Fourier ptychographic microscopy (FPM), a new microscopic imaging technology, skillfully combines the concepts of phase recovery algorithm and synthetic aperture, solving the problem of difficult combination of a large field of view with high resolution. In traditional calculations, the FPM process is often approximated as coherent imaging. Specifically, LED is regarded as a point light source and the coherent transfer function as the constraint of spectrum support domain for the optimal solution. However, strictly, LED is an extended incoherent light source, so this improper approximation will degrade the reconstructed image quality. For this reason, a new transfer function, apodized coherent transfer function weighted by the Bessel function (B-AC), is proposed as a support domain constraint in this paper. Experimental results show that the B-AC constraint is more suitable for the FPM imaging system and obviously reduces the ringing effect caused by the constraint of the coherent transfer function. Furthermore, the reconstructed image quality and robustness are better than those under the constraints of coherent transfer function and apodized coherent transfer function.