Within a Cylindrical Cell
A synopsis of the paper presented at the 9th International Conference on Photoacoustic and Photothermal Phenomena, Nanjing, P. R. China, 1996
Agnès Chartier and Stephen Bialkowski
email: firstname.lastname@example.org , Stephen.Bialkowski@usu.edu
This work was susbsequently published in Optical Engineering, 36 303-311 1997, under the title "Photothermal lens spectrometry of homogeneous fluids with incoherent white-light excitation using a cylindrical sample cell".
Difference Between Laser- and Lamp-Excited Apparatus
With the laser-excited photothermal lens apparatus, the laser beam is focused to a small volume. This spatial anisotropy results in an anisotropic temperature profile. This, in turn, results in thermal lens formation.
In the cylindrical sample cell apparatus, a small volume cell is illuminated by the image of an excitation source. The sample cell is illuminated with spatially constant irradiance. Thermal diffusion results in the spatial anisotropic temperature change. This, in turn, produces the thermal lens element.
Features of Photothermal Lens Spectrometry Using the Cylindrical Sample Cell
Cylindrical Cell Thermal Lens Theory
1 - The thermal diffusion equation
is solved for zero temperature change at the
2 - The temperature change, dT (K), for continuous excitation is
where a is the cell radius, Kf
is thermal conductivity of the sample medium, DT
is thermal diffusivity, and the Xn are
roots of the Bessel's function equation, J0(Xn)=0.
3 - The thermal lens strength obtained from
where tc=a2/4DT is the characteristic thermal diffusion time constant and
is the heat generated along the optical path. YH is the quantum yield for heat production.
4 - The maximum thermal lens strength for times much longer than the characteristic thermal diffusion time is
5 - The decay of the lens can be similarly
modeled for chopped sources.
6 - Accounting for the finite thermal conductivity of the cell (radiative heat transfer solution) yields the more complex solution
(m-1), is a relative thermal diffusion parameter, Ks
is sample cell thermal conductivity, and d (m) is the
thermal diffusion layer thickness.
7 - The long-time limited signal is the same as that for the "infinite" thermal conductivity approximation given in Point 4. However, the time constant for lens formation and decay depends on the thermal transfer characteristics of the sample cell.
Schematic of the apparatus used in these experiments. The optically filtered Xe arc lamp excitation source passes through a shutter and is imaged onto the entrance of the cylindrical sample cell. The near infrared diode probe laser is paraxially combined with the excitation source at the hot mirror, and is subsequently focused through the sample cell. The probe laser passes through the laser line filter and the pinhole aperture to develop the photothermal lens signal at the photodiode detector. The electronic signal is captured with an analog-to-digital converter and subsequently processed using the personal computer.
White-Light Lens Experiment
White Light Photothermal Lens Results*
* Measurements made using 7.5x103 W m2 (~6 mW through the 1 mm internal diameter stainless steel sample cell) distributed from 700 nm to 375 nm on pseudoisocyanin at average transmission of T~0.9 across the wavelength range.