An enhanced chromatic dispersion probe for simultaneous measurement of dual-axis absolute and relative displacement with nanometric resolutions

Abstract This paper presents an enhanced chromatic dispersion probe for simultaneous measurement of dual-axis absolute and relative displacement with nanometric resolutions based on a 4 f optical system and a signal processing algorithm. In the 4 f optical system, a light source is generated by a pinhole in such a way that the employed pinhole is placed on the focal planes of the two achromatic lenses, aimed at generating a low-pass filter in the frequency domain. With a smaller pinhole, side lobes of the measured spectra are effectively suppressed and the signal-to-noise ratio is optimized, resulting in an expanded absolute measurement range and improved resolution of the two axes, and an enhanced relative measurement resolution of the dual-axis. A signal processing algorithm is proposed in such a way that in the spectral curvature region of the dual-axis output spectra, the original fitted spectrum is replaced by a linear fitting line and a newly-intersected wavelength can be obtained, resulting in an expanded measurement range of the relative displacement of the dual-axis. Numerical simulation and experiments have indicated that the absolute measurement range has been expanded to 225 μm with an enhanced resolution of 40 nm, and the measurement range of the relative displacement of the dual-axis has been expanded to 370 μm with an enhanced relative measurement resolution of 90 nm.