Horiba Scientific Quanta-phi F-3029, Operation Manual

Page: 16 / 98

Quanta-
φ
rev. C (23 Apr 2010) Theory of Operation
1-2
where M is a factor called the sphere multiplier. The sphere multiplier takes into ac-
count the total fractional area f that the entrance and exit ports occupy (and thus reduce
the reflectance), plus multiple reflections:
 
f
ρ
ρ
M
 

1 1
(5)
For a typical integrating sphere whose
ρ
~ 0.95 and f ~ 0.03, M is between 10 and 30.
Time decay of signal
An incoming signal (such as a rapid fluorescence-decay) can be stretched temporally
because of the multiple diffuse reflections inside an integrating sphere. This can be im-
portant for fluorescence lifetime determinations. The impulse response of an integrating
sphere takes the form
τ
t
e

where
τ
is the time constant of the integrating sphere, and is
ρ
c
d
τ
sphere
ln
1
3
2
   
(6)
Equation (6) considers also the diameter of the integrating sphere,
d
sphere
, the average
reflectance,
ρ
, and the speed of light, c . A typical
τ
might range from several ns to sev-
eral dozen ns.
Coating of an integrating sphere
The interior reflective coating of an integrating sphere affects its overall performance.
The interior of the HORIBA Scientific integrating sphere is made from a proprietary
material known as Spectralon
®
, which has a very wide, flat reflectance of over 95%
from 250 nm to 2.5 μm (see graph below). Thus this integrating sphere is useful
throughout the
spectrofluorome-
ter’s scanning
range, from the
UV through the
near-IR.