Stochastic resonance and speed enhancement of thermoreflectance imaging for photonic device applications

Abstract

CCD-based thermoreflectance imaging is a powerful tool for high-resolution, 2D thermal imaging. Given the low signalto- noise ratio, thermoreflectance imaging is typically performed using a lock-in imaging, “4-bucket” algorithm that requires averaging over many (typically 10³-10⁴) sample modulation periods, leading to relatively long measurement times. However, averaging over multiple samples in the presence of noise also has the potential secondary effect of stochastic resonance enhancement, in which signals smaller than the bit depth of the camera can be measured, dramatically improving the thermal resolution. In this study, we develop a model of stochastic resonance enhancement of the image “buckets” through additive noise, quantization, and averaging. We demonstrate that for noise amplitudes greater than 1.25 least significant bits (LSB), the root mean square (RMS) error in an image bucket is independent of the input signal amplitude. In addition, we show that for input signals for which the image quantization error is greater than 0.5 LSB, the RMS error in an image bucket is minimized in the presence of small, non-zero, amounts of noise, demonstrating stochastic resonance enhancement. Our simulations confirm earlier results that an image bucket may be modeled as a Gaussian-distributed random variable, but the expected mean is offset due to the flooring quantization scheme. Finally, our results for experimentally reasonable noise and signal levels suggest that for measurements made using low numbers of iterations (<5000), a small tuning of the CCD camera noise could increase the stochastic resonance enhancement of the image bucket.