Single-wavelength Interferometry Research Articles

Impact of Cyclic Error on Absolute Distance Measurement Based on Optical Frequency Combs.

Absolute distance measurements based on optical frequency combs (OFCs) have greatly promoted advances in both science and technology, owing to the high precision, large non-ambiguity range (NAR), and a high update rate. However, cyclic error, which is extremely difficult to eliminate, reduces the linearity of measurement results. In this study, we quantitatively investigated the impact of cyclic error on absolute distance measurement using OFCs based on two types of interferometry: synthetic wavelength interferometry and single-wavelength interferometry. The numerical calculations indicate that selecting a suitable reference path length can minimize the impact of cyclic error when combining the two types of interferometry. Recommendations for selecting an appropriate synthetic wavelength to address the tradeoff between achieving a large NAR and minimizing the risk of failure when combining the two methods are provided. The results of this study are applicable not only in absolute distance measurements but also in other applications based on OFCs, such as surface profile, vibration analysis, etc.

Conjugate complex function coupling strategy of interferometric field: Synthetic-wavelength interferometric fringe extraction in simultaneous dual-wavelength interferometry

Simultaneous dual-wavelength interferometry (SDWI) supplies a better solution to extend the measurement range of traditional single-wavelength interferometry with higher efficiency. To decompose the needed longer beat-frequency synthetic-wavelength (λS) information from the generated moiré fringe pattern in SDWI, a conjugate complex function coupling strategy (CCFC) of interferometric field is proposed in this study. By the Fourier transform and the half-band filter in one side of the spectrum, the positive half spectrum is obtained. The inverse Fourier transform and conjugate operation are performed on the half spectrums to obtain the two conjugate complex functions of the interferometric field. Coupled by the multiplication for the conjugate complex functions, the lower beat-frequency synthetic-wavelength interferometric fringe pattern is derived directly. And if the SDWI is implemented with the π/2 phase shift at λS, the obtained phase-shift interferogram for λS could be demodulated by the conventional phase-shift algorithm. Compared with other spatial-domain Fourier transform demodulation theory, the half-band filter used in CCFC method is appropriate for the different spectral width and carrier spatial frequency. The necessary introduced linear carrier is merely about 0.0947 times of the carrier in the former numerically. And it is only used to pursue the separation between the ±1 order phase lobes instead of the separation between the different wavelength phase lobes. The feasibility and applicability of the CCFC method are verified using simulation and experimental results.

Measurement of the free electron line density in a spherical theta-pinch plasma target by single wavelength interferometry

A single wavelength heterodyne interferometer has been set up to investigate the free electron density integrated axially along the line of sight (line density) in a theta-pinch plasma to determine its applicability as a plasma target for ion beam stripping. The maximal line density reached in this experiment was cm−2 at 80 Pa and 20 kV. The findings demonstrate the pulsed character of the line density and its increase by raising the load voltage and the working gas pressure. Additionally, the results were compared with spectroscopic free electron density estimations, which were carried out by H-line broadening and peak separation. The time behavior of the line density indicates that its peak value is delayed by about 10 µs compared to the spectroscopic results. This effect is due to the formation of an extended, magnetically compressed plasma column in the vicinity of the current maximum, although the highest volumetric free electron density is reached near the current zero crossing. Since the line density is an essential parameter in describing the stripping capabilities of the plasma target, the interferometric diagnostic is superior to a spectroscopic diagnostic, because it directly provides integrated values along the line of sight. Furthermore, the measurements of the line density in this experiment partially show nonphysical negative values, which is due to gaseous effects and residual shot vibrations.

Quantitative phase imaging in dual-wavelength interferometry using a single wavelength illumination and deep learning.

In this manuscript, we propose a quantitative phase imaging method based on deep learning, using a single wavelength illumination to realize dual-wavelength phase-shifting phase recovery. By using the conditional generative adversarial network (CGAN), from one interferogram recorded at a single wavelength, we obtain interferograms at other wavelengths, the corresponding wrapped phases and then the phases at synthetic wavelengths. The feasibility of the proposed method is verified by simulation and experiments. The results demonstrate that the measurement range of single-wavelength interferometry (SWI) is improved by keeping a simple setup, avoiding the difficulty caused by using two wavelengths simultaneously. This will provide an effective solution for the problem of phase unwrapping and the measurement range limitation in phase-shifting interferometry.

Simultaneous dual-wavelength phase-shifting interferometry for surface topography measurement

To deal with vibration disturbance in interferometric measurement of surface topography, we present a simultaneous dual-wavelength phase-shifting interferometry (SDWPSI). SDWPSI collects phase-shifting interferograms of two wavelengths simultaneously with two cameras to accelerate data collection. The optical phases are retrieved from dual-wavelength interferograms with an iterative algorithm that is tolerant of phase-shifting error caused by vibration. And then the measured surface topography is reconstructed by fusing the phases of two wavelengths. Simulations and experiments verify that SDWPSI has a lower measurement noise than single-wavelength interferometry and extends the discontinuity limit to several micrometres. SDWPSI has advantages of high speed, vibration resistance, and low cost, and could be applied to in-workshop and on-machine measurement.

Carrier squeezing interferometry with π/2 phase shift at the synthetic wavelength: Phase extraction in simultaneous dual-wavelength interferometry

Dual-wavelength interferometry (DWI) could extend the measured range of each single-wavelength interferometry. The synchronization of the two working wavelengths in DWI is of high efficient, and the generated moiré fringe indirectly represents the information of the measured long synthetic-wavelength (λS) phase. However, the extraction of the measured synthetic-wavelength phase is rather arduous from the moiré fringe. To retrieve the synthetic-wavelength phase from the moiré fringe patterns, we present a carrier squeezing dual-wavelength interferometry method (CSDI) in simultaneous DWI (SDWI). After the mathematical square of the moiré fringe patterns, the multiplicative moiré phase-shift fringe patterns with π/2 phase shift at λS are combined into a single spatial-temporal fringe (STF). By converting the temporal phase shift into spatial carrier and the introduction of the carrier, the measured synthetic wavelength phase is retrieved by the filter and inverse Fourier transform of the STF spectrum. Compared with other methods, CSDI method could suppress the influence of the phase-shift error and only requires 4 frame phase-shift interferograms. Numerical simulations are executed to demonstrate the performance of the CSDI method in SDWI with the peak-to-valley (PV) value of 1.46 nm and the root mean square (RMS) values of 0.23 nm for the demodulated error. And the precision is better than PV of 20 nm (0.0059λs) and RMS of 6 nm (0.0017λs) even when the distribution range of the phase-shift error is as high as ± 10% relative to the π/2 phase shift step at λS. Finally, our experimental results indicate that the measurement accuracy is better than 1.3% for a step with the height of 7.8 µm, and 0.5% for the step height of 6.233 µm for a Fresnel lens.

Phase retrieval from the phase-shift moiré fringe patterns in simultaneous dual-wavelength interferometry

Simultaneous dual-wavelength interferometry (SDWI) could extend the measured range of each single-wavelength interferometry. The moiré fringe generated in SDWI indirectly represents the information of the measured long synthetic-wavelength phase, thus the phase demodulation is rather arduous. To address this issue, we present a method to convert the moiré fringe pattern into a synthetic-wavelength interferogram (moiré to synthetic-wavelength, MTS). After the square of the moiré fringe pattern in the MTS method, the additive moiré pattern is turned into a multiplicative one. And the synthetic-wavelength interferogram could be obtained by a low-pass filtering in spectrum of the multiplicative moiré fringe pattern. Therefore, when the dual-wavelength interferometer is implemented with the π/2 phase shift at a sequence of synthetic-wavelength phase-shift interferograms with π/2 phase shift could be obtained after the MTS method processing on the captured moiré fringe patterns. And then the synthetic-wavelength phase could be retrieved by the conventional phase-shift algorithm. Compared with other methods in SDWI, the proposed MTS approach could reduce the restriction of the phase shift and frame numbers for the adoption of the conventional phase-shift algorithm. Following, numerical simulations are executed to evaluate the performance of the MTS method in processing time, frames of interferograms and the phase shift error compensation. And the necessary linear carrier for MTS method is less than 0.11 times of the traditional dual-wavelength spatial-domain Fourier transform method. Finally, the deviations for MTS method in experiment are 0.97% for a step with the height of 7.8 μm and 1.11% for a Fresnel lens with the step height of 6.2328 μm.

Phase extraction for dual-wavelength phase-shift Fizeau interferometry in the presence of multi-beam interference

Dual-wavelength interferometry could extend the measured range of single-wavelength interferometry by combining the two single wavelength phases, particularly for the measurement of step height. When testing the high-reflectivity surfaces with the single wavelength Fizeau interferometer, we have presented the π∕4 phase-shift carrier squeezing interferometry (QCSI) method for phase extraction with multi-beam interference (Appl. Opt. 55, 1920–1928, 2016). In this paper, we propose an integer and decimal portions synthetization (IDS) method for the multi-beam interference in the dual-wavelength Fizeau interferometer. One of the single wavelength wrapped phases is demodulated by the multi-beam interference QCSI algorithm, while the second of the single wavelength wrapped phases is extracted by the conventional two-beam interference phase-shift algorithm, so the equivalent wavelength unwrapped phase is derived from the two single wavelength wrapped phase. The decimal portion of synthesized phase is then obtained directly from the first single wavelength wrapped phase, and the integer portion of synthesized phase is obtained from the fringe order of the first single wavelength wrapped phase determined by the equivalent wavelength unwrapped phase. The proposed non-iterative IDS method avoids the common error magnification effect in the two-wavelength techniques, and only requires no more than 8 frame phase-shift interferograms for each single wavelength. Its robust performance is validated by both simulations and experiments in the presence of multi-beam interference as well as phase-shift error for measuring objects with height discontinuities.

High Precision Double-Interferometry for Large Step-Height On-Line Measurement Using Waveform Transforming Technology

This paper focuses on obtaining high measurement precision for large step-height by double-interferometry using waveform transforming technology. The interferometer performing the measurement, which is stabilized by a feedback loop and is robust enough for on-line measurement, works simultaneously in both modes of single-wavelength interferometry (SWI) and two-wavelength interferoemetry (TWI). In order to make the peak point of the TWI signal prominent and unique, the cosine-amplitude-modulated TWI signal has been transformed to be a triangular signal with the same frequency as the cosine-amplitude modulating and being in phase with it. The positions of the one-to-one corresponding peaks of the TWI signal and the triangular signal are the same. As the peak point of the triangular signal can be addressed much more precisely than that of the TWI signal, by employing the shifting range of the peak of the triangular signal instead of that of the TWI signal to determine the amplitude of the step height while using the SWI signal to measure the value of it, the system could measure the height with high precision. The standard deviation of measuring a gauge block with the height of 0.5mm is 0.8nm.

Frequency-comb-referenced multi-wavelength profilometry for largely stepped surfaces

3-D profiles of discontinuous surfaces patterned with high step structures are measured using four wavelengths generated by phase-locking to the frequency comb of an Er-doped fiber femtosecond laser stabilized to the Rb atomic clock. This frequency-comb-referenced method of multi-wavelength interferometry permits extending the phase non-ambiguity range by a factor of 64,500 while maintaining the sub-wavelength measurement precision of single-wavelength interferometry. Experimental results show a repeatability of 3.13 nm (one-sigma) in measuring step heights of 1800, 500, and 70 μm. The proposed method is accurate enough for the standard calibration of gauge blocks and also fast to be suited for the industrial inspection of microelectronics products.

White light interferometry for surface profiling with a colour CCD

In laser based interferometry, the unambiguous measurement range is limited to half a wavelength. Multiple wavelength or white light interferometer is used to overcome this difficulty. In this paper a white light interferometer with a colour CCD camera is discussed. We access interference intensity information from the three channels of the colour CCD simulating three-wavelength measurement. This makes the data acquisition as simple as in single wavelength interferometry. The unambiguous measurement range however gets limited by the coherence length of the CCD. The usefulness of the proposed method is demonstrated on a micro-sample.

Red-Green-Blue wavelength interferometry and TV holography for surface metrology

Surface discontinuities greater than half a wavelength can not be measured unambiguously using single wavelength interferometry. In TV holography, it is difficult to quantify the data under relatively large loading conditions due to the overcrowding of fringes with a single wavelength. Further, single wavelength does not reveal the contour of rough surfaces with TV holography. Multiple wavelengths measurements using red, green, and blue wavelengths can overcome these problems. In this paper a multiple wavelength interferometric system with colour CCD is demonstrated for such measurements. The interference patterns are recorded by a single chip colour CCD camera which makes the data acquisition as simple as in single wavelength case. The interference pattern is decomposed into its R G B components to evaluate the phase at individual wavelengths. An eight step phase shifting algorithm is used to simplify the application of phase shifting technique in the multiple wavelength system. Experimental results on an etched silicon sample for the measurement of large discontinuities and on a MEMS pressure sensor for the measurement of shape and relatively large deflection are presented.

Two-wavelength micro-interferometry for 3-D surface profiling

Three-dimensional non-contact optical techniques for rapid and accurate mapping of micro-machined surfaces are important for the optoelectronic industry. Interferometry is a well-established technique for 3-D surface profiling. The conventional interferometric surface profilers using a single wavelength offer excellent vertical resolution, but a serious limitation to their use is that they can only handle smooth profiles and step heights less than half a wavelength. In this paper we describe a two-wavelength micro-interferometric setup for 3-D surface profile characterization of smooth as well as rough micro-specimens. The method removes ambiguity associated with the single-wavelength data and also extends the phase measurement range compared to the conventional single-wavelength interferometry. Seven-phase step algorithm is used for quantitative fringe analysis. The design of the system along with experimental results on smooth and rough micro-specimens is presented.

Multiwavelength interferometry and competing optical methods for the thermal probing of thin polymeric films

AbstractMultiple‐wavelength interferometry (MWI), a new optical method for the thermal probing of thin polymer films, is introduced and explored. MWI is compared with two standard optical methods, single‐wavelength interferometry and spectroscopic ellipsometry, with regard to the detection of the glass transition temperature (Tg) of thin supported polymer films. Poly(methyl methacrylate) films are deposited by spin coating on Si and SiO2 substrates. MWI is also applied to the study of the effect of film thickness (25–600 nm) and polymer molecular weight (1.5 × 104 to 106) on Tg, the effect of film thickness on the coefficients of thermal expansion both below and above Tg, and the effect of deep UV exposure time on the thermal properties (glass transition and degradation temperatures) of the films. This further exploration of the MWI method provides substantial insights about intricate issues pertinent to the thermal behavior of thin polymer films. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 102: 4764–4774, 2006

Interferometric measurements of dynamic polarizabilities for metal atoms using electrically exploding wires in vacuum

Measurements within 10% accuracy of the dynamic dipole polarizabilities $\ensuremath{\alpha}(\ensuremath{\lambda})$ for five nonrefractory metal atoms (Mg, Ag, Al, Cu, and Au) at laser wavelengths of $\ensuremath{\lambda}=532$ and $1064\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ are presented using electrical explosion of thin wires in vacuum and a novel laser probing integrated-phase technique. The technique is based on single-wavelength interferometry and does not require axial symmetry of the tested object. Theoretical prediction of $\ensuremath{\alpha}(\ensuremath{\lambda})$ for wavelengths $\ensuremath{\lambda}=355$, 532, and $1064\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$, as well as the static dipole polarizabilities ${\ensuremath{\alpha}}_{\mathrm{st}}$, are also presented. An agreement within 20% was obtained between calculated data, recommended static polarizabilities ${\ensuremath{\alpha}}_{\mathrm{st}}$, and the measured dynamic polarizabilities $\ensuremath{\alpha}(532\phantom{\rule{0.3em}{0ex}}\mathrm{nm})$ and $\ensuremath{\alpha}(1064\phantom{\rule{0.3em}{0ex}}\mathrm{nm})$.

Determining large step heights using zero-order interference fringe identification and an external cavity diode laser

Zero-order interference fringe identification is a powerful tool for measuring large step heights. In contrast to white light scanning interferometry, this study utilizes an external cavity diode laser as the light source. The zero-path difference point can be accurately identified by combining wavelength scanning interferometry, in which the laser wavelength is continuously changed, with single wavelength interferometry, in which the laser wavelength is fixed. The experimental apparatus is a two-arm interferometer containing the sample in the measurement arm. The step height denotes the distance between two locations of a zero-order interference fringe, which are obtained by continuously varying the length of the reference arm. The accuracy of a sample of 10mm step height was found to be 0.33μm.

A new method for low-powered laser reflectance and scattering monitoring of MOVPE growth with narrow optical access

During metalorganic vapor phase epitaxy (MOVPE) growth of layers of CdS/CdTe, two different sets of data has been extracted in situ at normal incidence, with only a narrow optical access to the sample, using a charge coupled device (CCD) array as the detector. When growing CdTe on Si (0 0 1) in a 2″ single wafer reactor, the growth rate was determined through reflectance interferometry, and film roughness through scattering measurements. A dual wavelength method has been used, where the wavelengths have been chosen to match the CCD detector elements for green and red light in an Agilent HDCS1000 CCD-array. The second wavelength has been used to correct for the absorption/scattering extinction problem of single wavelength interferometry. The relative high intensity of the laser light relative to the ambient minimised the need for filtering of ambient light. The result has been a very simple and robust instrument. The blue light pixels were used for ambient light correction, but could be used for blue laser light detection. The interferograms have been recorded by simple integration of the imaging data sets. The growth rate for both wavelengths was 0.83 nm/s. Through creating a diffused laser spot on a surface, and correlating this to the initial state, roughness data were also accessible. Roughness could be determined quantitatively through correlating scattering data from the interferograms with AFM micrographs of the samples.

Measurement of Excitation Equilibrium Departure Evolution in an Argon Pulsed Plasma

This work reports information about the temporal evolution of the excitation equilibrium departure in a high current pulsed arc. An argon plasma has been created in a linear lamp by discharging a capacitor bank on its electrodes. Spatially and temporally-resolved measurements have allowed us to determine electron density N e and excitation temperature T with great accuracy. Single-wavelength interferometry and H α -Stark broadening have been used to measure N e (0.2–0.98× 10 23 m -3 ). Excitation temperature has been obtained from Boltzmann-plot of ArII lines and ranges in this experiment from 13500 to 26500 K. By assuming this temperature is equal to kinetic electron temperature and by comparing the theoretically predicted and the experimental ArII/ArI intensities ratios at each instant of the plasma life, it is possible to measure the departure of the excitation processe from local them dynamic equilibrium (LTE) conditions and to show the ionizing characteristics of this close-to-LTE plasma. Different t...

Experimental Stark Widths and Shifts of Several NeiSpectral Lines

This work reports data of Stark widths and shifts of 37 Ne I lines that have been measured as functions of electron density and temperature in the ranges (0.07-1.85)×1023 m-3 and 13,900-20,700 K, respectively. A pulsed arc was used as a plasma source. The electron density was measured by single-wavelength interferometry using the 488.0 nm transition of an Argon ion laser and has also been determined from Hα Stark broadening. The plasma temperature has been determined from the Boltzmann plot of Ne I lines and estimated from the Saha law. Linear fits have been performed between Stark parameters and electron density, and possible dependencies on temperature have been checked. The measured parameters are compared with theoretical and experimental data taken from the literature.

Temporal investigation of a fast spark discharge in chemically inert gases

The evolution of a fast pin-to-pin spark discharge in nitrogen is studied during the first s of its development with a single-wavelength interferometry method. The growth of the plasma kernel, the particle number densities, the temperature distribution and shock-wave position are measured with this technique. The energy dissipated into the gap is measured with a calorimetric bomb. The voltage across the gap and the electrical current flowing through the gap are measured simultaneously. The measured waveform of the electrical current is used as an input to a two-dimensional simulation model based upon the equations from continuum mechanics. The model successfully describes the shock-wave position, the particle number densities and the temperature. The model can therefore be used to produce realistic initial conditions for studies of ignition of combustible gases.