Absolute distance measurement of optically rough objects using asynchronous-optical-sampling terahertz impulse ranging

Terahertz Time-of-Flight Ranging with Adaptive Clock Asynchronous Optical Sampling

We propose and implement a terahertz time-of-flight ranging system based on adaptive clock asynchronous optical sampling, where the timing jitter is corrected in real time to recover the depth information in the acquired interferograms after compensating for laser instabilities using electronic signal processing. Consequently, the involved measurement uncertainties caused by the timing jitter during the terahertz sampling process and the noise intensity of the terahertz electric field have been reduced by the utilization of the adaptive clock. The achieved uncertainty range is about 2.5 μm at a 5 cm distance after averaging the acquisition time of 1876 ms 5000 times, showing a significant improvement compared with the asynchronous optical sampling using a constant clock. The implemented terahertz ranging system only uses free-running mode-locked lasers without any phase-locked electronics, and this favors simple and robust operations for subsequent applications that extend beyond the laboratory conditions.

Modelling two-laser asynchronous optical sampling using a single 2-section semiconductor mode-locked laser diode

We present a theoretical overview and a proposed methodology which demonstrates SLASOPS (single laser asynchronous optical sampling) as a single-laser alternative to the conventional two-laser ASOPS technique. We propose the optical and electronic setup in which SLASOPS may be achieved experimentally with a single 2-section mode-locked laser diode as the pulsed-laser source and simulate how asynchronous optical sampling is generated and detected theoretically. We highlight the technique's ability to provide customizable scan ranges, scan rates and scan resolutions through variation of the imbalance in the interferometer arms and by tuning the repetition rate of the pulsed-laser source, which we present as optical cross-correlations between pulse pairs. We incorporate jitter into the system mathematically to assess the limitations on resolving both intensity and interferometric cross-correlation traces and to investigate the effects of averaging such traces in real-time. Analysis is then carried out on cross-correlation trace amplitude, width, and temporal positioning in order to discuss the technique's ability for deployment in typical optical sampling applications. In particular we note SLASOPS' ability to conduct asynchronous optical sampling using only a single laser, halving both the expense and technical requirements, doing so at megahertz scan rates, and within a spatial precision of just a few microns.

Fast optical sampling by electronic repetition-rate tuning using a single mode-locked laser diode

This paper demonstrates optical sampling by electronic repetition-rate tuning (OSBERT): a single-laser optical sampling technique capable of fast scan rates and customisable scan ranges. The method has no moving parts and is based on the electronic modulation of the repetition rate of a passively mode-locked laser diode, simply by varying the reverse bias applied directly to the saturable absorber section of the laser. Varying the repetition rate in a system built as a highly imbalanced interferometer results in pairs of (pump, probe) pulses with successive increasing delay. The resulting scan range is proportional to the magnitude of the repetition rate modulation and is scaled by the chosen length of the imbalance. As a first proof of concept, we apply the method to distance measurement, where the displacement of a target across 13.0 mm was detected with ∼0.1 mm standard deviation from an equivalent free-space distance of 36 m and at a real-time scan rate of 1 kHz. The customizable scan range and competitive scan rate of the method paves the way for single ultrafast semiconductor laser diodes to be deployed as fast, low-cost, and compact optical sampling systems in metrology, biomedical microscopy, and sensing applications.

Segment-Resolved Gas Concentration Measurements by a Time Domain Multiplexed Dual Comb Method

Locating gas concentration changes in widespread locations can be conducive to environmental atmospheric detection, gas emissions monitoring, production process control, etc. A time domain multiplexed dual-comb system for segment-resolved gas concentration measurement is reported in this work. Both absorption spectra and path lengths for multiple path-segments in a target path can be derived from the time domain separated interferograms and then the equivalent gas concentrations in each segment can be retrieved separately. A benchtop experiment aiming at a target path with three path-segments of different gases has been demonstrated. The relative deviation of gas concentration retrieval is 1.08% in 1 s. Besides, additional numerical simulations prove that the crosstalk between the interference signals affects the spectrum analysis by no more than 0.1% for a kilometer-long atmospheric absorption detection. Therefore, achieving a gridded measurement of regional gas concentration in the open air can be foreseen using this method.

Error Analysis and Modeling for an Absolute Capacitive Displacement Measuring System with High Accuracy and Long Range

We proposed a novel kind of absolute capacitive grating displacement measuring system with both high accuracy and long range in a previous article. The measuring system includes both a MOVER and a STATOR, the contact surfaces of which are coated by a thin layer of dielectric film with a low friction coefficient and high hardness. The measuring system works in contact mode to minimize the gap changes. This paper presents a theoretical analysis of the influence of some factors, including fabrication errors, installation errors, and environment disturbance, on measurement signals. The measuring signal model was modified according to the analysis. The signal processing methods were investigated to improve the signal sensitivity and signal-to-noise ratio (SNR). The displacement calculation model shows that the design of orthogonal signals can solve the dead-zone problem. Absolute displacement was obtained by a simple method using two coarse signals and highly accurate displacement was further obtained while using two fine signals with the help of absolute information. According to the displacement calculation model and error analysis, the error in fine calculation functions mainly determines the model's accuracy and is locally affected by coarse calculation functions. It was also determined that amplitude differences, non-orthogonality, and signal offsets are not related to the accuracy of the displacement calculation model. The experiments were carried out to confirm the abovementioned theoretical analysis. The experimental results show that the displacement resolution and error in the displacement calculation model reach ±4.8 nm and ±34 nm, respectively, in the displacement range of 5 mm. The experiments and the theoretical analyses both indicate that our proposed measuring system has great potential for achieving an accuracy of tens of nanometers and a range of hundreds of millimeters.

Dual terahertz comb spectroscopy with a single free-running fibre laser

Dual terahertz (THz) comb spectroscopy enables high spectral resolution, high spectral accuracy, and broad spectral coverage; however, the requirement for dual stabilized femtosecond lasers hampers its versatility. We here report the first demonstration of dual THz comb spectroscopy using a single free-running fibre laser. By tuning the cavity-loss-dependent gain profile with an intracavity Lyot filter together with precise management of the cavity length and dispersion, dual-wavelength comb light beams with slightly detuned repetition frequencies are generated in a single laser cavity. Due to sharing of the same cavity, such comb light beams suffer from common-mode fluctuation of the repetition frequency, and hence the corresponding frequency difference between them is passively stable around a few hundred hertz within millihertz fluctuation. While greatly reducing the size, complexity, and cost of the laser source by use of a single free-running fibre laser, the dual THz comb spectroscopy system maintains a spectral bandwidth and dynamic range of spectral power comparable to a system equipped with dual stabilized fibre lasers, and can be effectively applied to high-precision spectroscopy of acetonitrile gas at atmospheric pressure. The demonstrated results indicate that this system is an attractive solution for practical applications of THz spectroscopy and other applications.

Measurement of absolute frequency of continuous-wave terahertz radiation in real time using a free-running, dual-wavelength mode-locked, erbium-doped fibre laser

A single, free-running, dual-wavelength mode-locked, erbium-doped fibre laser was exploited to measure the absolute frequency of continuous-wave terahertz (CW-THz) radiation in real time using dual THz combs of photo-carriers (dual PC-THz combs). Two independent mode-locked laser beams with different wavelengths and different repetition frequencies were generated from this laser and were used to generate dual PC-THz combs having different frequency spacings in photoconductive antennae. Based on the dual PC-THz combs, the absolute frequency of CW-THz radiation was determined with a relative precision of 1.2 × 10⁻⁹ and a relative accuracy of 1.4 × 10⁻⁹ at a sampling rate of 100 Hz. Real-time determination of the absolute frequency of CW-THz radiation varying over a few tens of GHz was also demonstrated. Use of a single dual-wavelength mode-locked fibre laser, in place of dual mode-locked lasers, greatly reduced the size, complexity, and cost of the measurement system while maintaining the real-time capability and high measurement precision.

Parameter optimization of a dual-comb ranging system by using a numerical simulation method

Dual-comb system parameters have significant impacts on the ranging accuracy. We present a theoretical model and a numerical simulation method for the parameter optimization of a dual-comb ranging system. With this method we investigate the impacts of repetition rate difference, repetition rate, and carrier-envelope-offset frequency on the ranging accuracy. Firstly, the simulation results suggest a series of discrete zones of repetition rate difference in an optimal range, which are consistent with the experimental results. Secondly, the simulation results of the repetition rate indicate that a higher repetition rate is very favorable to improve the ranging accuracy. Finally, the simulation results suggest a series of discrete optimal ranges of the carrier-envelope-offset frequency for the dual-comb system. The simulated results were verified by our experiments.

Double-modulation reflection-type terahertz ellipsometer for measuring the thickness of a thin paint coating

We constructed a double-modulation, reflection-type terahertz (THz) ellipsometer for precise measurement of the thickness of a paint film which is coated on a metal surface and which is not transparent to visible or mid-infrared light. The double-modulation technique enabled us to directly obtain two ellipsometric parameters, Δ(ω) and Ψ(ω), as a function of angular frequency, ω, with a single measurement while reducing flicker noise due to a pump laser. The bias voltage of a photoconductive antenna (PCA) used as a THz pulse emitter was modulated at 100 kHz, and a first lock-in amplifier (LA1) was connected to the output of an electro-optic (EO) signal-sampling unit. In addition, a wire-grid polarizer (WGP) was rotated at 100 Hz to conduct polarization modulation with a frequency of 200 Hz. The output signal from LA1 was fed into a second lock-in amplifier (LA2) that worked in synchronization with the rotating WGP (RWGP). By operating LA2 in a quadrature phase-detection mode, we were able to obtain in-phase and out-of-phase signals simultaneously, from which the two ellipsometric parameters for an isotropic sample could be derived at the same time while cancelling common-mode noise. The lower detection limit of the thickness measurement and the relative standard deviation (RSD) of a black paint film coated on an aluminum substrate were 4.3 µm and 1.4%, respectively. The possibility of determining all elements of the Jones matrix for an anisotropic material is also discussed.

Phase-slope and phase measurements of tunable CW-THz radiation with terahertz comb for wide-dynamic-range, high-resolution, distance measurement of optically rough object

Phase measurement of continuous-wave terahertz (CW-THz) radiation is a potential tool for direct distance and imaging measurement of optically rough objects due to its high robustness to optical rough surfaces. However, the 2π phase ambiguity in the phase measurement of single-frequency CW-THz radiation limits the dynamic range of the measured distance to the order of the wavelength used. In this article, phase-slope measurement of tunable CW-THz radiation with a THz frequency comb was effectively used to extend the dynamic range up to 1.834 m while maintaining an error of a few tens µm in the distance measurement of an optically rough object. Furthermore, a combination of phase-slope measurement of tunable CW-THz radiation and phase measurement of single-frequency CW-THz radiation enhanced the distance error to a few µm within the dynamic range of 1.834 m without any influence from the 2π phase ambiguity. The proposed method will be a powerful tool for the construction and maintenance of large-scale structures covered with optically rough surfaces.

Comparison of length measurements provided by a femtosecond optical frequency comb

This paper presents a comparison of length measurements between the wavelength and the adjacent pulse repetition interval length (APRIL) provided by a femtosecond optical frequency comb. A theoretical estimation of the frequency stability for stabilizing the wavelength and APRIL, the frequency parameters that affect the stability of the APRIL in air, and the ambiguity in the length measurement by the APRIL are investigated. We find that the APRIL can be used as a low-cost measurement for the absolute length over a range of hundreds of meters in laboratory conditions.

Continuous-wave terahertz phase imaging using a far-infrared laser interferometer

Terahertz phase imaging can reveal the depth information of an optically opaque object and provide much better contrast for weak-absorption materials. We demonstrate a continuous-wave terahertz interferometric imaging method in which a far-infrared laser interferometer is used to measure the phase distribution with diffraction-limited lateral resolution and subwavelength axial resolution. An improved four-step phase-shifting algorithm is introduced to retrieve the phase map with very high accuracy and low distortion. The relative depth profiles of two transparent samples are successfully extracted by using this method. Experimental results verify that terahertz interferometric imaging in combination with the phase-shifting technique enables effective reconstruction of the phase image of the object under test.