KEYWORDS: Phase shifting, Phase measurement, Measurement uncertainty, Model based design, Interferometers, Data modeling, Distance measurement, Signal intensity
An electro-optic comb has a wide frequency mode spacing of more than several tens of GHz, making it possible to resolve each comb mode by using commercial spectrometers. The individual frequency modes of the electro-optic comb can be employed as the multiple stabilized lasers required for a multi-wavelength interferometer in absolute distance measurements. For absolute distance measurements, the phase information for each frequency mode, i.e., wavelength, is necessary for determining the absolute distance using the excess fraction method, and this requires a phase shifting process. Typically, the phase shifting is implemented through the sequential translation of a reference mirror by an equal distance. However, since the wavelength values corresponding to every frequency mode are different, even the same amount of shifting of the reference mirror generates different phase change for each wavelength. In such a situation, to accurately measure the phase for each wavelength, a model-based analysis method for phase shifting intensity signals itself was adopted. In the model-based analysis of phase shifting intensity signals, the phase determination uncertainty can vary depending on the number of the phase shifting step. Therefore, in this study, we aim to estimate the phase determination uncertainty according to the number of the phase shifting step through numerical simulations.
Absolute distance measurement has been widely required not only in various industrial fields such as semiconductors, displays, and heavy industry, but also in fundamental and applied research sites. Among the various optical methods for measuring absolute distances, the most widely used method with high precision is multi-wavelength interferometry. In general, multi-wavelength interferometry uses three or more frequency-stabilized lasers to solve the phase ambiguity problem from a large amount of phase information corresponding to several wavelengths. However, despite the high measurement precision of multi-wavelength interferometers, it is practically not easy to install and maintain several frequency-stabilized lasers in terms of cost and maintenance. In this work, we aim to implement a multi-wavelength interferometer using an electro-optic comb with wide spacing between frequency modes. Because the frequency mode spacing of the electro-optic comb is wide enough to be resolved by commercial spectrometers, each frequency mode can be considered as a single frequency-stabilized laser. Through this concept, several frequency-stabilized lasers for multiwavelength interferometer can be replaced with a single electro-optic comb. Absolute distance measurement was performed using the proposed method, and measurement uncertainty evaluation was also performed to evaluate the proposed method. When the electro-optic comb is stabilized by being locked to an atomic clock being traceable to the time standard, so it is expected that it can be easily used to realize length standards or measure ultra-precise absolute distances in the future.
A multi-layered structure is being extensively applied in the high-tech devices fabrication in the semiconductor and display industries. For measuring the thin-film thicknesses of the multi-layered structure, various techniques like spectral reflectometry, spectral ellipsometry, and SEM/TEM have been used depending on the application fields. Among them, the spectral reflectometry is being widely used because of the advantages of simple configuration, non-destructive characteristics, and high-speed measurement. In spectral reflectometry, the reliability of the reflectance model is very important, because the higher the agreement of the modeled reflectance to the measured one, the lower the measurement uncertainty of the thin-film thicknesses determined by the reflectance model. In case of the single-layer thin-film sample, the thickness can be verified using a certified reference material, but the multi-layer thicknesses are not easy to be verified unlike single-layer case. In this study, to check the reliability of the multi-layer reflectance model, two different methods were used; (1) the extension of the single-layer model and (2) the multi-layer model based on the transfer matrix. The first one is to sequentially determine the thin-film thicknesses from layer to layer. The second one is to simultaneously determine all the thin-film thicknesses of a multi-layer structure. By applying two methods to double-layered thin-film sample(SiO2-SiN), the thin-film thicknesses of both layers were determined and compared to each other by considering the measurement uncertainty. The applicability of the theoretical reflectance model can be confirmed according to whether the thin-film thickness measurement results are agreed within the uncertainty.
Ultrafast laser frequency microcombs provide equidistant coherent frequency markers over a broad spectrum, enabling new frontiers in chip-scale frequency metrology, laser spectroscopy, dense communications, precision metrology. Measuring and understanding the fundamental noise parameters in these high-clock-rate frequency microcombs are essential to advance the underlying physics and the precision microwave-optical clockwork. In this talk we describe the noise characteristics and timing jitter in adiabatic laser frequency microcombs. We compare and contrast the fundamental noise and fluctuation parameters for a series of laser frequency microcomb states, from multiple soliton to soliton crystals and single-soliton regimes. Each of the noise families and their noise coupling mechanisms are examined with our theoretical models. This aids the understanding of frequency, intensity and phase noise characteristics of frequency microcombs towards the precision limits.
In this talk, first, we describe chip-scale coherent mode-locking in microresonator frequency combs, verified by interferometric femtosecond timing jitter measurements and phase-resolved ultrafast spectroscopy. Normal dispersion sub-100-fs mode-locking is also observed, supporting by nonlinear modeling and analytics. Second we describe the noise limits in full microcomb stabilization, locking down both repetition rate and one comb line against a reference. Active stabilization improves the long-term stability to an instrument-limited residual instability of 3.6 mHz per root tau and a tooth-to-tooth relative frequency uncertainty down to 50 mHz and 2.7×10−16. Third we describe graphene-silicon nitride hybrid microresonators for tunable frequency modes, variants of soliton mode-locked states and crystals, and controllable Cerenkov radiation. Our studies provide a platform towards precision spectroscopy, frequency metrology, timing clocks, and coherent communications.
We measure absolute distances by performing multi-wavelength interferometry (MWI) using four different wavelengths generated simultaneously from the frequency comb of a femtosecond laser. The measurement precision is estimated to be less than 63 nm in peak-to-valley over a distance of 1 m as compared to an incremental HeNe laser interferometer. We also evaluate the operational stability and robustness of the interferometer hardware system over a time period of 12 hours. Finally, it is concluded that the proposed frequency-comb-referenced multi-wavelength interferometry is capable of providing fast, precise and high stable absolute distance measurements, being well suited for industrial precisionengineering applications and near-future space missions.
Absolute distance measurement (ADM) with high precision is required for various fields of precision engineering, which has long been implemented by means of time-of-flight measurement of a pulsed laser, intensity or frequency modulation of a continuous-wave laser, and cross-correlation of pseudo-random micro-wave signals. Recently, in response to increasing demands on the measurement precision and range beyond conventional limits, femtosecond pulse lasers began to draw attention as a new light source that permits realizing various advanced ADM principles such as synthetic radiofrequency wavelength generation, Fourier-transform-based dispersive analysis and multi-wavelength interferometry. In this talk, we present the state-of-the-art measurement principles and performance demonstrated by exploiting the unique temporal and spectral characteristics of femtosecond laser pulses for high-precision ADM applications.
We revisit the method of synthetic wavelength interferometry (SWI) for absolute measurement of long distances using the radio-frequency harmonics of the pulse repetition rate of a mode-locked femtosecond laser. Our intention here is to extend the nonambiguity range (NAR) of the SWI method using a coarse virtual wavelength synthesized by shifting the pulse repetition rate. The proposed concept of NAR extension is experimentally verified by measuring a ∼13-m distance with repeatability of 9.5 μm (root-mean-square). The measurement precision is estimated to be 31.2 μm in comparison with an incremental He–Ne laser interferometer. This extended SWI method is found to be well suited for long-distance measurements demanded in the fields of large-scale precision engineering, geodetic survey, and future space missions.
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