The adaptive optics system for the second-generation VLT-interferometer (VLTI) instrument GRAVITY consists of a novel cryogenic near-infrared wavefront sensor to be installed at each of the four unit telescopes of the Very Large Telescope (VLT). Feeding the GRAVITY wavefront sensor with light in the 1.4 to 2.4 micrometer band, while suppressing laser light originating from the GRAVITY metrology system, custom-built optical components are required. In this paper, we present the development of a quantitative near-infrared point diffraction interferometric characterization technique, which allows measuring the transmitted wavefront error of the silicon entrance windows of the wavefront sensor cryostat. The technique can be readily applied to quantitative phase measurements in the near-infrared regime. Moreover, by employing a slightly off-axis optical setup, the proposed method can optimize the required spatial resolution and enable real time measurement capabilities. The feasibility of the proposed setup is demonstrated, followed by theoretical analysis and experimental results. Our experimental results show that the phase error repeatability in the nanometer regime can be achieved.