Ptychographic iterative engine (PIE) is an ideal phase microscopic method for imaging with short wavelength including X-ray and electron beam. The traditional PIE algorithm requires a purely coherent illumination. Since the coherencies of X-ray and electron beam are always much lower than coherency of the laser, it is greatly important to develop new algorithm for enhancing the capability of PIE in handling the incoherence of the illumination. A method, named polyCDI (coherent diffraction imaging), which can generate clear reconstruction with the illumination of partial coherency, was proposed recently, however due to the use of tiny pinhole in the data acquisition the view field of the reconstructed image is limited. The polyPIE algorithm, which combines the principles of polyCDI with PIE, can realize the imaging of large object with partially coherent illumination. In this paper, an improved polyPIE algorithm is developed to realize the high-resolution phase imaging under incoherent illumination by bringing the shape of the illuminating pinhole and the spectral distribution of the light source into the iterative computation. The image of the object and the illuminating probe are reconstructed for each spectral component, and the shape of the pinhole forming the illumination is used as the same spatial constraint for all the reconstructed probes on the pinhole plane. With this method a very high convergence speed and reconstruction accuracy as well as a wide view field can be achieved. This method can find many applications in the imaging with X-ray and electron beam, which are of low coherence in most of cases. The influence of the spectral width on reconstruction accuracy is also analyzed by imaging the object with illuminations of different spectral widths. It is found that the improved polyPIE algorithm can accurately reconstruct the phase and modulus images of the object when the width of the incoherent illuminating source is smaller than 10% of the central wavelength, otherwise, the convergence speed and reconstruction accuracy will become remarkably lower. By bringing the shape of the pinhole into the iterative computation, the relevance of the reconstructed illuminating probes of different spectral components is used and accordingly the reconstruction speed can be obviously accelerated. The feasibility of this suggested method is verified by a series of numerical simulations.