A resolution evaluation of displacement measuring interferometer using a sinusoidal phase modulation (SPM) and a
modified phase-locked loop (PLL) is discribed in this presentation. Displacement measuring interferometer with frequency
stabilized light source has advantages of high resolution and traceable to the definition, and the combination of the SPM
and modified PLL is one of the interpolation methods to improve the resolution of displacement measuring interferometer.
The resolution is evaluated by noise floor measurement and small step displacement measurement. The results show that
the measurement system could observe step displacement as small as 0.1 nm, but the noise floor contains drift and noise
peaks at certain frequencies.
In this presentation, we discuss noise floor comparisons of an optical displacement measuring interferometer between air
and vacuum environments. A heterodyne interferometer and its phasemeter, with the resolution of 10-6 radian, implemented
in a field programmable gate array (FPGA) are utilized for the comparison. A heterodyne laser source consists of a frequency
stabilized He-Ne laser and two acoustic optic modulators (AOMs). The interferometer optics and a piezoelectric (PZT)
flexure stage which drives the moving retroreflector of the interferometer are placed in a vacuum chamber. In the vacuum
environment at 3 mPa, the noise floor of 1 pm/ÖHz or less is attained in the frequency range of 0.01 ~ 100 Hz.
A resolution evaluation of displacement measuring interferometer using a sinusoidal phase modulation (SPM) and a
modified phase-locked loop (PLL) is discribed in this presentation. Displacement measuring interferometer with frequency
stabilized light source has advantages of high resolution and traceable to the definition, and the combination of the SPM
and modified PLL is one of the interpolation methods to improve the resolution of displacement measuring interferometer.
The resolution is evaluated by noise floor measurement and small step displacement measurement. The results show that
the measurement system could observe step displacement as small as 0.1 nm, but the noise floor contains drift and noise
peaks at certain frequencies.
We propose a clustering-analysis approach that addresses the bandpass filter (BPF) detection problem in the analysis of the peak position of the interference envelope in vertical-scanning wideband interferometry. Our approach exploits the fact that the fringe signal formed by a wideband light source is a superposition of deterministic fringe signals and noise. Consequently, two clusters can be specified in advance for use in the k-means clustering analysis. We describe our measurement procedure and its development using a two-means method-based spectrum selection scheme based on the constituent characteristics of interference fringes. The details of our approach are introduced within the framework of femtosecond optical frequency comb-based interferometry. Our experimental results demonstrate the superiority of the proposed algorithm over the conventional heuristic threshold-based BPF estimation for envelope peak determination.
A new demodulation method for sinusoidal frequency/phase modulation (SFM/SPM) interferometers using an artificial harmonic series signal and a phase-locked loop (PLL) is proposed in the paper. Utilizing a laser diode (LD) as the light source and an electric optic modulator (EOM), frequency/phase modulations of the LD light can be achieved by modulating the LD injection current or the driving voltage to the EOM. The SFM/SPM interference signals for the displacement measurement has have the form of cos(msinωmt+θ), where m, ωm and φ are a modulation index, a modulation frequency and a phase change due to optical path movement, respectively. Therefore, the SFM/SPM interference signals is composed by a series of harmonics of the modulation frequency. The two adjacent (2k and 2k+1: k is integer) harmonics include the displacement information. By using the two harmonics, a Lissajous diagram can be drawn to obtain the displacements. In the conventional way, the two harmonics can be demodulated by two lock-in amplifiers. In this paper, we propose new demodulation method for SFM/SPM interferometers using an artificial hormonic series signal and the PLL, which are installed in field programable gate array (FPGA), to obtain sub-picometer (μrad) resolution. An artificial hormonic signals with the form of sin(msinωmt+θ) can be made virtually by the FPGA, where θ is the target phase controlled by the PLL. The output signal from the interferometer will be firstly digitized by the FPGA, and the digitized output signal and the artificial harmonic series signal are multiplied by a mixer, then the mixer output signal is inserted to a low pass filter (LPF). Then the LPF output signal should be -sin(φ-θ)~-(φ-θ) (if (φ-θ) is sufficiently small). In the system, modulation index should be fixed to some value. To set the LPF output signal (-(φ-θ)) to null, the target phase θ of the virtual artificial harmonic signal is controlled by the PLL. In the paper, we discuss the principle, experimental system and results.
In a pulse-train interferometer, the position of zero optical path difference (OPD) between the reference and object mirror can be obtained using the envelope peak of the interference fringe signal. Based on communication theory, frequency/phase information can provide higher accuracy compared to envelope/amplitude information. We propose a phase information-assisted method to obtain the position of zero OPD for a pulse-train interferometer. We demonstrate and verify that this phase approach can be used to determine the position of zero OPD with high accuracy using experimental data. This method is reliable and provides good performance for length measurement.
As nanotechnology have been developed rapidly, it is strongly needed to measure a displacement accurately and precisely. A sinusoidal frequency modulation (SFM) and a sinusoidal phase modulation (SPM) applied interferometers could be good candidates. In the SFM, a frequency of a light source is modulated sinusoidal way. In the SPM, a phase is modulated. Characteristics of these interferometers are defined by a modulation index. The modulation index is a function of both a frequency excursion and an initial optical path difference in the SFM, and is an amplitude of phase in the SPM. For displacement measurement, the displacement is obtained by a phase of an interference signal. A phase determination method using a phase-locked loop (PLL) is reported and a few pico-meters resolution is achieved for displacement measurement with a restriction of a specific modulation index. For precise and high resolution interferometer, a stabilizing the frequency of the light source is necessary. Because the modulation index is an essential parameter in the frequency stabilization, performing phase determination with the PLL in the arbitral modulation index must be developed. The nonlinear relationship between the phase and the displacement is a problem in arbitral modulation index. We have proposed a PLL for arbitral modulation index which successively changes the relationship from the nonlinear to the linear. PC-based calculations with a theoretical and an actual interference signals have been conducted to check the feasibility of proposed PLL. In this report, displacement measurements using PC-based calculation with actual interference signals are described.
In this paper, direct phase determination method which is based on the phase-locked loop technique and the null method is proposed for heterodyne-displacement-measuring interferometers. The requirement of the proposed method is to detect high-speed phase changes in the phase shift between two sinusoidal input signals, leading to measuring high-speed displacements in industrial applications. The method is estimated for two situations that include the use of (a) two pure sinusoidal signals from a function generator and (b) two interferometric signals from a heterodyne interferometer, which is integrated to an electro-optic modulator for phase modulation. The experimental results of the method provide the phase-variation-measuring speed with a modulation frequency of 20kHz in the 2.7MHz-input sinusoid. The principle, signal-processing program, experiments and results of the method are presented in the paper.
This study presents an algorithm for automatic selection of a frequency domain filter for the Fourier transform method of interference fringe analysis in a pulse-train interferometer. In this approach, the equality between the interference-fringe envelope peak point and the phase-crossing point of different frequency components is used to distinguish between the signal and noise in the frequency domain. The efficacy of the proposed technique is demonstrated by numerical experiments.
A new demodulation method for sinusoidal frequency/phase modulation (SFM/SPM) interferometers, which can be suitable for displacements/3D profiles of targets, is proposed in the paper. Utilizing a laser diode (LD) as the light source and an electric optic modulator (EOM), frequency/phase modulations of the LD light can be achieved by modulating the LD injection current or the EOM. The SFM/SPM interference signal for the displacement measurement is composed by a series of harmonics of the modulation frequency. The two adjacent (2nd and 3rd) harmonics include the displacement information. By using the two harmonics, a Lissajous diagram can be drawn to obtain the displacements. Normally, the two harmonics can be demodulated by two lock-in amplifiers. In this paper, we propose a signal demodulation method to acquire the 2nd and 3rd harmonics without any lock-in amplifiers, for reducing a cost of lock-in amplifiers. In the proposed method, the data acquisition system is synchronized to the modulation frequency such that the sampling points are exactly at the maximum and minimum points of the 2nd and the 3rd harmonics, respectively. By addition/subtraction calculations of the data at the maximum/minimum points, the 2nd and 3rd harmonics can be obtained for drawing the Lissajous diagram. We first show displacement measurements of the target mirror in the SFM interferometer with 20 kHz modulation frequency. Secondly, we show 3D profile (=2D displacement) measurements of the moving target in the modified SFM interferometer using the high speed camera with 128*128 pixels and 180k frames/s. Thirdly, we discuss the feasibility of the proposed method. The authors will introduce experimental results of SPM interferometers at the oral presentation.
The national standard of length in Japan changed to a femtosecond optical frequency comb (FOFC) in July 2009. The center frequency of the FOFC standard is 1560 nm, which is in the transmission band (C-band) of the communication optical fiber. Thanks to this fact, through the communication fiber networks, an FOFC can be delivered to everywhere at anytime. That means everyone at everywhere may access the high-accuracy length standard via communication fiber networks at anytime.
An FOFC is a stabilized pulse laser. In other words, an FOFC is a phase-coherent combination of several hundreds of thousands of wavelengths. Therefore, this fact means that there are several hundreds of thousands of different wavelengths and their combination, adjacent pulse repetition interval length (APRIL), which can be used as a length scale. Based on this idea, we proposed the APRIL-based method. APRIL-based length measurement method uses an APRIL (the physical length associated with the pulse repetition period) as a ruler for measuring distance. In this work, we show how the uncertainty in length conversion is affected by the change in environmental parameters via the sensitivity coefficients of refractive index under an actual experimental environment.
The conventional method of measuring the radial, axial and angular spindle motion is complicated and needs large spaces. Smaller instrument is better in terms of accurate and practical measurement. A method of measuring spindle error motion using a sinusoidal phase modulation and a concentric circle grating was described in the past. In the method, the concentric circle grating with fine pitch is attached to the spindle. Three optical sensors are fixed under grating and observe appropriate position of grating. The each optical sensor consists of a sinusoidal frequency modulated semiconductor laser as the light source, and two interferometers. One interferometer measures an axial spindle motion by detecting the interference fringe between reflected beam from fixed mirror and 0th-order diffracted beam. Another interferometer measures a radial spindle motion by detecting the interference fringe between ±2nd-order diffracted beams. With these optical sensor, 3 axial and 3 radial displacement of grating can be measured. From these measured displacements, axial, radial and angular spindle motion is calculated concurrently. In the previous experiment, concurrent measurement of the one axial and one radial spindle displacement at 4rpm was described. In this paper, the sinusoidal frequency modulation realized by modulating injection current is used instead of the sinusoidal phase modulation, which contributes simplicity of the instrument. Furthermore, concurrent measurement of the 5 axis (1 axial, 2 radial and 2 angular displacements) spindle motion at 4000rpm may be described.
Frosted glass (FG) diffusers are used for various purposes in optical experiments and are qualitatively classified based on the particle size of the grit used to polish them. Moreover, their surface topographies are known to affect their optical ability. However, a quantitative relationship between the surface topography (especially the surface amplitude parameters) and the polishing grit size is yet to be established. In the present study, a contact-type surface roughness measurement instrument was used to measure the surface amplitude parameters of a variety of commercial FG diffusers. The determined parameters, which are defined in ISO 4287-1997, were then compared with the root mean square of the grit size and the quantitative relationships were investigated. The parameters that were most strongly correlated with the root mean square of the grit size were identified. The established relationships, which statistically reflect the optical properties of an FG diffuser, may be used to optimally select a diffuser for a particular optical experiment or numerical calculation.
In this paper, we propose the sinusoidal frequency modulation on a laser diode (LD) to achieve both frequency stabilization of the LD and displacement measurement with a homodyne interferometer. The central frequency of the LD is stabilized to a Doppler broadened absorption line of an iodine (I2) molecule near the wavelength of 633 nm. The frequency of the LD is modulated across the absorption line and synchronous detection is utilized to detect the absorption signal. A simple and low-cost homodyne displacement-measuring interferometer can be constructed that can attain high measurement resolution.
We propose a new concept for an unconventional type of two-color method for interferometry-based length
measurements based on the adjacent pulse repetition interval length (APRIL), which is the physical length associated
with the pulse repetition period. We demonstrate by numerical simulations that if the wavelength-based two-color
method can eliminate the inhomogeneous disturbance of effects caused by the phase refractive index, then the APRIL-based
two-color method can eliminate the air turbulence of errors induced by the group refractive index. We show that
our analysis will benefit the pulse-laser-based two-color method, which secures traceability to the definition of the meter.
Correction of refraction index is important for length measurement. The two-color method has been widely used for correction. The wavelengths of lasers have been used as a ruler of that. Based on the analogy between the wavelength and the adjacent pulse repetition interval length (APRIL), in this paper we investigate the possibility of two-color method based on adjacent pulse repetition interval lengths. Since the wavelength-based two-color method can eliminate the inhomogeneous disturbance of effects caused by the phase refractive index, therefore the APRIL-based two-color method can eliminate the air turbulence of errors induced by the group refractive index. Our analysis will contribute to high-precision length measurement.
A unique absolute length measurement method is proposed and demonstrated for the first time. Since it takes advantage of both the high-accuracy measurement capability of a pulse train interference method and the ability of a two-color method to compensate for environmental changes, the present method is expected to be useful for high-precision length measurement for not only the purposes of laboratory science but also for satisfying the requirements of industry. A length measurement was performed to demonstrate the feasibility of the proposed method.
The second harmonic generation (SHG) of a femtosecond optical frequency comb (FOFC) has been studied. This work focuses on the SHG frequencies that are generated by the mixing of even-numbered frequency components from the original comb with odd-numbered components. It is observed that the generation of those frequencies is the reason the original FOFC and FOFC-based SHG signal have the same repetition frequency. The theoretical derivation agrees with the result of an optical experiment. Our results may be of use with the high-harmonic-generation process and FOFC-based SHG applications, including high-resolution spectroscopy, attosecond pulse generation, and precision length measurement.
This paper describes the characteristics of the adjacent pulse repetition interval length (APRIL), which is used as a scale for femtosecond optical frequency comb (FOFC)-based length measurements. This approach is based on the analogy between the phase refractive index and the group refractive index. Because the former influences the wavelength, which is the basic parameter used to describe monochromatic light in terms of length measurement, we investigated the latter to analyze the theoretical properties of the APRIL when used as a length standard. The results of theoretical analyses and numerical investigations show that when the air parameters change, the changes in the wavelength of a He–Ne laser and the APRIL of an FOFC laser are of the same order of magnitude. The difference between the effects of the phase refractive index on the wavelength and the group refractive index on the APRIL was also confirmed. The proposed concept and analysis pave the way for developing a length traceability system based on the APRIL via optical fibers.
In the conventional methods to measure radial, axial and angular motions of spindles, complicated artifacts with relative
large volume (such as two balls linked with a cylinder) are required. Small volume artifact is favorable from the
viewpoint of the accurate and practical measurement of the spindle motion. This paper describes a concurrent
measurement of spindle radial, axial and angular motions using concentric circle grating and phase modulation
interferometers. In the measurement, the concentric circle grating with fine pitch is installed on top of the spindle of
interest. The grating is a reference artifact in the method. Three optical sensors are fixed over the concentric circle
grating, and observe the proper positions of the grating. The optical sensor consists of a frequency modulated laser diode
as a light source, and two interferometers. One interferometer observes an interference fringe between reflected light
form a fixed mirror and 0-th order diffraction light from the grating to measure the axial motion. Another interferometer
observes an interference fringe between ±2nd diffraction lights from the grating to measure the radial motion. Using
three optical sensors, three radial displacements and three axial displacements of the proper observed position of the
grating can be measured. From these measured displacements, radial, axial and angular motions of the spindle can be
calculated concurrently. In the paper, a measurement instrument, a novel fringe interpolation technique by sinusoidal
phase modulation and experimental results are discussed.
In the article, we propose a measurement method for a fluctuation of the air air-refractive refractive-index from the frequency
measurement by combining a phase modulation homodyne interferometer (PMHI), an external cavity laser diode
(ECLD) as the light source and a frequency stabilized laser (FSL) as the frequency reference. The PMHI, which is set in
air environment, utilizes a Michelson interferometer and low low-thermal thermal-exp expansion ansion-glass (LTEG: the thermal expansion
ratio: 2×10 10-7 K-1) for its main supporting structure. In the PMHI, a dark (or bright) interference fringe with a specific
) integer order N is converted to a null point by utilizing the phase modulation and the loc lock-in detection, and must be kept
by use of the null null-method and the control on the ECLD frequency. Geometrical path change in the PMHI is neglected
because of the ultra ultra-low low-thermal thermal-expansion condition. Therefore, at the null point for N-th order in the suff sufficient thermal
icient condition, a fluctuation of the air air-refractive refractive-index can be measured by the ECLD frequency change, which is derived
from a beat signal between the ECLD and the FSL. In the article, a measurement principle, instrumentation and
experimental re results are discussed.
sults
This paper presents a practical 3-dimensional measurement system which is applied to geometrical accuracy measurenient for large-scale steel bridge members. The measuring niethod is based on stereo vision using precision CCD-cameras linked with a personal computer. The developed system can automatically recognize every target point in its view field and determine theX Y and Z coordinates within a remarkable short time and the measurement accuracy of the system is better than 0. 5 mm for a view field of about 3 m(H) by 2. 3 m(v). This system is applied to an inspection station for the measurement of steel bridge members. The inspection station can measure the geometrical and dimensional accuracy of a steel bridge member of about 3 m x 4 m x 20 in in maximum size with an acceptable measurement accuracy and the results obtained from practical runs for the last three years verify the feasibility of the developed system.
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