White-light Spectral Interferometry Research Articles

White-Light Spectral Interferometry for Characterizing Inhomogeneity in Solutions and Nanocolloids.

We demonstrate the use of white-light spectral interferometry as an effective technique involving only linear optical interactions and a partially coherent light source to measure the complex transmission response function of optical resonance and to determine the corresponding variation in the refractive index relative to a reference. We also discuss experimental arrangements to increase the accuracy and sensitivity of the technique. The superiority of the technique over single-beam absorption measurements is demonstrated by the accurate determination of the response function of the chlorophyll-a solution. The technique is then applied to chlorophyll-a solutions of varying concentrations and gold nanocolloids to characterize inhomogeneous broadening. Results on the inhomogeneity of gold nanocolloids are also supported by transmission electron micrographs, showing distributions of the size and shape of the constituent gold nanorods.

Measuring the refractive index of a methanol - water mixture according to the wavelength

The refractive index of the methanol-water mixture depending on the wavelength at different concentrations was determined by our experimental method using a Michelson interferometer system. A comparative study of Gladstone-Dale, Arago–Biot and Newton relations for predicting the refractive index of a liquid has been carried out to test their validity for the methanol-water mixture with the different concentrations 30%, 40%, 50%, 60%, 80%, and 100%. The comparison shows the good agreement between our experimental results and the results in the expressions studied over the wavelength range approximately from 450 to 850 nm. Full Text: PDF ReferencesS. Sharma, P.B. Patel, R.S. Patel, "Density and Comparative Refractive Index Study on Mixing Properties of Binary Liquid Mixtures of Eucalyptol with Hydrocarbons at 303.15, 308.15 and 313.15 K", E-Journal of Chemistry 4(3), 343 (2007). CrossRef A. Gayathri, T. Venugopal, R. Padmanaban, K. Venkatramanan, R. Vijayalakshmi, "A comparative study of experimental and theoretical refractive index of binary liquid mixtures using mathematical methods", IOP Conf. Series: Materials Science and Engineering 390, 012116 (2018). CrossRef A. Jahan, M.A. Alam, M.A.R. Khan, S. Akhtar, "Refractive Indices for the Binary Mixtures of N, N-Dimethylformamide with 2-Butanol and 2-Pentanol at Temperatures 303.15 K, 313.15 K, and 323.15 K", American Journal of Physical Chemistry 7(4), 55 (2018). CrossRef N. An, B. Zhuang, M. Li, Y. Lu, Z. Wang, "Combined Theoretical and Experimental Study of Refractive Indices of Water–Acetonitrile–Salt Systems", J. Phys. Chem. B 119(33), 10701 (2015). CrossRef M. Upadhyay, S.U. Lego, "Refractive Index of Acetone-Water mixture at different concentrations", American International Journal of Research in Science, Technology, Engineering & Mathematics 20(1), 77 (2017). CrossRef T.H. Barnes, K.Matsumoto, T. Eiju, K. Matsuda, N. Ooyama, "Grating interferometer with extremely high stability, suitable for measuring small refractive index changes", Appl. Opt. 30, 745 (1991). CrossRef B. W. Grange, W. H. Stevenson, R. Viskanta, "Refractive index of liquid solutions at low temperatures: an accurate measurement", Applied Optics 15(4), 858 (1976). CrossRef P. Hlubina, "White-light spectral interferometry with the uncompensated Michelson interferometer and the group refractive index dispersion in fused silica", Optics Communications 193(1-6), 1 (2001). CrossRef P. Hlubina, W. Urbanczyk, "Dispersion of the group birefringence of a calcite crystal measured by white-light spectral interferometry", Meas. Sci. Technol. 16(6), 1267 (2005). CrossRef P. Hlubina, D. Ciprian, L. Knyblová, "Direct measurement of dispersion of the group refractive indices of quartz crystal by white-light spectral interferometry", Optics Communications 269(1), 8 (2007). CrossRef S. R. Kachiraju, D. A. Gregory, "Determining the refractive index of liquids using a modified Michelson interferometer", Optics & Laser Technology 44(8), 2361 (2012). CrossRef F. Gladstone, D. Dale, "XXXVI. On the influence of temperature on the refraction of light", Philos. Trans. R. Soc. 148, 887 (1858). CrossRef D.F.J. Arago, J.B. Biot, Mem. Acad. Fr. 15, 7 (1806). CrossRef Kurtz S S and Ward A L J, "The refractivity intercept and the specific refraction equation of Newton. I. development of the refractivity intercept and comparison with specific refraction equations", Franklin Inst. 222, 563-592 (1936). CrossRef K. Moutzouris, M. Papamichael, S. C. Betsis, I. Stavrakas, G. Hloupis, D. Triantis, "Refractive, dispersive and thermo-optic properties of twelve organic solvents in the visible and near-infrared", Appl. Phys. B 116, 617 (2013). CrossRef S. Kedenburg, M. Vieweg, T. Gissibl, H. Giessen, "Linear refractive index and absorption measurements of nonlinear optical liquids in the visible and near-infrared spectral region", Opt. Mater. Express 2(11), 1588 (2012). CrossRef

Analysis of the synchronous phase-shifting method in a white-light spectral interferometer.

For white-light spectral interferometry, the phase information is usually retrieved via the Fourier transform method and the temporal phase-shifting method. In comparison, the synchronous phase-shifting method can be used to synchronously acquire interferometric signals with good accuracy and reduced noise. Therefore, it has potential for online measurement and is suitable for application in precision industries and for ultrahigh-speed measurement. In this work, a white-light spectral interferometer for synchronous phase shifting based on polarization interference was built, and the two-step phase-shifting algorithm was used to retrieve phase information. A variety of spectral interferometric signals were simulated based on the mathematical model of the two-step phase-shifting algorithm to illustrate the effects of differences in intensity and envelope shape, random noise, and phase-shift error on measurement of the absolute distance. Measurements of the absolute distance were conducted, and they indicated that the system had high accuracy.

Fine, Reversible and Broadband Tuning of the Group Velocity Dispersion of Tapered Silica Fibers in a Thermo-Optic Polymer Matrix

The development of tapered optical fibers embedded in a thermo-optic polymer matrix with reversibly tailored group velocity dispersion is hereby presented. Dispersion measurements for these tapered fibers were performed using white light spectral interferometry. The tapered fibers exhibit reversible thermo-optic group velocity dispersion tuning in both the normal and the anomalous regime in a broad spectral window extending from the E-band to the L-band of the telecommunication laser bandwidth. Group delay dispersion can be controlled thermo-optically within tuning ranges of up to −2230 fs2 in the anomalous and 2090 fs2 in the normal dispersion regime for single tapered fibers. Connecting a few of these polymer-embedded tapered fibers together offers even wider delay ranges that can be reversibly controlled. Thus, the polymer embedded tapers can be used as a versatile and modular dispersion management toolbox with the advantage of seamless integration with standard fiber optic systems. Such a dispersion management toolbox can be of use in the development of cavities for ultrafast fiber lasers and in other applications requiring fine and reversible dispersion control.

Nonlinear phase error analysis of equivalent thickness in a white-light spectral interferometer

Abstract A white light spectral interferometry based on a Linnik type system was established to accurately measure the thin film thickness through transparent medium. In practical work, the equivalent thickness of a beam splitter and the mismatch of the objective lens introduce nonlinear phase errors. Adding a transparent medium also increases the equivalent thickness. The simulation results show that the equivalent thickness has a significant effect on thin film thickness measurements. Therefore, it is necessary to perform wavelength correction to provide a constant equivalent thickness for beam splitters. In the experiments, some pieces of cover glasses as the transparent medium were added to the measured beam and then a standard thin film thickness of 1052.2±0.9 nm was tested through the transparent medium. The results demonstrate that our system has a nanometer-level accuracy for thin film thickness measurement through transparent medium with optical path compensation.

Modeling the Temperature-Dependent Material Dispersion of Imidazolium-Based Ionic Liquids in the VIS-NIR

A thorough analysis of the refractive index of 11 1-alkyl-3-methylimidazolium-based ionic liquids with three different anions, tetrafluoroborate (BF4), bis(trifluoromethylsulfonyl)imide (NTf2), and trifluoromethanesulfonate (OTf), is reported. Refractive indices were estimated, in the temperature interval from 298.15 to 323.15 K, using an Abbe refractometer to determine the value at the sodium D line and white light spectral interferometry to obtain dispersion in the range of wavelengths from 400 to 1000 nm. The first part of the manuscript is focused on the dependence of refractive index with wavelength, temperature, cation alkyl chain length, and anion nature. Once the main features are detailed, and in order to explain the experimental trends, a model for the refractive index is considered where its square is expressed by a single resonance Sellmeier dispersion formula. This formula has two coefficients: the first one identifies the position of the resonance in the spectral axis, and the second one spe...

Single point Linnik white-light spectral microscopic interferometer for surface measurement

According to the requirement for high precision surface measurement in complex situations, a single point Linnik type measuring system with long working distance is built based on white-light spectral interferometry. Five-step phase-shifting algorithm is used to extract accurate phase information in the measuring system. Several experiments are conducted to measure the absolute distance and film thickness, verifying the feasibility of the system. It has been achieved that the system can measure the surface form and film thickness with nanoscale accuracy.

Refractive index retrieval in the UV range using white light spectral interferometry

Continuous refractive index measurement in the UV spectral region and a small part of the Vis region (up to 520 nm) is performed by using white light spectral interferometry. The main limitations of operating in this region are the high dispersion and high absorption. The problems derived from high dispersion are overcome taking the data in several shots, that is, recording several interferograms that must be partially overlapped. Whereas, high absorbers require the use of thinner samples, while still keeping a precise measurement of the sample width. We show the capacity of the technique with well characterized reference materials such as BK7, quartz and deionised water.

Film thickness measurement based on nonlinear phase analysis using a Linnik microscopic white-light spectral interferometer.

Based on white-light spectral interferometry and the Linnik microscopic interference configuration, the nonlinear phase components of the spectral interferometric signal were analyzed for film thickness measurement. The spectral interferometric signal was obtained using a Linnik microscopic white-light spectral interferometer, which includes the nonlinear phase components associated with the effective thickness, the nonlinear phase error caused by the double-objective lens, and the nonlinear phase of the thin film itself. To determine the influence of the effective thickness, a wavelength-correction method was proposed that converts the effective thickness into a constant value; the nonlinear phase caused by the effective thickness can then be determined and subtracted from the total nonlinear phase. A method for the extraction of the nonlinear phase error caused by the double-objective lens was also proposed. Accurate thickness measurement of a thin film can be achieved by fitting the nonlinear phase of the thin film after removal of the nonlinear phase caused by the effective thickness and by the nonlinear phase error caused by the double-objective lens. The experimental results demonstrated that both the wavelength-correction method and the extraction method for the nonlinear phase error caused by the double-objective lens improve the accuracy of film thickness measurements.

Refractive index measurements in absorbing media with white light spectral interferometry

White light spectral interferometry is applied to measure the refractive index in absorbing liquids in the spectral range of 400-1000 nm. We analyze the influence of absorption on the visibility of interferometric fringes and, accordingly, on the measurement of the refractive index. Further, we show that the refractive index in the absorption band can be retrieved by a two-step process. The procedure requires the use of two samples of different thickness, the thicker one to retrieve the refractive index in the transparent region and the thinnest to obtain the data in the absorption region. First, the refractive index values are retrieved with good accuracy in the transparent region of the material for 1-mm-thick samples. Second, these refractive index values serve also to precisely calculate the thickness of a thinner sample (~150 µm) since the accuracy of the methods depends strongly on the thickness of the sample. Finally, the refractive index is recovered for the entire spectral range.

The phase ambiguity in dispersion measurements by white light spectral interferometry

In this work, we address the phase ambiguity in white light spectral interferometry. This ambiguity prevents one from obtaining the refractive index over a broad spectral range with high accuracy. We first determine the error when the refractive index is fitted to a linear combination of power functions. We demonstrate that the error is proportional to wavelength and independent of sample thickness. We show how to reduce the error over the entire spectral band by measuring the spectral phase at the output of the interferometer for some suitable wavelengths as a function of sample orientation.

Initial estimation of thin film thickness measurement based on white light spectral interferometry

White-light interferometry has been extended into the spectral domain for many years. The authors discuss a white light spectral interferometer using a Michelson interferometric objective and spectrometer to measure the film thickness and propose two methods for initial estimation which are based on the frequency of the nonlinear phase and the overall visibility of the spectral signal. Both of the methods are capable of obtaining good, rapid, initial estimates in these measurements: our proposed methods are quicker than the commonly used global algorithms (simulated annealing algorithm and genetic algorithm). In terms of the speed and precision, the proposed methods are suited to in-line, high-speed measurement. In general, when the film thickness is more than 1μm, it is better to use the method based on the nonlinear phase to estimate the initial value, and when the film thickness is <1μm, the method based on overall visibility is more applicable.

Measurement of Step Height Using White Light Spectral Interferometry

The development of micro-nanomanufacturing technology leads to higher requirement for measurement technology, which gives birth to the ultra-precision measurement technology. As a kind of low coherence interferometry technology, spectral interferometry has been proposed. In this paper, the theory and system of white light spectral interferometry were described in detail, and the measurement principle of micro-structure was analyzed. The spectral interference signal was recorded and the phase information was retrieved from it by using five-step phase shifting algorithm, which includes the phase change on reflection from the stucture. So the optical path difference (OPD) can be obtained, which represents the height information. Three methods including slope method, single wavelength method and least square method were discussed based on the theory deduction and the experimental analysis. A step height standard was measured and the results show that this method has a good accuracy.

Ultrabroadband Airy light bullets

We present the measurements of the spatiotemporal impulse responses of two optical systems for launching ultrashort Airy pulses, including ultrabroadband nonspreading Airy beams whose main lobe size remains invariantly small over propagation. First, a spatial light modulator and, second, a custom refractive element with continuous surface profile were used to impose the required cubic phase on the input field. A white-light spectral interferometry setup based on the SEA TADPOLE technique was applied for full spatio-temporal characterization of the impulse response with ultrahigh temporal resolution approaching a single cycle of the light wave. The results were compared to the theoretical model.

White light spectral interferometry as a spectrometer calibration tool.

For this paper, we used a white light interferometer in combination with spectral lamps to perform the wavelength calibration of a dispersive spectrometer. Illuminating the spectrometer with suitable spectral lamps gives the wavelength-pixel number relationship at discrete positions of the spectrometer detector array, and the wavelength-dependent phase difference at the output of the white light interferometer allows for a complete spectral calibration at any point on the detector (i.e., for every wavelength in the spectral range of the spectrometer). The details of this new calibration procedure are discussed, and two practical examples exhibiting the robustness of the method are presented. In addition, certain issues relating to minimizing the number of spectral lines used in the calibration procedure are examined.

Ultrabroadband Airy light bullets

We present the measurements of the spatiotemporal impulse responses of two optical systems for launching ultrashort Airy pulses, incl. ultrabroadband nonspreading Airy beams whose main lobe size remains invariantly small over propagation. First, a spatial light modulator and, second, a custom refractive element with continuous surface profile were used to impose the required cubic phase on the input field. White-light spectral interferometry setup based on the SEA TADPOLE technique was applied for full spatio-temporal characterization of the impulse response with ultrahigh temporal resolution approaching a single cycle of the light wave. The results were compared to the theoretical model.

Surface Plasmon Resonance Sensor Using Spectral Interference

This paper presents a novel surface plasmon resonance (SPR) sensor based on whitelight spectral interferometry. The experimental arrangement employs a white-light source (bandwidth from 350 nm to 1000 nm), a polarizer and a birefringent quartz crystal for SPR excitation. SF10 Kretschmann SPR sensor prism is inserted into the beam path and one measures both the corresponding SPR phase change and reflectivity at a suitable fixed angle of incidence across the visible spectrum. The prism (sensing surface) is coated with gold film of 44 nm nominal thickness and the incident angle is approximately 58 . In our case of the SPR effect, the useful phase information is encoded in the spectral interferogram. Thereby, p- and s-polarized spectra interfere among themselves and the interferograms are obtained by using an analyzer when only p-polarized waves are affected by the SPR effect. Spectral interference signals are then used in corresponding phase retrieval [1]. In order to calculate the SPR induced differential phase change, a windowed Fourier transform (WFT) [2] was adopted to extract the phases from two spectral interferograms, one corresponding to the reference material and the other corresponding to the analyte. The pilot measurements were tested with water as an analyte and air as a reference material and the measurement results were compared with the results of theoretical models. The first results show good agreement between a calculated resonance wavelength and a resonance wavelength determined from reflectivity measurements. The second results show good agreement for phase change measurements. The proposed technique offers a much simpler experimental arrangement than was recently presented in a paper [3].

Measuring the suppression of ultrashort pulses into Airy-Bessel light bullets with almost single-cycle temporal resolution

We have achieved ~3 fs and ~3 μm resolutions for full spatio-temporal characterization of impulse responses of optical systems using a white-light spectral interferometry set-up and demonstrate how a circular diffraction grating temporally focuses an Airy-Bessel wave-packet.

In-Process Fast Surface Measurement Using Wavelength Scanning Interferometry

A wavelength scanning interferometry system for fast areal surface measurement of micro and nano-scale surfaces which is immune to environmental noise is introduced in this paper. It can be used for surface measurement of discontinuous surface profiles by producing phase shifts without any mechanical scanning process. White light spectral scanning interferometry, together with an acousto-optic tuneable filtering technique, is used to measure both smooth surfaces and those with large step heights. An active servo control system is used to serve as a phase compensating mechanism to eliminate the effects of environmental noise. The system can be used for on-line or in-process measurement on a shop floor.

Temporal focusing of ultrashort pulsed Bessel beams into Airy–Bessel light bullets

We present measurements of the impulse response of a circular phase diffraction grating in dependence of the field point location behind it. These measurements were carried out using a white-light spectral interferometry set-up, which employs photonic crystal fibers in both the signal and reference arms, and achieves a few micron spatial and almost one-wave-cycle temporal resolution. Our study shows that the grating as a simple and robust single-element optical device (i) suppresses the material-induced spread of ultrashort pulses, (ii) thereby generates the Airy–Bessel light bullets, and (iii) enables temporal focusing of the pulses at the prescribed propagation depth.