A unified and accurate fast diffraction calculation between a pair of concentric cylindrical surfaces is proposed. Analysis of the obliquity factor shows that the physical meaning of it is the projection of the unit complex amplitude in the propagation direction onto the outer normal of the observation point. Therefore, a unified and accurate diffraction calculation formula for both inside-out and outside-in propagation models is achieved. Furthermore, it is accurately accelerated by a fast calculation method using fast Fourier transformation with a speed-up over 3.9×10, which is compared with the direct calculation method under resolution of 512×512 pixels. Through analysis and comparison, it is found that the computing error is significant in the approximate method of the inside-out propagation model, which releases the limitation of the ratios of the outer radius and the height to the inner radius of the cylinders. The simulation results are presented to verify the correctness and accuracy of our proposal.

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