Horiba Scientific Quanta-phi F-3029, Operation Manual

Page: 20 / 98

Quanta-
φ
rev. C (23 Apr 2010) Theory of Operation
1-6
Because the integration time constant used to collect E
a
and E
c
was 8 times longer than
for L
a
and L
c
, we need to divide the difference between E
a
and E
c
by 8 to calculate the
quantum yield,
υ
, below using the four parameters E
c
, E
a
, L
a
, and L
c
,.
6 5
6 6
[( ) / 8]
100%
[(2.51648 10 3.29376 10 ) / 8]
100%
2.27954 10 1.9856 10
93.01%
c a
a c
E E
L L


 

  
 
  

This
υ
is slightly lower compared to some literature reports for rhodamine 101 in aci-
difed ethanol (~ 96–99%) primarily due to the anhydrous ethanol used as the solvent.
Error-propagation analysis
In addition to the calculation of
υ
, the Quanta-φ software performs an error-propagation
analysis to help evaluate when signal levels are not properly balanced. This may occur
with dilute concentrations of the sample, or when samples exhibit very low quantum ef-
ficiency. The error propagation is based on the Poissonian statistics of photon-counting,
where the standard deviation
σ
is equal to the square-root of the photon-count value,
i.e. ,
The error propagation is performed in a stepwise manner.
First, find the standard deviations for
E
a
, E
c
, L
a
, and L
c
, respectively as ,
, and .
Second, evaluate the standard deviation of the numerator
num = [( E
c
– E
a
)/8] of the
υ
equation (considering the constant factor of 8 in the integration time) as
Then evaluate the standard deviation of the denominator
den = ( L
a
– L
c
), as
Propagation of the respective relative (
σ
rel
) and absolute errors (
σ
abs
) of
υ
is as follows: