In this paper we present the theory and the experimental setup used to transfer a standard frequency, to synchronize two clocks linked by an optical fiber. In order to verify the accuracy on frequency transfer over fiber link, we prepared an experiment that allows testing the performance of the setup for a variable set of environmental conditions, namely associated to temperature and vibration variations. The experimental setup shows the fiber optic link between one laboratory, where the standard frequency is generated, and another laboratory, where the equipment for simulating temperatures and vibrations are installed. The standard frequency, traceable to UTC(IPQ), is used to modulate two lasers with different wavelength,, injected in the optical fiber. At the end of the optical fiber the signals will be out of phase due to the inherent chromatic dispersion, which is also dependent on the temperature of the propagation media. Measuring the phase variations, caused by temperature gradients in the fiber, we can compensate the frequency transfer and synchronize the clocks. Evaluating all uncertainty components in this model, allows the metrological characterization of the synchronization and obtain the associated uncertainty of this quantity.

The Portuguese Institute for Quality is responsible for the realization and dissemination of the frequency standard in Portugal. There are several techniques for frequency transfer, but we use a frequency mixer to detect phase variations between two light signals with different wavelengths, traveling along an optical fibre. In this paper, we present the development of a digital twin (DT) that replicates the use of a frequency mixer to improve the frequency transfer problem. A setup was built to train and validate the technique: a frequency mixer was used to determine the phase difference between the two signals, which are caused by temperature gradients in the fibre, together with real-time temperature data from sensors placed along the fibre and on the mixer itself. The DT was trained with two machine learning algorithms, in particular, ARIMA and LSTM networks. To estimate the accuracy of the frequency mixer working as a phasemeter, several sources of uncertainty were considered and included in the DT model, with the goal of obtaining a phase value measurement and its uncertainty in real time. The JCGM 100:2008 and JCGM 101:2008 approaches were used for the estimation of the uncertainty budget. With this work, we merge DT technology with a frequency mixer used for phase detection to provide its value and uncertainty in real time.

Digital transformation in metrology, essential for Industry 4.0 and digital quality infrastructure, is driving the development of digital twins (DTs) to improve accuracy, traceability, and automation. In this work, we developed and experimentally validated a DT at the Portuguese National Metrology Institute to monitor and optimize standard frequency transfer through an optical fibre link, with the aim of reducing phase instability induced by thermal disturbances, the main uncertainty source in such systems. The DT combines real-time sensor data, simulation, and machine learning algorithms to reproduce the physical link. A long short-term memory network predicts ambient temperature, which feeds a neural network to forecast phase drift. These predictions are used to calculate fractional frequency offsets and apply compensating corrections every 5 and 30 min. Measurement uncertainty from the physical and digital components, including the ML models, was quantified using Monte Carlo dropout to capture random and epistemic contributions. The global expanded uncertainty for phase measurements was estimated as 2.10 ps ( k = 2). The performance was evaluated using a special form of Allan deviation (ADEVS) and TIE_rms. Periodic corrections significantly improved link stability. At τ = 60 s, ADEVS decreased from 1.64 × 10 ⁻¹¹ s without correction to 4.48 × 10 ⁻¹² s with 5 min corrections and 4.94 × 10 ⁻¹² s with 30 min corrections. The 5 min scheme performed better at short integration times below 120 s, whereas the 30 min scheme gave lower ADEVS between τ = 240 s and τ = 1200 s. Up to 1200 s, both compensated signals improved by more than 50% compared with the uncorrected signal. This work demonstrates, for the first time, that a DT incorporating machine learning–based phase prediction and uncertainty quantification can act as a low-cost, algorithm-driven compensation mechanism for optical frequency transfer links used as secondary links, where primary-laboratory accuracy is not required.