A method of polishing a substrate is disclosed. The method includes irradiating the substrate with light; measuring intensity of the reflected light; producing spectral waveform representing relationship between relative reflectance and wavelength of the light; performing a Fourier transform process on the spectral waveform to determine a thickness of the film and a corresponding strength of frequency component; determining whether the determined thickness of the film is reliable or not by comparing the strength of frequency component with a threshold value; calculating a defective data rate representing a proportion of the number of unreliable measured values to the total number of measured values; and changing the threshold value based on the defective data rate.