Dispersive Interferometer Research Articles

Performance enhancement approach for a snapshot interferometer sensor of surface inspection

Due to the high level of interest recently accorded to online surface measurement methods by academia and industry, engineers can now measure engineered surfaces rapidly and accurately. The present work involved illumination and individually examining a snapshot dispersive optical interferometer sensor with two different types of high-powered super-luminescent diodes (SLDs). Fringe pattern visibility is crucial to the effectiveness of this kind of interferometer. Two scenarios were introduced to examine the interference pattern visibility for the first-order (scanning range). Compared to the zero-order (reference beam), the first-order (diffraction/measurement beam) is less intense. Undesirable outcomes are generated by the dispersive line beam, like increased noise at a reduced intensity at the scanning range margin. Noise is among the parameters adversely impacting effective signal in all classes of optical measurement sensors; subsequently, sensor resolution measurement is influenced by any elevation in first-order intensity. The measurement noise peak to peak of the analyzed sample was developed from 28 to 20 nm. Consequently, it is possible to apply the snapshot sensor to a next-generation snapshot fiber link interferometry sensor for surface inspection.

Phase-encoding of loosely bound soliton molecules

Dissipative soliton molecules (DSMs) are of great interest for studying the complexity of nonlinear optical problems as they can map with the matter molecules for making interdisciplinary analogies. In contrast to strongly bound DSMs that have a short time separation between the bound solitons, the complex dynamics and underlying binding mechanism of loosely bound soliton molecules (LBSMs) with orders of magnitude longer time separation remain open questions. To this end, here, we explore real-time spectroscopy using a dispersive temporal interferometer (DTI) to visualize the dynamics of LBSMs in a mode-locked fiber laser and unveil their underlying phase-evolving mechanism. The DTI enables fringe-resolved spectroscopy in real time of the LBSM’s evolution by creating duplicates of the LBSM that results in a much closer time separation between the individual solitons of the LBSM. The real-time evolution of the LBSM’s phase exhibits a diverging sliding landscape, which is theoretically and experimentally proved to be closely associated with gain dynamics. Based on the understanding of its phase dynamics, we finally demonstrate programmable phase-encoding modulation of the LBSM through gain control. These efforts not only shed light on understanding the mechanism of long-range interactions in LBSMs but also provide an alternative approach for all-optical information processing.

Enhanced Data-Processing Algorithms for Dispersive Interferometry Using a Femtosecond Laser.

Dispersive interferometry based on a femtosecond laser is extensively utilized for achieving absolute distance measurements with high accuracy. However, this method cannot measure arbitrary distances without encountering a dead zone, and deviations in its output results are inevitable due to inherent theory limitations. Therefore, two enhanced data-processing algorithms are proposed to improve the accuracy and reduce the dead zone of dispersive interferometry. The principles of the two proposed algorithms, namely the truncated-spectrum algorithm and the high-order-angle algorithm, are proposed after explaining the limitations of conventional methods. A series of simulations were conducted on these algorithms to show the improved accuracy of measurement results and the elimination of the dead zone. Furthermore, an experimental setup based on a dispersive interferometer was established for the application of these proposed algorithms to the experimental interference spectral signals. The results demonstrated that compared with the conventional algorithm, the proposed truncated-spectrum algorithm could reduce the output distance deviations derived from direct inverse Fourier transforming by eight times to reach as low as 1.3 μm. Moreover, the unmeasurable dead zone close to the zero position of the conventional algorithm, i.e., the minimum working distance of a dispersive interferometer, could be shortened to 22 μm with the implementation of the proposed high-order-angle algorithm.

Real-time revealing of Cherenkov radiation evolution in optical fibers.

The generation of Cherenkov radiation (CR) is determined by the phase-matching condition, but the experimental observation on the phase change of its transient process is still incomplete. In this paper, we use the dispersive temporal interferometer (DTI) technique to real-time reveal the buildup and evolution of CR. Experiments show that when the pump power varies, the phase-matching conditions also change, which is mainly affected by the nonlinear phase shift caused by the Kerr effect. Further simulation results propose that both pulse power and pre-chirp management have a significant impact on phase-matching. The CR wavelength can be shortened and the generation position can be moved forward by adding a suitable positive chirp or increasing the incident peak power. Our work directly reveals the evolution of CR in optical fibers and provides a method for optimizing it.

Improved Algorithms of Data Processing for Dispersive Interferometry Using a Femtosecond Laser

Two algorithms of data processing are proposed to shorten the unmeasurable dead-zone close to the zero-position of measurement, i.e., the minimum working distance of a dispersive interferometer using a femtosecond laser, which is a critical issue in millimeter-order short-range absolute distance measurement. After demonstrating the limitation of the conventional data processing algorithm, the principles of the proposed algorithms, namely the spectral fringe algorithm and the combined algorithm that combines the spectral fringe algorithm with the excess fraction method, are presented, together with simulation results for demonstrating the possibility of the proposed algorithms for shortening the dead-zone with high accuracy. An experimental setup of a dispersive interferometer is also constructed for implementing the proposed data processing algorithms over spectral interference signals. Experimental results demonstrate that the dead-zone using the proposed algorithms can be as small as half of that of the conventional algorithm while measurement accuracy can be further improved using the combined algorithm.

Radiation shielding design of the CFETR polarimeter interferometer and CO2 dispersion interferometer

A three-wave based laser polarimeter/interferometer and a CO2 laser dispersion interferometer are used to determine the electron and current density profiles on a Chinese fusion engineering test reactor (CFETR). Radiation shielding is designed for the combination of polarimeter/interferometer and CO2 dispersion interferometer. Furthermore, neutronics models of the two systems are developed based on the engineering-integrated design of CFETR polarimeter/interferometer and CO2 dispersion interferometer and the major material components of CFETR. The polarimeter/interferometer and CO2 dispersion interferometer’s neutron and photon transport simulations were performed using the Monte Carlo neutral transport code to determine the energy deposition and neutron energy spectrum of the optical mirrors. The energy depositions of the first mirrors on the polarimeter/interferometer are reduced by three orders with the whole shielding. Since the mirrors of CO2 dispersion interferometer are very close to the diagnostic first wall, shielding space is limited and the CO2 dispersion interferometer energy deposition is higher than that of the polarimeter/interferometer. The dose rate after shutdown 106 s in the back-drawer structure has been estimated to be 83 μSv h−1 when the radiation shield is filled in the diagnostic shielding modules, which is below the design threshold of 100 μSv h−1. Radiation shielding design plays a key role in successfully applying polarimeter/interferometer and CO2 dispersive interferometer in CFETR.

Real time revealing relaxation dynamics of ultrafast mode-locked lasers

Single-shot measurement of ultrashort time with a dispersive temporal interferometer (DTI) paves the way for exploring intracavity dynamics in ultrafast lasers. Here, we report observations of pulse evolution dynamics after mode-locking buildup in ultrafast lasers. We observe the roundtrip time and phase evolution of the mode-locked pulses after buildup, and we unveil that the pulse experiences three different stages before stabilization, i.e., the soliton breathing stage, the relaxation oscillation stage, and the long-term relaxation stage. We find that the gain depletion effect makes the pulse move forward but does not shift its phase, and it can be distinguished by a DTI from the refractive index change. With this, the dynamics of the three stages is analyzed. Moreover, it is unveiled that the gain relaxation dynamics can intensively affect a laser's stability. These results provide additional perspectives on the intracavity dynamics of mode-locked lasers and of complex nonlinear systems, and they can help to improve the laser stability, which may impact laser design, ultrafast diagnostics, and nonlinear optics.

Dispersive Temporal Interferometry toward Single‐Shot Probing Ultrashort Time Signal with Attosecond Resolution

With the intensive research on ultrafast dynamics in physics and chemistry, the single‐shot measurement of ultrashort time change has become increasingly important. The most advanced oscilloscope with the time‐lens technique possesses subpicosecond resolution, while the interferometer can single‐shot probe time event within one optical cycle. However, the single‐shot measurement of time difference beyond optical cycle but less than time‐lens’ resolution is still inaccessible. Herein, a technique, the dispersive temporal interferometer (DTI), to break through the gap between interferometer and time lens on single‐shot time measurement, is reported. The concept is an analogy to the spatial interference: a pulse passes two paths to assemble into a pulse pair, and temporal interference arises after large dispersion, which can single‐shot record the imposed time change. Experimentally, it is measured that its resolution is sub‐20 as (0.004 optical cycle) over a range of larger than 2 ps (400 optical cycle), with a range‐to‐resolution ratio of 105 and sampling rate of 42.8 MHz. Moreover, a DTI‐based gyroscope with sensitivity of 348 as/(deg s−1) is fabricated to demonstrate its applications in optical sensors. This technique can precisely single‐shot monitor ultrashort time change in attosecond resolution and has a prosperous application prospect in capturing ultrafast process.

High-accuracy simultaneous measurement of surface profile and film thickness using line-field white-light dispersive interferometer

White-light dispersive interferometry (WLDI) is an instantaneous, high-resolution optical metrological technique for measuring precise and complicated surfaces. This method enables nondestructive inspection of transparent-film-structure devices that are widely used in semiconductor packaging. We propose in this paper to use a home-built WLDI system with line-by-line spectral calibration, phase-shifting algorithm, and single-wave-number method for high-accuracy, simultaneous measurements of surface profiles and film thickness. By calibrating the relationship between wave-number and pixel position on each line of a two-dimensional detector, the line-by-line calibration method improves the measurement accuracy by correcting the spectral distortion caused by the optical system. Moreover, the spectral signal phase is obtained by the phase-shifting algorithm instead of by the Fourier transform method. The single-wave-number method is applied to the computation process by introducing the fringe order, and the measurement result indicates that it enhances the system immunity to environmental noise. A 1.806-µm-high standard step and a 1052.2-nm-thick standard film are measured to verify the system performance and show that the system is highly accurate and reliable.

Application of Clustering Filter for Noise and Outlier Suppression in Optical Measurement of Structured Surfaces

In comparison to tactile sensors, optical techniques can provide a fast, nondestructive profile/areal surface measurement solution. Nonetheless, high measurement noise, unmeasured points, and outliers are often observed in optical measurement, particularly for structured surfaces. To alleviate their detrimental impacts on the characterization of surface topography as well as the examination of micro/nanoscale geometries, a post processing filtering technique, i.e., the clustering filter, which is essentially an iterative process to find the aggregation center of a cluster of points, is implemented. The clustering filter is particularly useful for noises and outlier suppression for optical measurement of structured surfaces due to its edge-preserving capability. Five surface samples with structured features are measured by an in-house developed dispersive interferometer and a commercial white light interferometer, thereafter the measured surface data are filtered by the clustering filter. Both noise and outliers are suppressed, which not only facilitates the visualization and characterization of surface topography, but also enables the accurate evaluation of local functional geometries.

Spatial Heterodyne Raman Spectrometer (SHRS) for In Situ Chemical Sensing Using Sapphire and Silica Optical Fiber Raman Probes.

A spatial heterodyne Raman spectrometer (SHRS), constructed using a modular optical cage and lens tube system, is described for use with a commercial silica and a custom single-crystal (SC) sapphire fiber Raman probe. The utility of these fiber-coupled SHRS chemical sensors is demonstrated using 532 nm laser excitation for acquiring Raman measurements of solid (sulfur) and liquid (cyclohexane) Raman standards as well as real-world, plastic-bonded explosives (PBX) comprising 1,3,5- triamino- 2,4,6- trinitrobenzene (TATB) and octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine (HMX) energetic materials. The SHRS is a fixed grating-based dispersive interferometer equipped with an array detector. Each Raman spectrum was extracted from its corresponding fringe image (i.e., interferogram) using a Fourier transform method. Raman measurements were acquired with the SHRS Littrow wavelength set at the laser excitation wavelength over a spectral range of ∼1750 cm-1 with a spectral resolution of ∼8 cm-1 for sapphire and ∼10 cm-1 for silica fiber probes. The large aperture of the SHRS allows much larger fiber diameters to be used without degrading spectral resolution as demonstrated with the larger sapphire collection fiber diameter (330 μm) compared to the silica fiber (100 μm). Unlike the dual silica fiber Raman probe, the dual sapphire fiber Raman probe did not include filtering at the fiber probe tip nearest the sample. Even so, SC sapphire fiber probe measurements produced less background than silica fibers allowing Raman measurements as close as ∼85 cm-1 to the excitation laser. Despite the short lengths of sapphire fiber used to construct the sapphire probe, well-defined, sharp sapphire Raman bands at 420, 580, and 750 cm-1 were observed in the SHRS spectra of cyclohexane and the highly fluorescent HMX-based PBX. SHRS measurements of the latter produced low background interference in the extracted Raman spectrum because the broad band fluorescence (i.e., a direct current, or DC, component) does not contribute to the interferogram intensity (i.e., the alternating current, or AC, component). SHRS spectral resolution, throughput, and signal-to-noise ratio are also discussed along with the merits of using sapphire Raman bands as internal performance references and as internal wavelength calibration standards in Raman measurements.

Analysis of main parameters of spectral interferometry ranging using optical frequency comb and animproved data processing method

<sec>With the rapid development of modern technology, high-precision absolute distance measurement is playing an important role in many applications, such as scientific research, aviation and industry measurement. Among the above various measurement methods, how to realize higher-accuracy, larger-scale, and faster-speed measurement is particularly important. In the traditional technique for long-distance measurement, the emergence of optical frequency comb (OFC) provides a breakthrough technology for accurately measuring the absolute value of distance. The OFC can be considered as a multi-wavelength source,whose phase and repetition rate are locked. The OFC is a very useful light source that can provide phase-coherent link between microwave and optical domain, which has been used as a source in various distance measurement schemes that can reach an extraordinary measurement precision and accuracy. A variety of laser ranging methods such as dual-comb interferometry and dispersive interferometer based on femtosecond laser have been applied to the measuring of absolute distance.</sec><sec>In this paper, the factors affecting the resolution and the non-ambiguous range of spectral interferometry ranging using OFC are particularly discussed. We also analyze the systematic errors and the limitations of traditional transform methods based on Fourier transform, which can conduce to the subsequent research.</sec><sec>To address the problem caused by low resolution and unequal frequency interval, we propose a data processing method referred to as equal frequency interval resampling. The proposed method is based on cubic spline interpolation and can solve the error caused by the frequency spectrum broadening with the increase of distance. Moreover, we propose a new method based on least square fitting to calibrate the error introduced by the low resolution of interferometry spectrum obtained with fast Fourier transform (FFT). With the proposed method, the simulation results show that the systematic error is less than 0.2 μm in the non-ambiguity range and the system resolution is greatly improved. Finally, anabsolute distance measurement system based on Michelson interferometer is built to verify theproposed method. The measurement results compared with those obtained by using a high-precision commercial He-Ne laser interferometer show that the distance measurement accuracy is lower than 3 μm at any distancewithin the non-ambiguity range. The experimental results demonstrate that our data processing algorithm is able to increase the accuracy of dispersive interferometry ranging with OFC.</sec>

Optimization methods of pulse-to-pulse alignment using femtosecond pulse laser based on temporal coherence function for practical distance measurement

An interferometer technique based on temporal coherence function of femtosecond pulses is demonstrated for practical distance measurement. Here, the pulse-to-pulse alignment is analyzed for large delay distance measurement. Firstly, a temporal coherence function model between two femtosecond pulses is developed in the time domain for the dispersive unbalanced Michelson interferometer. Then, according to this model, the fringes analysis and the envelope extraction process are discussed. Meanwhile, optimization methods of pulse-to-pulse alignment for practical long distance measurement are presented. The order of the curve fitting and the selection of points for envelope extraction are analyzed. Furthermore, an averaging method based on the symmetry of the coherence function is demonstrated. Finally, the performance of the proposed methods is evaluated in the absolute distance measurement of 20 µ m with path length difference of 9 m. The improvement of standard deviation in experimental results shows that these approaches have the potential for practical distance measurement.

Refraction and dispersion measurement using dispersive Michelson interferometer

A new approach to a dispersive Michelson interferometer (DMI) is introduced. Rings of Equal Chromatic Order (RECO) are formed by a DMI illuminated by a white light source and crossed with an auxiliary dispersion spectrograph. The theoretical foundations are developed and then applied to different glass plates (BAK1, BK7, N-LAF35 and SK4) of thicknesses (12.101, 12.473, 9.930 and 6.602mm), respectively. The sample is introduced in one of the arms of the interferometer. The refraction and dispersion of the samples are deduced from a single RECO interferogram. The refractive index and its variation are measured across the spectral range: 0.500–0.650µm with relative errors of 10−3 and 1.6 ×10−4, respectively. A good agreement between our measurements and reference data is found.

Improving Spectral Results Using Row-by-Row Fourier Transform of Spatial Heterodyne Raman Spectrometer Interferogram.

This work describes a method of applying the Fourier transform to the two-dimensional Fizeau fringe patterns generated by the spatial heterodyne Raman spectrometer (SHRS), a dispersive interferometer, to correct the effects of certain types of optical alignment errors. In the SHRS, certain types of optical misalignments result in wavelength-dependent and wavelength-independent rotations of the fringe pattern on the detector. We describe here a simple correction technique that can be used in post-processing, by applying the Fourier transform in a row-by-row manner. This allows the user to be more forgiving of fringe alignment and allows for a reduction in the mechanical complexity of the SHRS.

Measurements of refractive indices and thermo-optical coefficients using a white-light Michelson interferometer.

A dispersive white-light Michelson interferometer was used to determine the wavelength dependence of the refractive index (n) in the visible range from 425 to 775 nm and the thermo-optical coefficient (dn/dT) of fused silica (FS) and borosilicate glass (BK7). For FS, the values obtained for n and dn/dT at 546 nm were 1.46079 and 11.3×10-6 K-1, respectively, while the values for BK7 glass were 1.51825 and 2.2×10-6 K-1, respectively, which is in good agreement with the literature. The accuracy of the methodology used for n was almost 10-6, enabling precise spectroscopic characterization of materials across a wide spectral range.

Efficient processing of reaction-sintered silicon carbide by anodically oxidation-assisted polishing

Reaction-sintered silicon carbide (RS-SiC) is a promising optical material for the space telescope systems. Anodically oxidation-assisted polishing is a method to machine RS-SiC. The electrolyte used in this study is a mixture of hydrogen peroxide (H2O2) and hydrochloric acid (HCl), and the oxidation potential has two modes: constant potential and high-frequency-square-wave potential. Oxide morphologies are compared by scanning electron microscope/energy dispersive x-ray spectroscopy and scanning white-light interferometer. The results indicate that anodic oxidation under constant potential can not only obtain a relatively smooth surface but also be propitious to obtain high material removal rate. The oxidation depth in anodic oxidation under constant potential is calculated by comparing surface morphologies before and after hydrofluoric acid etching. The theoretical oxidation rate is 5.3 nm/s based on the linear Deal–Grove model. Polishing of the oxidized RS-SiC is conducted to validate the machinability of the oxide layer. The obtained surface roughness root-mean-square is around 4.5 nm. Thus, anodically oxidation-assisted polishing can be considered as an efficient method, which can fill the performance gap between the rough figuring and fine finishing of RS-SiC. It can improve the machining quality of RS-SiC parts and promote the application of RS-SiC products.

High-sensitivity dispersive Mach-Zehnder interferometer based on a dissimilar-doping dual-core fiber for sensing applications.

A dual-core fiber in which one of the cores is doped with germanium and the other with phosphorus is used as an in-line Mach-Zehnder dispersive interferometer. By ensuring an equal length but with different dispersion dependencies in the interferometer arms (the two cores), high-sensitivity strain and temperature sensing are achieved. Opposite sensitivities for high and low wavelength peaks were also demonstrated when strain and temperature was applied. To our knowledge this is the first time that such behavior is demonstrated using this type of in-line interferometer based on a dual-core fiber. A sensitivity of (0.102±0.002) nm/με, between 0 and 800 με and (-4.2±0.2) nm/°C between 47°C and 62°C is demonstrated.

Surface profile measurement using spatially dispersed short coherence interferometry

Improved online techniques for surface profile measurement can be beneficial in high/ultra-precision manufacturing, in terms of enabling manufacture and reducing costs. This paper introduces a spatially dispersed short-coherence interferometer sourced by a super luminescent diode. This technique uses a broadband light source, which is spatially dispersed across a surface using a reflective grating and a scan lens. In this way, the phase data pertaining to surface at height is spectrally encoded. The light reflected from the surface is interfered with a reference beam in a Michelson interferometer, after which the resulting fringes are interrogated by a spectrometer. Phase shifting interferometry is used to extract the spectrally encoded phase information by analysing four captured frames using a Carré algorithm procedure; in this way, surface height can be determined across a profile on a sample. The short coherent light utilized in this interferometric technique means it has the potential for an application as a remote probe through an optical fibre link. This paper describes the concept of a spatially dispersed short coherence interferometer and provides some of the initial experimental results.

Dispersed reference interferometry

Dispersed reference interferometry (DRI) is a potentially useful technique for applications such as absolute displacement, surface topography and film thickness measurement. A bulk optic implementation of a short coherence dispersed reference interferometer is described with the chromatic dispersion applied using two matched transmission gratings in one arm. Such an interferometer can provide absolute knowledge of position by tracking a symmetrical fringe pattern produced by a spectrometer. An operating principle is presented and validation provided through empirical data from optical apparatus. We present experimental results for the resolution, linearity and repeatability of the investigated interferometer apparatus.