Golay code modulation in low-power laser-ultrasound

The current work presents a correlation-based detection technique with application in modulated laser-ultrasonics. In standard use of coded sequences the impulse response of a system is recovered in the time domain with improved signal to noise ratio (SNR). The presented method is an extension of this technique, where the response to a chirped waveform is restored with improved SNR; hence, the response is in a well-defined frequency range. To achieve this goal the chirped waveforms are modulated by Golay codes. It will be shown that the response to this bandlimited carrier waveform can be recovered in the time domain with improved signal to noise ratio using a cross-correlation technique. Improvement in the SNR is discussed analytically and it is shown that this improvement is proportional to the square root of the length of the applied sequences. Experimental applications in laser-ultrasound are shown using modulated laser diodes as excitation sources with an output power of ∼1 W. In the experiments a plate with a thickness of 50 μm is investigated using Lamb waves in the MHz range to confirm the predicted improvement in the SNR. Golay codes with three different lengths were used with 7, 9 and 11 bits resulting in 27 = 128, 29 = 512, and 211 = 2048 repetitions in an individual signal, respectively. The predicted improvements of 2 in the SNR between the 7 and 9 bits, and between the 9 and 11 bits waveforms, respectively, were well approximated by the experimentally obtained values of 1.83 and 2.17. As Lamb wave dispersion curves can be used for the characterization of plates or layered samples by inverse problems, it is also shown that by using multiple measurement points the recovered waveforms can be utilized in the evaluation of the dispersion relation