In non-telecentric structured light projection measurement system，the frequency mismatch problem between the designed virtual grating and the captured carrier frequency fringe for single-shot spatial phase detection（SPD）will degrade the measurement accuracy and the range of the method. We propose a new demodulation frequency acquisition method by calculating the frequency value at the local peak points to fit the frequency function to obtain the virtual grating that can match the carrier frequency of the deformed fringe well. In addition，the piecewise Hilbert transform is proposed to eliminate the fringe background to be ease to spatial filtering. The improvements not only nearly expand two times measurement range but bring higher measurement accuracy of single-shot SPD method because more detail of the tested object can be obtained. Simulation and experimental results demonstrate the effectiveness of the proposed method. The results show that the maximum error of the single-shot SPD method is reduced by almost half after removing the fringe background. This method provides a reference for spatial fast 3D detection based on structured light projection.