Compact field programmable gate array (FPGA)-based multi-axial interferometer for simultaneous tilt and distance measurement in the sub-nanometre range

Quantitative determination of microstructure and nanostructure properties is essential in research, development and in control of the production process. In instruments for dimensional nanometrology the positioning stage is the key component, since the characteristics of the position acquisition and control determine directly the achievable precision of the complete system. Compact commercial positioning systems usually employ capacitive or inductive position sensors. Both technologies not only offer a resolution in the nanometre range, but also require a (periodic) calibration. To achieve traceable measurements, interferometric sensors need to be implemented into the metrology system. However, currently available commercial interferometers turned out to be too large to be installed in miniature positioning stages easily. Therefore, a new highly compact interferometer to allow for traceability and an uncertainty in the Angstrom range was developed. One of its first applications will be the new metrological low-noise atomic force microscope at the Physikalisch-Technische Bundesanstalt. The new interferometer is based on a modified homodyne Twyman–Green interferometer concept. It uses a novel signal processing approach based on a field programmable gate array, whereby a spatial interferogram is acquired by a high-speed CMOS line sensor and transformed into its frequency spectrum through a discrete Fourier transform. The spectral representation is analyzed for its major components; the phase information bears a direct connection to the displacement of the positioning unit. Furthermore, a possible stage tilt during the scan gives rise to a shift of the peak magnitude in the frequency spectrum. In addition, the developed system proved to be easily extendable to multiple axes by superimposing multiple interferograms on a single line sensor.