Optical coherent detection is widely used for highly sensitive sensing applications, but nonlinearity issues pose challenges in accurately interpreting the system outputs. Most existing compensation methods require access to raw measurement data, making them not useful when only demodulated data are available. In this study, we propose a compensation method designed for direct application to demodulated data, effectively addressing the 1st and 2nd-order nonlinearities in both homodyne and heterodyne systems. The approach involves segmenting the distorted signal, fitting and removing baselines in each section, and averaging the resulting distortions to obtain precise distortion shapes. These shapes are then used to retrieve compensation parameters. Simulation shows that the proposed method can effectively reduce the deviation caused by the nonlinearities without using the raw data. Experimental results from a silicon-photonics-based homodyne laser Doppler vibrometry prove that this method has a similar performance as the conventional Heydemann correction method.