The present paper aimed at the question that the beam cross-section changes according to the rotation of concave grating during the measuring process, and the appropriate supplement to the principle of the program was done. The appropriate supplement to the principle lay the foundation for the derivation of the beam cross-section k(theta), and the whole analytical expression of changes factor of the beam cross-section k(theta) for concave grating was derived. Because of the relationship between the theoretical values and the factors which affect the diffraction efficiency measuring accuracy was nonlinear, the quadratic nonlinear regression analysis was introduced and the compensating formula was established. The results show further correction to diffraction efficiency measurements for concave grating, the range of differences between the compensated values and the theoretical values was reduced from +/-2. 5% to less than +/-0. 3%, compared with the linear regression analysis, and the quadratic nonlinear regression analysis significantly reduces the variation between the compensated values and the theoretical values, which further ensures the accurate measurement of the diffraction efficiency for concave gratings. The compensating process is embedded in the measurement program; this method is strongly real-time, which can satisfy the requirements of simple operation, testing speediness and preciseness.
