Heterodyne Interferometer Research Articles

Thermally stable monolithic Doppler asymmetric spatial heterodyne interferometer: optical design and laboratory performance.

We report on a thermally stable monolithic Doppler asymmetric spatial heterodyne (DASH) interferometer with field-widening prisms for thermospheric wind measurements by observing the Doppler shift of the airglow emission. Analytical deduction and numerical simulation are applied to determine the central optical path difference, the thermal compensation condition and the field-widening design. A monolithic interferometer with optimized configuration was built and tested in the laboratory. Laboratory tests show that the best visibility of 0.94 was realized with the 9 ° field-of-view illumination, while the thermal responses of the spatial frequency and the optical phase offset are 0.0154 cm-1/°C and 0.469 rad/°C, respectively.

A compact high-precision periodic-error-free heterodyne interferometer

We present the design, bench-top setup, and experimental results of a compact heterodyne interferometer that achieves picometer-level displacement sensitivities in air over frequencies above 100 MHz. The optical configuration with spatially separated beams prevents frequency and polarization mixing, and therefore eliminates periodic errors. The interferometer is designed to maximize common-mode optical laser beam paths to obtain high rejection of environmental disturbances, such as temperature fluctuations and acoustics. The results of our experiments demonstrate the short- and long-term stabilities of the system during stationary and dynamic measurements. In addition, we provide measurements that compare our interferometer prototype with a commercial system, verifying our higher sensitivity of 3 pm, higher thermal stability by a factor of two, and periodic-error-free performance.

Determination of silicon wafer site flatness using dual heterodyne interferometers with sub-nanometer precision.

Precise measurement of wafer flatness with high sensitivity and high spatial resolution is essential to realize high yields in nano-scale lithography because the depth of focus in this technology is relatively small. We report on a highly precise site flatness measurement system that employs a pair of heterodyne interferometers and achieves sub-nanometer precision for polished 300-mm silicon wafers. The determined overall mean standard deviation for the site flatness front-surface least-squares fit range is 0.21 nm. Furthermore, this system allows us to obtain images of the wafer flatness via scanning with a high spatial resolution of approximately 12 µm. These results suggest that the heterodyne interferometer-based system is a suited candidate for use at the next-generation 16-nm half-pitch technology node.

A Displacement Measuring Interferometer Based on a Frequency-Locked Laser Diode with High Modulation Frequency

Laser interferometers can achieve a nanometer-order uncertainty of measurements when their frequencies are locked to the reference frequencies of the atom or molecule transitions. There are three types of displacement-measuring interferometers: homodyne, heterodyne, and frequency modulation (FM) interferometers. Among these types of interferometer, the FM interferometer has many advantageous features. The interference signal is a series of time-dependent harmonics of modulation frequency, so the phase shift can be detected accurately using the synchronous detection method. Moreover, the FM interferometer is the most suitable for combination with a frequency-locked laser because both require frequency modulation. In previous research, low modulation frequencies at some tens of kHz have been used to lock the frequency of laser diodes (LDs). The low modulation frequency for the laser source means that the maximum measurement speed of the FM interferometers is limited. This paper proposes a novel contribution regarding the application of a high-frequency modulation for an LD to improve both the frequency stability of the laser source and the measurement speed of the FM interferometer. The frequency of the LD was locked to an I2 hyperfine component at 1 MHz modulation frequency. A high bandwidth lock-in amplifier was utilized to detect the saturated absorption signals of the I2 hyperfine structure and induce the signal to lock the frequency of the LD. The locked LD was then used for an FM displacement measuring interferometer. Moreover, a suitable modulation amplitude that affected the signal-to-noise ratio of both the I2 absorption signal and the harmonic intensity of the interference signal was determined. In order to verify the measurement resolution of the proposed interferometer, the displacement induced by a piezo electric actuator was concurrently measured by the interferometer and a capacitive sensor. The difference of the displacement results was less than 20 nm. To evaluate the measurement speed, the interferometer was used to measure the axial error of a high-speed spindle at 500 rpm. The main conclusion of this study is that a stable displacement interferometer with high accuracy and a high measurement speed can be achieved using an LD frequency locked to an I2 hyperfine transition at a high modulation frequency.

Heterodyne interferometry at ultra-high frequencies with frequency-offset-locked semiconductor lasers

Modern broadband telecommunications require microelectromechanical filters which mechanically vibrate at ultra-high frequencies up to several gigahertz. Heterodyne interferometers, so-called laser-Doppler vibrometers (LDVs), provide a sensitive and contactless measurement technique for vibrations in such filters, but are limited in GHz heterodyning by the efficiency drop of acousto-optic frequency shifters. Heterodyning by frequency-offset locking of two lasers in an optoelectronic phase-locked loop (OPLL) overcomes this limitation. This is demonstrated with our LDV setup with heterodyning up to via offset locking of two semiconductor lasers at visible wavelength. The experiments show a vibration-amplitude resolution of less than per for frequencies higher than up to . The bandwidth is only limited by our photodetectors. This amplitude resolution already qualifies our LDV for vibration measurement of microelectromechanical filters at ultra-high frequencies. We present a comprehensive model for the vibration-amplitude resolution of a LDV with this technique including the laser linewidths, the OPLL transfer function, and interferometer delays. The experiments with our LDV validate the model predictions from numerical simulations. Finally, we discuss the collapse of the heterodyne carrier at vanishing mutual coherence due to interferometer delays, the transition to shot-noise-limited detection, and provide design recommendations.

Real-time compensation of nonlinearity in heterodyne interferometers based on quadrature demodulation and extremum operation

The existing compensation methods for nonlinearity in heterodyne interferometers tend to be time-consuming, which limits their application in real time. To solve this problem, a real-time compensation method is proposed. First, dual-channel quadrature demodulation is used to transform the error signals in interference signals into the traditional three errors (direct current offsets, unequal amplitude errors, and phase nonorthogonal errors) in the demodulated signals. Second, the three errors are dynamically corrected by a simple algorithm based on the extremums extracted from the demodulated signals. To verify the effectiveness of the proposed method, experiments employing the proposed method were carried out to process simulated signals and to conduct actual displacement measurements. The results demonstrate that the nonlinearity in the heterodyne interferometer can be reduced down to a subnanometer level.

An improved differential-grating plane-mirror heterodyne interferometer for small roll angle measurement of a linear motion.

In the previous studies on roll angle (ROLL) measurements which are based on the concept of the combination of a diffraction grating displacement technique and a laser heterodyne interferometry, there is always a lack of ideally functional retro-reflectors and corresponding optical configurations resulting in misalignment and unconfident monitoring. To overcome this problem, a differential-grating plane-mirror heterodyne interferometer is proposed in this paper, in which the grating displacement sensing method is utilized to promote angular interferometry as a reliable ROLL measurement. The working mechanism is thoroughly demonstrated through the theoretical derivation and performance analysis. In particular, the exploited configuration here including a differential grating with excellent robustness and a plane mirror with doubled resolution enables improved performance compared with the existing methods. Furthermore, a corresponding prototype is also developed to validate the proposed method successfully. So, it features merits such as an ultra-high resolution up to 1 nrad, a high sampling rate of kHz and easy practicability, which is significant for high-accuracy and real-time ROLL monitoring and compensation for advanced manufacturing and scientific instruments.

Vibration amplitude range enhancement method for a heterodyne interferometer

Scanning heterodyne interferometers are widely used in micro-vibration measurements due to its high sensitivity and high resistivity to environment change. However, the amplitude range of scanning heterodyne interferometers is limited by the approximation in the theory to several nanometers. To solve this problem, a method for vibration amplitude range enhancement is proposed. By exploiting the Bessel functions, the interferometer is able to measure vibration amplitude ranging up to several hundred nanometers. The method was validated by measuring a micro-cantilever and the results were desirable. To further demonstrate the method, measurements were performed on a piezoelectric micromachined ultrasonic transducer (PMUT) with the maximum amplitude up to ∼300 nm.

Design for A Highly Stable Laser Source Based on the Error Model of High-Speed High-Resolution Heterodyne Interferometers.

Heterodyne interferometers with two opposite Doppler shift interference signals have been proposed for high-resolution measurement with high measurement speed, which can be used in the background of high-speed high-resolution measurement. However, a measurement error model for high-speed high-resolution heterodyne interferometers (HSHR-HIs) has not yet been proposed. We established a HSHR-HI measurement error model, analyzed the influence of beat frequency stability with a simplified optical structure, and then designed an offset-locked dual-frequency laser source with a digital control system to reduce the impact of beat frequency drift. Experiments were used to verify the correction of the measurement error model and the validity of the laser source. The results show that the new laser source has a maximum beat frequency range of 45 MHz, which shows the improvements in the measuring speed and resolution.

Independent Component Analysis for Signal Crosstalk Elimination in Infrared Interferometry

Infrared interferometers are optical devices that can measure optical path-length differences by measuring changes in the refractive index. Several arrangements can be deployed, from single channel devices to multichannel double color heterodyne interferometers. These type of devices are typically used to recover the spatial electron density profile of fusion plasmas. This process involves measuring precisely the phase differences of the intermediate frequencies. A source of error that affects the measurements is the crosstalk that appears due to the coupling of the signals into the different channels of the interferometers. The inter-channel coupling of the signals is extremely difficult to eliminate specially when the probing frequencies are close to each other. In this paper it is shown that Independent Component Analysis effectively eliminates inter-crosstalk coupling in such devices. Furthermore, it is shown how the Signal-to-Noise ratio is dramatically increased when this technique is used.

19-picometer mechanical step displacement measurement using heterodyne interferometer with phase-locked loop and piezoelectric driving flexure-stage

In this paper, we discuss 20-picometer-order mechanical step displacement measurements using a heterodyne interferometer with a phase-locked loop (PLL) and two piezoelectric (PZT) driving flexure-stages. First, the phase meter for heterodyne interferometry using one simple digital PLL is developed. Two inputs and one output of the single PLL are the reference and measurement signals of the heterodyne interferometer and the phase shift due to the movement of the target mirror, respectively. The PLL includes an active phase shifter, a mixer (multiplier), a low-pass filter combined with an averaging operation, and an integrator. In electronics evaluation of the PLL, the PLL shows a phase resolution of 174 μrad with 4.2 μrad noise (standard deviation) and a phase noise floor of 3 μrad/√Hz above 0.2 Hz with an output sampling rate of 200 Hz. Using the single PLL, a four-pass normal commercial heterodyne interferometer, and high-stiff-parallel spring stage driven by PZT actuator, we demonstrate the actuations and measurements of mechanical step displacements of 19 pm (1.5 mrad) and a displacement noise floor of 1.1 pm/√Hz (90 μrad/√Hz) above 1 Hz in normal air. In the paper, the principle, instrumentation, and experimental results are discussed.

A versatile heterodyne interferometer for vibration measurement and analysis of micro-structures

AbstarctA versatile heterodyne interferometer for vibration measurements of microstructures is presented. The interferometer is able to measure absolute amplitude and phase from out-of-plane vibration fields. Its measurement range covers the vibration frequency up to 12 GHz with the current setup, and amplitude up to several hundred nanometers by combining the Bessel functions. To demonstrate the capabilities of the setup, measurements of A0 lamb wave mode and S1 lamb wave mode of a piezoelectric micromachined ultrasound transducer were implemented. The results show the versatility of the setup for vibration measurements of microstructures.

Software-defined optoacoustic tomography.

In this work we present what we believe is the first application of software-defined optoelectronics (SDO) for bidimensional optoacoustic tomography (OAT). The SDO concept refers to optoelectronic systems where the functionality associated with the conditioning and processing of optical and electrical signals are digitally implemented and controlled by software. This paradigm takes advantage of the flexibility of software-defined hardware platforms to develop adaptive instrumentation systems. We implement an OAT system based on a heterodyne interferometer in a Mach-Zehnder configuration and a commercial software-defined radio platform (SDR). Here the SDR serves as a function generator and oscilloscope, while at the same time providing perfect carrier synchronization between its transmitter and receiver in a coherent baseband modulator scheme. This carrier synchronization enables us to have much better phase recovery. We study the performance of the OAT SDO system using different bidimensional phantoms and carry out an analysis of the reconstructed images.

Heterodyne speckle interferometry for measurement of two-dimensional displacement.

This paper presented a heterodyne speckle interferometer (HSI) for the measurement of two-dimensional in-plane displacement. A diffraction grating is used to split the light source into four beams, which are then reflected into a non-mirror measurement surface at symmetrical incident angles, before being scattered to form an interference pattern. In accordance with the Doppler Effect, in-plane displacement of the surface causes phase variations in speckle interference patterns, from which displacement information can be obtained. Several experiments were performed to evaluate the feasibility of the proposed HSI. Experiment results demonstrate that the proposed system is capable of accurately measuring in-plane displacement with a resolution of approximately 1.5 nm.

Determination of absolute turbulence amplitude by CO2 laser phase contrast imaging

Phase contrast imaging (PCI) has the important advantages of good sensitivity and applicability for the measurements of fluctuation and turbulence in magnetically confined plasma. However, the determination of the absolute amplitude of fluctuation is not well established. In this article, we propose to determine the absolute amplitude of fluctuation with calibration. The fluctuation measured by CO2 laser PCI (CO2-PCI) was confirmed by simultaneous measurements by using a HeNe heterodyne interferometer (HeNe-HI). In the test experiments, CO2-PCI and HeNe-HI measured sound fields, which are produced by the audio speaker (f=6∼18 kHz, k=0.09∼0.33 mm−1) and the piezoelectric transducer (f=72 kHz, k=1.3 mm−1). At f=13∼18 kHz, k=0.24∼0.33 mm−1, the differences between CO2-PCI and HeNe-HI were 20∼30%. At f=72 kHz, k=1.3 mm−1, the difference was less than ∼10%. On the other hand, the difference between PCI and HI becomes larger at f<13 kHz, k<0.24 mm−1. This is because in these regions some parts of the scattered and non-scattered radiation were not clearly separated inside and outside the groove of the phase plate. The procedure of the absolute value determination was applied to the detached plasma of LHD and compared with the measurement by using a CO2 laser heterodyne interferometer (CO2-HI). The signal of CO2- HI at f>20 kHz is almost at the same as the level of noise. On the other hand, the 2D-PCI signal is clearly higher than the level of noise in all the entire frequency region. At f < 20 kHz, the difference between CO2-HI and CO2-PCI becomes large. This is likely to be due to the wavenumber cut-off of CO2-PCI. Combining two diagnostics, it is possible to measure a wide range of fluctuations from the macroscopic to the microscopic scale.

Picometer mechanical displacement measurement using heterodyne interferometer with phase-locked loop

In this paper, we show picometer-order mechnical displacmment measurements using a heterodyne interferometer with a phase-locked loop (PLL). A heterodyne light source for the interferometer is implemented with a frequency stabilized HeNe laser and two acousto-optic modulators. A real time phase measurement is performed by the PLL, whose software is programmed in a field-programmable gate array (FPGA). A stiff parallel spring stage combined with a high-voltage piezoelectric actuator is used to generate picometer-order mechanical motion. With the above implementations, mechanical displacement of 10 picometer or less can be measured.

Повышение быстродействия и разрешающей способности акустооптических гетеродинных лазерных интерферометров перемещений. Адаптивный лазерный интерферометр

Повышение быстродействия и разрешающей способности акустооптических гетеродинных лазерных интерферометров перемещений. Адаптивный лазерный интерферометр

A combined Phase Contrast Imaging and heterodyne interferometer for multiscale fluctuation measurements in tokamak plasmas

An upgrade to the Phase Contrast Imaging (PCI) diagnostic on the DIII-D tokamak has successfully combined PCI with density interferometry to provide electron density fluctuation measurements across an unprecedented range in wavenumber. The combined diagnostic uses a single laser and a single beam path through the tokamak, minimizing machine resources in anticipation of future reactor-scale devices where port access will be at a premium. The PCI multichannel detector provides low-noise, wavenumber-resolved detection of moderate-wavenumber turbulence, while the interferometer channel is sensitive to long-wavelength turbulence, including the peak of ion-scale turbulence and MHD. The overlap in wavenumber range between the two schemes allows for an in situ absolute calibration of the PCI.

Ultraviolet-Excitation Photothermal Heterodyne Interferometer as a Micro-HPLC Detector.

The first demonstration of a photothermal heterodyne interferometer (PHI) combined with micro-HPLC (high-performance liquid chromatography) is reported. A semiconductor laser (375 nm) was used for excitation, and the temperature change caused by heat released from photoexcited species was detected with a He-Ne laser (632.8 nm). The temperature-dependent refractive index change of the solvent modified the optical path of the probe beam. The phase difference between two arms of the interferometer, one passing through the heated sample and another as a reference, was sensitively detected with the PHI. The nitro-polycyclic aromatic hydrocarbon and vitamin mixture separated via micro-HPLC was successfully detected with the PHI as well as a UV detector. The detection limit of the PHI for riboflavin in the absorbance units was 77 times better than that of the commercial UV detector. The detection limit of the PHI with a small flow cell (6 nL) was the same as that with a large flow cell (18 nL) for 1-nitropyrene.

On the assembly and calibration of a spatial heterodyne interferometer for limb sounding of the middle atmosphere

Spatial heterodyne interferometers are an enabling technology to build highly miniaturized optical instruments for the observation of faint emissions in the atmosphere. They are particularly suited for the deployment on nano- or micro-satellite constellations. One application of the SHI technology is a middle atmosphere temperature sounder based on the measurement of relative intensities emitted by the O2 atmospheric band system. Beside basic design considerations, aspects of the opto-mechanical design and assembly of a monolithic SHI for a space application are addressed. For the characterization of such an instrument, a light stimulus based on a Köhler illuminator is presented.