Comparison of Single and Dual-Phase Lock-in Amplifiers for Photoacoustic Spectroscopy

Abstract

& Dual phase lock-in is usually used in photoacoustic research because it allows precise projection of the measured spectra. In this article, double and single phase lock-in amplifiers were used and the advantages and disadvantages of both were compared. Two liquid crystals were studied in this work: ethylo-and penthylo-cyanobiphenyl in cyclohexane, tetrahydrofuran, and acetonitrile. The red-shift of the maximum related to the polarity of solvents and a bigger shift for 4-penthylo-4 0 -cyanobiphenyl relative to 4-ethylo-4 0 -cyanobiphenyl were observed. In order to investigate the usefulness of the single-phase device, compared to the more expensive double-phase device, the frequency dependence measurements and photoacoustic spectra were recorded and compared. Small differences were observed (within the limit of error) in spectra obtained using the single and the double lock-in amplifier. The simpler single-phase lock-in device can be used to reliably measure frequency spectra without any loss of information.

Improving the computational efficiency of lock-in algorithms through coherent averaging

“…Although, from a mathematical point of view, equations 2 and 8 are equivalent, they don't involve the same operations. The constant term 1 N , and the final calculations of amplitude and phase will be ignored for the next deductions since they don't need to be calculated in real-time (they can be computed after the whole signal is obtained and processed).…”

“…This multiplication produces a signal with two frecuential components: one at 2ω r and one at base band. This base band component carries the information of the signal's module, so by low-pass filtering the multiplied signal, the module can be determined [1]. To recover the signal's phase an additional reference signal, phase-shifted at the quadrature of the original reference, may be used [2] [3] [4].…”