS Y10.18-1967 is a USA Standard prepared by Subcommittee 6 of Sectional Committee Y10 on Letter Symbols, in cooperation with the Illuminating Engineering Society, and approved by the USA Standards Institute on February 2, 1967. It establishes a uniform system of letter symbols for the radiometric and photometric quantities used in illuminating engineering, closely following the international agreements then being reached by the International Commission on Illumination (CIE), the International Organization for Standardization (ISO), the International Electrotechnical Commission (IEC), and the SUN Commission of the International Union of Pure and Applied Physics. As the Foreword states, the symbols in this Standard are consistent with the international agreements reached to date — a step toward worldwide acceptance of one set of terms and symbols.
💡 The outstanding feature of this Standard is the “one symbol, two uses” strategy: radiometric and photometric quantities share the same set of symbols, distinguished only by the subscripts e (energy) and v (visual) when differentiation is needed — a convention later adopted widely by CIE and international standards.
1. Scope and Background 📌
In the 1960s, the spread of fluorescent lamps, high-intensity discharge lamps, and photoelectric measurement created an urgent need for uniform lighting symbols. Close cooperation among CIE, ISO, IEC, and the SUN Commission was producing a globally unified set of terms and symbols; this Standard is the US contribution to that process.
The two outstanding features of the Standard are:
- Shared radiometric/photometric symbols: the same symbol works in both the radiation (physical energy) and light (visually weighted) contexts, distinguished by the subscripts e and v when needed;
- Spectral concentration and wavelength-function conventions: subscript λ designates a spectral concentration, while parentheses (λ) designate a function of wavelength — in English the adjective “spectral” covers both meanings, while in French “spectrique” is substituted for “spectral” for the first meaning to avoid ambiguity.
The significance: radiometric and photometric formulas have identical structure and differ only in the weighting function, so shared symbols greatly simplify the formula system.
⚠️ A fine distinction in spectral quantities: the subscript λ means “quantity per unit wavelength interval” (spectral concentration), whereas parentheses (λ) mean “function of wavelength.” For example, spectral irradiance Eλ and the wavelength-dependent irradiance E(λ) have different meanings — write them precisely.
2. Core Lighting Quantity Symbols 🧮
The table below gives the core quantities of the Standard system in their radiometric and photometric forms (subscripts e/v distinguish the radiation/light contexts, subscript λ denotes spectral concentration):
| Quantity | Radiometric Symbol | Photometric Symbol | Units |
|---|---|---|---|
| Energy | Qe | Qv | J / lm·s |
| Power / flux | Φe (or P) | Φv (luminous flux) | W / lm |
| Intensity | Ie | Iv (luminous intensity) | W/sr / cd |
| Irradiance / illuminance | Ee | Ev (illuminance) | W/m² / lx |
| Radiance / luminance | Le | Lv (luminance) | W/(m²·sr) / cd/m² |
| Exitance | Me | Mv | W/m² / lm/m² |
| Exposure | He | Hv | J/m² / lx·s |
| Spectral concentration | Eλ, Xe,λ, etc. | V(λ), Xv,λ, etc. | Quantity per unit wavelength interval |
On the photometric side, the Standard also covers luminous efficacy K, the spectral luminous efficiency function V(λ), and colorimetric quantities. This system is consistent with CIE standard terminology (e.g., CIE 17.4 International Lighting Vocabulary) and has become the common basis for lighting design, luminaire testing, and road-lighting evaluation.
💡 Unit relationships to remember: luminous flux lm, illuminance lx, luminous intensity cd, and luminance cd/m² are related by Φ = I·Ω, E = Φ/A, and L = I/Aprojected. As long as the subscript (e/v) is correct, the units follow automatically.
3. Symbol Rules and Engineering Practice ✍️
The Standard inherits the general Y10 principles: quantity symbols in italic, unit symbols in roman; subscripts e/v for the radiation/light contexts, subscript λ for spectral concentration, and parentheses (λ) for wavelength functions. These conventions have broad influence in practice:
- 🏭 Lighting design: illuminance Ev, luminance Lv, and uniformity are written with standard symbols in design calculations, easing communication with owners and luminaire manufacturers;
- 🔬 Photometric measurement: integrating-sphere luminous flux Φv and goniophotometer intensity Iv(θ,φ) use uniform symbols, avoiding ambiguity in test reports;
- ☀️ Daylighting and radiation assessment: solar radiation measurements use radiometric symbols such as Ee and He, linking directly to photovoltaic and solar-thermal calculations;
- 🌐 International alignment: following the CIE-consistent international symbols lets national lighting documents map one-to-one onto CIE/ISO/IEC documents.
🚨 Typical errors: confusing “luminous intensity I” with electric current I, or using “illuminance E” as an energy symbol. In cross-disciplinary documents (e.g., LED driver design covering both electrical and optical domains), define the symbol by context and subscripts, or the formulas become unreadable.
4. Frequently Asked Questions ❓
❓ Q: Why can radiometric and photometric symbols be shared?
A: Their formula structures and geometric definitions are exactly parallel; only the metric basis differs — radiometric quantities measure physical energy while photometric quantities weight by the human visual function V(λ). Sharing symbols with subscripts e/v preserves one unified formula system, an efficient approach endorsed by CIE.
A: Their formula structures and geometric definitions are exactly parallel; only the metric basis differs — radiometric quantities measure physical energy while photometric quantities weight by the human visual function V(λ). Sharing symbols with subscripts e/v preserves one unified formula system, an efficient approach endorsed by CIE.
❓ Q: What is the difference between Eλ and E(λ)?
A: Eλ is a spectral concentration (irradiance/illuminance per unit wavelength interval), while E(λ) is the irradiance/illuminance as a function of wavelength. The subscript λ means “quantity per unit wavelength interval”; the parentheses (λ) mean “function of wavelength” — they must not be interchanged.
A: Eλ is a spectral concentration (irradiance/illuminance per unit wavelength interval), while E(λ) is the irradiance/illuminance as a function of wavelength. The subscript λ means “quantity per unit wavelength interval”; the parentheses (λ) mean “function of wavelength” — they must not be interchanged.
❓ Q: How does this Standard relate to the CIE International Lighting Vocabulary?
A: It was developed in close cooperation with CIE, ISO, IEC, and the SUN Commission and is consistent with the international agreements reached at the time, serving as a bridging document between the CIE ILV and modern ISO 80000-7 (Light and Radiation).
A: It was developed in close cooperation with CIE, ISO, IEC, and the SUN Commission and is consistent with the international agreements reached at the time, serving as a bridging document between the CIE ILV and modern ISO 80000-7 (Light and Radiation).
❓ Q: How should luminous efficacy (lm/W) be written in reports?
A: Luminous efficacy is the ratio of luminous flux to electrical power; the symbol can be η or K (luminous efficacy), with the unit lm/W. It is recommended to list η, Φv, and P in the report’s symbol table and to state whether the value refers to the luminaire or the bare lamp.
A: Luminous efficacy is the ratio of luminous flux to electrical power; the symbol can be η or K (luminous efficacy), with the unit lm/W. It is recommended to list η, Φv, and P in the report’s symbol table and to state whether the value refers to the luminaire or the bare lamp.
