Spectral Interference Fringes Research Articles

Control of spectral interference patterns in broad Rabi sidebands toward quasi-comb structures.

The pattern of spectral interference fringes in broad dynamic Rabi sidebands allows for a considerable degree of control by shaping the picosecond driving pulse. We demonstrate experimental evidence of such control and report an analytic and numerical investigation of possibilities to control the fringe pattern to produce a comb-like optical structure. The temporal phase and amplitude shaping of a picosecond driving pulse influence the spectrum envelope, fringe contrast, and fringe spacing variation in the sideband spectra. The sideband spectrum envelope depends on the sharpness of the driving pulse, that is, on the rate at which the temporal distance between the leading and trailing edges grows away from the pulse maximum. Increasing this parameter reduces the variation of the envelope amplitude across the sideband. The fringe contrast, defined by the maximum-to-minimum difference, depends strongly on the asymmetry of the driving pulse. The imbalance between the leading and trailing edges leads to a decrease of the contrast. The variation of interpeak distance within a sideband was controlled using the temporal shape of the driving pulse. In the particular case of a blue-shifted sideband emitted by excited oxygen atoms driven by a picosecond pulse of 800 nm carrier wavelength and ∼5×10¹⁰ W cm⁻² intensity, a Gaussian pulse shape results in an interpeak distance increasing almost five times over the interval from 1.60 to 1.66 eV, whereas a super-Gaussian shape leads to almost equidistant fringes producing a comb-like spectrum.

Spectral interferometry based absolute distance measurement using frequency comb

Spectral interferometry using frequency comb has become a powerful approach to absolute distance measurement. In this paper, we analyze the principle of spectral interferometry in detail. With the consideration of dispersion, pulse chirp and the power ratio of the reference pulse and the measurement pulse, we develop a Gaussian model, which can be used to determine distances. The frequency of the spectral interference fringe is of key importance. The distances can be directly determined by the frequency of the spectral interference fringe through one-step fast Fourier transform with no filters during the data processing. The simulation results show that the maximum deviation is 1.5 nm when the distance is 1.5 mm theoretically. The comb consists of hundreds of thousands of teeth in the spectral domain, and each tooth can be regarded as a cw laser. We propose a method based on the phases of two close modes. The principle is introduced, and the maximum deviation is 8.7 nm with a distance of 1.5 mm while the minimum deviation is 0.3 nm corresponding to distance of 0.5 mm. We theoretically show that the linear pulse chirp can be used for distance measurement. The measurement principle is analyzed, and the simulation shows that the maximum deviation is 5.3 nm when the distance is 1.2 mm.

Carrier-envelope phase drift measurement of picosecond pulses by an all-linear-optical means.

Carrier-envelope phase (CEP) drift of a pulse train of 2 ps pulses has been measured by a multiple beam interferometer. The round trip time of the interferometer is slightly mistuned from the pulse sequence, leading to spectral interference fringes. We extract the pulse-to-pulse CEP drift from the position of the spectral interference pattern. The length of the interferometer has been actively stabilized to ±10 nm, which sets the ultimate limit on the accuracy of the measurement to 78 mrad, while the CEP-drift (rms) noise of the measurement was 127 mrad (at 800 nm).

Experimental Measurements of Electron-Bunch Trains in a Laser-Plasma Accelerator

Spectral measurements of visible coherent transition radiation produced by a laser-plasma-accelerated electron beam are reported. The significant periodic modulations that are observed in the spectrum result from the interference of transition radiation produced by multiple bunches of electrons. A Fourier analysis of the spectral interference fringes reveals that electrons are injected and accelerated in multiple plasma wave periods, up to at least 10 periods behind the laser pulse. The bunch separation scales with the plasma wavelength when the plasma density is changed over a wide range. An analysis of the spectral fringe visibility indicates that the first bunch contains most of the charge.

Common-path spectral-domain optical low coherence interferometric system for the measurement of small changes in refractive index of Liquid Crystal cell

We report the measurement of small changes in the refractive index of liquid crystal (LC) with applied voltage using a common-path spectral-domain optical low coherence interferometric system. Changes in the spectral modulations were observed as a function of voltage applied to the LC cell in steps. Hilbert transform fringe analysis was used for the extraction of the phase of the spectral interference fringe signal. The change in the refractive index of the LC material as a function of voltage was then determined from the phase information. The present system is common-path, yields a higher stability in measurement and compensates the optical length perturbation and hence can be used in real time.

Spectral-Domain Measurement of Strain Sensitivity of a Two-Mode Birefringent Side-Hole Fiber

The strain sensitivity of a two-mode birefringent side-hole fiber is measured in the spectral domain. In a simple experimental setup comprising a broadband source, a polarizer, a two-mode birefringent side-hole fiber under varied elongations, an analyzer and a compact spectrometer, the spectral interferograms are resolved. These are characterized by the equalization wavelength at which spectral interference fringes have the highest visibility (the largest period) due to the zero group optical path difference between the fundamental, the LP01 mode and the higher-order, the LP11 mode. The spectral interferograms with the equalization wavelength are processed to retrieve the phase as a function of the wavelength. From the retrieved phase functions corresponding to different elongations of a two-mode birefringent side-hole fiber under test, the spectral strain sensitivity is obtained. Using this approach, the intermodal spectral strain sensitivity was measured for both x and y polarizations. Moreover, the spectral polarimetric sensitivity to strain was measured for the fundamental mode when a birefringent delay line was used in tandem with the fiber. Its spectral dependence was also compared with that obtained from a shift of the spectral interferograms not including the equalization wavelength, and good agreement was confirmed.

Speckle reduction in parallel optical coherence tomography by spatial compounding

In this paper, we propose a novel method for speckle reduction by combining spatial compounding technique with parallel Fourier-domain optical coherence tomography (FDOCT). Through a two-dimensional (2-D) CCD camera, multiple spectral interference fringes for a single lateral point are acquired with adjacent pixels in parallel detection plane simultaneously. By compounding these spatial-resolved images, we can obtain a speckle-suppressed B-scan tomogram in a single shot without sacrificing axial resolution and imaging speed. The principle of our method is demonstrated by imaging a shrimp's telson in vivo and a pearl. A signal-to-noise ratio improvement close to a factor of two was achieved by averaging four spatial-resolved FDOCT images.

Tomographic and volumetric reconstruction of composite materials using full-field swept-source optical coherence tomography

We demonstrate tomographic and volumetric reconstruction of composite material using a full-field swept-source optical coherence tomographic (FF-SS-OCT) system. The FF-SS-OCT system is based on a co-axial and common-path optical interferometric system based on Mirau objective lens. By means of sweeping the frequency of the broad-band light source, multiple spectral interferograms are recorded and stacked in the X–Y–λ axes and processed in a computer. Optically sectioned images of the composite material at different depths are reconstructed. From the spectral interference fringe signal, the phase maps at various depths are also reconstructed. Due to its common path configuration, the present FF-SS-OCT system is highly stable and less sensitive to external vibration and does not require lateral B-scan leading to a large area measurement of the sample.

Preparation and Characterization of ZnO: In Transparent Conductor by Low Cost Dip Coating Technique

Transparent conducting oxide (TCO) based on indium doped zinc oxide films in the nano scale were successfully prepared using combination between dip coating and thermal decomposition process. Structural investigations confirm the polycrystalline ZnO hexagonal wurtzite phase grown along the c-axis with nano crystallite size about 10 nm. Morphology investigation shows that ZnO films consist of fine grains of average size 40 nm. This indicates that each grain contains several crystallites with different orientations. Cross sectional image presents good adhesion of the films with the substrate and the film thickness has been determined. Compositional analysis detects the indium content in the host ZnO matrix, the In/Zn ratio is close to the calculated concentration ratios of the precursor. The optical transmittance shows that the films are transparent in the UV and VIS-IR spectral region and interference fringes were observed to be thickness dependent. Preparation parameters were investigated and optimized such as dipping rate, number of deposition cycles, precursor concentration, annealing process and In/Zn ratio. Optimization process was investigated for low resistivity, high optical spectral window transmission and easy preparation process. Dipping rate in the range 2 - 38 mm/s is the most suitable range for good film quality while dipping rate range 30 - 38 mm/s produces thicker films in lower deposition cycles. The higher dipping rate produces films with lower transparency (milky films) while the small deposition rate rate requires large number of deposition cycles in order to increase the thickness. Besides, the higher dipping rate reflects lower resistivity of the deposited films. Precursor molar concentration was observed to have an essential effect on the film thickness, film quality and transparency. Lower precursor concentration requires also large number of deposition cycles for thickening the films. The higher concentration results also milky films (high scattering process by powder film). Precursor concentrations in the range 0.7 - 0.9 mol/liter were found to be the optimal for better quality and for faster deposition process. The resistivity of the films has been reduced from the range 1.5 - 2.5 kW?cm to the range 100 - 400 W.cm as the molar concentration reaches the range 0.07 - 0.09 mol/liter. The resistivity of films increases from 330 to 1686 .cm as the decomposition temperature increases from 200C to 350C. Annealing at 450C process after completing the decomposition at 200?C results the lowest resistivity with annealing time in the range 1.5 - 2 h. In/Zn percentage in the range 1.5% - 5% produces the lowest electrical resistivity. The absorption edge of the deposited films was observed to be critical affected by the preparation parameters. The band gap change was discussed through the degenerate semiconductors as well as nanostructured semiconducting materials of the energy gap confinement effect. Deposition of TCO based on ZnO:In was optimized depending on all deposition parameters forwide area, the lower cost and good performance TCO films.

Micrometer axial resolution OCT for corneal imaging

An optical coherence tomography (OCT) for high axial resolution corneal imaging is presented. The system uses 375 nm bandwidth (625 to 1000 nm) from a broadband supercontinuum light source. The system was developed in free space to minimize image quality degradation due to dispersion. A custom-designed spectrometer based on a Czerny Turner configuration was implemented to achieve an imaging depth of 1 mm. Experimentally measured axial resolution was 1.1 μm in corneal tissue and had a good agreement with the theoretically calculated resolution from the envelope of the spectral interference fringes. In vivo imaging was carried out and thin corneal layers such as the tear film and the Bowman’s layer were quantified in normal, keratoconus, and contact lens wearing eyes, indicating the system’s suitability for several ophthalmic applications.

Spectrally Resolved Maker Fringes in High-Order Harmonic Generation

We investigate macroscopic interference effects in high-order harmonic generation using a Ti:sapphire laser operating at a 100 kHz repetition rate. The structure and behavior of spectral and spatial interference fringes are explained and analytically described by transient phase matching of the long electron trajectory contribution. Time-frequency mapping due to the temporal chirp of the harmonic emission allows us to observe Maker fringes directly in the spectral domain.

Angular high-speed massively parallel detection spectral-domain optical coherence tomography for speckle reduction

We demonstrate speckle reduction based on angular compounding using parallel-detection spectral-domain optical coherence tomography (OCT). An ultrahigh-speed two-dimensional complementary metal-oxide semiconductor camera acquired angular and spectral interference fringes (128 × 1024 pixels) simultaneously at 15,000 frames/s for a single lateral point. A signal-to-noise ratio improvement of 8 dB was achieved for imaging human skin in vivo by averaging 121 angle-resolved OCT images.

Spectral-Domain Endoscopic Optical Coherence Tomography (EOCT) Using a Balloon Probe for Esophageal Imaging

Purpose: EOCT obtains micron-scale, cross-sectional structural images to depths exceeding 1mm in the esophagus. The 1st generation EOCT systems employed a time-domain OCT (TD-OCT) configuration with fiber-optic catheter probes that could be inserted through standard endoscopes. However, the low imaging speed of TD-OCT was an obstacle for 3D visualization of long segments. Also, these probes were designed for spot examination of focal lesions. This is not suitable for surveillance of Barrett's esophagus (BE) where the area of mucosa would be 20 sq cm or more. 1st generation EOCT only covers a few millimeters, which is similar to the normal hit-and-miss biopsy. With the advent of Fourier-domain OCT (FD-OCT) technology, imaging speeds increased 10-fold allowing rapid in-vivo imaging. We demonstrate here the 1st ballon-based high-speed SD-EOCT system for comprehensively imaging the esophagus in vivo with the potential for surveillance of long-segment BE within minutes. Methods: The balloon SD-OCT system employs a 12.5 mW, broadband light source with a full width at half maximum bandwidth of 60 nm centered at 1310 nm. The spectral interference fringes were detected by a custom-designed, linear-k spectrometer. The proximal end of the catheter consisted of a fiber rotary joint, which was driven at speeds approaching 570 rpm. A urethane low durometer balloon with a diameter of 18 mm and length of 25 mm was bound to the distal end of the catheter. During the scanning, the fiber probe was driven by the rotary joint to circumferentially scan the whole lumen of esophagus. Simultaneously, the pull-back system pulled the catheter longitudinally so that the probe scanned along a helical path to obtain 3D comprehensive images of the esophagus. The image acquisition and display was coordinated by a software program written in C++. The system was tested in anesthetized live swine as approved by the Case Animal Lab IRB. Results: A total of 10 swine were utilized for the study with successful OCT imaging in all animals. There were no equipment failures. There were no complications. Different layers could clearly be identified, including the squamous epithelium, lamina propria, muscularis mucosa, submucosa and muscularis propria. 3-D imaging was possible in all 10 swine. The images were displayed in real-time and the entire OCT examination of the esopagus took an average of 2.7 minutes. The SD-EOCT balloon system proved to be both feasible and safe. Conclusion: We report here a specially designed SD-EOCT balloon system that is capable of comprehensive imaging of long segments of the esophagus, and thus can be used for real-time, in-vivo, high-speed EOCT imaging for surveillance of BE.

Simultaneous measurement of multiparameters using a Sagnac interferometer with polarization maintaining side-hole fiber

A Sagnac interferometer with a section of a polarization maintaining side-hole fiber for multiparameter measurement is proposed. The sensor was experimentally demonstrated to be sensitive to torsion, temperature, and longitudinal strain, simultaneously. The birefringence in the investigated side-hole fiber is induced simultaneously by the elliptical shape of a germanium-doped core and by field overlap with the air holes surrounding the core. The latter effect is purely geometrical and causes high chromatic dispersion of the group birefringence in the long wavelength range, which results in a different period of spectral interference fringes. A different wavelength response is obtained for each interference fringe peak when the fiber is subjected to torsion, temperature, or longitudinal strain. A matrix equation for simultaneous measurement of the three parameters--torsion, temperature, and longitudinal strain--is also proposed.

An Improved Data Processing Method in Differential White Light Spectral Interferometry for the Measurement of Thickness of Ultra-Thin Metallic Foil

The accurate thickness measurement of Ultra-thin rolling metallic foil has an important role in industrial or some special applications. Unfortunately, commercial thickness meters do not provide high precision measurements non-destructively. A new spectral-domain interferometric method for measuring absolute thickness of Ultra-thin metallic foil is proposed here. The thickness is measured by differential white light spectral interferometer. Two differential Michelson Interferometers (MI) are used as basic measuring system to obtain the spectral interference fringes on the spectrometers. The spectral interference between both beams, which shows up a periodic modulation of the source spectrum with the period dependent on the OPD, serves as an illustration of a technique for measuring both OPDs and displacements in a range dependent on the source spectrum width. Therefore, the interference fringes only depend on the OPD due to the thickness of metallic foil and are unrelated to the position of the foils in the system, which is insensitive to the vibration. The spectral interference fringes are resolved over a wide spectral range and the absolute thickness of metallic foil can be calculated by measuring the OPD with a modified extremum method based on the least root mean square (RMS) deviation. The theoretical analysis and preliminary experiments indicate that the technique can measure the thickness of foils in the range of 1μm to 80μm, and it requires less than 50ms within the single measurement. Experimental results are presented.

Interference of white light in tandem configuration of birefringent crystal and sensing birefringent fiber

Spectral interference of white-light beams propagating through a tandem configuration of birefringent crystal and sensing birefringent fiber is analyzed theoretically and experimentally. The spectral interference law is expressed analytically under the condition of a Gaussian response function of a spectrometer taking into account the dispersion of birefringence in the crystal and in the fiber. Two types of spectral interferograms are modeled knowing dispersion characteristics of the sensing fiber and using a quartz crystal of the positive or a calcite crystal of the negative birefringence. The theoretical analysis is accompanied by two experiments employing a highly birefringent fiber and a birefringent quartz crystal of two suitable thicknesses. Within both experiments the spectral interference fringes are resolved in accordance with the theory with phases dependent on the fiber length.

Phase unwrapping of interference fringes using recursion and iteration algorithms of phase automatic frequency control

This paper presents the results of a study of methods for reconstructing the phase of the spectral interference fringes (the groove spectrum) obtained by means of a low-coherence interferometer and a spectrometer, based on the use of discrete methods of phase automatic frequency control for cases of randomly varying and a priori unknown fringe parameters. The unwrapped phase of the spectral interference fringes characterizes the group optical path difference, and this makes it possible to investigate the dispersion properties of materials and to measure the displacement of objects. © 2003 Optical Society of America

Slightly dispersive white-light spectral interferometry to measure distances and displacements

Summary A new spectral-domain interferometric technique of measuring distances and displacements is realized when the effect of low dispersion in a Michelson interferometer, which comprises two coated plates of a beam splitter and a compensator, is known and the spectral interference fringes are resolved over a wide wavelength range. First, processing the recorded spectral interferograms by an adequate method, the unmodulated spectrum, the spectral fringe visibility function and the unwrapped phase function are obtained. Then, knowing the dispersion relation for the fused-silica plates, the ambiguity of the unwrapped phase function is removed and the thickness of fused silica and the nonlinear phase function due to the effect of the coatings are determined by using a new procedure. It is based on the linear dependence of the overall optical path difference between interferometer beams on the refractive index of fused silica. Once the thickness and the nonlinear phase function are known, the positions of the interferometer mirror are determined precisely by a least-squares fitting of the theoretical spectral interferograms to the recorded ones.

Dispersive white-light spectral two-beam interference under general measurement conditions

Summary Spectral-domain interference of two beams from a white-light source is analysed theoretically and experimentally when the effects of both dispersion in an interferometer and the response function of a spectrometer are taken into account. The spectral interference law is expressed analytically under the condition of a Gaussian response function of a spectrometer. The theoretical analysis is accompanied by experiments employing a dispersive Michelson interferometer and a low-resolution spectrometer. Two experiments with different amounts of dispersion in the Michelson interferometer are realized giving rise to the spectral interference fringes resolved only in the vicinity of the so-called equalization wavelength, at which the group optical path difference between interfering beams is zero. The recorded spectral interferograms are in good agreement with the theoretical ones, which are modelled knowing dispersion in the interferometer and the bandpass of the spectrometer.

Evaluation of spectral modulated interferograms using a Fourier transform andthe iterative phase-locked loop method

Spectral modulated interference fringes are observed in the form of the periodicalmodulation of a broadband spectrum at the output of an interferometer providedwith a subsequent spectrometer. The group optical path difference ofinterfering light waves corresponding to the distance from the surfaceto be measured is characterized by the spectral fringe phase function.To recover the phase functions, a standard, Fourier-transform method,or parametric methods like a phase-locked loop (PLL) method, can beused. In the former case, the Fourier spectrum in the wavelength domainis computed and filtered out to obtain the reference spectrum and theoverall phase information using a phase-unwrapping algorithm. In thelatter case, the fringe phase deviations are traced dynamically in theindependent variable domain, i.e. in the wavelength domain when thePLL method is applied to spectral interferometry. The PLL method wasused to demodulate spectral fringes iteratively. A spectral fringe signalwith a priori unknown carrier fringe frequency is considered and at thefirst iteration step a fringe phase equal to zero is supposed. The seconditeration takes the demodulated phase found from the first iteration etc. As aresult, the unwrapped phase function of the spectral fringes is found.