The wavefront measuring range and recovery precision of a curvature sensor can be improved by an intensity compensation algorithm. However, in a focal system with a fast f-number, especially a telescope with a large field of view, the accuracy of this algorithm cannot meet the requirements. A theoretical analysis of the corrected intensity compensation algorithm in a focal system with a fast f-number is first introduced and afterwards the mathematical equations used in this algorithm are expressed.

The corrected result is then verified through simulation. The method used by such a simulation can be described as follows. First, the curvature signal from a focal system with a fast f-number is simulated by Monte Carlo ray tracing; then the wavefront result is calculated by the inner loop of the FFT wavefront recovery algorithm and the outer loop of the intensity compensation algorithm. Upon comparing the intensity compensation algorithm of an ideal system with the corrected intensity compensation algorithm, we reveal that the recovered precision of the curvature sensor can be greatly improved by the corrected intensity compensation algorithm.