In grating-based X-ray Talbot interferometry, the wave nature of X-ray radiation is exploited to generate phase contrast images of objects that do not generate sufficient contrast in conventional X-ray imaging relying on X-ray absorption. The phase sensitivity of this interferometric technique is proportional to the interferometer length and inversely proportional to the period of gratings. However, the limited spatial coherency of X-rays limits the maximum interferometer length, and the ability to obtain smaller-period gratings is limited by the manufacturing process. Here, we propose a new optical configuration that employs a combination of a converging parabolic micro-lens array and a diverging micro-lens array, instead of a binary phase grating. Without changing the grating period or the interferometer length, the phase signal is enhanced because the beam deflection by a sample is amplified through the array of converging-diverging micro-lens pairs. We demonstrate that the differential phase signal detected by our proposed set-up is twice that of a Talbot interferometer, using the same binary absorption grating, and with the same overall inter-grating distance.