Synchronous multi-color laser network with daily sub-femtosecond timing drift

Filming atoms in motion with sub-atomic spatiotemporal resolution is one of the distinguished scientific endeavors of our time. Newly emerging X-ray laser facilities are the most likely candidates to enable such a detailed gazing of atoms due to their angstrom-level radiation wavelength. To provide the necessary temporal resolution, numerous mode-locked lasers must be synchronized with ultra-high precision across kilometer-distances. Here, we demonstrate a metronome synchronizing a network of pulsed-lasers operating at different center wavelengths and different repetition rates over 4.7-km distance. The network achieves a record-low timing drift of 0.6 fs RMS measured with 2-Hz sampling over 40 h. Short-term stability measurements show an out-of-loop timing jitter of only 1.3 fs RMS integrated from 1 Hz to 1 MHz. To validate the network performance, we present a comprehensive noise analysis based on the feedback flow between the setup elements. Our analysis identifies nine uncorrelated noise sources, out of which the slave laser's inherent jitter dominates with 1.26 fs RMS. This suggests that the timing precision of the network is not limited by the synchronization technique, and so could be much further improved by developing lasers with lower inherent noise.Comment: 12 pages, 4 figure

Automatic Detection of Optic Disc in Retinal Image by Using Keypoint Detection, Texture Analysis, and Visual Dictionary Techniques

With the advances in the computer field, methods and techniques in automatic image processing and analysis provide the opportunity to detect automatically the change and degeneration in retinal images. Localization of the optic disc is extremely important for determining the hard exudate lesions or neovascularization, which is the later phase of diabetic retinopathy, in computer aided eye disease diagnosis systems. Whereas optic disc detection is fairly an easy process in normal retinal images, detecting this region in the retinal image which is diabetic retinopathy disease may be difficult. Sometimes information related to optic disc and hard exudate information may be the same in terms of machine learning. We presented a novel approach for efficient and accurate localization of optic disc in retinal images having noise and other lesions. This approach is comprised of five main steps which are image processing, keypoint extraction, texture analysis, visual dictionary, and classifier techniques. We tested our proposed technique on 3 public datasets and obtained quantitative results. Experimental results show that an average optic disc detection accuracy of 94.38%, 95.00%, and 90.00% is achieved, respectively, on the following public datasets: DIARETDB1, DRIVE, and ROC

Quantum diffusion of microcavity solitons

Coherently pumped (Kerr) solitons in an ideal optical microcavity are expected to undergo random quantum motion that determines fundamental performance limits in applications of the soliton microcombs. Here this random walk and its impact on Kerr soliton timing jitter are studied experimentally. The quantum limit is discerned by measuring the relative position of counter-propagating solitons. Their relative motion features weak interactions and also presents common-mode suppression of technical noise, which typically hides the quantum fluctuations. This is in contrast to co-propagating solitons, which are found to have relative timing jitter well below the quantum limit of a single soliton on account of strong correlation of their mutual motion. Good agreement is found between theory and experiment. The results establish the fundamental limits to timing jitter in soliton microcombs and provide new insights on multisoliton physics

Quantum diffusion of microcavity solitons

Coherently pumped (Kerr) solitons in an ideal optical microcavity are expected to undergo random quantum motion that determines fundamental performance limits in applications of the soliton microcombs. Here this random walk and its impact on Kerr soliton timing jitter are studied experimentally. The quantum limit is discerned by measuring the relative position of counter-propagating solitons. Their relative motion features weak interactions and also presents common-mode suppression of technical noise, which typically hides the quantum fluctuations. This is in contrast to co-propagating solitons, which are found to have relative timing jitter well below the quantum limit of a single soliton on account of strong correlation of their mutual motion. Good agreement is found between theory and experiment. The results establish the fundamental limits to timing jitter in soliton microcombs and provide new insights on multisoliton physics

Quantum diffusion of microcavity solitons

Coherently-pumped (Kerr) solitons in an ideal optical microcavity are expected to undergo random quantum motion that determines fundamental performance limits in applications of soliton microcombs. Here, this diffusive motion and its impact on Kerr soliton timing jitter is studied experimentally. Typically hidden below technical noise contributions, the quantum limit is discerned by measuring counter-propagating solitons. Their relative motion features only weak interactions and also presents excellent common mode suppression of technical noise. This is in strong contrast to co-propagating solitons which are found to have relative timing jitter well below the quantum limit of a single soliton on account of strong mutual motion correlation. Good agreement is found between theory and experiment. The results establish the fundamental limits to timing jitter in soliton microcombs and provide new insights on multi-soliton physic

The Coefficients of the Polynomial Interpolation in Terms of Finite Differences and Numerical Differentiations

In this note, the polynomial interpolation of degree n passing through n+1 distinct points is considered. The coefficients of the polynomial interpolation are investigated in terms of finite differences and numerical differentiations. The coefficients are formulated by the use of divided differences and correlated with forward, backward differences and numerical differentiations. It is seen that the coefficients of the polynomial interpolation can be found and computed by using finite differences, numerical differentiations and generating special formulae for equidistant points or not

Ultra-precise timing and synchronization for large-scale scientific instruments

Ultra-precise timing has become a prerequisite for many modern large-scale scientific instruments, and timing precision is a crucial enabling factor to achieve the ultimate goals of those instruments. Here, we review the recent progress in timing technologies, including timing characterization methods among different kinds of sources (optical lasers, microwaves and x-ray pulses), large-scale free-space timing synchronization, and fiber-based timing synchronization. Technical and fundamental limitations of fiber-based timing systems are also discussed to provide future directions