Frequency-modulated impulse response photothermal detection through optical reflectance. 1: Theory

Area of Science:

• Physics
• Materials Science
• Optical Engineering

Background:

• Photothermal detection relies on surface temperature changes.
• Understanding impulse response is crucial for accurate measurements.
• Opaque solids present unique challenges in photothermal analysis.

Purpose of the Study:

• To present a 3-D theory for impulse response photothermal detection in opaque solids.
• To extend the theory to account for the finite spatial extent of the laser source.
• To derive explicit expressions for the time-dependent temperature field.

Main Methods:

• Developed a 3-D theory based on surface temperature optical reflectance.
• Utilized the Green's function as the mathematical equivalent of an optical impulse.
• Extended the model to include finite laser source dimensions.
• Analyzed semi-infinite solids and finite-thickness solids with different backings.

Main Results:

• Presented a comprehensive 3-D theory for photothermal detection in opaque solids.
• Successfully incorporated the effects of finite laser source size.
• Obtained explicit expressions for time-dependent temperature fields.
• Addressed various boundary conditions relevant to experimental setups.

Conclusions:

• The presented 3-D theory provides a robust framework for photothermal detection in opaque solids.
• The inclusion of laser source extent enhances the applicability of the theory.
• The derived expressions are valuable for interpreting experimental data in diverse solid configurations.