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We present an annular illumination pattern optimization scheme for Fourier ptychographic microscopy (FPM) based on spectrum aliasing minimization. It has been found that an annular illumination light source could provide the highest phase retrieval accuracy while the oblique illumination angles matching the objective NA precisely. However, this conclusion is no longer valid when the Nyquist sampling criterion is not satisfied under the incoherent illumination case. In this paper, we investigate the spectrum aliasing characteristic with different spatial sampling rates. Then, an objective cost function related to the spectrum aliasing percentage and reconstruction error is established to bring about an annular illumination pattern optimization scheme. The reconstruction accuracy improvement of the proposed approach is demonstrated by achieving a full-pitch resolution of 548 nm across a wide FOV of 1.772 mm2 while the incoherent spatial sampling criterion is not satisfied.
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