Multiple wavelength interferometry for distance measurements of moving objects with nanometer uncertainty

Abstract

Optical measurement techniques offer great opportunities in diverse applications, such as lathe monitoring and microfluidics. Doppler-based interferometric techniques enable simultaneous measurement of the lateral velocity and axial distance of a moving object. However, there is a complementarity between the unambiguous axial measurement range and the uncertainty of the distance. Therefore, we present an extended sensor setup, which provides an unambiguous axial measurement range of 1 mm while achieving uncertainties below 100 nm. Measurements at a calibration system are performed. When using a pinhole for emulating a single scattering particle, the tumbling motion of the rotating object is resolved with a distance uncertainty of 50 nm. For measurements at the rough surface, the distance uncertainty amounts to 280 nm due to a lower signal-to-noise ratio. Both experimental results are close to the respective Cramér–Rao bound, which is derived analytically for both surface and single particle measurements.

A review of state-of-the-art 1D length scale calibration instruments

“…The two colour method, using the varying dispersion of two different wavelengths passing through the same path was first developed over 50 years ago [56] and shares the advantage of measuring the full beam path refractive index. The method has been applied to interferometry by various groups [57][58][59][60], with work from Wu et al [61] using an optical frequency comb achieving an uncertainty change of 5 × 10 −8 . A difficulty with the two-colour method is that it does not produce valid results when the air is moist.…”

A review of interferometry for geometric measurement

“…In this case, the larger synthetic wavelength results in a measuring range of Λ 23 /2 (≈145 μm), and the result is then used to determine the fringe order of the smaller synthetic wavelength (14 μm). Doppler-based technique MWI is also available for moving objects [110]. Four and more wavelengths are used for further improvements [111][112][113].…”

Optical, in situ, three-dimensional, absolute shape measurements in CNC metal working lathes

“…Hence, the required steep calibration function hinders a large measurement range for the distance measurement. In order to increase the measurement range, a third fringe system with a slightly different tilting angle is superposed, which results in an additional, unambiguous calibration function to resolve the ambiguity issue [27]. In Fig.…”

“…On the one hand, the SNR decreases, since less scattered light is detected by the sensor (SNR(γ = 0) = 10 dB, SNR(|γ | = 25 • ) = 0 dB). The SNR decrease leads to an increase of the measurement uncertainty [27,28]. On the other hand, the distance of the surface varies within the width w of the measurement volume.…”