Quantum-enhanced optical precision measurement assisted by low-frequency squeezed vacuum states

Stable low-frequency squeezed vacuum states at a wavelength of 1550 nm were generated.By controlling the squeezing angle of the squeezed vacuum states,two types of low-frequency quadrature-phase squeezed vacuum states and quadrature-amplitude squeezed vacuum states were obtained using one setup respectively.A quantum-enhanced fiber Mach–Zehnder interferometer(FMZI)was demonstrated for low-frequency phase measurement using the generated quadrature-phase squeezed vacuum states that were injected.When phase modulation was measured with the quantumenhanced FMZI,there were above 3 dB quantum improvements beyond the shot-noise limit(SNL)from 40 kHz to 200 kHz,and 2.3 dB quantum improvement beyond the SNL at 20 kHz was obtained.The generated quadrature-amplitude squeezed vacuum state was applied to perform low-frequency amplitude modulation measurement for sensitivity beyond the SNL based on optical fiber construction.There were about 2 dB quantum improvements beyond the SNL from 60 kHz to 200 kHz.The current scheme proves that quantum-enhanced fiber-based sensors are feasible and have potential applications in high-precision measurements based on fiber,particularly in the low-frequency range.

Precision frequency measurement of 1^S0–3^P1 intercombination lines of Sr isotopes

We report on frequency measurement of the intercombination（5s^2）^1S0–（5s5p）^3P1transition of the four natural isotopes of strontium, including88^Sr（82.58%）,87^Sr（7.0%）,86^Sr（9.86%）, and84^Sr（0.56%）. A narrow-linewidth laser that is locked to an ultra-low expansion（ULE） optical cavity with a finesse of 12000 is evaluated at a linewidth of 200 Hz with a fractional frequency drift of 2.8×10^-13 at an integration time of 1 s. The fluorescence collector and detector are specially designed, based on a thermal atomic beam. Using a double-pass acousto-optic modulator（AOM） combined with a fiber and laser power stabilization configuration to detune the laser frequency enables high signal-to-noise ratios and precision saturated spectra to be obtained for the six transition lines, which allows us to determine the transition frequency precisely.The optical frequency is measured using an optical frequency synthesizer referenced to an H maser. Both the statistical values and the final values, including the corrections and uncertainties, are derived for a comparison with the values given in other works.

First Evaluation and Frequency Measurement of the Strontium Optical Lattice Clock at NIM

An optical lattice clock based on 87Sr is built at National Institute of Metrology （NIM） of China. The systematic frequency shifts of the clock are evaluated with a total uncertainty of 2.3×10-16. To measure its absolute frequency with respect to NIM＇s cesium fountain clock NIM5, the frequency of a flywheel H-maser of NIM5 is transferred to the Sr laboratory through a 50-kin-long fiber. reference frequency of this H-maser, is used for the optical this Sr clock is measured to be 429228004229873.7（1.4）Hz. A fiber optical frequency comb, phase-locked to the frequency measurement. The absolute frequency of

Fringe Projection Measurement System in Reverse Engineering

Acquisition of physical data with high precision is a key step in reverse engineering (RE). It is an important stimulative for the progress of reverse engineering with which various digitizing devices are invent ed, developed and made applicable. This paper introduces a three dimensional opt ical measurement method based on digital fringe projection technique in RE to im prove the technique through its application. A practical example is presented an d the result demonstrates the applicability and feasibility of the measurement s ystem as well as the reliability and validity of relevant methods and algorithms .

Optics System Design of Microwave Imaging Reflectometry for the EAST Tokamak

A front-end optics system has been developed for the EAST microwave imaging reflectometry for 2D density fluctuation measurement.Via the transmitter optics system,a combination of eight transmitter beams with independent frequencies is employed to illuminate wide poloidal regions on eight distinct cutoff layers.The receiver optics collect the reflected wavefront and project them onto the vertical detector array with 12 antennas.Utilizing optimized Field Curvature adjustment lenses in the receiver optics,the front-end optics system provides a flexible and perfect matching between the image plane and a specified cutoff layer in the plasma,which ensures the correct data interpretation of density fluctuation measurement.

Erratum and Note: Measurement of Zeeman Shift of Cesium Atoms Using an Optical Nanofiber [Chin. Phys. Lett. 35(2018) 083201]

Our recent article (Chin. Phys. Lett. 35 (2018)083201) measured the Zeeman shift of cesium atoms using an optical nanofiber. Before our work, Watkins et al.(Ref.[17] in our article) had demonstrated the Zeeman shift also using an optical nanofiber in rubidium atoms. Watkins et al. reported on the observation

A method for phase reconstruction in optical three-dimensional shape measurement

In optical three-dimensional shape measurement, a method of improving the measurement precision for phase reconstruction without phase unwrapping is analyzed in detail. Intensities of any five consecutive pixels that lie in the x-axis direction of the phase domain are given. Partial derivatives of the phase function in the x- and y-axis directions are obtained with a phase-shifting mechanism, the origin of which is analysed. Furthermore, to avoid phase unwrapping in the phase reconstruction, we derive the gradient of the phase function and perform a two-dimensional integral along the x- and y-axis directions. The reconstructed phase can be obtained directly by performing numerical integration, and thus it is of great convenience for phase reconstruction. Finally, the results of numerical simulations and practical experiments verify the correctness of the proposed method.

Editorial: Advances in Optical Techniques for Mechanical Measurements

Recently, optical techniques have attracted great attention due to their excellent non-destructive, non-contact, high-resolution, and full-field characteristics. Applications can be found in diverse fields such as precision mechanics and manufacturing, aerospace and automotive testing and inspection, materials science, and biomedical engineering. Advances in Optical Techniques for Me- chanical Measurements presents the latest research progresses in several widely used optical techniques with applications in preci- sion mechanical engineering.

VIBRATION MEASUREMENT OF DOUBLE-ENDED TUNING FORKS RESONATOR

To enhance the coherence and reliability of the double-ended tuning fork （DETF） resonator, a measurement system of resonator vibration is presented to check its dynamic characteristics. Laser Doppler techniques are utilized and the relation between DETF vibration velocity and output current of photodetector is obtained. Resonator vibration equation is also analyzed and its driving power only depends on the direct current bias voltage and the amplitude of alternative voltage. Furthermore, a special resonator driving control circuit based on measurement is designed. The amplitude and frequency of circuit is controlled by a computer so that highly stable and strong driving signal can be output. Experiments on driving and measuring double-ended tuning fork have been done, The frequency of driving signal is 8 kHz and the peak-to-peak value of driving voltage is 140 V. Experimental results indicate resonator can be drived stably by driving control circuit and dynamic characteristics of DETF may be measured in real time.

Precise Optical Fiber Length Measurement System Based on Fresnel Reflection

In this study, a precise optical fiber length measurement system is proposed. The measurement technique is based on the measurement of relative Fresnel reflected light intensity in a test fiber. Time delayed optical reflected pulses are obtained from a single nanosecond pulse injected at the input due to the difference in lengths of the reference and test fibers. The lengths of the different optical fibers have been measured with this technique with high resolution and fast response time. The measured results show that, the proposed technique has a comparable performance with the well-known length measurement systems.

Measurement of Zeeman Shift of Cesium Atoms Using an Optical Nanofiber

Nanofibers have many promising applications because of their advantages of high power density and ultralow saturated light intensity. We present here a Zeeman shift of the Doppler-broadened cesium D2 transition using a tapered optical nanofiber in the presence of a magnetic field. When a weak magnetic field is parallel to the propagating light in the nanofiber, the Zeeman shift rates for different circularly polarized spectra are observed.For the ＋component, the typical linear Zeeman shift rates of = 3 and = 4 ground-state cesium atoms are measured to be 3.10（±0.19） MHz/G and 3.91（±0.16） MHz/G. For the -component, the values are measured to be-2.81（±0.25） MHz/G, and-0.78（±0.28） MHz/G. The Zeeman shift using the tapered nanofiber can help to develop magnetometers to measure the magnetic field at the narrow local region and the dispersive signal to lock laser frequency.

Analyzing the Effect of the Intra-Pixel Position of Small PSFs for Optimizing the PL of Optical Subpixel Localization

Subpixel localization techniques for estimating the positions of point-like images captured by pixelated image sensors have been widely used in diverse optical measurement fields.With unavoidable imaging noise,there is a precision limit(PL)when estimating the target positions on image sensors,which depends on the detected photon count,noise,point spread function(PSF)radius,and PSF’s intra-pixel position.Previous studies have clearly reported the effects of the first three parameters on the PL but have neglected the intra-pixel position information.Here,we develop a localization PL analysis framework for revealing the effect of the intra-pixel position of small PSFs.To accurately estimate the PL in practical applications,we provide effective PSF(e PSF)modeling approaches and apply the Cramér–Rao lower bound.Based on the characteristics of small PSFs,we first derive simplified equations for finding the best PL and the best intra-pixel region for an arbitrary small PSF;we then verify these equations on real PSFs.Next,we use the typical Gaussian PSF to perform a further analysis and find that the final optimum of the PL is achieved at the pixel boundaries when the Gaussian radius is as small as possible,indicating that the optimum is ultimately limited by light diffraction.Finally,we apply the maximum likelihood method.Its combination with e PSF modeling allows us to successfully reach the PL in experiments,making the above theoretical analysis effective.This work provides a new perspective on combining image sensor position control with PSF engineering to make full use of information theory,thereby paving the way for thoroughly understanding and achieving the final optimum of the PL in optical localization.

Time-resolution enhanced multi-path OTD measurement using an adaptive filter based incoherent OFDR

High accuracy and time resolution optical transfer delay(OTD)measurement is highly desired in many multi-path applications,such as optical true-time-delay-based array systems and distributed optical sensors.However,the time resolution is usually limited by the frequency range of the probe signal in frequency-multiplexed OTD measurement techniques.Here,we proposed a time-resolution enhanced OTD measurement method based on incoherent optical frequency domain reflectometry(I-OFDR),where an adaptive filter is designed to suppress the spectral leakage from other paths to break the resolution limitation.A weighted least square(WLS)cost function is first established,and then an iteration approach is used to minimize the cost function.Finally,the appropriate filter parameter is obtained according to the convergence results.In a proof-of-concept experiment,the time-domain response of two optical links with a length difference of 900 ps is successfully estimated by applying a probe signal with a bandwidth of 400 MHz.The time resolution is improved by 2.78times compared to the theoretical resolution limit of the inverse discrete Fourier transform(iDFT)algorithm.In addition,the OTD measurement error is below±0.8 ps.The proposed algorithm provides a novel way to improve the measurement resolution without applying a probe signal with a large bandwidth,avoiding measurement errors induced by the dispersion effect.

Error-CompensatingFive-SamplePhase-Shifting Algorithm Based on Phase-Shift Error Estimation

A new error compensating five sample phase shifting algorithm which is insensitive to phase shift error is proposed to retrieve the phase distribution of a fringe pattern. It includes two steps. First, the linear phase shift error is estimated using four sample images. Then, the phase distribution is calculated with error corrected by using the phase shift error estimated in the first step. As the equations of error estimation and phase calculation are simple, this new algorithm is practical as well as effective. Computer simulations were carried out to verify the effectiveness of the algorithm. Results of two other well known error compensating algorithms are also presented, which show the new algorithm is the least sensitive to phase shift error.

Cross-interference correction and simultaneous multi-gas analysis based on infrared absorption

In this paper, we present simultaneous multiple pollutant gases （CO2, CO, and NO） measurements by using the non-dispersive infrared （NDIR） technique. A cross-correlation correction method is proposed and used to correct the cross-interferences among the target gases. The calculation of calibration curves is based on least-square fittings with third-order polynomials, and the interference functions are approximated by linear curves. The pure absorbance of each gas is obtained by solving three simultaneous equations using the fitted interference functions. Through the interference correction, the signal created at each filter channel only depends on the absorption of the intended gas. Gas mixture samples with different concentrations of CO2, CO, and NO are pumped into the sample cell for analysis. The results show that the measurement error of each gas is less than 4.5%.

Accurate Phase Shift Extraction for Generalized Phase-Shifting Interferometry

An accurate phase shift extraction method for generalized phase-shifting interferometry is suggested. Based on the nearly random phase distribution of the diffraction field of the object, a singular formula is derived to calculate the unknown phase shift without the requirements of an iteration process or the selection of the correct value from two or more possible phase shift solutions as needed before. This method can be used in the cases of two or more frames with both smooth and diffusing object surfaces. Computer simulations and optical experiments have satisfactorily verified the efficiency and accuracy of this method.

Precise determination of characteristic laser frequencies by an Er-doped fiber optical frequency comb

Femtosecond optical frequency combs correlate the microwave and optical frequencies accurately and coherently.Therefore,any optical frequency in visible to near-infrared region can be directly traced to a microwave frequency.As a result,the length unit“meter”is directly related to the time unit“second”.This paper validates the capability of the national wavelength standards based on a home-made Er-doped fiber femtosecond optical frequency comb to measure the laser frequencies ranging from visible to near-infrared region.Optical frequency conversion in the femtosecond optical frequency comb is achieved by combining spectral broadening in a highly nonlinear fiber with a single-point frequencydoubling scheme.The signal-to-noise ratio of the beat notes between the femtosecond optical frequency comb and the lasers at 633,698,729,780,1064,and 1542 nm is better than 30 d B.The frequency instability of the above lasers is evaluated by using a hydrogen clock signal with a instability of better than 1×10^(-13)at 1-s averaging time.The measurement is further validated by measuring the absolute optical frequency of an iodine-stabilized 532-nm laser and an acetylenestabilized 1542-nm laser.The results are within the uncertainty range of the international recommended values.Our results demonstrate the accurate optical frequency measurement of lasers at different frequencies using the femtosecond optical frequency comb,which is not only important for the precise and accurate traceability and calibration of the laser frequencies,but also provides technical support for establishing the national wavelength standards based on the femtosecond optical frequency comb.

Optical spectroscopy and crystal-field strength of Cr^(3+) in various solid matrixes

The Cr^3＋：BeAl2O4 crystal, Cr^3＋：LiNbO3 crystal, and ZnO-Al2O3-SiO2 glass-ceramic were obtained by the Czochralski technique, Bridgman method, and melting processing, respectively. The optical absorption and emission spectra of the above Cr^3＋-incorporated solid-state materials were recorded. The technical parameters for growing high-quality Cr^3＋：BeAl2O4 and Cr^3＋：LINbO3 crystals were obtained. The results indicate that the optical absorption and fluorescence spectra of Cr^3＋ show quite a few differences in various matrixes. The sharp line emissions were observed in the Cr^3＋：BeAl2O4 and Cr^3＋：LiNbO3 crystals. The crystal-field parameters （Dq） for Cr^3＋. in different matrixes were calculated from their corresponding spectra. It is indicated that Cr^3＋：BeAl2O4 and Cr^3＋：LiNbO3 belong to the high-field site crystal, while the Cr^3＋ ZnO-Al2O3-SiO2 glass and glass-ceramic belong to the weak-field site crystal.

Automatic Recognition Method for Optical Measuring Instruments Based on Machine Vision

Based on a comprehensive study of various algorithms, the automatic recognition of traditional ocular optical measuring instruments is realized. Taking a universal tools microscope(UTM) lens view image as an example, a 2-layer automatic recognition model for data reading is established after adopting a series of pre-processing algorithms. This model is an optimal combination of the correlation-based template matching method and a concurrent back propagation(BP) neural network. Multiple complementary feature extraction is used in generating the eigenvectors of the concurrent network. In order to improve fault-tolerance capacity, rotation invariant features based on Zernike moments are extracted from digit characters and a 4-dimensional group of the outline features is also obtained. Moreover, the operating time and reading accuracy can be adjusted dy-namically by setting the threshold value. The experimental result indicates that the newly developed algorithm has optimal recognition precision and working speed. The average reading ratio can achieve 97.23%. The recognition method can automatically obtain the results of optical measuring instruments rapidly and stably without modifying their original structure, which meets the application requirements.

Automated Phase-measuring Profilometry of 3-D Diffuse Objects Using a Single Phase Step Method

The technique of phase measuring profilometry using a single phase step method is proposed.This method can automatically obtain phase value at each pixel by using a discret cosine transform algorithm.The method is able to automatically recognize any position between depression and elevation on an object surface.Theoretical analysis and experimental verification are presented.