Depth Profiling of Optical Absorption in Thin Films via the Mirage Effect and a New Inverse Scattering Theory. Part II: Experimental Reconstructions on Well-Characterized Materials

Abstract

Mirage effect spectrometry is experimentally evaluated in this work as a technique of optical depth profiling in thin films where no prior information is available about the sample properties. An apparatus suitable for performing quantitative measurements is described. High-precision experimental alignment procedures are introduced along with a new method for precise optical correction of the detector signal for experimental frequency response nonuniformities. Reconstructions were made of the heat source density and absorption coefficient depth profile in materials with known depth dependence. These included samples approximating weighted delta function arrays, and depth-continuous media known to obey Beer's law to a good approximation. The properties of these samples were examined independently by using a technique of depth-sensitive light microscopy. Mirage effect depth profiles reconstructed on samples containing discrete absorbers were effectively regularization limited, indicating that resolution is limited by random error in the data rather than experimental bias. Depth profiles obtained in continuously absorbing media show a good agreement with those obtained by reference methods.

Beam Deflection Photothermal Spectroscopy

“…p ½ 5 a 0 C . 21,22 The key geometric factor affecting depth resolution is the offset a 0 . 20 As the probe beam is aligned closer to the surface, the time lag in the deflection response becomes smaller, according to the approximate expression:…”

“…This is true for single-ended irradiation, An experimental means of determining a 0 involves placing an optically opaque, thin (<5 µm) marker layer on the sample surface near a region of interest for depth analysis. 21,22 Assuming thermal matching between fluid and sample, irradiation of the marker layer and reconstruction of p the estimate of a 0 returned by the marker. a 0 is further refined by fine tuning its value in the vicinity of the marker estimate, and observing where the data residual (fit of theory to experiment for the sample depth region) is minimized.…”

“…A diffraction theory reducible to the form of equation (14), provides an alternative expression for G e x, x 0 , t , with an agreement <1% RMS of full scale between theory and experiment. 21,22 Finally, p C must be related back to b x , the quantity of spectroscopic interest. If the sample's total optical transmission, T 0 , is available, optical transmission as a function of depth is then given by equation (16) 21 :…”

Depth Profiling of Optical Absorption in Thin Films via the Mirage Effect and a New Inverse Scattering Theory. Part I: Principles and Methodology

“…These techniques also have individual drawbacks for depth pro® ling, which will be examined in m ore detail later in this work. 20 Mirage effect spectrometry, of all phototherm al techniques, is among the best adapted for measurem ents at such interfaces. This technique uses an optically trans-parent¯uid m edium in contact with a thin-® lm sample.…”

“…When the sample is irradiated by an optical impulse, nonradiative processes following light absorption release heat into the sample as a function of depth, according to a depth integral form of Beer' s law. 20 A time delay is required for heat evolution at any given depth to cause a detectable change in the temperature of the¯uid m edium, so that depth of an absorbing feature is generally related to the transit time for heat conduction to the surface. Temperature changes in the¯uid medium cause corresponding refractive index changes, which are then sensed by a combination of de¯ection and diffraction induced in a probe beam aligned parallel with the sample surface.…”