Preserving subnanometer-scale ranging precision in advanced multiwavelength interferometry via elimination of error magnification

In this study, we comprehensively reveal the error magnification mechanism in multiwavelength interferometry (MWI) for absolute distance measurement. An ideal linear relationship (ILR) between the phases of two wavelengths is introduced. The phase measurement error in the orthogonal direction of the ILR is considerably magnified. To eliminate this error magnification, a coordinate transformation method is proposed to project the measured phase onto the ILR. Experimental results show that the measured Allan deviation decreases from 6.7 μm to 0.9 nm at an averaging time of 8 μs, reaching 22 pm at an averaging time of 40 ms. This advanced MWI approach enables subnanometer-scale high-precision, microsecond-scale high-speed absolute distance measurements without the need for additional hardware components, offering remarkable potential for future space missions and advanced manufacturing, such as synthetic aperture radars and segmented-mirror optical telescopes.