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Illuminance
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| Illuminance | |
|---|---|
Common symbols | Ev |
| SI unit | lux |
Other units | phot, foot-candle |
| In SI base units | cd·sr·m−2 |
| Dimension | |
In photometry, illuminance is the total luminous flux incident on a surface, per unit area.[1] It is a measure of how much the incident light illuminates the surface, wavelength-weighted by the luminosity function to correlate with human brightness perception.[2] Similarly, luminous emittance is the luminous flux per unit area emitted from a surface. Luminous emittance is also known as luminous exitance.[3][4]
In SI units illuminance is measured in lux (lx), or equivalently in lumens per square metre (lm·m−2).[2] Luminous exitance is measured in lm·m−2 only, not lux.[4] In the CGS system, the unit of illuminance is the phot, which is equal to 10000 lux. The foot-candle is a non-metric unit of illuminance that is used in photography.[5]
Illuminance was formerly often called brightness, but this leads to confusion with other uses of the word, such as to mean luminance. "Brightness" should never be used for quantitative description, but only for nonquantitative references to physiological sensations and perceptions of light.
The human eye is capable of seeing somewhat more than a 2 trillion-fold range. The presence of white objects is somewhat discernible under starlight, at 5×10−5 lux (50 μlx), while at the bright end, it is possible to read large text at 108 lux (100 Mlx), or about 1000 times that of direct sunlight, although this can be very uncomfortable and cause long-lasting afterimages.[citation needed]
Common illuminance levels
[edit]
| Lighting condition | Foot-candles | Lux |
|---|---|---|
| Sunlight | 10,000 [6] | 100,000 |
| Shade on a sunny day | 1,000 | 10,000 |
| Overcast day | 100 | 1,000 |
| Very dark day | 10 | 100 |
| Twilight | 1 | 10 |
| Deep twilight | 0.1 | 1 |
| Full moon | 0.01 | 0.1 |
| Quarter moon | 0.001 | 0.01 |
| Starlight | 0.0001 | 0.001 |
| Overcast night | 0.00001 | 0.0001 |
Astronomy
[edit]In astronomy, the illuminance stars cast on the Earth's atmosphere is used as a measure of their brightness. The usual units are apparent magnitudes in the visible band.[7] V-magnitudes can be converted to lux using the formula[8] where Ev is the illuminance in lux, and mv is the apparent magnitude. The reverse conversion is
Relation to luminance
[edit]
The luminance of a reflecting surface is related to the illuminance it receives: where the integral covers all the directions of emission ΩΣ, and
- Mv is the surface's luminous exitance
- Ev is the received illuminance, and
- R is the reflectance.
In the case of a perfectly diffuse reflector (also called a Lambertian reflector), the luminance is isotropic, per Lambert's cosine law. Then the relationship is simply
See also
[edit]References
[edit]- ^ "Illuminance, 17-21-060". CIE S 017:2020 ILV: International Lighting Vocabulary, 2nd edition. CIE - International Commission on Illumination. 2020. Retrieved 20 April 2023.
- ^ a b International Electrotechnical Commission (IEC): International Electrotechnical Vocabulary. ref. 845-21-060, illuminance
- ^ Luminous exitance Drdrbill.com
- ^ a b International Electrotechnical Commission (IEC): International Electrotechnical Vocabulary. ref. 845-21-081, luminous exitance
- ^ One phot = 929.030400001 foot-candles, according to http://www.unitconversion.org/unit_converter/illumination.html
- ^ "Illuminance - Recommended Light Level". The Engineering ToolBox. Archived from the original on April 3, 2022. Retrieved July 7, 2022.
- ^ Schlyter, Paul. "Radiometry and photometry in astronomy FAQ, section 7".
- ^ "Formulae for converting to and from astronomy-relevant units" (PDF). Archived from the original (PDF) on December 2, 2013. Retrieved Nov 23, 2013.
External links
[edit]- Illuminance Converter Archived 2010-02-10 at the Wayback Machine
- Knowledgedoor, LLC (2005) Library of Units and Constants: Illuminance Quantity
- Kodak's guide to Estimating Luminance and Illuminance using a camera's exposure meter. Also available in PDF form.
| Quantity | Unit | Dimension [nb 1] |
Notes | ||
|---|---|---|---|---|---|
| Name | Symbol[nb 2] | Name | Symbol | ||
| Luminous energy | Qv[nb 3] | lumen second | lm⋅s | T⋅J | The lumen second is sometimes called the talbot. |
| Luminous flux, luminous power | Φv[nb 3] | lumen (= candela steradian) | lm (= cd⋅sr) | J | Luminous energy per unit time |
| Luminous intensity | Iv | candela (= lumen per steradian) | cd (= lm/sr) | J | Luminous flux per unit solid angle |
| Luminance | Lv | candela per square metre | cd/m2 (= lm/(sr⋅m2)) | L−2⋅J | Luminous flux per unit solid angle per unit projected source area. The candela per square metre is sometimes called the nit. |
| Illuminance | Ev | lux (= lumen per square metre) | lx (= lm/m2) | L−2⋅J | Luminous flux incident on a surface |
| Luminous exitance, luminous emittance | Mv | lumen per square metre | lm/m2 | L−2⋅J | Luminous flux emitted from a surface |
| Luminous exposure | Hv | lux second | lx⋅s | L−2⋅T⋅J | Time-integrated illuminance |
| Luminous energy density | ωv | lumen second per cubic metre | lm⋅s/m3 | L−3⋅T⋅J | |
| Luminous efficacy (of radiation) | K | lumen per watt | lm/W | M−1⋅L−2⋅T3⋅J | Ratio of luminous flux to radiant flux |
| Luminous efficacy (of a source) | η[nb 3] | lumen per watt | lm/W | M−1⋅L−2⋅T3⋅J | Ratio of luminous flux to power consumption |
| Luminous efficiency, luminous coefficient | V | 1 | Luminous efficacy normalized by the maximum possible efficacy | ||
| See also: | |||||
- ^ The symbols in this column denote dimensions; "L", "T" and "J" are for length, time and luminous intensity respectively, not the symbols for the units litre, tesla and joule.
- ^ Standards organizations recommend that photometric quantities be denoted with a subscript "v" (for "visual") to avoid confusion with radiometric or photon quantities. For example: USA Standard Letter Symbols for Illuminating Engineering USAS Z7.1-1967, Y10.18-1967
- ^ a b c Alternative symbols sometimes seen: W for luminous energy, P or F for luminous flux, and ρ for luminous efficacy of a source.
Illuminance
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Fundamentals
Definition
Illuminance is a fundamental photometric quantity that describes the total luminous flux incident on a surface per unit area, where luminous flux represents the measure of visible light weighted by the spectral sensitivity of the human visual system.[9] This weighting accounts for the eye's varying response to different wavelengths, using the photopic luminous efficiency function V(λ) under normal daylight conditions or the scotopic function V'(λ) in low-light environments.[10] As such, illuminance quantifies the density of visible light reaching a given point on a surface, irrespective of the light's direction of incidence or the emitting source.[9] Mathematically, illuminance Ev is expressed as: where Φv is the luminous flux in lumens and A is the surface area in square meters.[9] Luminous flux itself is the total quantity of light emitted or received, perceived by the human eye.[10] The origins of illuminance trace back to 19th-century photometric investigations into light measurement, which sought to standardize visual perception of brightness. The term and its formal definition were established in the 1920s by the International Commission on Illumination (CIE), which introduced the standard spectral luminous efficiency functions to enable consistent photometric evaluations.Units and Standards
The primary unit of illuminance in the International System of Units (SI) is the lux (symbol: lx), defined as the illuminance produced by a luminous flux of one lumen (lm) uniformly distributed over a surface of one square meter (m²).[11] This coherent derived unit ensures consistency in photometric measurements worldwide, with the lux adopted by the 11th General Conference on Weights and Measures (CGPM) in 1960. Historically, illuminance was measured using non-SI units such as the foot-candle (fc), which originated in the late 19th century as the illuminance from a standard candle at a distance of one foot, standardized by the Illuminating Engineering Society in 1909 for practical lighting applications in the United States.[12] Another unit, the phot (ph), was coined in 1921 as part of the centimeter-gram-second (CGS) system, defined as one lumen per square centimeter (cm²), primarily used in scientific contexts before the widespread adoption of SI units. Both units have become obsolete in modern international standards due to the global shift to SI, though the foot-candle persists in some legacy engineering and photography practices in non-metric regions. Common conversions between these units are essential for transitioning measurements across systems. The table below summarizes key factors, based on exact definitions where 1 fc = 1 lm/ft² and 1 ph = 1 lm/cm².| Unit | Symbol | Relation to Lux (lx) |
|---|---|---|
| Lux | lx | 1 lx |
| Foot-candle | fc | 1 lx = 0.092903 fc |
| Phot | ph | 1 lx = 0.0001 ph |
Measurement
Instruments
Illuminance meters, commonly referred to as lux meters, are the primary instruments for measuring illuminance, the density of luminous flux incident on a surface. These devices typically utilize silicon photodiodes as detectors, paired with V(λ) correction filters to closely replicate the spectral sensitivity of the human eye under photopic conditions, as defined by the CIE 1924 luminosity function.[15][16] The photodiode generates a photocurrent proportional to the illuminance, which is then amplified and processed to provide readings in lux.[17] Common types include handheld digital illuminance meters, which offer portability and ease of use for field applications, featuring digital displays such as LCDs for direct readout of illuminance values.[18] For scenarios requiring uniform illumination measurement, integrating spheres are employed to create a homogeneous light field, facilitating accurate calibration and testing of illuminance meters by distributing light evenly across the detector surface.[19] Calibration of illuminance meters is essential for traceability and accuracy, with standards provided by organizations such as the National Institute of Standards and Technology (NIST) and the International Commission on Illumination (CIE).[18] These calibrations involve direct substitution against reference photometers under controlled conditions, ensuring compliance with SI units, and manufacturers typically recommend annual recalibration to account for potential drift in detector response.[17] Advanced variants, such as spectroradiometers, enable measurement of spectral illuminance by capturing the full spectral power distribution of incident light, allowing computation of illuminance weighted by V(λ). These instruments gained prominence in the 2000s for detailed analysis of complex sources like LED lighting, where spectral content affects perceived illuminance and color rendering.[20][21]Techniques
The basic procedure for measuring illuminance involves positioning the sensor of an illuminance meter perpendicular to the incident light rays to capture the total luminous flux on a surface accurately.[22] This orientation ensures that the measurement reflects the direct and diffuse components falling on the plane, with the sensor placed flat against the surface rather than suspended above it.[23] To account for variations in lighting conditions, multiple readings are taken at the same location and averaged, typically over several minutes or across repeated sessions to minimize temporal fluctuations. Illuminance measurements can be planar, targeting light on a specific surface, or hemispherical, integrating light from the entire surrounding environment; for diffuse lighting scenarios common in indoor or overcast conditions, cosine correction is essential to adjust for the angular dependence of light incidence according to the cosine law. This correction is achieved by attaching diffusers, such as opal glass or PTFE, to the meter sensor, which approximate an ideal cosine response and reduce errors from off-axis light rays.[24] Without proper cosine correction, readings can deviate significantly at oblique angles, particularly beyond 60 degrees from the normal.[25] In field techniques, illuminance mapping in rooms or spaces employs systematic grid patterns or cross-sections to evaluate lighting uniformity, with sensors moved methodically across predefined points on horizontal and vertical surfaces. Post-2020 advancements have integrated software for real-time data logging and visualization, enabling automated collection via mobile devices or robotic systems that generate detailed illuminance maps for analysis.[26] These methods facilitate comprehensive assessments, such as plotting contours of light distribution to identify hotspots or deficiencies.[27] Common error sources in illuminance measurement include stray light, which introduces unintended illumination from extraneous sources, and cosine errors from imperfect sensor angular responses. Stray light can be mitigated by shielding the sensor and conducting measurements in controlled environments, while cosine errors are quantified and corrected using quality indices like the directional response index (f₂) defined in ISO/CIE 19476.[28] Adherence to ISO 17025 accreditation protocols for calibration laboratories further ensures traceability and reduces overall measurement uncertainty through standardized verification procedures.Photometric Relations
Relation to Luminous Flux
Illuminance is fundamentally defined as the amount of luminous flux incident on a surface per unit area. Mathematically, for a small differential area where the illumination can be considered uniform, illuminance is expressed as the ratio of the differential luminous flux to the differential area : This relation, with measured in lux (lx) or lumens per square meter (lm/m²), quantifies how the total visible light power, weighted by human visual sensitivity, is distributed across the receiving surface.[29] For extended surfaces experiencing non-uniform illumination, the direct relation extends to an integrated form. The total luminous flux incident on the entire surface is then calculated by integrating the illuminance over the area: where denotes the surface. This inverse operation allows designers to compute the overall light output required from sources to achieve specified illuminance distributions, ensuring efficient use of luminous energy.[30] A practical derivation of this relation appears in the case of a point source, where illuminance decreases with the inverse square of the distance due to flux spreading over a spherical surface. For a point source with luminous intensity (in candela, cd, defined as luminous flux per unit solid angle in lumens per steradian, lm/sr), the illuminance at a perpendicular distance (in meters) is: This equation arises because the flux through a small solid angle yields . Luminous intensity itself incorporates the visibility factor , the spectral luminous efficiency function that weights radiant power by eye sensitivity, but for broadband sources, it is embedded in the photometric units.[2] This formula applies for normal incidence, where the surface is perpendicular to the line from the source. For oblique incidence, illuminance follows Lambert's cosine law, which reduces it by the cosine of the angle of incidence (the angle between the surface normal and the direction to the source): where is the distance from the source to the point on the surface. For a horizontal surface illuminated by an overhead source at vertical height , with horizontal distance to the point directly below the source, and , yielding: This is equivalent to the cosine-cubed law . Contributions from multiple point sources add linearly.[31] For example, consider two identical lamps each with luminous intensity cd at height m above a horizontal surface, with horizontal distances from point P to the points directly below the lamps of m and m. For the first lamp ( m): m, lx.For the second lamp ( m): m, lx.
Total: lx. In applications involving enclosed spaces, such as rooms, the conservation of luminous flux underpins lighting design principles. The total flux emitted by luminaires is conserved within the space, minus losses to absorption and transmission, allowing average illuminance to be estimated as , where is the utilization factor (fraction of flux reaching the workplane) and is the maintenance factor (accounting for depreciation). These methods, aligned with energy-efficient practices, were refined in recent CIE guidelines, including updates in CIE S 017:2020 for photometric quantities and related technical reports on flux measurement, to optimize installations while minimizing energy consumption.[32][33]
Relation to Luminance
Illuminance and luminance represent distinct aspects of light interaction with surfaces: illuminance measures the density of luminous flux incident on a surface, whereas luminance quantifies the luminous intensity emitted or reflected from that surface per unit projected area and per unit solid angle. This fundamental difference arises because illuminance describes incoming light without regard to directionality beyond the surface orientation, while luminance accounts for the directional distribution of outgoing light as perceived by an observer.[31] For opaque surfaces that reflect light diffusely, the relationship between illuminance and luminance is mediated by the surface's reflectance , which is the ratio of reflected to incident luminous flux. Under ideal conditions for a perfectly diffusing surface, the luminance is given by where arises from the geometry of diffuse reflection. This equation assumes uniform illumination and neglects specular components, focusing on the diffuse portion.[31][34] The equation derives from the properties of an ideal Lambertian surface, where luminance remains constant irrespective of viewing angle, obeying Lambert's cosine law such that observed brightness appears uniform. The luminous exitance from the surface, representing total outgoing flux per unit area, equals for a diffuse reflector. To connect to , integrate the differential flux over the emitting hemisphere: the flux element is , where is the zenith angle from the surface normal and is the solid angle element. The exitance is then Solving for luminance yields , highlighting the cosine dependence in the projected area and hemispherical integration.[35][31] These concepts were formalized in the 1930s by the International Commission on Illumination (CIE), which distinguished illuminance as an incident light metric from luminance as an emitted or reflected one to standardize photometry for lighting and vision applications. This separation enabled precise modeling of light propagation and surface interactions in engineering contexts.[36]Applications
Lighting Design
In lighting design, illuminance serves as a key metric for ensuring adequate visual performance, occupant comfort, and energy efficiency in architectural and interior spaces. The Illuminating Engineering Society (IES) provides recommended illuminance targets tailored to specific environments, such as 300–500 lx on the work plane for general office tasks to support reading and detailed work.[37] These levels balance visual acuity with glare control, drawing from extensive photometric research. Recent updates, including ANSI/IES RP-46-23, incorporate circadian considerations to support physiological effects of lighting in interior daytime environments.[38] Designers calculate target illuminance using established methods like the lumen method, which estimates average illuminance across a space by accounting for light output, distribution, and losses. The formula for average illuminance is: where is the total luminous flux from the luminaires in lumens, is the coefficient of utilization reflecting room geometry and surface reflectances, is the light loss factor for maintenance and depreciation, and is the area in square meters. This approach, part of the utilization factor method, enables preliminary layouts before detailed simulations, prioritizing uniform distribution to meet IES criteria. Advanced software tools facilitate precise 3D illuminance modeling, integrating photometric data from manufacturers with building geometry. DIALux, a free tool compliant with IES standards, supports detailed simulations of illuminance contours and daylight integration, with post-2015 versions adding modules for energy optimization and sustainable metrics like life-cycle assessments.[39] Similarly, Relux emphasizes sustainability through features for calculating energy-efficient layouts, enabling designers to visualize illuminance variations in real-time renders.[40] Integration with energy codes further embeds illuminance targets into sustainable practices, as seen in LEED v4.1 standards effective since 2020, which address daylight illuminance requirements (e.g., minimum 300 lx in occupied spaces for certain credits) and promote efficient lighting controls and sources to reduce overall energy use by up to 30% in certified buildings.[41] These guidelines prioritize adaptive systems that maintain required illuminance while minimizing consumption, aligning with broader environmental goals.[42]Photography and Cinematography
In photography and cinematography, illuminance is essential for calculating exposure to ensure images are neither underexposed nor overexposed. The exposure value (EV) at ISO 100 integrates the f-number (N) and exposure time (t in seconds) via the formula , which relates directly to scene illuminance in lux through .[43] This equivalence allows practitioners to determine settings based on measured light levels; for instance, the Sunny 16 rule adapts this for bright sunlight at approximately 100,000 lux, recommending f/16 aperture and 1/125-second shutter speed for proper exposure.[43] Such relations stem from photometric principles where total exposure is the product of illuminance and time, calibrated to sensor sensitivity. Historically, in the film era before the 1970s, illuminance measurements in photography and cinematography predominantly used foot-candles (1 foot-candle ≈ 10.76 lux) in the United States for lighting calculations and exposure determination.[44] This imperial unit facilitated on-set assessments with light meters, aligning with film stock sensitivities expressed in ASA speeds. The transition to digital workflows, accelerated by global standardization and SI unit adoption, shifted practices toward lux by the late 20th century, enabling seamless integration with international equipment and software.[45] In cinematography, illuminance ratios in three-point lighting setups—comprising key, fill, and backlight—define contrast and visual depth. A standard high-contrast configuration employs an 8:1 key-to-fill ratio, where the fill light provides one-eighth the illuminance of the key light to produce sharp shadows and dramatic mood, as seen in low-key styles for thrillers.[46] Lower ratios, like 2:1, yield softer, high-key effects for balanced scenes, with ratios adjusted via light intensity to suit narrative intent. Digital advancements since the 2010s have incorporated auto-exposure algorithms in cameras equipped with CMOS sensors, which evaluate scene illuminance through luminance histograms to dynamically adjust parameters like shutter speed and aperture.[47] These algorithms prioritize minimizing overexposed regions while preserving detail across varying light levels, marking a shift from manual metering to real-time computational control in both still and motion capture.[48]Common Levels and Contexts
Everyday Environments
In everyday environments, illuminance levels vary widely, influencing visual perception, task performance, and physiological responses. Indoor residential settings typically feature 100-300 lux for general living areas such as living rooms and bedrooms, sufficient for relaxation and basic navigation while minimizing energy use and glare. For instance, in a small 3x3 m bedroom or bathroom (area of 9 m²), a single 25 W clear incandescent bulb, producing approximately 200-250 lumens, would provide an average illuminance of about 22-28 lux. This level is very dim, suitable only for basic navigation or mood lighting, but insufficient for tasks such as reading or detailed work. For comfortable general lighting in such spaces, a total luminous flux of 400-900 lumens is recommended, corresponding to 50-100 lux, based on standards from the Illuminating Engineering Society (IES) and similar guidelines.[49][5] Office spaces require higher illuminance of 300-500 lux, with some standards recommending at least 500 lux, to support detailed work like reading documents or using computers, aligning with Illuminating Engineering Society (IES) recommendations for visual comfort and reduced fatigue.[5][6] Outdoor illuminance fluctuates dramatically with weather and time of day. Direct sunlight delivers up to 100,000 lux, enabling sharp visibility and vitamin D synthesis through skin exposure. An overcast sky diminishes this to about 1,000 lux, still adequate for outdoor activities but softer on the eyes. At night, full moonlight offers roughly 0.25 lux, providing minimal natural illumination for basic orientation. Urban streets at night are often lit to 10-20 lux to ensure pedestrian safety without excessive light pollution.[50][51] Health considerations underscore the importance of appropriate illuminance. Levels below 250 lux during prolonged reading can lead to eye strain and reduced visual acuity, as insufficient light increases pupil dilation and contrast demands on the retina. Exposure to at least 250 lux (melanopic equivalent daylight illuminance), especially blue-enriched light in the morning, supports circadian entrainment by suppressing melatonin and enhancing alertness, with the 2022 study confirming benefits for sleep quality and mood regulation.[6][52] The following table summarizes typical illuminance levels in select everyday environments:| Environment | Typical Illuminance (lux) | Source/Context |
|---|---|---|
| Residential general areas | 100-300 | IES standards for comfort[5] |
| Office workspaces | 300-500 | IES for task visibility (some standards ≥500 lux)[6] |
| Full sunlight | 100,000 | Clear day peak[50] |
| Overcast day | 1,000 | Diffuse natural light[50] |
| Urban street at night | 10-20 | Safety standards[51] |
| Full moonlight | 0.25 | Natural night low |
| Reading tasks | 250+ | Minimum to avoid strain[6] |