Homodyne Michelson Interferometer Research Articles

Digital Demodulation Using I/Q Signals and Optical Phase Control Applied to a Vibrometer

An efficient and cost effective optical phase detection vibrometer based on a modified closed loop homodyne Michelson interferometer is presented. Real-time phase demodulation is carried out, using an embedded platform that performs data acquisition, signal processing, PI (proportional-integral) control and the generation of signals that drive the electrooptic Pockels cell phase shifter and the piezoelectric actuator under test. Two phase quadrature signals are generated from a single interferometric output, using the interleaving action, in alternation, of a digitally generated modulating signal, and then the well-known differential-cross-multiplication technique is applied to perform the computation of the phase shift of interest. The quadrature condition is reached using the PI loop based on an error signal obtained from a Lissajous figure derived from out-of-phase signals. The vibrometer is capable of measuring nanometric displacements, and is simple, inexpensive, accurate, immune to fading and self-consistent. The new method was used to determine the displacement frequency response curves of two prototypes of multi-actuated flextensional piezoelectric actuators. Measurements were made between 500 Hz and 15 kHz, and the results agreed with those obtained by the standard SCM-Signal Coincidence Method.

Investigation of position detectors for atomic force microscopes

This paper presents different possibilities of determination of cantilever deflection using the beam theory and finite element method. It is proved that the cantilever can be described as an elementary beam with the force point within the neutral fibre, and its deflection can be determined according to Euler–Bernoulli beam theory. The determined analytical relationship between the inclination angle of the cantilever beam and displacement of its end is used for further calculations of the output signal of the atomic force microscope (AFM) position detector optical lever. Such position detectors as an interferometer, optical lever, and focus sensor are compared for application in an AFM. Analytical and numerical position detector models are developed here for determination of characteristic curves of detector output signals and their sensitivities. The comparison shows that the interferometer is by far the most sensitive and the optical lever is similarly sensitive to the focus sensor. Furthermore, a combined deflection-detection system that contains a homodyne Michelson interferometer and an optical lever is discussed.

Dynamic vacuum measurement by an optical interferometric technique

A homodyne Michelson interferometer was developed to realize a dynamic vacuum standard. The interferometer measures variation in optical path due to refractive index changes related to the pressure of the gas. The measurement arm of the interferometer is formed by two quasi-parallel mirrors which act as a multiplication set-up to allow an increment of the optical path and consequently of the sensitivity. The interference signal is detected by a high speed camera: starting from the recorded interference pattern, two quadrature regions are identified and analyzed by custom software to obtain the quadrature phase signals.The dynamic vacuum system is mainly composed of a large low-pressure chamber VA (about 800 L) connected by a valve and a replaceable orifice to a high pressure chamber VB of about 2 L, hosting the interferometer. The fast pressure drop from 100 kPa to 100 Pa is obtained by a gas expansion from VB to VA. The velocity of the expansion process can be easily varied by substituting the orifice connecting the two chambers.The response of the system was first tested with a slow process of about 40 s at different gains of the measurement arm of the interferometer. Subsequently, a fast process (< 3 s) was considered and the result of the optical device was compared to the measurements performed by two capacitance diaphragm gauges (133 kPa and 1.33 kPa full scale). The gauges are equipped with special electronics to give each nominal reading every 0.7 ms. The two measurements performed by the dynamic vacuum standard and capacitance diaphragm gauges showed an agreement better than 12%.

A high dynamic range method for the direct readout of a dynamic phase change in homodyne interferometers

Piezoelectric flextensional actuators (PFAs) are an efficient alternative to systems that demand nano-positioning of devices, such as in nanotechnology. Optical techniques constitute an excellent choice for contactless measurement of nano-displacements. In particular, optical interferometry constitutes an adequate choice for characterizing PFAs. There are several types of interferometers, as well as optical phase demodulation methods, used in practice. One interesting class of demodulation methods uses the spectrum of the photo-detected signal and its intrinsic properties when there is a harmonically varying time-domain modulating signal. In this work, a low cost homodyne Michelson interferometer, associated with simple electronic circuits for signal conditioning and acquisition, is used. A novel dynamic phase demodulation method, named Jm&Jm + 2, is proposed, which uses only the magnitude spectrum of the photo-detected signal, without the need to know its phase spectrum. The method is passive, direct, self-consistent, without problems of phase ambiguity and immune to fading, and presents a dynamic range from 0.45 to 100 rad displacements (between 22.6 nm and 5 µm, for λ = 632.8 nm). When applied to the measurement of half-wave voltage in a proof-of-concept Pockels cell, it presents errors smaller than 0.9% when compared to theory. For the estimation of PFA displacement, it allows the measurement of linearity and frequency response curves, with excellent results.

Phase sensitive absolute amplitude detection of surface vibrations using homodyne interferometry without active stabilization

A detection scheme for obtaining phase and absolute amplitude information of surface vibrations on microacoustic components using homodyne laser interferometry is described. The scheme does not require active stabilization of the optical path length of the interferometer. The detection setup is realized in a homodyne Michelson interferometer configuration, and selected measurements on a 374 MHz surface acoustic wave fan-shaped filter and two different piezoelectrically actuated micromechanical resonators are presented to demonstrate the performance of the instrument. With the current detection electronics, the interferometer is capable of detecting out-of-plane surface vibrations up to 2 GHz with a lateral resolution of better than 1 μm and with a minimum detectable vibration amplitude of ∼1 pm.

High-resolution parallel multipass laser interferometer with an interference fringe spacing of 15 nm

We present a high-resolution laser interferometer based on the parallel multipass configuration with a pair of right-angle prisms to increase the optical fringe subdivision order up to 21. In the experiment, a multipass homodyne Michelson interferometer (MHMI) with the fringe spacing of 15nm was demonstrated, resulting in the displacement measurement with a measurement resolution of 180pm limited by the sampling rate of the employed analog-to-digital converter. We show that the ultimate resolution of the demonstrated MHMI scales with 1/N and it is estimated to be 8.7pm for N=21.

A Compact Signal Processing with Position Sensitive Detectors Utilized for Michelson Interferometer

Interferometric signals of a homodyne Michelson interferometer appear in sinusoidal forms. In this investigation, new concepts for signal processing of Michelson interferometer are demonstrated. With the utilization of detection of position sensitive detector (PSD) and by the procedure of differential signals and the characteristic of symmetric waveform, a compact signal processing for homodyne Michelson interferometer has been developed. Its advantages include simplified procedure, fast processing and few electronic hardware. For experiment tests of the signal processing, a conventional homodyne Michelson interferometer has been constructed. Major components of the interferometer consist of laser light source, beam splitter, mirrors, PSD and piezo transducer for driving measurement mirror. To verify the performance of the signal processing, a commercial nanopositioning stage as reference standard has been utilized for comparison measurements. Through theoretical analysis and experiment tests, it can be proved that by the developed signal processing an interferometer possesses the optical resolution of 79 nm. With support of the developed signal processing, interferometers will possess the benefits of simply structure, few components and lower cost.

Analysis of Linearity and Frequency Response of a Novel Piezoelectric Flextensional Actuator Using a Homodyne Interferometer and the $J_{1}{-}J_{4}$ Method

Piezoelectric transducers are widely used in high-resolution positioning systems. This paper reports the experimental analysis of a novel piezoelectric flextensional actuator (PFA), which is designed by using the topology-optimization method through a low-cost homodyne Michelson interferometer. By applying the J1-J4 method for signal demodulation, which provides a linear and direct measurement of dynamic optical phase shift independent of fading, the nanometric displacements of the PFA were determined. Linearity and frequency response of the PFA were evaluated up to 50 kHz. PFA calibration factor and amplification rate were determined for the PFA operating in the quasi-static regime. To confirm the observed frequencies of resonance, an impedance analyzer is also utilized to measure the magnitude and phase of the PFA admittance

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.

Scanning Michelson interferometer for imaging surface acoustic wave fields

A scanning homodyne Michelson interferometer is constructed for two-dimensional imaging of high-frequency surface acoustic wave (SAW) fields in SAW devices. The interferometer possesses a sensitivity of ~10(-5)nm/ radicalHz , and it is capable of directly measuring SAW's with frequencies ranging from 0.5 MHz up to 1 GHz. The fast scheme used for locating the optimum operation point of the interferometer facilitates high measuring speeds, up to 50,000 points/h. The measured field image has a lateral resolution of better than 1 mu;m . The fully optical noninvasive scanning system can be applied to SAW device development and research, providing information on acoustic wave distribution that cannot be obtained by merely electrical measurements.

Combined optical and X–ray interferometry for high–precision dimensional metrology

The requirement for calibrating transducers having subnanometre displacement sensitivities stimulated the development of an instrument in which the displacement is measured by a combination of optical and X–ray interferometry. The need to combine both types of interferometry arises from the fact that optical interferometry enables displacements corresponding to whole numbers of optical fringes to be measured very precisely, but subdivision of an optical fringe may give rise to errors that are significant at the subnanometre level. The X–ray interferometer is used to subdivide the optical fringes. Traceability to the meter is achieved via traceable calibrations of the lattice parameter of silicon and of the laser frequency. Polarization encoding and phase modulation allow the optical interferometer to be precisely set on a specific position of the interference fringe—the null point setting. The null point settings in the interference fringe field correspond to dark or bright fringes. Null measurement ensures maximum possible noise rejection. However, polarization encoding makes the interferometer nonlinear, but all nonlinearity effects are effectively zero at the fringe set point. The X–ray interferometer provides the means for linear subdivision of optical fringes. Each X–ray fringe corresponds to a displacement that is equal to the lattice parameter of silicon, which is ca .0.19 nm for the (220) lattice planes. For displacements up to 1 m the measurement uncertainties at 95% confidence level are ± 30 pm, and for displacements up to 100 m and 1 mm the uncertainties are ± 35 and ± 170 pm, respectively. Important features of the instrument, which is located at the National Physical Laboratory, are the silicon monolith interferometer that both diffracts X–rays and forms part of the optical interferometer, a totally reflecting parabolic collimator for enhancing the usable X–ray flux and the servo–control for the interferometers.

Testing of the quality of solder joints through the analysis of their thermal behaviour with an interferometric laser probe

We present an optical contactless method for testing the quality of solder joints in surface mounted components by measuring their thermal dynamic behaviour. We detect surface normal displacements induced by Joule heating with a high resolution interferometnc laser probe. This probing method, based upon a homodyne Michelson interferometer, is an interesting tool for investigating the mechanisms of heat deposition and flow inside electronic devices. It allows the precise time evolution of the surface normal displacement to be measured (the laser probe has subnanometric resolution). This new approach of thermal behaviour laser testing is based upon the analysis of the diffusion of heat produced by the Joule effect in the structure (lead, solder and copper strip) from short current pulses and will influence heat diffusion. Solder joint failures (intermetallics, hidden voids, etc. ) behave as a thermal barrier. The optical test consists of measuring the dynamics of the solder joint expansion, and the variations from a standard response (good quality solder joints) will reveal defects. Important variations have been observed in solder joints that have undergone thermal cycling ageing tests. We have also investigated the thermal response of joints on IMS (insulated metallic substrate) and epoxy substrates. They show a very different time response.