Theoretical and experimental investigation of the thermal resolution and dynamic range of CCD-based thermoreflectance imaging

Abstract

We demonstrate thermal imaging using a charge-coupled device (CCD) thermoreflectance lock-in technique that achieves a record temperature resolution of 18 mK, 44 dB below the nominal dynamic range of the camera (from 72 to 116 dB) for 10(5) periods of measurement. We show that the quantization limit of the CCD camera does not set the lower bound on the precision of the technique. We present a theoretical description of the measurement technique, accounting for the effects of noise and nonideal analog-to-digital conversion, resulting in analytic expressions for the probability distribution function of the measured signals, and allowing for explicit calculation of resolution and error bars. The theory is tested against parametrically varied measurements and can be applied to other sampled lock-in measurements. We also experimentally demonstrate sub-quantization-limit imaging on a well-characterized model system, joule heating in a silicon resistor. The accuracy of the resistor thermoreflectance measurement is confirmed by comparing the results with those of a standard 3omega measurement.

Detection of nanoscale defects in optical films by photothermal reflectance microscopy

“…The proposed photothermal reflectance microscopy (PTRM) system consists of a standard CCD-based thermoreflectance microscopy (TRM) system [12][13][14] using the off-axis two-beam configuration as shown in Fig. 1.…”

“…It measures the local variation of the refractive index as a function of temperature change ΔT, which manifests as a relative change in optical reflectivity ΔR. The resulting temperature of the material can be derived from the simple relationship of ΔR/R 0 = κΔT where R 0 and κ are the background reflectivity at ambient temperature and an intrinsic thermoreflectance coefficient for the material, respectively [14]. In this experiment, we measured the relative reflectivity ratio rather than the thermal mapping because the κ value of the defects was unknown, but this was enough to identify the presence of defects within the optical materials.…”

Thermoreflectance imaging of sub 100 ns pulsed cooling in high-speed thermoelectric microcoolers

“…Temperature resolutions down to 10 mK are achievable. 18 For steady-state characterizations, we supply a sinusoidal bias signal to the DUT with period several orders of magnitude larger than the relevant thermal time constants of the sample. The phase-locked CCD takes 4 images over every cycle under constant illumination from which the magnitude and phase of the slowly oscillating temperature field can be determined.…”

Time and frequency domain CCD-based thermoreflectance techniques for high-resolution transient thermal imaging

“…This image is sampled by the CCD running at frame rate 4 f and processed in exactly the same way as for the homodyne case. It has been demonstrated [2] that with this heterodyne technique a temperature resolution about 10 mK can be achieved, with a spatial resolution down to 250 nm when blue light is used. It should, however, be noted that achieving such supreme temperature resolutions come at the cost of extremely long averaging times in the order of 10 hours or more, which may be unsuitable for practical purposes.…”

“…However, noise usually causes the signal to fluctuate over several levels. Through averaging over a sufficient number of exposures, the effective temperature resolution can be largely enhanced [2]. This phenomenon, known as stochastic resonance, is able to extend the dynamic range of a 12-bit CCD to over 18 effective bits, allowing measurements with temperature resolutions of 10 mK [2].…”