Absolute Phase Measurement Research Articles

Color-coding and phase-shift method for absolute phase measurement

In this paper, a novel color-coding method for absolute phase measurement is proposed. A three steps phase-shift algorithm was adopted to calculate the relative phase (wrapped phase) because of the least need of images. Color strips were used to mark each 2π phase-change period and three neighboring colors as a group were used as codewords to identify the fringe orders. With the two parts, relative phase and fringe orders, the absolute phase can be obtained directly. We selected five colors (black, red, green, blue, and white) to test our algorithm, and nearly 60 different codewords were embedded in one image. The fringe orders and the relative phase are calculated simultaneously, and this algorithm can circumvent the phase unwrapping process. Moreover, errors will not diffuse, because the relative phase and fringe orders are uncorrelated. Besides, no need of unwrapping processing will lead to high speed in 3D profile measurement. In addition, large object can be measured with high precision using this method owe to enormous codewords can be embedded in one color image. One experiment with a small object and a big complex object was designed to test the algorithm for separate objects, and experimental results showed the validity of our algorithm for absolute phase measurement.

Composite phase-shifting algorithm for absolute phase measurement

This paper presents a method to recover absolute phase by using only four images: three phase-shifted patterns and one stair pattern. The stair pattern is designed in such a way that the stair changes are perfectly aligned with the phase jumps, and thus absolute phase can be recovered by referring to the stair pattern. Due to system noises and camera and/or projector blurring, a computational framework is also proposed. Because this technique only requires four fringe images for absolute phase recovery, it has the merit of measurement speed. And since the absolute phase is obtained, this technique is suitable for measuring step-height objects. We have developed a digital fringe projection system to verify the performance of the proposed technique.

Improved technique for measuring full-field absolute phases in a common-path heterodyne interferometer

When an asymmetric triangle voltage signal is applied to drive an electro-optic modulator, interference signals with two groups of periodic sinusoidal segments with different frequencies are obtained. An improved method is proposed to fit these two groups of segments, and their associated phases can be determined. The absolute phase can be obtained by subtracting the initial phase from the phases of these two groups. This technique is applied to all pixels, and the full-field absolute phase measurements can be achieved. The validity of this method is demonstrated.

Indole Adsorption to a Lipid Monolayer Studied by Optical Second Harmonic Generation

Adsorption of indole from an aqueous subphase to a lipid (DPPC) monolayer at the air/water interface is studied by nonresonant second harmonic generation (SHG) with lambda = 800 nm and by observation of compression isotherms with a Langmuir trough. The nonlinear susceptibilities of the monolayers have been carefully measured, including corrections for the contributions of the lipid monolayer and subphase, calibration of absolute values by comparison with a quartz reference, and measurement of absolute phase by comparison with a clean air/water interface. Details of the calibrations involving z-cut quartz and the clean air/water interface are presented. The number density of adsorbed indole molecules has been estimated by comparison of nonlinear susceptibilities with a reference monolayer of hexadecyl 3-indoleacetate. The extent of adsorption of indole to the lipid monolayer is maximum at low surface pressure, decreasing from an indole/DPPC ratio near 2:1 as the monolayer is compressed. The free energy change for adsorption of indole to the monolayer is estimated as -8.1 kcal/mol, which is similar to a result reported previously for a lipid bilayer. Information on the orientation of adsorbed indole is derived by comparison of observed ratios of nonlinear susceptibilities with calculated ratios for model indole monolayers with assumed orientational distributions. Measurement and analysis procedures are described in detail for effective nonlinear susceptibilities in a s/p polarization basis. The calculations use as input the molecular hyperpolarizability tensor of indole, which is obtained by using several computational approaches including sum-over-states calculations and time-dependent Hartree-Fock and density functional methods. The analysis shows that the pyrrole ring of indole points toward the water subphase, and the tilt angle of the long axis of indole increases from near 50 degrees to near 60 degrees as the monolayer is compressed. The analysis also suggests that the plane of indole lies more nearly parallel than perpendicular to the plane of the interface.

Absolute Orientation of Molecules with Competing Hydrophilic Head Groups at the Air/Water Interface Probed with Sum Frequency Generation Vibrational Spectroscopy

The constructive or destructive spectral interference between the molecular groups oriented up and down at the interface in the sum-frequency generation (SFG) spectra provides a direct measurement of the absolute orientation of these molecular groups. This simple approach can be employed to interrogate absolute molecular orientations other than using the complex absolute phase measurement in the SFG studies. We used the CN group in the p-cyanophenol (PCP) molecule as the internal phase standard, and we measured the phases of the SFG fields of the CN groups in the 3,5-dimethyl-4-hydroxy-benzonitrile (35DMHBN) and 2,6-dimethyl-4-hydroxy-benzonitrile (26DMHBN) at the air/water interface by measuring the SFG spectra of the aqueous surfaces of the mixtures of the PCP, 35DMHBN, and 26DMHBN solutions. The results showed that the 35DMHBN had its CN group pointing into the aqueous phase; while the 26DMHBN, similar to the PCP, had its CN group pointing away from the aqueous phase. The tilt angles of the CN group for both the 35DMHBN and 26DMHBN molecules at the air/water interface were around 2545 from the interface normal. These results provided insights on the understanding of the detailed balance of the competing factors, such as solvation of the polar head groups, hydrogen bonding and hydrophobic effects, etc., on influencing the absolute molecular orientation at the air/water interface.

Method for determining full-field absolute phases in the common-path heterodyne interferometer with an electro-optic modulator

When a sawtooth voltage signal with the amplitude lower than its half-wave voltage is applied to drive an electro-optic modulator, the interference signals become a group of periodic sinusoidal segments. A new algorithm is proposed to modify these segments to an associated continuous sinusoidal wave, and then its initial phase can be determined. Subtracting the characteristic phase of the modulator from the initial phase, the absolute phase can be obtained. This technique is applied to all pixels, and full-field absolute phase measurements can be achieved. The validity of this method is demonstrated.

Use of the absolute phase in frequency modulated continuous wave plasma reflectometry

In frequency modulated continuous wave reflectometry, used for density profile measurement in fusion plasmas, it is usual to measure the beat frequency between the launched wave and the reflected wave, and from this to calculate the position of the reflecting layer in the plasma. The absolute phase of the beat signal is usually neglected. The reason is that the phase shift between sweeps is usually comparable with or more than 2pi, leading to an ambiguity that is impossible to resolve. However, recent observations on the MAST tokamak have shown that, under quiet plasma conditions (this term has to be defined), the phase shift between sweeps is small compared with 2pi and the phase ambiguity can be readily resolved. The reflectometer signal is then being analyzed as an interferometer signal would normally be, and there is a substantial improvement in spatial resolution. The method is illustrated by application to small edge localized mode precursor and allows what is believed to be the first quantitative measurement of the displacement of the plasma boundary by such a precursor mode. The errors in both the absolute phase measurement and the more conventional frequency measurement are also estimated.

Scanning heterodyne laser interferometer for phase-sensitive absolute-amplitude measurements of surface vibrations

We describe a scanning heterodyne interferometer for imaging surface vibrations with a wide frequency range, with current electronics, up to 6GHz. The heterodyne operation facilitates measurement of absolute amplitude and phase of the surface vibration without calibration. Currently, the setup allows detection of vibration amplitudes down to ∼1pm with a lateral resolution of <1μm. The interferometer is designed to accommodate the different sample types, e.g., surface and bulk acoustic wave devices and micromechanical resonators. The absolute-amplitude and phase information allows for a thorough characterization of surface vibrations in such components and provides direct information of the vibration fields not obtainable via electrical measurements.

A generalized temporal phase unwrapping algorithm for three-dimensional profilometry

A generalized temporal phase unwrapping algorithm is proposed for absolute phase measurement of object surfaces with complex topography. We first make comments on error analysis of various temporal phase unwrapping (TPU) algorithms and point out problems existing in these techniques. We present a generalized TPU algorithm (GTPU), which eliminates some limitations imposed on the fringe sequence for the classical TPU algorithms. So the desired number of fringes can be determined according to practical situation, leading to a flexible method for phase reconstruction. In addition, compared with the classical TPU algorithms, GTPU has better noise immunity and less computational complexity. Theoretical analysis and experiment results are presented to show the validity of the proposed algorithm.

Wide frequency range measurements of absolute phase and amplitude of vibrations in micro- and nanostructures by optical interferometry

A heterodyne interferometer has been built in order to characterize vibrations on micro- and nanostructures. The interferometer offers the possibility of both absolute phase and high resolution absolute amplitude vibrational measurements. By using two acousto-optic modulators (AOMs) in one of the interferometer arms and varying the frequency inputs of both, the setup is designed to measure vibrations in the entire frequency range 0 - 1.2GHz. The system is here demonstrated on Capacitor Micromachined Ultrasonic Transducers (CMUTs) and a PZT transducer to show measurements from 5kHz up to 35MHz. We have measured absolute amplitudes with picometer resolution.

Orientation of 1-Dodecyl-4-phenylpyridinium Ions Constituting an Ionic Liquid at the Ionic Liquid|Water Interface Studied by Second Harmonic Generation

A hydrophobic room-temperature ionic liquid (RTIL) of 1-dodecyl-4-phenylpyridinium (C12ppy+) ions, the cations with high first hyperpolarizability, was prepared in combination with bis(pentafluoroethylsulfonyl)imide, and the orientation of C12ppy+ at the RTIL|water and RTIL|air interfaces was analyzed using optical second harmonic generation (SHG). From polarization-dependence measurements and absolute phase measurements, it was found that C12ppy+ ions at the RTIL|air interface are orientated with the main axis of 4-phenylpyridinium moiety (from phenyl to pyridinium direction) tilted at 53° from the surface normal (from RTIL to air direction) and that the dodecyl chain is protruding to the air. At the RTIL|water interface, it was suggested that C12ppy+ is orientated at the tilt angle of 131° from the surface normal (from RTIL to water direction) with the dodecyl chain protruding away from the aqueous phase.

Inverse projected-fringe technique based on multi projectors

The inverse projected-fringe technique based on multi projectors is proposed. By an absolute phase measurement on the master object, different inverse fringes are generated, for projectors placed in different directions. During the inspection process, inverse fringes are projected simultaneously. If the test object and the master object are identical, an optimized sine fringe is obtained on the camera. Otherwise, every faulty area of the test object causes distortions of the fringe. The deformations can be evaluated quantitatively by simple Fourier transformation and phase unwrapping. Therefore, we can complete the inspection of complex and discontinuous objects with only one fringe image, and solve the problems of shadow and break to a large extent, and consequently realize the fast on-line inspection. The principle of this technique is expatiated, and we prove the validity of it on the example of a two-projector system. The analysis of error and prerequisites of application are also presented.

Absolute phase measurements using geometric constraints between multiple cameras and projectors

The method of phase shift with the projection of multiple cyclic patterns enables 3D measurement that is highly accurate, dense, and fast. However, this measurement is only possible for the wrapped phase value, which has ambiguities in its multiples of cycles. Two particular problems are that conventional methods require additional patterns to be projected to determine the absolute phase and that unwrapping the phase tends to fail where depth varies abruptly. Two methods are proposed: the first is to determine the absolute phase without additional patterns being projected by observing the projected pattern with multiple cameras and applying the geometric constraints between them, and the second is to prevent failure in unwrapping the phase by referring to continuities in the relative phases of multiple projected patterns. The proposed methods were achieved with a 3D scanner that can measure approximately a 180 degrees field of view within 0.5 s, with an accuracy of 0.14 mm in depth.

Optical 3D Surface Reconstruction by a Multi-Period Phase Shift Method

One problem of classical phase shifting for optical 3D surface reconstruction is the occurrence of ambiguities due to the use of fringe projection. We generally derive a number-theoretical approach to calculate absolute phase measurements which can be used as a base for a reliable surface reconstruction without any ambiguity. The essence of our method is the application of pattern sequences with different periods whereby we homogeneously use all pictures which were taken for the measurement. This leads to a higher average accuracy in the surface reconstruction. Furthermore we propose a technique to avoid typical calculation errors that are produced in classical phase shifting caused by discontinuities, occlusions and reflections on the surface.

Absolute phase measurement in heterodyne detection of transient gratings.

We present a method of measuring the absolute phase in heterodyne-detected transient grating experiments. The method permits direct and sensitive characterization of the amplitude and phase of the grating parameters. We also present a convenient implementation of this technique and demonstrate its efficacy in a cuprate superconductor.

Time efficient Chinese remainder theorem algorithm for full-field fringe phase analysis in multi-wavelength interferometry

We present a computationally efficient method for solving the method of excess fractions used in multi-frequency interferometry for absolute phase measurement. The Chinese remainder theorem, an algorithm from number theory is used to provide a unique solution for absolute distance via a set of congruence's based on modulo arithmetic. We describe a modified version of this theorem to overcome its sensitivity to phase measurement noise. A comparison with the method of excess fractions has been performed to assess the performance of the algorithm and processing speed achieved. Experimental data has been obtained via a full-field fringe projection system for three projected fringe frequencies and processed using the modified Chinese remainder theorem algorithm.

Absolute phase-measurement technique based on number theory in multifrequency grating projection profilometry

A simple and robust technique for absolute phase measurement based on number theory is presented. The new, to our knowledge, technique, which is compared with the Gushov-Solodkin algorithm, surmounts the shortcomings in the Gushov-Solodkin algorithm. The technique permits the three-dimensional shape measurement of objects that have discontinuous height steps and has resulted in a new and more powerful method of measuring surface absolute profile. Experimental results are presented that demonstrate the validity of the principle.

Guest Editorial: Special Section on Optical Methods for Shape Measurement

In industry, there is a need for accurately measuring the 3-D shape of objects to speed up and ensure product development and manufacturing quality. There are a variety of applications of 3-D shape measurement, such as: control for intelligent robots, obstacle detection for vehicle guidance, dimension measurement for die development, stamping panel geometry checking, and accurate stress/ strain and vibration measurement. Moreover, automatic online inspection and recognition issues can be reduced to the 3-D shape measurement of, for example, body panel paint defects and dent inspection. The principles of triangulation, structured light, and interferometry have been in existence for decades. However, it is only with the recent availability of advanced and low cost computers, electro-optical elements, and lasers that such techniques have reached the breakthrough point to be commercialized, and ever increasingly be applied in industry. To make it even more acceptable in industry and to strive to achieve 10 to 10 accuracy, there are still some challenges that need to be addressed, such as: the shading issue, the specular surface headache, accurate data patching from different view directions, geometric parameter determination and calibration, absolute phase measurement, local and global coordinates tracking and transforming, real-time computing, sensor planing, and optimization. This special section is designed to promote research activity and to serve as a forum both for academia and industry. This special section includes a variety of development and application examples such as: optimization of an optical system which results in one part in 20,000 accuracy, new techniques using a diffraction grating or defocus to overcome the shading issue, direct digital wavefront reconstruction combined with wavelength scanning to attack the absolute phase measurement issue, and develop-

Characterization of air-coupled ultrasound transducers in the frequency range 40 kHz–2 MHz using light diffraction tomography

The aim of this work was to show the applicability of light diffraction tomography on airborne ultrasound in the frequency range 40 kHz–2 MHz. Seven different air-coupled transducers were measured to show the method's performance regarding linearity, absolute pressure measurements, phase measurements, frequency response, S/N ratio and spatial resolution. A calibrated microphone and the pulse–echo method were used to evaluate the results. The absolute measurements agreed within the calibrated microphone's uncertainty range. Pulse waveforms and corresponding FFT diagrams show the method's higher bandwidth compared with the microphone. Further, the method offers non-perturbing measurements with high spatial resolution, which was especially advantageous for measurements close to the transducer surfaces. The S/N ratio was higher than or in the same range as that of the two comparison methods.

Ultrastable absolute-phase common-path optical profiler based on computer-generated holography

A new scanning common-path interferometric profiler capable of absolute-phase measurement is described. The key element is a computer-generated hologram, which acts as the beam-splitting element. Unlike most absolute phase systems, it can be made entirely common path with respect to piston microphonics and is thus exceptionally stable. In addition to operating in scanning mode, the optical configuration permits simultaneous operation as a single-shot phase measuring interferometer and is thus capable of simultaneous form and texture measurements. The operation and stability of the scanning profiler are demonstrated experimentally.