Refractive index determination of transparent samples by noniterative phase retrieval

We present a simple method to determine the refractive indices of transparent specimens. The refractive index of an object under investigation is received by evaluating the optical path difference introduced by the object, while taking into account geometric parameters. The optical path difference that corresponds to the phase distribution is obtained by a noninterferometric, noniterative phase retrieval method based on Green's functions. It will be shown that this technique is a highly accurate and quantitative method for refractive index determination.     

Complex refractive-index measurement based on Fresnel's equations and the uses of heterodyne interferometry

The phase difference between s and p polarization of the light reflected from a material is used for measuring the material's complex refractive index. First, two phase differences that correspond to two different incidence angles are measured by heterodyne interferometry. Then these two phase differences are substituted into Fresnel's equations, and a set of simultaneous equations is obtained. Finally, the equations are solved by use of a personal computer by a numerical analysis technique, and the complex refractive index of the material can be estimated.     

Phase geographical map for determining the material type of a right-angle prism

A phase geographical map for determining a right-angle prism is presented. The proposed method is based on total-internal-reflection effects and chromatic dispersion. Under the total-internal-reflection condition, the phase difference between the S and P polarizations, as a function of the wavelength and refractive index, can be extracted and measured using heterodyne interferometry. Various wavelengths correspond to various refractive index values. The proposed map is convenient in ensuring the prism material using a specific V number. The method has the following merits: high stability, ease of operation, and rapid measurement.     

Determination of the refractive index and the chiral parameter of a chiral solution based on chiral reflection equations and heterodyne interferometry

This study develops a method for determining the chiral parameter and the refractive index of an isotropic chiral medium using chiral reflection equations and critical angle phenomena. Linearly polarized light propagates back and forth in a parallelogram prism between two parallel compartments with chiral solutions. A beam splitter then divides the light that emerges from the prism into a reflected light beam and a transmitted light beam. The two beams pass through a compensator and an analyzer, respectively, to cause phase compensation and interference of s and p polarizations. The phase difference between the two interference signals are initially optimized by a suitable optical arrangement and subsequently measured by heterodyne interferometry. Additionally, the refractive index of the solution is determined from the critical angle that occurred at the discontinuity of the phase difference between the two interference signals. These results are substituted into derived equations to calculate the chiral parameter. The approach has the merits of both common-path interferometry and heterodyne interferometry.     

Quantitative phase and refractive index analysis of optical fibers using differential interference contrast microscopy

A systematic and straightforward image processing method to extract quantitative phase and refractive index data from weak phase objects is presented, obtained using differential interference contrast (DIC) microscopy. The method is demonstrated on DIC images of optical fibers where a directional integration routine is applied to the DIC images to extract phase and refractive index information using the data obtained across the whole DIC image. By applying the inverse Abel transform to the resultant phase images, an accurate refractive index profile is obtained. The method presented here is compared to the refracted near-field technique, typically used to obtain the refractive index profile of optical fibers, and shows excellent agreement. It is concluded that through careful image processing procedures, DIC microscopy can be successfully implemented to obtain quantitative phase and refractive index information of optical fibers.     

Digital Hilbert transformation for separation measurement of thicknesses and refractive indices of layered objects by use of a wavelength-scanning heterodyne interference confocal microscope

A wavelength-scanning heterodyne interference confocal microscope quickly accomplishes the simultaneous measurement of the thickness and the refractive index of a sample by detection of the amplitude and the phase of the interference signal during a sample scan. However, the measurement range of the optical path difference (OPD) that is obtained from the phase changes is limited by the time response of the phase-locked loop circuit in the FM demodulator. To overcome this limitation and to improve the accuracy of the separation measurement, we propose an OPD detection using digital signal processing with a Hilbert transform. The measurement range is extended approximately five times, and the resolution of the OPD is improved to 5.5 from 9 microm without the electrical noise of the FM demodulator circuit. By applying this method for simultaneous measurement of thickness and the refractive index, we can measure samples 20-30-microm thick with refractive indices between 1 and 1.5.     

Method for measuring the refractive index and the thickness of transparent plates with a lateral-shear,wavelength-scanning interferometer

A new method for measuring simultaneously the thickness and the refractive index of a transparent plate is proposed. The method is based on a simple, variable lateral-shear, wavelength-scanning interferometer. To achieve highly accurate measurements of both refractive index n and thickness d we use several means to determine these two quantities. We finely tune a distributed-feedback diode laser light source to introduce a phase shift into the detected signal, whereas we make the sample rotate to produce variable lateral shearing. Phase shifting permits precise determination of the optical thickness, nd, whereas refractive index n is obtained from the retrieved phase of the overall interference signal for all incidence angles.     

A new refractometer by combining a variable length vacuum cell anda double-pass Michelson interferometer

A new refractometer with a variable length vacuum cell has been developed to eliminate errors caused by deformations in optical windows of the cell. The refractive index of air is determined by measuring the changes in the optical path difference between the air of interest and a vacuum as a function of the changes in the cell length. An optical phase modulation technique and a dark fringe detection method are used to obtain a high resolution in measuring the optical path difference by a double-pass Michelson interferometer. A combined standard uncertainty of 5×10^-9 in the measurement of the refractive index of air has been achieved     

Influence of internal refractive index gradients on size measurements of spherically symmetric particles by phase Doppler anemometry

A model based on geometric optics for predicting the response of interferometric (phase Doppler) instruments for size measurements of particles with radially symmetric but inhomogeneous internal refractive index profiles is developed. The model and results are important for applications in which heat or mass transfer from the particles or droplets is significant, for example, in liquid-fuel combustion. To quantify the magnitude of potential bias errors introduced by the classical assumption of uniform internal properties on phase Doppler measurements, we compute calibration curves for a sequence of times during the evaporation of a decane droplet immersed in an environment of T = 2000 K and p = 10 bars. The results reveal considerable effects on the relation between phase difference and droplet diameter caused by the refractive index gradients present. The model provides an important tool to assess sizing uncertainties that can be expected when applying conventional (based on uniform properties) phase Doppler calibration curves in spray combustion and similar processes.     

Optical fiber design and the trapping of Cerenkov radiation

Cerenkov radiation is generated in optical fibers immersed in radiation fields and can interfere with signal transmission. We develop a theory for predicting the intensity of Cerenkov radiation generated within the core of a multimode optical fiber by using a ray optic approach and use it to make predictions of the intensity of radiation transmitted down the fiber in propagating modes. The intensity transmitted down the fiber is found to be dominated by bound rays with a contribution from tunneling rays. It is confirmed that for relativistic particles the intensity of the radiation that is transmitted along the fiber is a function of the angle between the particle beam and the fiber axis. The angle of peak intensity is found to be a function of the fiber refractive index difference as well as the core refractive index, with larger refractive index differences shifting the peak significantly toward lower angles. The angular range of the distribution is also significantly increased in both directions by increasing the fiber refractive index difference. The intensity of the radiation is found to be proportional to the cube of the fiber core radius in addition to its dependence on refractive index difference. As the particle energy is reduced into the nonrelativistic range the entire distribution is shifted toward lower angles. Recommendations on minimizing the quantity of Cerenkov light transmitted in the fiber optic system in a radiation field are given.     

Effect of interfacial refractive index on optical molecular orientation measurements

The sensitivity of optical molecular orientation measurements to assumptions regarding thin film refractive index was investigated. Specifically, the influence of the interfacial refractive index on second harmonic generation (SHG) and linear dichroism measurements made in a total internal reflection (TIR) geometry was probed for five distinct molecular systems. The five molecular thin films ranged from weakly adsorbed species in equilibrium with solution to covalently bound molecules. Polarization data from the two techniques were fit using a range of assumed interfacial refractive indices. Surprisingly, a linear relationship between the difference in calculated apparent orientation angle and the difference in solvent-prism refractive index was observed. The trend indicates that for a TIR geometry, the error introduced by the thin film refractive index is negligible when the difference in solvent and prism refractive indices is less than approximately 0.08. However, there are clearly cases, such as a glass/air interface, in which assumptions regarding the thin film refractive index can result in significant error in the extracted orientation angle.     

Non-interferometric methods of phase estimation for application in optical tomography

Abstract

We describe here two non-interferometric methods for the estimation of the phase of transmitted wavefronts through refracting objects. The phase of the wavefronts obtained is used to reconstruct either the refractive index distribution of the objects or their contours. Refraction corrected reconstructions are obtained by the application of an iterative loop incorporating digital ray tracing for forward propagation and a modified filtered back projection (FBP) for reconstruction. The FBP is modified to take into account non-straight path propagation of light through the object. When the iteration stagnates, the difference between the projection data and an estimate of it obtained by ray tracing through the final reconstruction is reconstructed using a diffraction tomography algorithm. The reconstruction so obtained, viewed as a correction term, is added to the estimate of the object from the loop to obtain an improved final refractive index reconstruction.     

Optical phase contrast measurement of ultrasonic fields

This report describes an optical phase contrast imaging technique for the measurement of wide bandwidth ultrasound fields in water. In this method, a collimated optical wavefront (λ_l = 810 nm) impinges on a wide bandwidth ultrasound pulse. The method requires that refractive index perturbations induced by the ultrasound field be sufficiently small. Specifically, on exit from the acoustic field, the phase of the optical wavefront must be proportional to the ray sum of local density taken in the direction of propagation of the incident optical wave. A similar restriction is placed on the dimensions of the ultrasound pulse. Repeated measurement of this phase as the ultrasound field is rotated through 180° about an axis normal to the direction of propagation of the incident optical wave generates the Radon transform of the ultrasonically induced refractive index perturbation. Standard tomographic reconstruction techniques are used to reconstruct the full three-dimensional refractive index perturbation. A simple two-lens imaging system and an optical signal processing element from phase contrast microscopy provide a method of directly measuring an affine function of the desired optical phase for small optical phase shifts. The piezo- and elasto-optic coefficients (the first partial derivatives of refractive index with respect to density and pressure) relate refractive index to density and pressure via a linear model. The optical measurement method described in this paper provides a direct, quantitative measurement of the piezo- and elasto-optic coefficients (from the density or pressure fields)     

Kramers-Kronig analysis of infrared reflection spectra with perpendicular polarization

The application of Kramers-Kronig analysis for reflection spectra from a single interface with perpendicular (s) polarization has been studied theoretically with regard to a phase correction term. The errors in phase shift and complex refractive index obtained by the use of Kramers-Kronig analysis have been examined for such techniques as external, internal, and total internal reflection spectroscopies by the use of spectral simulation and the complex refractive index based on dispersion theory. The advantages and disadvantages of the various measurement techniques used to obtain the complex refractive index of a sample material have been compared. It is concluded that the external reflection technique can be used until the sample thickness becomes too thin to provide the edge shape necessary to avoid the detection of reflection from the back surface. The total internal reflection technique should be used only for a thin-film sample because knowledge of the refractive index at some frequency is required and bcause this technique may yield larger errors than the other techniques in the complex refractive index obtained by the use of Kramers-Kronig analysis.     

Probe transit effect in interferometry of fast moving samples

When a fast moving transparent sample (with a speed close to c) is probed with a laser pulse, some artifacts can occur from data analysis. These artifacts are connected to the transit time of the probe through the sample and can mask the presence of a steep gradient of refractive index in the sample. We study this problem in the case of interferometry. In fact, the problem can affect the femtosecond interferometry of the media under ultrafast ionization by a propagating laser pulse. Two algorithms are introduced: the first based on the phase difference and the second based on visibility. Both algorithms allow for the reconstruction, under suitable assumptions, of an approximated refractive index profile from the distorted fringes.     

High quality ZnO layers with adjustable refractive indices for integrated optics applications

Thin ( 1 μm) crystalline ZnO films with a good optical quality and good (0002) texture are grown under two considerably different process parameter sets using a r.f. planar magnetron sputtering unit. The optical parameters of the two corresponding ZnO layers are distinctly different: high refractive index ( 2.0 at λ = 632.8 nm) ZnO films resembling the single crystal form, and ZnO films with considerably lower (typical difference 0.05) refractive indices. The refractive index of the latter ZnO layers is adjustable ( 1.93–1.96 at λ = 632.8 nm) through the process deposition parameters. It is shown that the difference in refractive index between the two ZnO types most probably results from a difference in package density of the crystal columns. The optical waveguide losses of both ZnO types are typically 1–3 dB/cm at λ = 632.8 nm, however the low refractive index ZnO layers need a post-deposition anneal step to obtain these values. The two ZnO types are used to fabricate optical channel-and slab waveguides with small refractive index differences.     

微纳Taper光纤干涉传感器的折射率测量理论研究

利用微纳taper光纤干涉方程和微纳光纤传输模式函数关系,建立了微纳taper光纤干涉波长随环境折射率变化的数学模型,指出微纳taper光纤干涉波长的响应规律由基模高阶模有效折射率差、色散因子和环境折射率3个因素所决定.详细研究了微纳taper光纤传感器的灵敏度变化规律,结果表明,传感器的灵敏度随光纤半径变小而急速增大,并随环境折射率的增大而非线性增加,而且探测波长越长,其灵敏度越大.     

Three-dimensional phase imaging with the intensity transport equation

Phase can be retrieved from intensity measurements with the intensity transport equation. Three-dimensional image formation of weak phase objects based on this method is investigated. It is shown that, although the refractive index of a thin object can be measured, the three-dimensional variation of refractive index of an arbitrary object cannot, in general, be reconstructed, as spatial frequencies with a zero-axial component are not detected. However, this may not be a problem if regions with known refractive index are present in the sample.     

Gold nanorods as nanotransducers to monitor the growth and swelling of ultrathin polymer films

In this work, we demonstrate that plasmonic nanostructures can be employed as nanoscale transducers to monitor the growth and phase transitions in ultrathin polymer films. In particular, gold nanorods with high refractive index sensitivity (~150 nm/refractive index unit (RIU)) were employed to probe the growth and swelling of polyelectrolyte multilayers (PEM). By comparing the wavelength shift and extinction intensity increase of the localized surface plasmon resonance (LSPR) of the gold nanorods coated with PEM in air and water, the swelling of PEM was estimated to be 26% ± 6%. The swelling was quantitatively confirmed with independent thickness measurement of PEM in dry and swollen states using AFM. The deployment of shape-controlled metal nanostructures with high refractive index sensitivity represents a novel and facile approach for monitoring the phase transition in polymers with nanoscale resolution.     

Accuracy of the Double Variation Technique of Refractive Index Measurement

Errors in the double variation teclinique of refractive index measurement are analyzed using a new approach. The ability to measure matching wavelength is characterized, along with the effect on the calculated refractive index. Refractive index accuracy and precision are very dependent on the specifics of each calibration set, particularly the difference in dispersion between the liquid and solid. Our best precision (±1 or 2×10⁻⁴) is attained only when the difference in dispersion between liquid and solid is small, and is dependent on an individual operator’s ability to perceive changes in relief. This precision is impossible to achieve for the other glass/liquid combinations, where we are limited by a precision of approximately 1 nm in the selection of matching wavelength. A bias in the measurement of matching wavelength exists that affects the accuracy of the calculated refractive indices. The magnitude of the bias appears to be controlled by the bandpass of the graded interference filter. The errors in refractive index using a graded interference filter with a bandpass of 30 nm FWHM (full width at half maximum intensity) are an order of magnitude larger than the errors using a filter with a bandpass of 15 nm FWHM.