We establish a theoretical model of dispersion mismatch in absolute distance measurements using swept-wavelength interferometry (SWI) and propose a novel dispersion mismatch compensation method called chirp decomposition. This method separates the dispersion coefficient and distance under test, which ensures dispersion mismatch compensation without introducing additional random errors. In the measurement of a target located at 3.9 m, a measurement resolution of 45.9 μm is obtained, which is close to the theoretical resolution, and a standard deviation of 0.74 μm is obtained, which is better than the traditional method. The measurement results are compared to a single-frequency laser interferometer. The target moves from 1 m to 3.7 m, and the measurement precision using the new method is less than 0.81 μm.
The laser frequency scanning interferometer has several advantages, such as non-contact, high accuracy and low signal to noise ratio in detection. In order to achieve higher resolution of the laser frequency scanning interferometer, increasing the tuning range of the light source and reducing the tuning non-linearity have become the key factors. The commonly used method is to correct the non-linearity of the wide bandwidth external cavity tuning laser by a fiber optical auxiliary interferometer constructed external frequency sampling clock. When using the broadband external cavity tuning laser and the auxiliary interferometer with an optical path difference of 220 m, it is found experimentally that the single-mode fiber dispersion makes the frequency of sampled signals change over time, causing the spectrum to broaden and resolution to decline. This paper has established the dispersion mismatch model which shows that the fiber dispersion of the auxiliary interferometer causes linear chirp frequency changes during the measurement of signals. The linear chirp frequency is proportional to the tuning bandwidth and measured distance. The phenomenon and theoretical model of dispersion mismatch is verified by experiments. The results for targets in the air are shown to linearly decrease as the tuning range increases with the maximum offset of 156.3 µm for the 20 nm tuning bandwidth. The experiment also proves the peak broadening intensifies with increasing distance measured, and thus verifies as the time delay of free space increase, and the peak broadening and distortion also increases. This result means that it will limit the ranging distance and make large errors in measurement result for long distance targets. The dispersion of the auxiliary interferometer should be compensated in the laser frequency scanning interferometer for large-sized high resolution measurements. In this paper, phase dispersion compensation method based on the evolution of peak variation distortion elimination is proposed, by taking the peak amplitude variation as the criterion; the phase compensation can offset the dispersion and improve the resolution. The original signal is multiplied by the complex phase compensation term, then regulating the phase compensation factor, the chirp becomes smaller as the phase compensation factor is approaching the distortion factor. Under the condition that the phase compensation factor is equal to the distortion factor, the chirp is offset. Then, the relationship between the amplitude and the peak FWHM is studied. It is found that the peak FWHM decreases while the amplitude shows a gradually increasing trend. Therefore, the amplitude can be referred to in order to determine whether the peak FWHM reaches the minimum. The resolution for target's peak can be improved by searching for the maximum amplitude of the spectrum and adjusting the phase distortion coefficient. The experiment shows that the peak FWHM of the target is obviously narrowed after dispersion compensation. The peak value becomes close to the theoretical resolution, and the static target at a distance of 975.216254 mm from the laser frequency scanning interferometer is measured. Results show the measurement accuracy of the interferometer is 584 nm. To further verify the accuracy of the laser frequency scanning interferometer, the laser frequency scanning interferometer is compared with the Renishaw laser interferometer in the measurement range of 0692 mm. The standard deviation between them is 4.5 µm. The proposed method is put forward to provide basis for future studies on the large size high resolution laser frequency scanning interferometer.
The influence of a fiber dispersion calibration interferometer on the measurement results for a largescale high-resolution broadband frequency-modulated continuous wave (FMCW) measurement system was studied. A model was constructed to simulate the influences of fiber dispersion on the measurements when using a frequency sampling method that corrects the tuning nonlinearity. The results indicated that a broadband external cavity tunable laser, in comparison with a semiconductor laser, causes linear variations in the measurement results because of the effect of the fiber dispersion in the calibration interference path for large-scale high-resolution measurements, and these variations decreased the resolution of the measurements. A method that combines chirp slope calibration and phase compensation to reduce the effects of the fiber dispersion was proposed. A gauge block with a height difference of 200 μm at a distance of 2.43 m was measured during the experiments. Before calibrating the fiber dispersion, the frequency spectrum showed false peaks, and it was difficult to distinguish the peaks of the targets. After compensating for the dispersion, the peaks of the targets could be clearly distinguished, and a height difference of 199.6 μm was measured. Using this model and the method to compensate for the dispersion will provide a reference for large-scale high-resolution broadband FMCW laser measurements.
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