We present a new method for the extraction of quantitative phase data from microscopic phase samples by use of partially coherent illumination and an ordinary transmission microscope. The technique produces quantitative images of the phase profile of the sample without phase unwrapping. The technique is able to recover phase even in the presence of amplitude modulation, making it significantly more powerful than existing methods of phase microscopy. We demonstrate the technique by providing quantitatively correct phase images of well-characterized test samples and show that the results obtained for more-complex samples correlate with structures observed with Nomarski differential interference contrast techniques.

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A new technique is proposed for the recovery of optical phase from intensity information. The method is based on the decomposition of the transport-of-intensity equation into a series of Zernike polynomials. An explicit matrix formula is derived, expressing the Zernike coefficients of the phase as functions of the Zernike coefficients of the wave-front curvature inside the aperture and the Fourier coefficients of the wave-front boundary slopes. Analytical expressions are given, as well as a numerical example of the corresponding phase retrieval matrix. This work lays the basis for an effective algorithm for fast and accurate phase retrieval.