Flattened Gaussian focal spot with uniform phase produced by photon sieve

The equivalent pupil and the point spread function constitute the Fourier-Bessel transform relation. Based on this, we established the equivalent pupil function theory of rotating symmetric photon sieve and derived the Fourier transform of the flattened Gaussian function. The focal spot produced by this type of photon sieve exhibits a uniform intensity and phase distribution. According to the numerical results, the flattened Gaussian field distribution is consistent with the designed function. In addition, the nonuniformity in intensity and phase is approximately 1% and less than 1/170 wavelength, respectively.