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Realization of the NIST Total Spectral Radiant Flux Scale
Y. Ohno and Y. Zong
National Institute of Standards and Technology, Gaithersburg, Maryland USA
Abstract. The total spectral radiant flux scale has been
realized at National Institute of Standards and Technology
using a goniospectroradiometer for the 360 nm to 800 nm
region. The construction of the goniospectroradiometer
and results of the scale realization as well as the
uncertainty budget are presented.
Introduction. There are increasing needs for total
spectral radiant flux standards, which are required to
calibrate integrating sphere systems employing a
spectroradiometer. Such integrating sphere systems are
increasingly used for measurement of color and total
luminous flux of light sources such as discharge lamps and
light-emitting diodes (LEDs) as well as for measurement
of total radiant flux of ultraviolet (UV) sources.
A realization of total spectral radiant flux in the visible
region using a gonio-colorimeter was reported (Goodman,
1991), which was based on measurement of the correlated
color temperature of a test lamp in many directions, and
the average spectral distribution of the lamp was derived
based on Planck’s equation. No further developments have
been reported. Since then, new methods and technologies
have become available to realize the scale more directly,
possibly with lower uncertainties.
To address the strong needs for total spectral flux
standards in the U.S. (CORM, 2001), a project has started
at National Institute of Standards and Technology (NIST)
to realize the total spectral radiant flux scale from the UV
to visible region. Two independent methods are employed
to realize the scale, allowing cross-check of the realized
scales. The first method uses a goniospectroradiometer
designed and built at NIST. The second method uses the
NIST 2.5 m integrating sphere, applying the principles of
the Absolute Integrating Sphere (AIS) method, which is
successfully used for the realization of the lumen since
1995 at NIST (Ohno, 1996).
For the first phase of the project, NIST total spectral
radiant flux scale has been realized in the 360 nm to
800 nm region using the goniospectroradiometer. This
paper presents the principles of the methods of realization,
the construction of the goniospectroradiometer, and the
results of the realization of the scale as well as its
uncertainty budget.
Methods for Scale Realization
Goniospectroradiometric method
The spectral radiant intensity of a light source is measured
in many directions (θ, φ) over 4π steradian using a
goniospectroradiometer. The total spectral radiant flux
Φ λ (λ) of the light source is given by
2π π
Φ λ (λ) = ∫ ∫ I λ (λ,θ,φ) sinθ dθ dφ , (1)
φ=0
θ =0
where I λ (λ,θ,φ) is the spectral radiant intensity
distribution of the source on spherical coordinates (θ, φ).
If the goniospectroradiometer measures spectral irradiance,
the total spectral radiant flux Φ λ (λ) of the light source is
given by
Φ λ (λ) = r 2 2π π
∫ ∫ E λ (λ,θ,φ) sinθ dθ dφ , (2)
φ=0 θ =0
where E λ (λ,θ,φ) is the spectral irradiance distribution on
the spherical surface with radius r around the light source
being measured.
The realization of the scale can be done more easily if the
absolute scale is brought from the luminous flux unit. Then
the spectral irradiance measurements can be done
relatively. In such a method, the total spectral radiant flux
of a lamp is given by
and
Φ λ (λ) = k scale
∫
2π
φ=0
k scale =
∞
K m V(λ)
∫
λ=0
∫
π
∫ S(λ,θ,φ) sinθ dθ dφ , (3)
θ =0
2π
φ=0
∫
Φ v
π
θ =0
S(λ,θ,φ) sinθ dθ dφ dλ
(4)
where S(λ,θ,φ) is the relative spectral and spatial
distribution of the lamp as given by
S(λ,θ,φ) = k ⋅ E λ (λ,θ,φ)
(k : an arbitrary constant) , (5)
and Φ v is the total luminous flux (lumen) of the lamp,
determined using other methods. With this relative
method, errors in the rotation radius r of the
goniospectroradiometer, the positioning of lamp and
detector, stray light from surrounding walls, and the
absolute scale calibration of the spectroradiometer are
mostly not relevant.
Absolute Integrating Sphere Method
The AIS method is applied spectrally. Figure 1 shows the
arrangement of an integrating sphere system for this
application. The flux from the spectral irradiance
standard lamp is introduced through a calibrated aperture
placed in front of the opening. The internal source, a lamp
to be calibrated, is mounted in the center of the sphere.
The external source and the internal source are operated
alternately. The flux Φ λ,ref (λ) introduced from the
external source is given by,
Φ λ,ref (λ) = A ⋅ E λ (λ) , (6)
where E λ (λ) is the average spectral irradiance from the
external source over the limiting aperture of known area A.
The total spectral radiant flux Φ λ,test (λ) of the test lamp
is obtained by comparison to the external radiant flux:
Φ λ,test (λ) = y test (λ)
y ref (λ) ⋅ k cor (λ) ⋅Φ λ,ref (λ), (7)
Proceedings NEWRAD, 17-19 October 2005, Davos, Switzerland 337