A scattering spectrometer for white light interferometry

White light interferometry is a non-contact method to measure surface topography. The depth profile of the surface is typically encoded in the spectrum of the reflected light, and a spectrometer is used to decode this signal. In this work, we demonstrate a new form of spectral interferometry, a subset of white light interferometry, in which the conventional spectrometer is replaced with an engineered scattering chip and a camera. The chip is created using laser direct writing to controllably embed scattering centres within a bulk silica substrate, forming a highly stable optical scattering element. Calibration of our device is straight-forward: we circumvent the need for spectral characterisation and computational extraction of the spectrum, and instead directly measure the relationship between surface depth and the white light speckle pattern. Using our technique, we demonstrate surface profile measurements with a resolution of 27 nm over a range of 0.5 mm. Our work provides a new route to the development of potentially compact and low-cost white light interferometers with implications for the measurement of distance, strain, temperature, pressure, and more.