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The theoretical approach to describe the defocusing microscopy technique byU. Agero et al. [Phys. Rev. E {\bf 67}, 051904 (2003)] assumes that the size ofthe objective lens aperture is infinite. This treatment gives that theintensity at the image plane depends on the laplacian of the phase introducedin the field by a pure phase object. In the present paper, we consider anarbitrary size for the aperture of the objective lens and we conclude that theintensity at the image plane depends also on the gradient of the phaseintroduced by the object and the phase itself. In this case, even an objectthat introduces only linear variations in the phase can be detected.Furthermore, we show that the contrast of the image of the phase objectincreases with the use of smaller objective apertures.

Defocusing microscopy with an arbitrary size for the aperture of the objective lens