Photothermal technology: common-path (single beam) interferometry

How it works

Photothermal Common-path Interferometry uses a single probe beam. Nevertheless, it reaches interferometric sensitivity to the index change (or thermal expansion) induced in the object by the heating pump beam. The interference pattern does not suffer from drifts. Therefore sensitive tests can be done efficiently in a normal environment.

When the pump is on, the probe experiences phase distortion in the heated area. If the distortion is small (up to 0.1 rad of distortion could be considered as small enough to secure the linear response) the phase distortion term in the complex amplitude of the probe expands into two terms

This expression actually shows 2 waves: the unity represents undistorted probe while the second term stands for a weak wave originated by the distortion. The weak wave, at its origin, is -p/2 shifted relatively to the undistorted one. There is no interference and hence no amplitude contrast yet.

The effective interference happens at some distance from the object and only when the distortion occupies a small part of the probe wavefront. The weak wave quickly diffracts then, acquires on-axis phase shift with respect to the slowly changing undistorted probe. Fig.1 illustrates this situation. Even with white probe there will be good interference pattern since both waves are coherent being actually two parts of the same beam.

Surprisingly, the maximum possible amplitude contrast at the center of the probe beam is simply

which equals the two-beam interferometer maximum response. The above expression is valid for an infinitely wide probe and for Gaussian distortion shape. This maximum contrast happens in the near field, at the Rayleigh range for the weak wave. In practice it is not hard to be within a factor of two of this maximum. One historical name for instrument based on this principle is Photothermal Common-path Interferometer (PCI) which is reflected in the names of first models designed by Stanford Photo-Thermal Solutions in years 2002-2003.

To use the full potential of the pump/probe setup the following popular arrangements are used:

• -CW pump is chopped at some frequency to provide periodic heating of the object
• -Probe crosses pump at an angle thus giving adjustable 3D resolution
• -Periodic distortion of the probe is detected after an aperture
• -Lock-in is used to sense the detected AC-signal at the frequency of the chopper

In a photothermal setup the detected signal is proportional to absorption losses which means that PCI systems resolution is limited by noise (shot noise of the photodetector being a natural floor). The linearity of photothermal instruments is exceptional, stretching over six orders of magnitude. Contrary to that spectrophotometers rely on calculation of absorption from transmission which results in many problems with low absorption measurements. Besides photo thermal common-path interferometers obviously detect only thermalized component of absorption which excludes any mistake for scattering inherent to other methods.

Laser sources rather than broad-band lamps are used with PCI to generate absorption signal. This gives a great gain in dynamic range on one hand and possibility to use several lasers at the same time for studying induced absorption on the other. This makes PCI a powerful instrument for materials characterization.