Xuejian Wu

Absolute distance measurement using frequency-sweeping heterodyne interferometer calibrated by an optical frequency comb.

We present a frequency-sweeping heterodyne interferometer to measure an absolute distance based on a frequency-tunable diode laser calibrated by an optical frequency comb (OFC) and an interferometric phase measurement system. The laser frequency-sweeping process is calibrated by the OFC within a range of 200 GHz and an accuracy of 1.3 kHz, which brings about a precise temporal synthetic wavelength of 1.499 mm. The interferometric phase measurement system consisting of the analog signal processing circuit and the digital phase meter achieves a phase difference resolution better than 0.1 deg. As the laser frequency is sweeping, the absolute distance can be determined by measuring the phase difference variation of the interference signals. In the laboratory condition, our experimental scheme realizes micrometer accuracy over meter distance.

Absolute distance measurement by dual-comb nonlinear asynchronous optical sampling.

A dual-comb nonlinear asynchronous optical sampling method is proposed to simplify determination of the time interval and extend the non-ambiguity range in absolute length measurements. Type II second harmonic generation facilitates curve fitting in determining the time interval between adjacent pulses. Meanwhile, the non-ambiguity range is extended by adjusting the repetition rate of the signal laser. The performance of the proposed method is compared with a heterodyne interferometer. Results show that the system achieves a maximum residual of 100.6 nm and an uncertainty of 1.48 μm in a 0.5 ms acquisition time. With longer acquisition time, the uncertainty can be reduced to 166.6 nm for 50 ms and 82.9 nm for 500 ms. Moreover, the extension of the non-ambiguity range is demonstrated by measuring an absolute distance beyond the inherent range determined by the fixed repetition rate.

Phase-shifting interferometer using a frequency-tunable diode laser calibrated by an optical frequency comb

We present a phase-shifting interferometer based on a frequency-tunable diode laser calibrated by an optical frequency comb and the Carré algorithm. By use of the frequency control strategies of locking the diode laser to different comb modes and scanning the repetition rate, an arbitrary single optical frequency synthesizer is obtained. The relative laser frequency uncertainty is 5.7 × 10(-12) for 1 s averaging time with tracing to an Rb clock and accurate phase steps are achieved by optical frequency tuning. The surface topography of a standard sphere is measured by this phase-shifting interferometer based on a flat reference. The phase measurement repeatability is λ/200. With this technique, phase measurement uncertainties from the laser frequency and phase steps are negligible.

Reliable non-ambiguity range extension with dual-comb simultaneous operation in absolute distance measurements

We report an absolute distance measurement scheme using two simultaneous optical frequency combs with different repetition rates for reliable non-ambiguity range extension. Since the non-ambiguity range extension is susceptible to distance drift during the repetition rate adjustment, pulse trains with two different repetition rates are coupled and directed simultaneously onto a target for coincident distance measurement. The simultaneous measurement avoids the process of adjusting the repetition rate and suppresses the influence of distance drift therein. The distances measured by the two repetition rates are distinguished by type II second harmonic generation. Target movement and atmospheric variation are made to imitate the distance drift, and experimental results show that the non-ambiguity range extension remains effective along the measurement.

Subnanometer absolute displacement measurement using a frequency comb referenced dual resonance tracking Fabry–Perot interferometer

Fabry-Perot (F-P) interferometry is a traceable high-resolution method for displacement metrology that has no nonlinearity. Compared with the single resonance tracking F-P interferometry, the dual resonance tracking (DRT) F-P interferometer system is able to realize tens of millimeters measurement range while maintaining the intrinsic high resolution. A DRT F-P system is thus developed for absolute displacement measurement in metrology applications. Two external cavity diode lasers (ECDLs) are simultaneously locked to two resonances of a high-finesse F-P cavity using the Pound-Drever-Hall locking scheme. The absolute optical frequencies of the locked ECDLs are measured using a reference diode laser, with the frequency stabilized and controlled by an optical frequency comb. The absolute cavity resonance order numbers are investigated. The measurement range is experimentally tested to achieve 20 mm, while the resolution reaches ~10 pm level, mainly limited by the mechanical stability of the F-P cavity. Compared with the measurement results from a self-developed displacement-angle heterodyne interferometer, the displacement residuals are within 10 nm in the range of 20 mm. This high-resolution interferometer may become a candidate for length metrology such as in Watt balance or Joule balance projects.

Determining mean thickness of the oxide layer by mapping the surface of a silicon sphere

To determine Avogadro constant with a relative uncertainty of better than 2 x 10(-8), the mean thickness of the oxide layer grown non-uniformly on the silicon sphere should be determined with about 0.1 nm uncertainty. An effective and flexible mapping strategy is proposed, which is insensitive to the angle resolution of the sphere-rotating mechanism. In this method, a sphere-rotating mechanism is associated with spectroscopic ellipsometer to determine the distribution of the layer, and a weighted mean method based on equal-area projection theory is applied to estimate the mean thickness. The spectroscopic ellipsometer is calibrated by X-ray reflectivity method. Within 12 hours, eight hundred positions on the silicon sphere are measured twice. The mean thickness is determined to be 4.23 nm with an uncertainty of 0.13 nm, which is in the acceptable level for the Avogadro project.

Optically stabilized Erbium fiber frequency comb with hybrid mode-locking and a broad tunable range of repetition rate.

We present an optically stabilized Erbium fiber frequency comb with a broad repetition rate tuning range based on a hybrid mode-locked oscillator. We lock two comb modes to narrow-linewidth reference lasers in turn to investigate the best performance of control loops. The control bandwidth of fast and slow piezoelectric transducers reaches 70 kHz, while that of pump current modulation with phase-lead compensation is extended to 32 kHz, exceeding laser intrinsic response. Eventually, simultaneous lock of both loops is realized to totally phase-stabilize the comb, which will facilitate precision dual-comb spectroscopy, laser ranging, and timing distribution. In addition, a 1.8-MHz span of the repetition rate is achieved by an automatic optical delay line that is helpful in manufacturing a secondary comb with a similar repetition rate. The oscillator is housed in a homemade temperature-controlled box with an accuracy of ±0.02  K, which not only keeps high signal-to-noise ratio of the beat notes with reference lasers, but also guarantees self-starting at the same mode-locking every time.

Improved full-field rotating analyzer ellipsometry method for ultrathin film characterization

Abstract. We describe an improved approach for accurately characterizing the thickness distribution of ultrathin films by using full-field rotating analyzer ellipsometry. The significant improvements originate from the combination of angle optimization and error compensation. Angle optimization is achieved by fixing the polarizer and the quarter wave plate (QWP) at the averaged values of a series of optimal angles, which correspond to a certain thickness range of the sample. At the same time, error compensation further improves the accuracy by determining and removing the nonuniform impact of the QWP. To verify the applicability of the proposed method, experiments based on varied ultrathin films are implemented and compared with the results of two conventional methods. The results from the proposed method are in accord with those obtained using commercial instrument and the design value in thermal evaporation system. Further investigation shows that the uncertainties of the ellipsometric angles, both Ψ and Δ, are less than 0.045 deg, with a lateral resolution of 4.65  μm. Because of its improved accuracy, this method offers a feasible route for characterizing film thickness, especially in the case of monitoring the growth of thin layers from a bare substrate or following changes in the sample parameters during a kinetic process.

Compact Dual-Comb Absolute Distance Ranging With an Electric Reference

To exploit the potential of a dual-comb absolute distance ranging system outside a well-controlled laboratory, a compact dual-comb structure is proposed. A beat frequency generated by the repetition rates of two frequency combs serves as an electric reference, which is easily built and maintains a long range and high resolution compared with traditional dual-comb systems. The performance of the proposed method is compared with that of a heterodyne interferometer. The residuals range within -116.6 to 117.2 nm, the standard deviations vary from 46.3 to 137.9 nm, and the non-ambiguity range extension remains reliable throughout a 10-m test. Compared with Michelson-type dual-comb interferometers, this compact dual-comb system omits the redundant optical reference arm, promising practical applications of distance ranging.

Note: Periodic error measurement in heterodyne interferometers using a subpicometer accuracy Fabry-Perot interferometer

Periodic error is the major problem that limits the accuracy of heterodyne interferometry. A traceable system for periodic error measurement is developed based on a nonlinearity free Fabry-Perot (F-P) interferometer. The displacement accuracy of the F-P interferometer is 0.49 pm at 80 ms averaging time, with the measurement results referenced to an optical frequency comb. Experimental comparison between the F-P interferometer and a commercial heterodyne interferometer is carried out and it shows that the first harmonic periodic error dominates in the commercial heterodyne interferometer with an error amplitude of 4.64 nm.