ABSTRACT
In laser-induced ›uorescence (LIF), the wavelength corresponding to the electronic energy difference of a molecule is selected as an incident light. Following the absorption of this incident light, the molecule undergoes collision, emission, predissociation, and other processes to transfer into other energy states. The LIF energy transfer process contains many energy levels and energy transfer types, but there are several cases in which a simple twolevel model is applicable for the evaluation of the measurement results. The energy transfer process in the two-level model is shown in Figure 3.1. The transfer process is given by the following rate equations:[3.1],[3.2]
dn dt
n W n W Q A1 1 12 2 21 21 21= − + + +( )
(3.1)
dn dt
n W n W Q A P2 1 12 2 21 21 21 2= − + + +( )
(3.2)
where n1 and n2 are the number densities in states 1 and 2 respectively, UL the energy density, A the Einstein A coef—cient, Q21 the quenching rate, and P2 the predissociation rate. W12 and W21 are the stimulated emission and absorption rates, respectively, and they are proportional to the incident laser light intensity. In the case of a steady state, the number density of the measured molecule at the upper excited level n2 is obtained by the following equation:
n W n W Q A P1 12 2 21 21 21 2 0− + + + =( ) (3.3)
When the number density of the lower excited level prior to the laser excitation n01 has a relation n01 = n1 + n2, which means the loss of number density by predissociation is negligible, Equation (3.3) becomes
n n
W W W
Q A P W W
1= +
+ + +
+ =
( ) 1 0 1n
(3.4)
where K1 is the proportional constant. The ›uorescence intensity I is proportional to n2
I K n A= 2 2 21 (3.5)
Here, K2 is a proportional constant. n01 has a relation with the species number density n by the Boltzmann distribution
n n g e g e
ng e Z
= ∑ = −
(3.6)
where gi and Ei are the degeneracy and energy of i state, and Z the partition function. Using Equations (3.4) through (3.6), n can be estimated by the ›uorescence intensity I
n
n Z g e
ZI K A g eE kT E kT
= = − −
(3.7)
The two different energy states i and j have to be excited to measure temperature
n
n Z g e
ZI K A g e
= = − −
(3.8)
n
n Z g e
ZI K A g e
= = − −
(3.9)
Using Equations (3.8) and (3.9), temperature T is given by
T E E k
=
−
( )ln ,,2121αα (3.10) Equation (3.7) is used for concentration measurements and Equation (3.10) for temperature.
