Homodyne photothermal spectrometry (HPS) is a very wide bandwidth signal recovery technique which uses many of the elements of lock-in detection at very low cost. The method uses a frequency sweep, with a high-frequency bandwidth of up to 10 MHz, to excite a linear photothermal system. The response sweep of the photothermal system is downshifted into a bandwidth of a few kilohertz by means of in-phase mixing with the excitation sweep with the use of a four-quadrant double-balanced mixer and a low-pass filter. Under conditions derived from theory, the filter output gives a good approximation to the real part of the photothermal system's frequency response, dispersed as a function of time. From a recording of this signal, the frequency and impulse response of the photothermal system are rapidly recovered at very high resolution. The method has been tested with the use of laser photopyroelectric effect spectrometry and provides an inexpensive, convenient method for the recovery of high-frequency photothermal signals.
Estimating the leverage parameter of continuous‐time stochastic volatility models using high frequency S&P 500 and VIX