Beat Frequency Technique Research Articles

Possibility to break through limitation of measurement range in dual-wavelength digital holography* *Project supported by the Foundation of Science and Technology Department of Shaanxi Province, China (Grant No. 2018JQ6009), the Foundation of Education Department of Shaanxi Province, China (Grant No. 17JK1165), the Beijing Natural Science Foundation, China (Grant No. Z190004), the National Natural Science Foundation of China (Grant No. 61575197),

By using the beat frequency technique, the dual-wavelength digital holography (DWDH) can greatly increase the measurement range of the system. However, the beat frequency technique has a limitation in measurement range. The measurement range is not larger than a synthetic wavelength. Here, to break through this limitation, we propose a novel DWDH method based on the constrained underdetermined equations, which consists of three parts: (i) prove that the constrained underdetermined equation has a unique integer solution, (ii) design an algorithm to search for the unique integer solution, (iii) introduce a third wavelength into the DWDH system, and design a corresponding algorithm to enhance the anti-noise performance of DWDH. As far as we know, it is the first time that we have discovered that the problem of DWDH can belong in a problem of contained underdetermined equations, and it is also the first time that we have given the mathematical proof for breaking through the limitation of the measurement range. A series of results is shown to test the theory and the corresponding algorithms. More importantly, since the principle of proposed DWDH is based on basic mathematical principles, it can be further extended to various fields, such as dual-wavelength microwave imaging and dual-wavelength coherent diffraction imaging.

Linearized segmentation method for measuring the phase transfer function of a silicon Mach-Zehnder modulator by using the beat-frequency technique.

A linearity segmentation method for measuring the phase shift curve of silicon Mach-Zehnder modulators (SMZMs) as a function of applied electric field is presented. Applying a small sinusoidal signal to the traveling-wave electrode of the SMZM, the upper and lower arms of the SMZM produce differential phase modulation effect. Meanwhile, a local oscillator source with a wavelength-adjustable function is employed to heterodyne the intensity modulated optical signal of the SMZM; thus, the modulated intensity signal in the optical field domain is transformed into the low-frequency electric field domain. Meanwhile, a balanced detector with a low-speed transimpedance amplifier is exploited to realize photoelectric conversion, which can suppress the direct-current component and improve the anti-noise ability. Extracting the beat-frequency and first-order harmonic sideband signals in the case of phase bias is 0 and π, respectively, the phase shift slopes of the upper and lower arms can be calculated under different reverse PN voltages, and we can achieve the phase shift as a function of the modulation frequency and reverse PN voltage. The proposed method is supported by the simulation and measurement results and the key parameters of the SMZM, such as the radio frequency half-wave voltage, chirp characteristic, 3 dB bandwidth, etc., can be acquired from the phase shift curves of the upper and lower arms.

Fiber birefringence measurement by an external applied strain method and a polarimetric fiber laser sensor.

In this work, a high-sensitivity and low-cost sensing scheme for measuring intrinsic and induced fiber birefringence change is reported based on a polarimetric fiber laser sensor interrogated by the beat frequency technique. The fiber birefringence measurement is achieved by an external applied strain method. A detailed theoretical analysis of the principle for fiber birefringence measurement is carried out. Two alternative equations are given for determining the change of fiber birefringence, which make it very convenient for users to choose different order beat signals. To verify the performance of the sensing system, the external applied strain-induced fiber birefringence change is measured experimentally. The experiment result shows that the fiber birefringence experiences a linear increase with the increase of applied strain. A strain response coefficient of 4.646×10-11/μϵ is obtained. Furthermore, the repeatability and stability performances of the polarimetric fiber laser sensor are also investigated.

Fiber Birefringence Measurement of Single-Mode Fiber by a Polarimetric Fiber Ring Laser

A novel and low-cost fiber birefringence measurement scheme is proposed and studied by a polarimetric fiber ring laser interrogated by the beat frequency technique. For the fiber ring laser, modes splitting occur between two orthogonal polarization modes because of intrinsic fiber birefringence. As a result, two types of beat frequency signals (i.e., longitudinal mode beat frequency and polarization mode beat frequency signals) are generated simultaneously. The principle of measurement of fiber birefringence by the fiber ring laser has been analyzed theoretically in detail. Two alternative expressions for fiber birefringence change are obtained, which is very convenient for users to choose different order longitudinal and polarization mode beat frequency signals. The variation of fiber birefringence caused by applied strain has been calculated in terms of beat frequency shift. To validate the proposed sensing system, the strain-induced fiber birefringence change in commercial Erbium-doped fiber is investigated and obtained by measuring frequency shift of two types of beat frequency signals. The experimental results show that the fiber birefringence experiences a linear decrease when the applied strain is increased. A strain response coefficient of –1.756 × 10–11/μe is obtained. The proposed sensing scheme has obvious advantages of simple structure, low cost, and high sensitivity and it will provide great convenience for measuring fiber birefringence for short-length single mode fiber.

Design of a Beat Frequency Oscillator Metal Detector

This paper discusses the design,construction,and simulation of a beat frequency oscillator metal detector. Over the years, it has become an important issue to limit, the entry of people into certain places with weapons or instruments of harm and destruction.in this paper is a design of an effective means of detecting dangerous weapons made of metal in order to reduce crime rate in the society. It uses the principle of electromagnetic induction and adopts a digital beat frequency technique. The system uses a search coil to detect metallic objects at a close range and gives a visual, auditory and vibratory indication once the metallic object is detected. The search coil forms part of an LC oscillation circuit. The activation frequency of the LC oscillator is primarily determined by the value of involved inductor and capacitor. In case an inductance is altered, the frequency does not remain the same by changing its value through the introduction of a metallic object.

Generation of electron bunches at low repetition rates using a beat-frequency technique

Even at a continuous wave facility such as CEBAF at Jefferson Lab, an electron beam with long time intervals (tens of ns) between individual bunches can be useful, for example to isolate sources of background via time of flight detection or to measure the energy of neutral particles that cannot be separated with a magnetic field. This paper describes a demonstrated method to quickly and easily deliver bunches with repetition rates of 20 to 100 MHz corresponding to time intervals between 10 to 50 ns (respectively). This is accomplished by changing the ON/OFF frequency of the RF-pulsed drive laser by a small amount (f/f < 20%), resulting in a bunch frequency equal to the beat frequency between the radio frequencies of the drive laser and the photoinjector chopper system.

Demonstration of RSFQ digitizer on a multichip module

A 1-b slice of a rapid single-flux quantum (RSFQ) digitizer with interchip communications on a multichip module (MCM) has been successfully designed, fabricated using 3-/spl mu/m Nb technology, and tested. We placed a flash comparator followed by an enable switch and an MCM transmitter circuit on one side of the chip, and an MCM receiver circuit followed by a memory buffer on the other side. The 5 /spl times/ 5 mm chip was flip-chip mounted on a 10 /spl times/ 10 mm carrier chip by a solder bump technique. During circuit operation, the comparator output signal and the clock signal left the chip, moved to the carrier chip, and returned back to the chip into the memory buffer. We operated the circuit with a beat frequency technique where the data input frequency was slightly off from the clock frequency by the beat frequency of 10 kHz. The circuit operated correctly up to 10 GHz. The critical circuit operation margin was observed to be the bias current to the SQUID in the MCM receiver circuit and was about /spl plusmn/6% at 10 GHz.

Absolute measurement of the hyperfine splittings of six molecular 127I2 lines around the He-Ne/I2 wavelength at λ = 633 nm

With the aid of two diode-laser narrowband spectrometers around 633 nm, we report the measurement of the iodine hyperfine components of the R(60) 8-4, R(125) 9-4 and P(54) 8-4 transitions located −12 GHz from the classical red He-Ne laser stabilized on the R(127) 11-5 transition of 127I2, the P(33) 6-3 transition roughly −1 GHz away, the P(39) 6-3 transition 3.4 GHz above, and the R(59) 8-4 and P(53) 8-4 transitions roughly 19 GHz above. The Doppler-free absorption signals were resolved using a third-harmonic detection technique and hyperfine frequency splittings were measured by beat-frequency techniques. The individual hyperfine transitions were linked to a 633 nm He-Ne laser by direct frequency measurements up to 16 GHz. The experimental standard uncertainty was typically below 5 kHz (i.e. relative uncertainty <1 × 10−11).

Iodine-stabilized extended cavity diode laser at λ=633 nm

An extended cavity diode laser at 633 nm has been frequency stabilized to I/sub 2/-Doppler-free absorption signals of the P(33)6-3 transition using a third-harmonic detection technique. The frequency was measured by the beat-frequency technique with an iodine-stabilized He-Ne laser as reference. A minimum value for the two-probe relative standard uncertainty of 1/spl times/ 10/sup -11/ (5 kHz) is reached after 100 s. We also report measurements of the hyperfine splittings of the P(33)6-3 transition and laser frequency dependence on modulation amplitude and iodine pressure.

International comparison of stabilized He-Ne lasers by the saturated absorption of 127I2 at λ ≈ 633 nm involving the CEM (Spain), the IPQ (Portugal) and the BIPM

The results of an international comparison of iodine-stabilized He-Ne lasers at λ ≈ 633 nm, made by beat-frequency techniques, between the CEM (Spain), the IPQ (Portugal) and the BIPM are presented. Four lasers took part in the ten-day period of measurements, and were compared once or twice a day. The frequency differences between the lasers were all less than 6 kHz and the highest standard uncertainty of the mean of the frequency differences between two lasers was 7 kHz. These results lie inside the standard uncertainty given in the mise en pratique of the definition of the metre. Parameters which affect the frequency of the lasers, such as modulation width, iodine pressure and laser power, were also investigated.

International Comparison of Two Iodine-stabilized He-Ne Lasers at λ ≈ 543 nm

An intercomparison of two 127I2 stabilized He-Ne lasers at λ ≈ 543 nm, recommended as length standards, has been made between the DFM and the PTB, and is the first international comparison at this wavelength reported so far. Both lasers use saturated absorption of iodine in an external cell, one (PTB) using frequency-modulation spectroscopy, the other (DFM) using the first or third harmonic detection techniques. The range of the frequency differences between the two lasers was from 11,8 kHz to 18,4 kHz, with a mean of Δf = 14,2 kHz and a standard uncertainty of 1,9 kHz. A minimum value for the two-probe relative standard uncertainty of 2,5 × 10-13 (140 Hz) is reached after 5 000 s. The hyperfine line splittings were measured by the beat-frequency technique, and good agreement was found between the two completely different laser systems. Measurements of frequency dependence on modulation amplitude, iodine pressure, and pump power are also reported.

Iodine-stabilized 543 nm HeNe lasers

Internal-mirror 543 nm HeNe lasers are frequency-stabilized on the iodine hyperfine transitions. The Allen standard deviation of 1×10 −12 is reached after a 10 second integration time. The hyperfine spectrum originating from the R (12) 26-0 and R (106) 28-0 lines of the B-X system of 127I 2 has been studied. The frequency differences between hyperfine components have been measured by beat frequency techniques, and the hyperfine coupling constants are fitted for the R (106) 28-0 line.

Frequency-stabilized 543 nm HeNe laser systems: A new candidate for the realization of the metre?

The first results are reported of high-accuracy beat-frequency measurements between HeNe lasers stabilized on an iodine transition at 543 nm. The frequency difference between two such systems was found to be (14±5) kHz. A minimum value of the Allan standard deviation of 2.5×10 -12 is reached after 50 s. A part of the hyperfine spectrum originating from the R(12) 26-0 and R(106) 28-0 lines of the B-X system of 127I 2 has been studied. The frequency differences between hyperfine components have been measured by beat frequency techniques. A study of modulation and pressure effects has also been carried out.

Comparison of the 127I2 Stabilized He-Ne Lasers at 633 nm Wavelength of the National Research Laboratory of Metrology of Japan and the Bureau International des Poids et Mesures

The results of an international comparison of iodine-stabilized He-Ne lasers at 633 nm, made by beat-frequency techniques, between the NRLM (Japan) and the BIPM are presented. During two weeks the frequency of the two lasers NRLM1 and BIPM4 were compared twice a day. The mean frequency difference was determined to be Δf = [0.9 ± 2.6] kHz, corresponding to a relative frequency difference of [2 ± 5] · 10-12. Parameters which affected the frequency of the lasers such as modulation width, iodine pressure and laser power were also investigated. As the laser BIPM4 was compared with the laser BIPM2 at the BIPM before and after the travel to the NRLM, we can link our results to the previous international comparisons in which the BIPM has participated.

Characteristics of a 127I2 - Stabilized Dye Laser at 576 nm

Two dye lasers have been stabilized to component "o" of the 17-1 P(62) line in 127I2 at 576 nm. The reproducibility of these lasers has been measured by beat-frequency techniques and the dependence of the laser frequency on depth of modulation, power, and iodine pressure determined. The frequency ratio between this laser and a He-Ne laser stabilized to component "i" of the 11-5 R(127) line at 633 nm in 127I2 has been measured interferometrically with an uncertainty of ±1 × 10-10. Some iodine hyperfine component separations at 576 nm are also given.

2-bit 1-Gsample/s electro-optic guided-wave analogue-to-digital convertor system

An electro-optic analogue-to-digital convertor system has been demonstrated at 1 Gsample/s. This system has been tested with low-frequency waveforms and by means of a beat-frequency technique with a 499 MHz test signal. Digital outputs are slowed in time and then fed into 125 MHz digital-toanalogue convertors which accurately reconstruct the beat signal, proving the compatibility of electra-optic signal processing with digital circuits.

Results of international comparisons using methane-stabilized He-Ne lasers at 3.39 μm and iodine-stabilized He-Ne lasers at 633 nm

The results of international comparisons of methane-stabilized He-Ne lasers at λ = 3.39 μm and iodine-stabilized He-Ne lasers at 633 nm, made by beat frequency techniques, between Bureau International des Poids et Mesures (BIPM) and eleven national laboratories are presented. Generally, the measured frequency differences were inside /spl I.chemo/4 × 10-11; but greater frequency differences were observed with some iodine cells (probably as a result of contamination) or when the output power of one laser was two or three times greater than the power of the other laser.

2-bit 1 Gsample/s electrooptic guided-wave analog-to-digital converter

An electrooptic analog-to-digital converter which uses a pulsed GaAlAs diode laser for sampling, a LiNbO 3 Ti-indiffused-waveguide interferometric array for conversion, a Si APD, and a special 1 GHz Si integrated circuit for digital processing has been demonstrated at 1 Gsample/s. Individual bit channels of this 2-bit device have been tested by a beat-frequency technique with a 499.2 MHz test signal. This represents the highest frequency conversion of an analog waveform reported to date.

高い周波数領域で作動するFM復調素子および流体信号発生器の開発

In fluidics, frequency demodulating circuits (f/a converters) have been used in temperature sensors and revolutional speed sensors. The conventional types of the circuits were constructed by using some fluidic devices which were connected by transmission lines, and the operating frequencies were usually under 1kHz.In this experiment, the frequency demodulation was conducted by only one fluidic element and the frequency range was up to 10kHz without using beat frequency technique.The developed element was constructed by acting the main jet of the first stage to the main jet of the second stage directly without transmission line. By this method, the element with excellent frequency characteristics was obtained.A fluid signal genarator which was able to obtain high frequency fluid signals was also developed in this study. The signal generator produced up to 10kHz with a nearly constant amplitude.By applying the fluid signal to the fluidic element directly without using beat frequency technique, the operation up to 10kHz was recognized. The output pressure change was about 17Pa/Hz.

Digital thickness monitor using only one crystal oscillator

A digital thickness monitor which measures the thickness of a film deposited on a quartz crystal by measuring the change of frequency of a single oscillator controlled by the resonance of the crystal is described. Conventional beat-frequency techniques involving two precision oscillators are avoided by means of circuits including a presettable memory and an up-down counter. The monitor is easily reset at the start of a deposition, can display either frequency change or frequency, and can be easily modified to display film thickness directly. Film thickness determined by the monitor is compared favorably to thickness values determined interferometrically.