NIST: Candela, the Lumen, and Other Photometric Units

Realization of the Candela, the Lumen, and Other Photometric Units

Figure 1. FEL and photometer.

The Optical Technology Division of NIST is responsible for the realization of the SI base unit, the candela. The candela is realized based on the absolute responsivity of detectors and maintained on a group of eight standard photometers. The standard photometers are annually calibrated traceable to Division's reference cryogenic radiometer (POWR). The lumen is realized from the candela using the Absolute Integrating Sphere Method implemented in the NIST 2.5 m integrating sphere. Calibrations of luminous flux as well as luminous intensity of lamps are performed using detector-based measurement procedures. The unit of illuminance (lux) is maintained directly on the standard photometers. The luminance unit (cd/m²) is derived using an integrating sphere source equipped with a calibrated aperture.

Introduction

The aim of photometry is to measure light in such a way that the results correlate with human vision. While radiometry covers all spectral regions from ultraviolet to infrared, photometry deals with only the spectral region from 360 nm to 830 nm (the visible region) where human eyes are sensitive. Photometry is essential for evaluation of light sources and objects used for lighting, signaling, displays, and other applications where light is seen by the human eye.

In order to achieve the aim of photometry, one must take into account the characteristics of human vision. The relative spectral responsivity of the human eye was first defined by the Commission Internationale de l'Éclairage (CIE, the International Commission on Illumination) in 1924. It is called the spectral luminous efficiency for photopic vision, with a symbol V(λ) defined in the domain from 360 nm to 830 nm, and is normalized to unity at its peak, 555 nm.

Figure 2. The CIE spectral luminous efficiency function, V(λ).

This model has gained wide acceptance. The values were republished by CIE in 1983, and adopted by Comité International des Poids et Mesures (CIPM, the International Committee on Weights and Measures), in 1983 to supplement the 1979 definition of the candela. The tabulated values of the function at 1 nm increments are available in CIE references. In most cases, the region from 380 nm to 780 nm suffices for calculation with negligible errors since the value of the V(λ) function falls below 10^-4 outside this region. As specified in the definition of the candela in 1979 and a supplemental document from CIPM in 1983, a photometric quantity X_v is now defined in relation to the corresponding radiometric quantity $X_{\rm e,\lambda}(\lambda)$ by the equation:

$X_{\rm v}=K_{\rm m}\int_{360{\rm nm}}^{830{\rm nm}}X_{\rm e\lambda}(\lambda)V(\lambda){\rm d}\lambda .$

The constant, K_m, relates the photometric quantities and radiometric quantities, and is called the maximum spectral luminous efficacy of radiation for photopic vision. The value of K_m is given in the 1979 definition of candela, which defines the spectral luminous efficacy of radiation at the frequency 540 × 10¹² Hz (at the wavelength 555.016 nm in standard air) to be 683 lm/W. Note that this is not exactly at the peak of V(λ) at 555 nm. The value of K_m is calculated as 683 × V(555.000 nm)/V(555.016 nm) = 683.002 lm/W. K_m is normally rounded to 683 lm/W with negligible error for all practical applications.

Detector-based realization of the candela

The Optical Technology Division at NIST is responsible for the realization of the SI base unit, the candela. The candela is the unit of luminous intensity, and represents a unit of measure of the intensity of a light source as observed by the human eye. The candela is realized with a detector-based method that is directly traceable to the Division's Reference Cryogenic Radiometer (POWR), and maintained on a set of well-characterized filtered detectors (NIST standard photometers). The standard photometers are constructed to emulate the CIE spectral luminous efficiency function for photopic vision, consisting of a silicon photodiode, a V(λ)-correction filter, and a precision aperture.

Figure 3. Detector based candela.

The absolute spectral power responsivity s(λ) (in A/W) of the entire photometer (as an average over the aperture area) is calibrated against the spectral responsivity scale based on an absolute cryogenic radiometer. The area of the aperture A is calibrated by using a dimension-measuring instrument. The illuminance responsivity s_v (in A/lx) of the photometer is then obtained by

$s_{\rm v}[{\rm A/lx}]=\frac{A\int_\lambda S(\lambda)s(\lambda){\rm d}\lambda}{K_{\rm m}\int_\lambda S(\lambda)s(\lambda){\rm d}\lambda}$

where S(λ) is the relative spectral power distribution of the light to be measured, V(λ) is the spectral luminous efficiency function, and K_m is the maximum spectral luminous efficacy (683 lm/W). Planckian radiation at 2856 K (CIE Standard Illuminant A) is normally used for S(λ).

When a light source having spectral distribution S(λ) is measured with the photometer at a distance d, the luminous intensity I_v (in cd) of the source is given, according to the inverse square law, by

$I_{\rm v}=E_{\rm v}d^2\cdot\frac{1}{\Omega_0}=\frac{y}{s_{\rm v}}\cdot\frac{d^2}{\Omega_0}$

where y is the output current of the photometer, and Ω₀ is the unit solid angle (=1 sr). This establishes the luminous intensity unit, the candela.

The uncertainty in determining the candela value at NIST is currently 0.4 % (k = 2). Based on the base unit, the candela, other photometric units are derived.

Realization of the lumen

The unit of total luminous flux, the lumen, is normally calibrated using a goniophotometer at most national laboratories. A unique method was developed by NIST in 1995 to realize the lumen using an integrating sphere (referred to as the Absolute Integrating-Sphere Method).

The total flux of a lamp inside the sphere is calibrated against the known amount of flux introduced into the sphere from an external source through a calibrated aperture. The introduced flux from the external source is determined by the illuminance E measured at the aperture plane and the aperture area A. The total flux of an internal source is measured against the flux from the external source as

$\Phi_{\rm int}=c_{\rm f}\Phi_{\rm ext}\cdot\frac{y_{\rm int}}{y_{\rm ext}}=c_{\rm f}E\cdot A\cdot\frac{y_{\rm int}}{y_{\rm ext}}$

where y_int is the photometer head signal for the internal source, and y_ext is the photometer head signal for the external source. The parameter c_f is a correction factor for various non-ideal behaviors of the integrating sphere.

The key element of the correction factor is the correction for the spatial nonuniformity of the integrating sphere and is obtained from the spatial mapping of the sphere responsivity, measured by a rotating beam sphere scanner. The uncertainty of the NIST luminous flux unit is 0.50 % (k = 2).

This Absolute Integrating Sphere Method is now applied to the routine calibration measurements of total luminous flux using the NIST 2.5 m sphere. The sphere system is automated so that the sphere responsivity is calibrated for each test lamp measured, based on the illuminance measurement of the external source by the standard photometers, allowing for calibration with no need for luminous flux standard lamps. This brings the luminous flux calibration into a detector-based measurement procedure, thereby eliminating the uncertainties associated with the use of working standard lamps. Lower uncertainties are achieved by shortening the calibration chain. In addition, the measurement is simplified with the self-absorption of test lamps automatically corrected.

Figure 4. Arrangement of the NIST 2.5 m integrating sphere for the detector-based total luminous flux calibration.

Figure 5. Spatial uniformity mapping of the NIST 2.5 m integrating sphere responsivity.

Figure 6. NIST 2.5 m integrating sphere facility used for realization of the lumen and calibration services of luminous flux.

References

Photometry in general and candela realization

Y. Ohno, Recent Developments in Detector-Based Photometry and Future Needs in Photometry (48 kB) , Proc. CIE Symposium '99 - 75 Years of CIE Photometry, Budapest, 109-114 (1999).
Y. Ohno, T. Goodman, and G. Sauter, Trilateral Intercomparison of photometric units maintained by NPL (UK), PTB (Germany), and NIST (USA) (93 kB) , J. Res. Natl. Inst. Stand. Technol. 104, 47-57 (1999).
Y. Ohno, High Illuminance Calibration Facility and Procedures (84 kB) , J. IES, 27(2), 132-140 (1998).
Y. Ohno and M. Navarro, New Photometric Calibration Programs at the National Institute of Standards and Technology (48 kB) , Metrologia 35(4), 317-321 (1998).
Y. Ohno, NIST Measurement Services: Photometric Calibrations, NIST Spec. Publ. 250-37 (1997).
Y. Ohno, Improved Photometric Standards and Calibration Procedures at NIST (135 kB) , J. Res. Natl. Inst. Stand. Technol. 102(3), 323-331 (1997).
A.C. Parr, A National Measurement System for Radiometry, Photometry, and Pyrometry Based Upon Absolute Detectors, NIST Tech Note 1421 (1996).
Y. Ohno and J.K. Jackson, Characterization of modified FEL quartz-halogen lamps for photometric standards (143 kB) , Metrologia 32(6), 693-696 (1996).
Y. Ohno, Improved Photometric Standards and Calibration Procedures at NIST, Proc. NCSL 1996 Workshop and Symposium, Vol. 1, 343-353 (1996).
C.L. Cromer, G. Eppeldauer, J.E. Hardis, T.C. Larason, Y. Ohno, and A.C. Parr, The NIST Detector-Based Luminous Intensity Scale (143 kB) , J. Res. Natl. Inst. Stand. Technol. 101(2), 109-132 (1996).
Y. Ohno and G. Sauter, 1993 Intercomparison of Photometric Units Maintained at NIST (USA) and PTB (Germany) (839 kB) , J. Res. Natl. Inst. Stand. Technol. 100(3), 227-239 (1995).
Y. Ohno, C.L. Cromer, J.E. Hardis, and G. Eppeldauer, The Detector-based Candela Scale and Related Photometric Calibration Procedures at NIST (149 kB) , J. IES, 23(1), 88-98 (1994).

Sphere photometry and lumen realization

Y. Ohno and R. Bergman, Detector-referenced integrating sphere photometry for industry, J. IES 32(2), 21-26 (2003).
Y. Ohno and R.O. Daubach, Integrating Sphere Simulation on Spatial Nonuniformity Errors in Luminous Flux Measurement, J. IES, 30(1), 105-115 (2001).
Y. Ohno, R. Köhler, and M. Stock, AC/DC Technique for the Absolute Integrating Sphere Method, Metrologia 37, 583-586 (2000).
Y. Ohno, Detector-Based Luminous Flux Calibration using the Absolute Integrating-Sphere Method (146 kB) , Metrologia, 35(4), 473-478 (1998).
Y. Ohno, NIST Measurement Services: Photometric Calibrations, NIST Spec. Publ. 250-37 (1997).
Y. Ohno, Realization of NIST 1995 Luminous Flux Scale using Integrating Sphere Method (41 kB) , J. IES, 25(1), 13-22 (1996).
Y. Ohno, Realization of NIST Luminous Flux Scale Using an Integrating Sphere with an External Source (61 kB) , Proc. CIE 23rd Session, New Delhi, 1, 87-90 (1995).
Y. Ohno, New Method for Realizing a Total Luminous Flux Scale using an Integrating Sphere with an External Source (109 kB) , J. IES, 24(1), 106-115 (1995).
Y. Ohno, Integrating Sphere Simulation - Application to Total Flux Scale Realization, Appl. Opt. 33(13), 2637-2647 (1994).

Optical Sensor Group

For technical information or questions, contact:
Yuqin Zong Phone: (301) 975-2332 Email: yzong@nist.gov	Steve Brown Phone: (301) 975-5167 Email: swbrown@nist.gov	Yoshi Ohno Phone: (301)-975-2321 Email: ohno@nist.gov

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Online: September 1997 - Last updated: February 2008