Frequency-sweeping Interferometry Research Articles

Absolute distance measurement using frequency sweeping interferometry with large swept range and target drift compensation

Frequency sweeping interferometry (FSI) is an attractive absolute distance measurement (ADM) method because of the advantages of large unambiguity range, simple structure and excellent flexibility. By using a reference interferometer (RI), the calibration of the frequency sweeping range in FSI can be avoided, and the complexity and cost of the system can be further reduced. Then, the measurement accuracy is associated with the accuracy of phase demodulation, the range of frequency sweeping and the compensation of target drift. In this paper, ADM using FSI with large swept range and target drift compensation is presented. A frequency stabilized HeNe laser that travels along the same optical path with the swept source laser was employed to monitor the target drifts of the measurement interferometer and RI. Interference phases of the corresponding interferometers were extracted simultaneously using phase generated carrier demodulation technique, and an accuracy better than 1° was verified by nanometer displacement measurement. Comparative experiments of ADM at a distance of ∼4.5 m with different swept ranges before and after target drift compensation were carried out, and the results demonstrated that larger swept range and target drift compensation could greatly improve the stability and accuracy of measurement.

Increased Spurious-Free Dynamic Range in Frequency Sweeping Interferometry by Suppression of Parasitic Amplitude Modulation

We propose an envelope detrending method to correct parasitic amplitude modulation (AM) in frequency sweeping interferometry (FSI). Parasitic AM arises from effects such as device spectral response and residual AM of laser. The periodic component in parasitic AM introduces spurious harmonics, which degrade the spurious-free dynamic range (SFDR) and interfere with information analysis. The proposed method employs a Hilbert transform to obtain a time-varying amplitude fluctuation curve from an auxiliary interferometer. This curve is then employed to detrend the parasitic AM in the main interferometric signal, thus restoring the point spread function and improving the SFDR. An optimal SFDR can be obtained when the optical path differences (OPDs) of the two interferometers are equal, while mismatched OPDs lead to a rapid degradation of the SFDR correction. Experimental results demonstrate the effectiveness of the proposed method and the optimal matching condition. A maximum SFDR of 90.2dB can be achieved when the OPD matching condition is satisfied. By applying the method to an optical frequency domain polarimeter, we realized a measured 81.1dB polarization extinction ratio. We believe that the proposed method can also help to improve the SFDR in other FSI systems.

Phase Unwrapping and Frequency Points Subdivision of the Frequency Sweeping Interferometry Based Absolute Ranging System.

Frequency sweeping interferometry (FSI) based absolute distance ranging has high precision and no ranging blind area. It can be used to realize large-scale and non-cooperative target measurement. However, the nonlinear frequency modulation of the laser seriously affects the ranging accuracy. In this manuscript, a measurement method assisted by Hilbert Transform (HT) and Chirp-z Transform (CZT) is proposed, which can realize the phase unwrapping of the beat signal, the length reduction in the delay fiber of auxiliary optical path, and the improvement of the frequency resolution. The narrow-band frequency suitable for HT is further studied. In the experiment, the ranging resolution is 70 μm and the standard deviation is 12.6 μm within a distance of 4005 mm.

Dynamic absolute distance measurement by frequency sweeping interferometry based Doppler beat frequency tracking model

Abstract We propose a frequency-sweeping interferometry (FSI) with single external cavity diode laser that can be used to measure the absolute distances of a dynamic target. Generally, the FSI-Doppler effect induced by target drift restricts the measurement accuracy severely, but the Doppler effect can also be used to measure the actual movement during optical frequency sweeps. Thus, a mathematical model of the Doppler effect in FSI is presented and a novel FSI method based on Doppler beat frequency tracking model is proposed to realize the absolute distance measurement of a dynamic target. The method was verified successfully by measuring vibrating targets of 50 ∼ 5000 Hz at 38 mm in the laboratory.

Sinusoidal phase modulating absolute distance measurement interferometer combining frequency-sweeping and multi-wavelength interferometry.

A sinusoidal phase modulating absolute distance measurement (ADM) interferometer combining frequency-sweeping interferometry (FSI) and multi-wavelength interferometry (MWI) is proposed in this paper. The swept frequency in FSI and the wavelengths for MWI are calibrated by an optical frequency comb, so the distance measurement can be directly traced back to the SI definition of a meter. With a simple optical structure, an ADM interferometer consisting of a measurement interferometer and a monitor interferometer is constructed without polarization optics. A near-infrared external cavity diode laser (ECDL) calibrated by an optical frequency comb is used as a work source of the measurement interferometer for frequency sweeping and hopping. The monitor interferometer using a He-Ne laser runs parallel to the measurement interferometer to monitor the fluctuation of the measured distance during the measurement. Experiments for absolute distance measurements in a range of 8.25 m were carried out to verify the feasibility of the proposed ADM interferometer. The experimental results show that the maximum measurement error is less than 1 μm compared with an incremental-type laser interferometer.

Comb-referenced frequency-sweeping interferometry for precisely measuring large stepped structures.

A precise 3D surface measurement method for large stepped structures without height ambiguity is proposed based on optical-frequency-comb-referenced frequency-sweeping interferometry and Fourier-transformed fractional phase retrieval. Unlike other interferometry that depends on the absolute phase value for several certain wavelengths, this method obtains results from the phase change during frequency sweeping and thus remains free from the confined non-ambiguity range. By reference to an optical frequency comb, the relative uncertainty from the tunable laser frequency was reduced by three orders of magnitude, and the sweeping frequency range can be precisely determined. Besides, the fractional phase can be rapidly retrieved in only one step using a Fourier transform method, with advantages of high accuracy and immunity to light intensity fluctuation and mechanical vibration noise. Samples of step heights from 1μm to 1mm were measured, and the standard uncertainty was 45nm. This permits applications such as quality assurance in microelectronics production and micro-electro-mechanical system (MEMS) manufacture.

Frequency comb calibrated frequency-sweeping interferometry for absolute group refractive index measurement of air.

The absolute group refractive index of air at 194061.02GHz is measured in real time using frequency-sweeping interferometry calibrated by an optical frequency comb. The group refractive index of air is calculated from the calibration peaks of the laser frequency variation and the interference signal of the two beams passing through the inner and outer regions of a vacuum cell when the frequency of a tunable external cavity diode laser is scanned. We continuously measure the refractive index of air for 2h, which shows that the difference between measured results and Ciddor's equation is less than 9.6×10-8, and the standard deviation of that difference is 5.9×10-8. The relative uncertainty of the measured refractive index of air is estimated to be 8.6×10-8. The data update rate is 0.2Hz, making it applicable under conditions in which air refractive index fluctuates fast.

Dynamic high-resolution spectroscopic frequency referencing for frequency sweeping interferometry

A spectroscopic reference for the intrinsic frequency calibration of a ranging system based on frequency-sweeping interferometry (FSI) is presented. Saturation spectroscopy of iodine transitions at 636.8 nm is used to generate well-defined frequency markers. The experimental and analytic implementation is shown to enable in principle a frequency determination with an uncertainty of 0.17 MHz for a coverage factor k = 1. This corresponds to a relative standard uncertainty of as contribution to the combined measurement uncertainty of the FSI-based length measurement. But the analysis also reveals the high sensitivity of the actually achievable measurement uncertainty to the quality of the spectroscopic reference data.

Interferometric diameter determination of a silicon sphere using a traceable single laser frequency synthesizer

To determine the absolute diameter of a silicon sphere for the Avogadro constant project, we present a phase-shifting interferometer based on a flat etalon and a traceable single laser frequency synthesizer. By using an optical frequency comb to calibrate a frequency-tunable diode laser, the single laser frequency synthesizer can produce an arbitrary laser frequency with a relative uncertainty of 9.2 × 10−12 in the range of 4 THz. According to the laser frequency tuning system, the Carré algorithm with arbitrary but equal phase steps is employed to calculate the fractional interference phases. The absolute diameter is obtained by measuring the fractional and integral parts based on the principles of phase-shifting interferometry and frequency-sweeping interferometry, respectively. The uncertainty of a single diameter measurement in air is estimated to be 5 nm, whose uncertainty sources from the laser frequency and the phase-shifting algorithm are negligible.

Dual-frequency sweeping interferometry for absolute metrology of long distances

Frequency sweeping interferometry (FSI) is a technique where absolute distance measurements are made without ambiguity, using synthetic wavelengths resulting from frequency sweeps. Accuracy is mainly dependent on the synthetic wavelength measurement using a Fabry-Perot interferometer to count resonances as frequency sweeps. Measurement uncertainty increases with distance due to propagation of uncertainty in the synthetic wavelength measurement. For large distances, the number of fringes dominates performance, leading to a linear decrease of accuracy with range. To overcome this problem, the dual FSI concept was introduced, where the measurement process for large distances is reduced to the close-range case, by limiting the interferometer optical path difference. This is achieved by increasing the reference arm with a long reference fiber, and using an ancillary interferometer to calibrate the fiber length continuously. This dual FSI concept was implemented and fully tested in view of ESA-PROBA3 space mission. The sensor is composed of an external cavity diode laser, a high-finesse Fabry-Perot interferometer, and a dual measurement system. Accuracies better than 32 µm for a measurement range from 51 to 61 m were achieved using a reference fiber with 71 m, while maintaining the reduced complexity inherent to FSI technique, which is mandatory for space applications.

Accuracy of frequency-sweeping interferometry for absolute distance metrology

Coherent interferometric absolute distance metrology is one of the most interesting techniques for length metrology. Without movement, measurements are made without ambiguity, by using either one or several synthetic wavelengths resulting from the beating of two or more wavelengths (multiple-wavelength interferometry), or a frequency sweep (frequency-sweeping interferometry). Sensors based on the latter are relatively simple devices and can fulfill an important role in dimensional metrology. In addition, their parameterization flexibility allows trade-offs to be performed, either technology-driven or application-related. We present in detail a theoretical model of frequency-sweeping interferometry and its uncertainty budget, discuss different parameterizations, present a method for drift error compensation, and demonstrate and evaluate sensor performance and robustness with a prototype sensor composed of a mode-hop-free frequency-sweep external-cavity diode laser, a high-finesse Fabry-Perot interferometer (to measure accurately the frequency sweep range), homodyne detection, and data processing. Results have shown that the inaccuracy will not exceed 10 µm for distances up to 1 m, at an affordable degree of complexity.

Calibration of the Fabry-Pérot free spectral range using a tunable laser in a Michelson interferometer

Coherent interferometric absolute distance metrology enables different techniques for length metrology. Measurements are made without ambiguity, by using either one or several synthetic wavelengths resulting from the beating of two or more wavelengths or, in the case of frequency sweeping interferometry (FSI), from a frequency sweep. These techniques require accurate measurements of the frequency variation, a task which is usually performed with a Fabry-Pérot (FP) interferometer. Sensor performances are highly dependent on the FP free spectral range (FSR), which must be accurately known. We describe a method to measure the FSR of an FP using a tunable laser in a Michelson interferometer, using both absolute and relative distance measurements. The optical setup is based on a frequency-sweeping sensor and a controlled translation table. An uncertainty of 45 ppm in the measurement of a 1-GHz FSR is obtained. The method is indicated for the calibration of the FP in the frequency-sweep-range-measuring subsystem of a frequency sweeping sensor absolute distance sensor as it does not require any addition hardware, configuring a self-calibration approach.

Correcting movement errors in frequency-sweeping interferometry

Absolute distance measurements can be performed with an interferometric method that uses only a single tunable laser. This method has one major drawback, because a small target movement of the order of one wavelength during a measurement will be interpreted as a movement of one synthetic wavelength. This effect is usually mitigated by adding a second (nonscanning) laser. We show that absolute distance measurements can be performed with only one laser if the movements encountered are smooth, on the time scale of one measurement. In this case the movement errors can be compensated with a simple algorithm that combines several subsequent measurements. First experimental results show good agreement with theory.