Non-interferometric accurate phase imaging via linear-convergence iterative optimization

•A non-interferometric accurate phase imaging method based on small-window phase modulation is reported.•A spectrum-modulated algebraic phase retrieval solution is built to obtain a good phase recovery.•An efficient iteration algorithm is developed to improve the algebraic phase recovery into an accurate one.•The iteration exhibits an intrinsic linear-convergence property so that a high-accuracy phase recovery is ensured.•The optical configuration is simple, which is modified from the classical phase-contrast imaging platform.•Experiments verified the power of the method in detecting diverse phase objects with high accuracy.