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At least 433 records · Page 24
All sourcesNASA NTRSDOE OSTI
NASA NTRS1994

Measurement of the frequency stability of responders in aircraft

Measurement on an aircraft orbit, such as a satellite launching orbit, is made by the responder in the aircraft along with several remote track stations on the ground. During the launching, the system is required to have precise time synchronization and frequency accuracy. At the same time, accurate measurement of aircraft velocity requires high frequency stability of the system. However, atomic frequency standards in the ground stations supply time and frequency reference standard with excellent long term and short term frequency stability for the above-mentioned goals. The stability of responder is also an important factor affecting the performance of the system and there are more requirements for the corresponding time/frequency measurements. In the system, the responders do not use continuous wave (CW) but narrow pulse modulated wave; consequently, the characterization theory of their stability is more complicated and the measurement technique is more difficult for pulsed wave than that for CW. A systematic characterization theory of the frequency stability for pulsed wave is demonstrated and the measuring methods are discussed. The measurement systems, which have been set up in Beijing Institute of Radio Metrology and Measurement (BIRMM) and can be used to test the frequency stability of pulse coherent responders in time domain and frequency domain with high sensitivity and accuracy, are described. Using these measurement systems, successful measurements for the responders were made with which the satellite launching orbits were precisely obtained and tracked.

Liu, Xiaofan↗
NASA NTRS1996

Robust Stabilization of Uncertain Systems Based on Energy Dissipation Concepts

Robust stability conditions obtained through generalization of the notion of energy dissipation in physical systems are discussed in this report. Linear time-invariant (LTI) systems which dissipate energy corresponding to quadratic power functions are characterized in the time-domain and the frequency-domain, in terms of linear matrix inequalities (LMls) and algebraic Riccati equations (ARE's). A novel characterization of strictly dissipative LTI systems is introduced in this report. Sufficient conditions in terms of dissipativity and strict dissipativity are presented for (1) stability of the feedback interconnection of dissipative LTI systems, (2) stability of dissipative LTI systems with memoryless feedback nonlinearities, and (3) quadratic stability of uncertain linear systems. It is demonstrated that the framework of dissipative LTI systems investigated in this report unifies and extends small gain, passivity, and sector conditions for stability. Techniques for selecting power functions for characterization of uncertain plants and robust controller synthesis based on these stability results are introduced. A spring-mass-damper example is used to illustrate the application of these methods for robust controller synthesis.

Gupta, Sandeep↗
NASA NTRS1999

Influence of Buoyant Convection on the Stability of Enclosed Laminar Flames

Enclosed diffusion flames are commonly found in practical combustion systems, such as the power-plant combustor, gas turbine combustor, and jet engine after-burner. In these systems, fuel is injected into a duct with a co-flowing or cross-flowing air stream. In combustors, this flame is anchored at the burner (i.e., fuel jet inlet) unless adverse conditions cause the flame to lift off or blow out. Investigations of burner stability study the lift off, reattachment, and blow out of the flame. There have been numerous studies of flame stability. Relatively few studies have investigated the stability of flames with an oxidizer co-flow, compared with the number of studies on (nearly) free jet diffusion flames. The air flow around the fuel jet can significantly alter the lift off, reattachment and blow out of the jet diffusion flame. In normal gravity, however, the effects of the air flow on flame stability are often complicated by the presence of buoyant convection. A comparison of normal-gravity and microgravity flames can provide clear indication of the influence of forced and buoyant flows on the flame stability. The overall goal of the Enclosed Laminar Flames (ELF) research, described at the following URL site: http://zeta.lerc.nasa.gov/expr/elf.htm, is to improve our understanding of the effects of buoyant convection on the structure and stability of co-flow diffusion flames.

Brooker, John E.↗
NASA NTRS1998

Sufficient Conditions for the Stability of a Lur'e System With Two Nonzero Inputs Based on Lyapunovs Direct Method

The Lur'e problem is a famous problem in nonlinear control theory. The analysis of this system is usually restricted to Lur'e systems in which the external input is zero. One form of this problem involves the stability analysis of the Lur'e system with two nonzero inputs. The stability analysis of this type of system is traditionally performed based on L stability theory. The objective of this paper is to present sufficient conditions for the stability of this system based on Lyapunov's direct method. This is a conceptually simpler approach to the existing analysis based on L stability theory and it provides some additional information about the stability of the system.

Adetona, Olawale↗
NASA NTRS1996

Effects of vestibular loss on head stabilization in response to head and body perturbations

Control of head position during postural responses is important to facilitate both the interpretation of vestibular signals and the stabilization of gaze. In these experiments, we compared head stabilization for two different postural tasks: 1) in response to perturbations at the head, and 2) in response to perturbations induced at the support surface, which perturb both body and head position. To determine whether normal vestibular function is necessary for head stabilization in these two tasks, responses to forward and backward mechanical perturbations of the head and body were compared for 13 normal subjects and 4 patients with profound bilateral vestibular loss (two with vestibular loss in adulthood and two in infancy). Normal subjects showed little neck muscle activity for body perturbations, but large, early activations in both neck extensors and flexors for head perturbations. In contrast, vestibular patients showed excessive neck muscle activation for body perturbations and reduced or absent neck muscle activity for head perturbations. Patients with vestibular loss in adulthood also showed increased head acceleration in response to both head and body perturbations, but patients with vestibular loss in infancy showed more normal head accelerations. For body perturbations, the differences in head acceleration between patients and normals were greater for later head acceleration peaks, indicating poor head control during the execution of the postural response. Trunk angle changes were also higher in the patients for forward body perturbations, indicating that poorer control of trunk position could have contributed to their poorer head stabilization. These results indicate that the vestibular system plays an important role in head and trunk stabilization for both head and body perturbations. However, the more normal head accelerations of the patients with infant vestibular loss also indicate that other mechanisms, possibly involving neck reflexes, can at least partially substitute for the vestibular system to provide head and trunk stabilization.

NASA Discipline Neuroscience↗
NASA NTRS1948

Measurements of the Lateral and Directional Stability and Control Characteristics of a P-51H Airplane (AAF No. 44-64164)

Flight tests of a P-51H airplane with two different vertical-tail assemblies were made to determine lateral and directional stability and control characteristics. The airplane had satisfactory directional stability in the landing, approach, and wave-off conditions with either tail. In the power-on clean and glide conditions, however, the airplane had weak directional stability with the original tail. The production tail, which had a 7-inch fin extension and a shorter span rudder, improved the directional stability in the power-on clean and glide conditions, but the stability was still weak in the power-on clean condition. Increased altitude in either case caused a slight decrease in the stability. The rudder-trim-force change with speed with either vertical-tail assembly was high. The general aileron control characteristics were satisfactory but the aileron effectiveness failed to meet the Army handling-qualities requirements.

Kraft, Christopher C., Jr.↗
NASA NTRS1951

Investigation of the Low-Speed Stability and Control Characteristics of a 1/10-Scale Model of the Douglas XF4D-1 Airplane in the Langley Free-Flight Tunnel TED No. NACA DE 349

An investigation of the low-speed, power-off stability and control characteristics of a 1/10-scale model of the Douglas XF4D-1 airplane has been made in the Langley free-flight tunnel. The model was flown with leading-edge slats retracted and extended over a lift-coefficient range from 0.5 to the stall. Only relatively low-altitude conditions were simulated and no attempt was made to determine the effect on the stability characteristics of freeing the controls. The longitudinal stability and control characteristics of the model were satisfactory for all conditions investigated except near the stall with slats extended, where the model had a slight nosing-up tendency. The lateral stability and control characteristics of the model were considered satisfactory for all conditions investigated except near the stall with slats retracted, where a change in sign of the static- directional-stability parameter Cn(sub beta) caused the model to be directionally divergent. The addition of an extension to the top of the vertical tail did not increase Cn(sub beta) enough to eliminate the directional divergence of the model, but a large increase in Cn(sub beta) that was obtainable by artificial means appeared to eliminate the divergence and flights near the stall could be made. Artificially increasing the stability derivative-Cn(sub r) (yawing moment due to yawing) and Cn(sub p) (yawing moment due to rolling) had little effect on the divergence for the range of these parameters investigated. Calculations indicate that the damping of the lateral oscillation of the airplane with slats retracted or extended will be satisfactory at sea level but will be only marginally satisfactory at 40,000 feet.

Johnson, Joseph L.↗
NASA NTRS1995

Concept Designed and Developed for Distortion- Tolerant, High-Stability Engine Control

Engine Control Future aircraft turbine engines, both commercial and military, must be able to successfully accommodate expected increased levels of steady-state and dynamic engine-face distortion. Advanced tactical aircraft are likely to use thrust vectoring to enhance their maneuverability. As a result, the engines will see more extreme aircraft angles-of-attack and sideslip levels than are currently encountered with present-day aircraft. Also, the mixed-compression inlets needed for the High Speed Civil Transport will likely encounter disturbances similar to those seen by tactical aircraft, in addition to planar pulse, inlet buzz, and high distortion levels at low flight speed and off-design operation. The current approach of incorporating a sufficient component design stall margin to tolerate these increased levels of distortion would significantly reduce performance. The objective of the High Stability Engine Control (HISTEC) program is to design, develop, and flight demonstrate an advanced, high-stability, integrated engine-control system that uses measurement-based, real-time estimates of distortion to enhance engine stability. The resulting distortion-tolerant control reduces the required design stall margin, with a corresponding increase in performance and decrease in fuel burn. The HISTEC concept has been designed and developed, and the software implementing the concept has successfully accommodated time-varying distortion. The NASA Lewis Research Center is currently overseeing the development and validation of the hardware and software necessary to flight test the HISTEC concept. HISTEC is a contracted effort with Pratt & Whitney of West Palm Beach, Florida. The HISTEC approach includes two major systems: A Distortion Estimation System (DES) and Stability Management Control (SMC). DES is an aircraft-mounted, high-speed processor that estimates the amount and type of distortion present and its effect on the engine. It uses high-response pressure measurements at the engine face to calculate indicators of the type and extent of distortion in real time. From these indicators, DES determines the effects of distortion on the propulsion systems and the corresponding engine match point necessary to accommodate it. DES output consists of fan and compressor pressure ratio trim commands that are passed to the SMC. In addition, DES uses maneuver information, consisting of angle-of-attack and sideslip from the flight control, to anticipate high inlet distortion conditions. The SMC, which is contained in the engine-mounted, Improved Digital Electronic Engine Control (IDEEC), includes advanced control laws to directly control the fan and compressor transient operating line (pressure ratio). These advanced control laws, with a multivariable design, have the potential for higher bandwidth and the resulting more precise control of engine match. The ability to measure and assess the distortion effects in real time coupled with a high-response controller improves engine stability at high levels of distortion. The software algorithms implementing DES have been designed, developed, and demonstrated, and integration testing of the DES and SMC software has been completed. The results show that the HISTEC system will be able to sense inlet distortion, determine the effect on engine stability, and accommodate distortion by maintaining an adequate margin for engine surge. The Pratt &Whitney Comprehensive Engine Diagnostic Unit was chosen as the DES processor. An instrumented inlet case for sensing distortion was designed and fabricated. HISTEC is scheduled for flight test on the ACTIVE F-15 aircraft at the NASA Dryden Flight Research Center in Edwards, California, in late 1996.

Source record↗
NASA NTRS2004

The Stability of Two Connected Pendant Drops

The stability of an equilibrium system of two drops suspended from circular holes is examined. The drop surfaces are disconnected surfaces of a connected liquid body. For holes of equal radii and identical pendant drops axisymmetric perturbations are always the most dangerous. The stability region for two identical drops differs considerably from that for a single drop. Loss of stability leads to a transition from a critical system of identical drops to a stable system of axisymmetric non-identical. This system of non-identical drops reaches its own stability limit (to isochoric or non-isochoric paturbations). For non-identical drops, loss of stability results in dripping or streaming from the holes. Critical volumes for non-identical drops have been calculated as functions of the Bond number, B. For unequal hole radii, stability regions have been constructed for a set of hole radius, K. The dependence of critical volumes on K and B is analyzed.

Slobozhanin, Lev A.↗
NASA NTRS2006

Stability Limits of a PD Controller for a Flywheel Supported on Rigid Rotor and Magnetic Bearings

Active magnetic bearings are used to provide a long-life, low-loss suspension of a high-speed flywheel rotor. This paper describes a modeling effort used to understand the stability boundaries of the PD controller used to control the active magnetic bearings on a high speed test rig. Limits of stability are described in terms of allowable stiffness and damping values which result in stable levitation of the nonrotating rig. Small signal stability limits for the system is defined as a nongrowth in vibration amplitude of a small disturbance. A simple mass-force model was analyzed. The force resulting from the magnetic bearing was linearized to include negative displacement stiffness and a current stiffness. The current stiffness was then used in a PD controller. The phase lag of the control loop was modeled by a simple time delay. The stability limits and the associated vibration frequencies were measured and compared to the theoretical values. The results show a region on stiffness versus damping plot that have the same qualitative tendencies as experimental measurements. The resulting stability model was then extended to a flywheel system. The rotor dynamics of the flywheel was modeled using a rigid rotor supported on magnetic bearings. The equations of motion were written for the center of mass and a small angle linearization of the rotations about the center of mass. The stability limits and the associated vibration frequencies were found as a function of nondimensional magnetic bearing stiffness and damping and nondimensional parameters of flywheel speed and time delay.

Kascak, Albert F.↗
NASA NTRS2008

Changes in Head Stability Control in Response to a Lateral Perturbation while Walking in Older Adults

Falling is a main contributor of injury in older adults. The decline in sensory systems associated with aging limits information needed to successfully compensate for unexpected perturbations. Therefore, sensory changes result in older adults having problems maintaining balance stability when experiencing an unexpected lateral perturbation (e.g. slip) in the environment. The goal of this study was to determine head stability movement strategies used by older adults when experiencing an unexpected lateral perturbation during walking. A total of 16 healthy adults, aged 66-81 years, walked across a foam pathway 6 times. One piece of the foam pathway covered a movable platform that translated to the left when the subject stepped on the foam. Three trials were randomized in which the platform shifted. Angular rate sensors were placed on the center of mass for the head and trunk segments to collect head and trunk movement in all three planes of motion. The predominant movement strategies for maintaining head stability were determined from the results of the cross-correlation analyses between the head and trunk segments. The Chi square test of independence was used to evaluate the movement pattern distributions of head-trunk coordination during perturbed and non-perturbed walking. When perturbed, head stabilization was significantly challenged in the yaw and roll planes of motion. Subjects demonstrated a movement pattern of the head leading the trunk in an effort to stabilize the head. The older adult subjects used this head stabilization movement pattern to compensate for sensory changes when experiencing the unexpected lateral perturbation.

Buccello, Regina R.↗
NASA NTRS2009

Application of Bounded Linear Stability Analysis Method for Metrics-Driven Adaptive Control

This paper presents the application of Bounded Linear Stability Analysis (BLSA) method for metrics-driven adaptive control. The bounded linear stability analysis method is used for analyzing stability of adaptive control models, without linearizing the adaptive laws. Metrics-driven adaptive control introduces a notion that adaptation should be driven by some stability metrics to achieve robustness. By the application of bounded linear stability analysis method the adaptive gain is adjusted during the adaptation in order to meet certain phase margin requirements. Analysis of metrics-driven adaptive control is evaluated for a second order system that represents a pitch attitude control of a generic transport aircraft. The analysis shows that the system with the metrics-conforming variable adaptive gain becomes more robust to unmodeled dynamics or time delay. The effect of analysis time-window for BLSA is also evaluated in order to meet the stability margin criteria.

Bakhtiari-Nejad, Maryam↗
NASA NTRS2009

Stability of Pharmaceuticals in Space

Stability testing is a tool used to access shelf life and effects of storage conditions for pharmaceutical formulations. Early research from the International Space Station (ISS) revealed that some medications may have degraded while in space. This potential loss of medication efficacy would be very dangerous to Crew health. The aim of this research project, Stability of Pharmacotherapeutic Compounds, is to study how the stability of pharmaceutical compounds is affected by environmental conditions in space. Four identical pharmaceutical payload kits containing medications in different dosage forms (liquid for injection, tablet, capsule, ointment and suppository) were transported to the ISS aboard a Space Shuttle. One of the four kits was stored on that Shuttle and the other three were stored on the ISS for return to Earth at various time intervals aboard a pre-designated Shuttle flight. The Pharmacotherapeutics laboratory used stability test as defined by the United States Pharmacopeia (USP), to access the degree of degradation to the Payload kit medications that may have occurred during space flight. Once these medications returned, the results of stability test performed on them were compared to those from the matching ground controls stored on Earth. Analyses of the results obtained from physical and chemical stability assessments on these payload medications will provide researchers additional tools to promote safe and efficacious medications for space exploration.

Nguyen, Y-Uyen↗
NASA NTRS2007

Computing a Stability Spectrum by Use of the HHT

The Hilbert-Huang transform (HHT) is part of the mathematical basis of a method of calculating a stability spectrum. This method can be regarded as an extended and improved version of a prior HHT-based method of calculating a damping spectrum. In the prior method, information on positive damping (which leads to stability) and negative damping (which leads to instability) becomes mixed into a single squared damping loss factor. Hence, there is no way to distinguish between stability and instability by examining a damping spectrum. In contrast, in the present stabilityspectrum method, information on the mathematical sign of the damping is retained, making it possible to identify reThe Hilbert-Huang transform (HHT) is part of the mathematical basis of a method of calculating a stability spectrum. This method can be regarded as an extended and improved version of a prior HHT-based method of calculating a damping spectrum. In the prior method, information on positive damping (which leads to stability) and negative damping (which leads to instability) becomes mixed into a single squared damping loss factor. Hence, there is no way to distinguish between stability and instability by examining a damping spectrum. In contrast, in the present stabilityspectrum method, information on the mathematical sign of the damping is retained, making it possible to identify regions of instability in a spectrum. This method is expected to be especially useful for analyzing vibration-test data for the purpose of predicting vibrational instabilities in structures (e.g., flutter in airplane wings).

Huang, Norden E.↗
NASA NTRS2010

Absolute Stability Analysis of a Phase Plane Controlled Spacecraft

Many aerospace attitude control systems utilize phase plane control schemes that include nonlinear elements such as dead zone and ideal relay. To evaluate phase plane control robustness, stability margin prediction methods must be developed. Absolute stability is extended to predict stability margins and to define an abort condition. A constrained optimization approach is also used to design flex filters for roll control. The design goal is to optimize vehicle tracking performance while maintaining adequate stability margins. Absolute stability is shown to provide satisfactory stability constraints for the optimization.

Jang, Jiann-Woei↗
NASA NTRS2002

Stability of Pseudobrookite-Type Titanium Oxides

Orthorhombic, (Bbmm), (Al, Fe, Cr, Ti)(sub 2) TiO5-(Mg, Fe)Ti2O5 solid solutions (pseudobrookites, s.l.) are found either as an oxidation product of ilmenite and/or spinel or a primary crystallizing phase in igneous and metamorphic rocks on Earth (e.g., basalt flows, crustal and mantle xenoliths, hornfels), and basaltic rocks on the Moon. Moreover, orthorhombic oxides are often part of the crystalline matrix in glass/ceramics with useful applications, and play a major role in the industrial production of TiO2. To fully exploit the potential of these compounds as petrogenetic indicators and/or useful materials we need to quantitatively understand the factors controlling their properties and stability, and thus, to extrapolate beyond the calibrating experiments. For that purpose, we need to combine thermochemistry, phase equilibrium, and in situ P-V-T-cation disorder experimental data that presently either are incomplete or lacking. Perhaps, the most complete data set is that for MgTi2O5 (karrooite) which allows the calibration of models for the Gibbs free energy of the MgTi2O5 as a function of pressure, temperature, and the Mg2+-Ti4+ distribution between the two nonequivalent octahedral sites. Consequently, the effect of cation disorder on MgTi2O5 stability, and the phase relations among MgTi2O5, other titanium oxides, and silicate minerals can be examined. Calculated phase relations in the Mg-Ti-Si-O system and phase equilibrium experiments in Fe-bearing compositions suggest that pseudobrookite-type oxides may be a more common in rocks than previously realized. However, homogeneous and heterogeneous equilibria, and crystallization paths likely affect their stability. For example, isobaric increases in temperature favor disordering and thus entropy-stabilization, in contrast, isothermal increases in pressure have the opposite effect. Although, currently, the potential effect of composition to cation disorder cannot be fully explored, it appears that enrichment in trivalent cations probably enhances entropy-stabilization and thus may increase the stability of (Al, Fe, Cr, Ti)-rich pseudobrookites relative to that of (Mg, Fe)-rich ones. In addition, high-temperature, nearly isothermal, decompression paths of olivine+orthopyroxene+oxide assemblages may favor pseudobrookites (s.l.) over rutile and/or ilmenite, in contrast, cooling at low pressures seems to favor ilmenite and/or rutile. In the case of crustal and mantle xenoliths, the presence or absence of orthorhombic oxides is probably controlled by reactions with olivine, orthopyroxene, ilmenite, and rutile. In oceanic mantle xenoliths such reactions may also involve a TiO2-enriched but not SiO2-enriched melt/fluid, because pseudobrookites (s.l.) would react with the SiO2-enriched melt/fluid to form orthopyroxene and rutile. Parenthetically, experiments and model calculations in the Mg-Ti-Si-O system suggest that low degree partial melting of low-TiO2 bulk compositions may produce Ti-enriched liquids in equilibrium with olivine, orthopyroxen ad=nd MgTi2O5, rutile or ilmenite.

Xirouchakis, Dimistrios↗
NASA NTRS2011

A Quasi-Steady Flexible Launch Vehicle Stability Analysis Using Steady CFD with Unsteady Aerodynamic Enhancement

Launch vehicles frequently experience a reduced stability margin through the transonic Mach number range. This reduced stability margin is caused by an undamping of the aerodynamics in one of the lower frequency flexible or rigid body modes. Analysis of the behavior of a flexible vehicle is routinely performed with quasi-steady aerodynamic lineloads derived from steady rigid computational fluid dynamics (CFD). However, a quasi-steady aeroelastic stability analysis can be unconservative at the critical Mach numbers where experiment or unsteady computational aeroelastic (CAE) analysis show a reduced or even negative aerodynamic damping. This paper will present a method of enhancing the quasi-steady aeroelastic stability analysis of a launch vehicle with unsteady aerodynamics. The enhanced formulation uses unsteady CFD to compute the response of selected lower frequency modes. The response is contained in a time history of the vehicle lineloads. A proper orthogonal decomposition of the unsteady aerodynamic lineload response is used to reduce the scale of data volume and system identification is used to derive the aerodynamic stiffness, damping and mass matrices. The results of the enhanced quasi-static aeroelastic stability analysis are compared with the damping and frequency computed from unsteady CAE analysis and from a quasi-steady analysis. The results show that incorporating unsteady aerodynamics in this way brings the enhanced quasi-steady aeroelastic stability analysis into close agreement with the unsteady CAE analysis.

Bartels, Robert E.↗
NASA NTRS2006

Stabilizing Microwave Frequency of a Photonic Oscillator

A scheme for stabilizing the frequency of a microwave signal is proposed that exploits the operational characteristics of a coupled optoelectronic oscillator (COEO) and related optoelectronic equipment. An essential element in the scheme is a fiber mode-locked laser (MLL), the optical frequency of which is locked to an atomic transition. In this scheme, the optical frequency stability of the mode-locked laser is transferred to that of the microwave in the same device. Relative to prior schemes for using wideband optical frequency comb to stabilize microwave signals, this scheme is simpler and lends itself more readily to implementation in relatively compact, rugged equipment. The anticipated development of small, low-power, lightweight, highly stable microwave oscillators based on this scheme would afford great benefits in communication, navigation, metrology, and fundamental sciences. COEOs of various designs, at various stages of development, in some cases called by different names, have been described in a number of prior NASA Tech Briefs articles. A COEO is an optoelectronic apparatus that generates both short (picosecond) optical pulses and a steady microwave signal having an ultrahigh degree of spectral purity. The term "coupled optoelectronic" in the full name of such an apparatus signifies that its optical and electronic oscillations are coupled to each other in a single device. The present frequency-stabilization scheme is best described indirectly by describing the laboratory apparatus used to demonstrate it. The apparatus (see figure) includes a COEO that generates a comb-like optical spectrum, the various frequency components of which interfere, producing short optical pulses. This spectrum is centered at a nominal wavelength of 1,560 nm. The spectrum separation of this comb is about 10 GHz, as determined primarily by the length of an optical loop and the bandpass filter in the microwave feedback loop. The optical loop serves as microwave resonator having a very high value of the resonance quality factor (Q). The optical frequency of MLL is then stabilized by locking it to an atomic transition as described below. The COEO contains a tunable 1-nm band-pass optical filter and a piezoelectric-transducer (PZT) drum over which a stretch of fiber is wound. The 1-nm-wide pass band of the filter provides coarse tuning to overlap the frequency comb with the atomic transition frequency. Controlled stretching of the fiber by means of the PZT drum can be used in conjunction with temperature control for locking the laser frequency. To reference to an atomic resonance at 780 nm in this demonstration setup, the optical output of the COEO at 1,560 nm is fed through an erbium-doped-fiber amplifier (EDFA) to a frequency doubler in the form of a periodically poled lithium niobate (PPLN) crystal. The frequency-doubled output is combined with the output of a separate frequency-stabilized diode laser at a photodetector. As described thus far, the two 780-nm laser subsystems are nominally independent of each other and can, therefore, operate at different frequencies. Hence, at the photodetector, the two laser beams interfere, so that the output of the photodetector includes a beat note (a component at the difference between the two laser frequencies).

Maleki, Lute↗