We derive the expressions of the first and second harmonic signals on the basis of absorption spectral and lock-in theories, and determine the gas concentration according to the ratio of second and first harmonic signals. It is found that the X and Y components of the harmonic signals are influenced by the phase shift between the detection and reference signal, and the phase shift can be any value in a range from 0 to 2π, which is different from the results obtained previously. Meanwhile, an additional item caused by the residual amplitude modulation will make a great contribution to the second harmonic signal, and may not be neglected under low absorbance conditions. Theoretical analysis indicates that subtracting back-ground signal from the second harmonic signal can remove the influence of this item, and can improve the measurement accuracy of gas concentration. On this basis, we select the transition of CO2 at 6527.64 cm-1 to analyse the approximation errors during the derivation by numerical simulation and then measure the CO2 concentration under low absorbance conditions, with absorbance varying from 1‰ to 6‰.
