Subspace tracking for independent phase noise source separation in frequency combs

Advanced digital signal processing techniques in combination with ultra-wideband balanced coherent detection have enabled a new generation of ultra-high speed fiber-optic communication systems, by moving most of the processing functionalities into digital domain. In this paper, we demonstrate how digital signal processing techniques, in combination with ultra-wideband balanced coherent detection can enable optical frequency comb noise characterization techniques with novel functionalities. We propose a measurement method based on subspace tracking, in combination with multi-heterodyne coherent detection, for independent phase noise sources identification, separation and measurement. Our proposed measurement technique offers several benefits. First, it enables the separation of the total phase noise associated with a particular comb-line or -lines into multiple independent phase noise terms associated with different noise sources. Second, it facilitates the determination of the scaling of each independent phase noise term with comb-line number. Our measurement technique can be used to: identify the most dominant source of phase noise; gain a better understanding of the physics behind the phase noise accumulation process; and confirm, already existing, and enable better phase noise models. In general, our measurement technique provides new insights into noise behavior of optical frequency combs

An Efficient Cross-Correlation Method for a Digital Phase Noise Measurement System

In this paper, we propose a digital phase noise measurement using a 10-bit digital oscilloscope MXR608A from Keysight Technologies. The digital oscilloscope’s four channel data are used for digital phase noise measurement: two channels are assigned for the equally divided SUT (source under test), while the other two are assigned for the equally divided reference signals. First, we propose a cross correlation method to identify the phase noises added by the ADCs in the digital oscilloscope from the measured phase noises. Then, we propose a novel cross correlation method to extract the SUT phase noise. The cross-correlation output of the proposed method yields only the SUT phase noise and does not contain the reference signal phase noise unlike the traditional method. The proposed method was applied to measure the phase noises of the two SUTs, Keysight’s synthesized signal generator E8257D and function generator 33600A. The measured phase noises of the two SUTs were compared and found to show remarkable agreements with those measured using Keysight’s signal source analyzer E5052B. The phase noise floor of our digital phase noise measurement system is about −160 dBc/Hz

Digital instrumentation for the measurement of high spectral purity signals

Improvements on electronic technology in recent years have allowed the application of digital techniques in time and frequency metrology where low noise and high accuracy are required, yielding flexibility in systems implementation and setup. This results in measurement systems with extended capabilities, additional functionalities and ease of use. The Analog to Digital Converters (ADCs) and Digital to Analog Converters (DACs), as the system front-end, set the ultimate performance of the system in terms of noise. The noise characterization of these components will allow performing punctual considerations on the study of the implementation feasibility of new techniques and for the selection of proper components according to the application requirements. Moreover, most commercial platforms based on FPGA are clocked by quartz oscillators whose accuracy and frequency stability are not suitable for many time and frequency applications. In this case, it is possible to take advantage of the internal Phase Locked Loop (PLL) for generating the internal clock from an external frequency reference. However, the PLL phase noise could degrade the oscillator stability thereby limiting the entire system performance becoming a critical component for digital instrumentation. The information available currently in literature, describes in depth the features of these devices at frequency offsets far from the carrier. However, the information close to the carrier is a more important concern for time and frequency applications. In this frame, my PhD work is focused on understanding the limitations of the critical blocks of digital instrumentation for time and frequency metrology. The aim is to characterize the noise introduced by these blocks and in this manner to be able to predict their effects on a specific application. This is done by modeling the noise introduced by each component and by describing them in terms of general and technical parameters. The parameters of the models are identified and extracted through the corresponding method proposed accordingly to the component operation. This work was validated by characterizing a commercially available platform, Red Pitaya. This platform is an open source embedded system whose resolution and speed (14 bit, 125 MSps) are reasonably close to the state of the art of ADCs and DACs (16 bit, 350 MSps or 14 bit, 1 GSps/3GSPs) and it is potentially sufficient for the implementation of a complete instrument. The characterization results lead to the noise limitations of the platform and give a guideline for instrumentation design techniques. Based on the results obtained from the noise characterization, the implementation of a digital instrument for frequency transfer using fiber link was performed on the Red Pitaya platform. In this project, a digital implementation for the detection and compensation of the phase noise induced by the fiber is proposed. The beat note, representing the fiber length variations, is acquired directly with a high speed ADC followed by a fully digital phase detector. Based on the characterization results, it was expected a limitation in the phase noise measurement given by the PLL. First measurements of this implementation were performed using the 150 km-long buried fibers, placed in the same cables between INRiM and the Laboratoire Souterrain de Modane (LSM) on the Italy-France border. The two fibers are joined together at LSM to obtain a 300 km loop with both ends at INRiM. From these results the noise introduced by the digital system was verified in agreement with characterization results. Further test and improvements will be performed for having a finished system which is intended to be used on the Italian Link for Frequency and Time from Turin to Florence that is 642-km long and to its extension in the rest of Italy that is foreseen in the next future. Currently, a higher performance platform is under assessment by applying the tools and concepts developed along the PhD. The purpose of this project is the implementation of a state of the art phasemeter whose architecture is based on the DAC. In order to estimate the ultimate performance of the instrument, the DAC characterization is under development and preliminary measurements are also reported here

Implementation of spatial shift estimation approach for 3D profilometry based on digital fringe projection

Fringe Pattern Profilometry (FPP) based on Digital Fringe Projection (DFP) is a promising optical noncontact three-dimension (3D) profile measurement technologies due to its accuracy and flexibility. Popular FPP approaches retrieve the 3D profile information using the detection of phase difference, called the Phase Difference Estimation (PDE). Recently, a new kind of FPP approach, referred to as Spatial Shift Estimation (SSE) is introduced, which retrieves the 3D profile information using the detection of spatial shift instead of phase different. Compared with PDE approaches, SSE approaches are advantageous in that the projected fringe patterns do not need to be sinusoidal, and thus accurate reconstruction can be obtained even when nonlinear distortions exist on the fringe patterns. However, efficient implementation of SSE approaches is still an issue. This thesis work aims to implement the SSE approach for 3D profile measurement based on digital fringe projection. Firstly, a DFP system is designed and adopted in our laboratory, which is utilized as an experiment platform for the work presented in this thesis. SSE approaches are implemented on the system. Some problems associated with the implementation are studied and solved, including elimination of noise and distortion in the fringe patterns. Furthermore, an improved Inverse Function based Shift Estimation (IFSE) method is proposed to improve the performance of SSE approaches. Secondly, shift unwrapping problem associated with SSE is investigated. Through reviewing the phase unwrapping problem in PDE based FPP, we indicate that a similar shift unwrapping problem also exists in SSE approaches. A method for solving the problem has been proposed and the experiment results are presented to demonstrate the effectiveness of the proposed method. Finally, the research is carried out to improve the efficiency of SSE approaches. SSE approaches have the advantages that the projected fringe patterns are no longer required to be sinusoidal nor periodic. Therefore, we can choose a fringe pattern which has strong counter-interference capability against the noise and nonlinear distortion with simple implementation. Based on analysis of the limitations of traditional sinusoidal fringe, we propose to use sawtooth fringe pattern. Theoretical analysis has been given to evaluate the complexity of the proposed sawtooth fringe pattern based algorithms, and practical experiment are performed at last to prove the efficiency of this proposed fringe pattern

Direct strain and slope measurement using 2D DSPSI Title

Large variety of optical full-field measurement techniques are being developed and applied to solve mechanical problems. Since each technique possess its own merits, it is important to know the capabilities and limitations of such techniques. Among these optical full-field methods, interferometry techniques take an important place. They are based on illumination with coherent light (laser). In shearing interferometry the difference of the out of-plane displacement in two neighboring object points is directly measured. Since object displacement does not result in interferometry fringes, the method is suited for localization of strain concentrations and is indeed used in industry for this purpose. Used quantitatively DSPSI possesses the advantage over conventional out-of-plane displacement-sensitive interferometry that only a single difference of the unwrapped phase map is required to obtain flexural strains, thereby relieving problems with noise and reduction in the field of view. The first publication on (DSPSI) was made in 1973, but the emergence of a system providing quantitative measurements is more recent. This work aims to present the results of strain measurements using digital speckle pattern shearing interferometry (DSPSI).Comment: Communication \`a la Conf\'erence M\'editerran\'eenne sur les Mat\'eriaux Innovants et Applications -CIMA, Beyrouth, Liban-Mars 15-17, 2011; JM-CIMA.pd

Phase control and measurement in digital microscopy

The ongoing merger of the digital and optical components of the modern microscope is creating opportunities for new measurement techniques, along with new challenges for optical modelling. This thesis investigates several such opportunities and challenges which are particularly relevant to biomedical imaging. Fourier optics is used throughout the thesis as the underlying conceptual model, with a particular emphasis on three--dimensional Fourier optics. A new challenge for optical modelling provided by digital microscopy is the relaxation of traditional symmetry constraints on optical design. An extension of optical transfer function theory to deal with arbitrary lens pupil functions is presented in this thesis. This is used to chart the 3D vectorial structure of the spatial frequency spectrum of the intensity in the focal region of a high aperture lens when illuminated by linearly polarised beam. Wavefront coding has been used successfully in paraxial imaging systems to extend the depth of field. This is achieved by controlling the pupil phase with a cubic phase mask, and thereby balancing optical behaviour with digital processing. In this thesis I present a high aperture vectorial model for focusing with a cubic phase mask, and compare it with results calculated using the paraxial approximation. The effect of a refractive index change is also explored. High aperture measurements of the point spread function are reported, along with experimental confirmation of high aperture extended depth of field imaging of a biological specimen. Differential interference contrast is a popular method for imaging phase changes in otherwise transparent biological specimens. In this thesis I report on a new isotropic algorithm for retrieving the phase from differential interference contrast images of the phase gradient, using phase shifting, two directions of shear, and non--iterative Fourier phase integration incorporating a modified spiral phase transform. This method does not assume that the specimen has a constant amplitude. A simulation is presented which demonstrates good agreement between the retrieved phase and the phase of the simulated object, with excellent immunity to imaging noise

Phase control and measurement in digital microscopy

The ongoing merger of the digital and optical components of the modern microscope is creating opportunities for new measurement techniques, along with new challenges for optical modelling. This thesis investigates several such opportunities and challenges which are particularly relevant to biomedical imaging. Fourier optics is used throughout the thesis as the underlying conceptual model, with a particular emphasis on three--dimensional Fourier optics. A new challenge for optical modelling provided by digital microscopy is the relaxation of traditional symmetry constraints on optical design. An extension of optical transfer function theory to deal with arbitrary lens pupil functions is presented in this thesis. This is used to chart the 3D vectorial structure of the spatial frequency spectrum of the intensity in the focal region of a high aperture lens when illuminated by linearly polarised beam. Wavefront coding has been used successfully in paraxial imaging systems to extend the depth of field. This is achieved by controlling the pupil phase with a cubic phase mask, and thereby balancing optical behaviour with digital processing. In this thesis I present a high aperture vectorial model for focusing with a cubic phase mask, and compare it with results calculated using the paraxial approximation. The effect of a refractive index change is also explored. High aperture measurements of the point spread function are reported, along with experimental confirmation of high aperture extended depth of field imaging of a biological specimen. Differential interference contrast is a popular method for imaging phase changes in otherwise transparent biological specimens. In this thesis I report on a new isotropic algorithm for retrieving the phase from differential interference contrast images of the phase gradient, using phase shifting, two directions of shear, and non--iterative Fourier phase integration incorporating a modified spiral phase transform. This method does not assume that the specimen has a constant amplitude. A simulation is presented which demonstrates good agreement between the retrieved phase and the phase of the simulated object, with excellent immunity to imaging noise

Tile-Based Two-Dimensional Phase Unwrapping for Digital Holography Using a Modular Framework

A variety of physical and biomedical imaging techniques, such as digital holography, interferometric synthetic aperture radar (InSAR), or magnetic resonance imaging (MRI) enable measurement of the phase of a physical quantity additionally to its amplitude. However, the phase can commonly only be measured modulo 2π, as a so called wrapped phase map. Phase unwrapping is the process of obtaining the underlying physical phase map from the wrapped phase. Tile-based phase unwrapping algorithms operate by first tessellating the phase map, then unwrapping individual tiles, and finally merging them to a continuous phase map. They can be implemented computationally efficiently and are robust to noise. However, they are prone to failure in the presence of phase residues or erroneous unwraps of single tiles. We tried to overcome these shortcomings by creating novel tile unwrapping and merging algorithms as well as creating a framework that allows to combine them in modular fashion. To increase the robustness of the tile unwrapping step, we implemented a model-based algorithm that makes efficient use of linear algebra to unwrap individual tiles. Furthermore, we adapted an established pixel-based unwrapping algorithm to create a quality guided tile merger. These original algorithms as well as previously existing ones were implemented in a modular phase unwrapping C++ framework. By examining different combinations of unwrapping and merging algorithms we compared our method to existing approaches. We could show that the appropriate choice of unwrapping and merging algorithms can significantly improve the unwrapped result in the presence of phase residues and noise. Beyond that, our modular framework allows for efficient design and test of new tile-based phase unwrapping algorithms. The software developed in this study is freely available

Off-body wireless link simulation framework using deterministic channel modeling

Body-centric communication concerns wireless links in which the human body represents the central element, exchanging data by means of wearable antennas with a different node in the external environment or on the human body itself. During the link design phase, it is very advantageous to be able to model the link and predict its performance before its real implementation, resulting in reduction of design time and costs. In the present contribution, we propose a novel computer simulation framework to describe a complete off-body communication link between a human user and a remote base station, including all the components of the communication link such as wearable and fixed antennas, human body and propagation channel at the physical level, also taking into account the digital data transmission at link level. The proposed framework was constructed by applying the most appropriate modeling tools for each component, including ray tracing for the deterministic channel modeling. The framework provides as output the most common link performance parameters such as Bit-Error-Rate (BER), received Signal-to-Noise Ratio (SNR) and channel correlations. The validity of the proposed method was verified by comparing the figures of merit of a real off-body communication link, studied during a previous measurement campaign, with the ones obtained by the proposed simulation framework. A good agreement is obtained in terms of both BERs and SNRs

GPU-based Low-dose 4DCT Reconstruction via Temporal Non-local Means

Four-dimensional computed tomography (4DCT) has been widely used in cancer radiotherapy for accurate target delineation and motion measurement for tumors in thorax and upper abdomen areas. However, 4DCT simulation is associated with much higher imaging dose than conventional CT simulation, which is a major concern in its clinical application. Conventionally, each phase of 4DCT is reconstructed independently using the filtered backprojection (FBP) algorithm. The basic idea of our new algorithm is that, by utilizing the common information among different phases, the input information required to reconstruct image of high quality, and thus the imaging dose, can be reduced. We proposed a temporal non-local means (TNLM) method to explore the inter-phase similarity. All phases of the 4DCT images are reconstructed simultaneously by minimizing a cost function consisting of a data fidelity term and a TNLM regularization term. We utilized a forward-backward splitting algorithm and a Gauss-Jacobi iteration method to efficiently solve the minimization problem. The algorithm was also implemented on graphics processing unit (GPU) to achieve a high computational speed. Our reconstruction algorithm has been tested on a digital NCAT thorax phantom in three low dose scenarios. Our new algorithm generates visually much better CT images containing less image noise and streaking artifacts compared with the standard FBP algorithm. Quantitative analysis shows that much higher contrast-to-noise ratio and signal-to-noise ratio can be obtained using our algorithm. The total reconstruction time for all 10 phases of a slice ranges from 90 to 140 seconds on an NVIDIA Tesla C1060 GPU card.Comment: 14 pages, 4 figures, and 2 tables, accepted by Med. Phy