Commercial Heterodyne Interferometer Research Articles

Self-calibrated free-running dual-comb ranging using subsampled repetition frequency information

Dual-comb ranging (DCR) is an emerging absolute distance measurement method with rapid speed, high precision, and wide ambiguity range. DCR has important applications in remote sensing, large-scale manufacturing, and aerospace exploration. However, the typical DCR system requires cumbersome phase-locking electronics for frequency stabilization and distance calibration, which hinders the practical application of DCR. In this paper, we demonstrate a free-running DCR scheme based on two free-running mode-locked fiber lasers. Two fiber lasers are environment-shared to improve the anti-aliasing capability. We then introduce a self-calibration technique that can directly extract the subsampled repetition frequency information from the interferograms (IGMs). By using this technique, real-time calibration of measured distance can be achieved without extra repetition frequency detection module and frequency counter. The system realizes a 5.3 µm precision for ∼1 m stand-off distance at ∼1 kHz acquisition speed. With averaging, the measurement precision drops to ∼101 nm at the averaging time of 3 s. The ambiguity range of our DCR system is ∼2.6 m due to the relatively small repetition frequency. For dynamic distance measurement, it shows good consistency with a commercial heterodyne interferometer. Our method provides a cost-effective scheme for high-performance absolute distance measurement, and it is promising for promoting DCR system out of the laboratory and realizing field-deployed applications.

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.

Polydyne displacement interferometer using frequency-modulated light.

A radio-frequency Frequency-Modulated (FM) signal is used to diffract a He-Ne laser beam through an Acousto-Optic Modulator (AOM). Due to the modulation of the FM signal, the measured spectra of the diffracted beams comprise a series of phase-synchronized harmonics that have exact integer frequency separation. The first diffraction side-beam emerging from the AOM is selected by a slit to be used in a polydyne displacement interferometer in a Michelson interferometer topology. The displacement measurement is derived from the phase measurement of selected modulation harmonic pairs. Individual harmonic frequency amplitudes are measured using discrete Fourier transform applied to the signal from a single photodetector. Phase signals are derived from the changes in the amplitudes of different harmonic pairs (typically odd-even pairs) with the phase being extracted using a standard quadrature method. In this study, two different modulation frequencies of 5 and 10 kHz are used at different modulation depths. The measured displacements by different harmonic pairs are compared with a commercial heterodyne interferometer being used as a reference for these studies. Measurements obtained from five different harmonic pairs when the moving mirror of the interferometer is scanned over ranges up to 10 μm all show differences of less than 50 nm from the reference interferometer measurements. A drift test was also used to evaluate the differences between the polydyne interferometer and reference measurements that had different optical path lengths of approximately 25 mm and 50 mm, respectively. The drift test results indicate that about half of the differences can be attributed to temperature, pressure, and humidity variations. Other influences include Abbe and thermal expansion effects. Rough magnitude estimates using simple models for these two effects can account for remaining observed deviations.

Simple digital phase-measuring algorithm for low-noise heterodyne interferometry

We present a digital algorithm for measuring the phase of a sinusoidal signal that combines the modified digital fringe-counting method with two-sample zero crossing to enable sequential signal processing. This technique can be applied to a phase meter for measuring dynamic phase differences between two sinusoidal signals with high resolution, particularly for heterodyne interferometry. The floor noise obtained from a demonstration with an electrical apparatus is at frequencies above approximately 0.1 Hz for 80 kHz signal frequency. In addition, by applying this method to a commercial heterodyne interferometer with a modulation frequency of 80 MHz, the floor-noise level is confirmed to be from 4 kHz to 1 MHz. We also confirm the validity of the algorithm by comparing its results with those from a standard homodyne interferometer for measuring shock-motion peak acceleration greater than and a 10 mm stroke.

Large-scale absolute distance measurement using inter-mode beat of a femtosecond laser

Large-scale absolute distance measurement system with high accuracy plays a significant role in science and engineering applications. In many fields such as aerospace technology, large-scale manufacture, geodetic survey and civil engineering, absolute distance measurement systems with a range of up to kilometers and accuracy of better than several micrometers are generally required. Traditional laser ranging methods such as the time-of-flight method and the interferometry method are difficult to achieve both large scale and high accuracy. With the development of femtosecond optical frequency comb technology, several ranging methods with larger range and higher accuracy are developed. In the frequency domain, the optical frequency comb has a large number of stable mode lines, or the longitudinal modes, at regular intervals, which generates the inter-mode beat signal. In this study, based on the inter-mode beat of a femtosecond laser, an absolute distance measurement system using multi-wavelength interferometric method is demonstrated. It has a simple experimental setup with high accuracy but in a limited range of 2.5 m due to the 2-period of phase detection. To achieve a large-scale measurement system, the measurement range of the experimental system is extended by using the synthetic wavelength generated by tuning the repetition frequency of the laser. With a repetition frequency change of 0.2 MHz, a synthetic wavelength of up to 1.5 km is realized, thus the measurement range of the experimental setup can be extended to 0.75 km. Besides the reference and measurement path beams, a monitor path beam and two alternately opened mechanical shutters are used to measure and compensate for the phase drift due to the unbalanced drift of the electronic circuit. By using this method, the standard deviation of the phase measurement results in 30 min is 0.022 in the experiment, and the phase drift can be compensated for very well. The measurement results from the experimental system are compared with the results from a commercial heterodyne interferometer, and the comparison between results shows a precision of better than 50 m in a displacement of 1125 mm. In the experiment, the repeatability of absolute distance measurement using the range extending method is better than 3 m, thus the range of the distance measurement system can be theoretically extended up to 7.5 km. In conclusion, we demonstrate that a large-scale absolute distance measurement system using inter-mode beat of a femtosecond laser, has a range of up to 7.5 km, an accuracy of better than 50 m and a repeatability of better than 3 m. The accuracy of the experimental system can be further improved by using photodetectors with higher bandwidth so that a higher inter-mode beat and a shorter wavelength can be used.

Non-Contact Photoacoustic Imaging Using a Commercial Heterodyne Interferometer.

Most current photoacoustic imaging (PAI) systems employ piezoelectric transducers to receive photoacoustic signals, which requires coupling medium to facilitate photoacoustic wave propagation and are not favored in many applications. Here, we report an all-optical non-contact PAI system based on a commercial heterodyne interferometer working at 1550 nm. The interferometer remotely detects ultrasound-induced surface vibration and does not involve any physical contact with the sample. The theoretically predicated and experimentally measured noise equivalent detection limits of the optical sensor are about 4.5 and 810 Pa over 1.2 MHz bandwidth. Using a raster-scan PAI system equipped with the non-contact design, stereotactic boundaries of an artificial tumor in a pig brain were accurately delineated. The non-contact design also enables the tomographic PAI of biological tissue samples in a non-invasive manner. The preliminary results and analyses reveal that the heterodyne interferometer-based non-contact PAI system holds good potential in biomedical imaging.

Note: Periodic error measurement in heterodyne interferometers using a subpicometer accuracy Fabry-Perot interferometer.

Periodic error is the major problem that limits the accuracy of heterodyne interferometry. A traceable system for periodic error measurement is developed based on a nonlinearity free Fabry-Perot (F-P) interferometer. The displacement accuracy of the F-P interferometer is 0.49 pm at 80 ms averaging time, with the measurement results referenced to an optical frequency comb. Experimental comparison between the F-P interferometer and a commercial heterodyne interferometer is carried out and it shows that the first harmonic periodic error dominates in the commercial heterodyne interferometer with an error amplitude of 4.64 nm.

Relative optical wavefront measurement in displacement measuring interferometer systems with sub-nm precision

Many error sources can affect the accuracy of displacement measuring interferometer systems. In heterodyne interferometry two laser source frequencies constitute the finally detected wavefront. When the wavefronts of these source frequencies are non-ideal and one of them walks off the detector, the shape of the detected wavefront will vary. This leads to a change in measured phase at the detector resulting in increased measurement uncertainty. A new wavefront measurement tool described in this publication measures the relative phase difference between the two wavefronts of the two source frequencies of a coaxial heterodyne laser source as used in commercial heterodyne interferometer systems. The proposed measurement method uses standard commercial optics and operates with the same phase measurement equipment that is normally used for heterodyne displacement interferometry. In the presented method a bare tip of a multimode fiber represents the receiving detection aperture and is used for locally sampling the wavefront during a line scan. The difference in phase between the beating frequency of the scanning fiber and a reference beating frequency that results from integration over the entire beam, is used for the reconstruction of the wavefront. The method shows to have a phase resolution in the order of ~25 pm or ~λ/25000 for λ 632.8 nm, and a spatial resolution of ~60 µm at a repeatability better than 1 nm over one week.

Polarimetric interferometer for measuring nonlinearity error of heterodyne interferometric displacement system

This letter presents a polarimetric interferometer (PI) that can measure the ellipsometric parameter θ with an accuracy of 0.01° leading to a potential accuracy of 17 pm. The PI is constructed and compared with a commercial heterodyne interferometer (HI). Given its low nonlinearity, the PI is used to measure the residual nonlinearity of a heterodyne interferometric displacement system. A rotating half-wave plate is used to compensate for a part of the nonlinearity error caused by the misalignment of the axis between input polarizing states and beamsplitter.

FPGA-Based Smart Sensor for Online Displacement Measurements Using a Heterodyne Interferometer

The measurement of small displacements on the nanometric scale demands metrological systems of high accuracy and precision. In this context, interferometer-based displacement measurements have become the main tools used for traceable dimensional metrology. The different industrial applications in which small displacement measurements are employed requires the use of online measurements, high speed processes, open architecture control systems, as well as good adaptability to specific process conditions. The main contribution of this work is the development of a smart sensor for large displacement measurement based on phase measurement which achieves high accuracy and resolution, designed to be used with a commercial heterodyne interferometer. The system is based on a low-cost Field Programmable Gate Array (FPGA) allowing the integration of several functions in a single portable device. This system is optimal for high speed applications where online measurement is needed and the reconfigurability feature allows the addition of different modules for error compensation, as might be required by a specific application.

Improving the accuracy of homodyne Michelson interferometers using polarisation state measurement techniques

We demonstrate a simple homodyne Michelson interferometer design capable of fringe interpolation accuracy of one part in 36,000 leading to a potential accuracy of 10 pm. This improvement becomes possible thanks to the significant advances in polarimetry that permit measurement of the ellipsometric parameters ψ and Δ with an accuracy of 0.01° with readily available commercial equipment. The proposed method has been set up and we make a direct comparison with a commercial heterodyne interferometer by measuring the displacement of the same target mirror. This latter has been displaced by steps of 20 nm using a high accuracy position control method.