Horiba Scientific Quanta-phi F-3029, Руководство по эксплуатации

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Quanta-
φ
rev. C (23 Apr 2010) Theory of Operation
1-1
1 : Theory of Operation
Introduction
An ideal integrating sphere is designed to integrate light for collection over all emission
angles from the sample. No integrating sphere is ideal, and so there are various approx-
imations required.
Spherical enclosures and radiance
When light hits a diffuse surface, such as the interior of an integrating sphere, radiation
exchange occurs. Imagine an area
dA
1
that reflects light to another area dA
2
. We can
write the exchange factor dF , the fraction of energy leaving dA
1
, traveling a distance S ,
and going to dA
2
.
2
2
2 1
cos cos
dA
S
π
θ θ
dF

(1)
For a spherical enclosure, the area
dA
1
actually exchanges light with an area A
2
of defi-
nite size. With geometrical considerations, we can integrate the differentials to get
sphere
A
A
r
π
A
F
2
2
2
4
 
(2)
Equation (2) tells us that the fraction of light
F that A
2
receives is just A
2
’s fraction of
the sphere’s total surface area. The parameter
F is independent of the viewing angle, is
the same when measured from anywhere within the integrating sphere, and is propor-
tional to the area of the sphere.
Radiance,
L , is the flux density of light emanating per unit solid angle. For a diffuse
surface receiving an incident flux Φ
i
,
A
π
ρ
L
i
Φ

(3)
where
A is the area under illumination,
ρ
is the reflectance, and
π
is the solid angle from
the surface. The main issue here is the reflectance for an integrating sphere. The reflec-
tance can be rewritten as a simplification of a power series from multiple reflections
within the sphere. Thus we rewrite the radiance as
M
A
π
L
i
 
Φ
(4)