Weak-measurement method for surface-roughness estimation

High-precision surface-roughness estimation plays an important role in many applications. However, the classical estimating methods are limited by shot noise and can only achieve a precision of 0.1 nm with a white-light interferometer. Here, we propose two weak-measurement schemes to estimate surface roughness through a spectrum analysis and intensity analysis. The estimating precision with the spectrum analysis is about 10(-5 )nm by using a currently available spectrometer with a resolution of Delta lambda = 0.04 pm and the corresponding sensitivity is better than 0.1 THz/nm. The precision and sensitivity of the light intensity analysis scheme achieved is as high as 0.07 nm and 1/nm, respectively. By introducing a modulated phase, we show that the sensitivity and precision achieved in our schemes can be effectively retained in a wider dynamic range. We further provide the experimental design of a surface profiler based on our schemes. It simultaneously meets the requirements of high precision, high sensitivity, and a wide measurement range, making it a promising practical tool.