Most optical characterization methods rely on measuring the complex optical fields emerging from the interaction between light and material systems. Nevertheless, inherent scattering and absorption cause ambiguities in both interferometric and noninterferometric attempts to measure phase. Here we demonstrate that the complete information about a probe optical field can be encoded into the states of polarization, and develop a topography measurement method by blindly varying the ambient refractive index surrounding the sample in a wedged cuvette, which is capable of simultaneously measuring the thickness and the ambient refractive index of the sample in real time, as well as extending the measurement range of the sample thickness. With the method, we have successfully measured the topography of a 136.7 µm thick coverslip by blindly changing the ambient refractive index by 0.001246, resulting in the thickest sample characterization ever achieved by quantitative phase imaging, to the best of our knowledge. An efficient and complete characterization of optical fields is critical for any high-resolution imaging approach and the technique demonstrated here should prove attractive for applications ranging from microscopy to remote sensing. Thanks to the high precision and fast response speed, this method may pave a new way for measuring the topography of the thick samples, such as biological tissues.