Bernard Drevillon

General and self-consistent method for the calibration of polarization modulators, polarimeters, and Mueller-matrix ellipsometers

Calibration of polarization-state generators (PSGs), polarimeters, and Mueller-matrix ellipsometers (MMEs) is an important factor in the practical use of these instruments. A new general procedure, the eigenvalue calibration method (ECM), is presented. It can calibrate any complete MME consisting of a PSG and a polarimeter that generate and measure, respectively, all the states of polarization of light. In the ECM, the PSG and the polarimeter are described by two 4 x 4 matrices W and A, and their 32 coefficients are determined from three or four measurements performed on reference samples. Those references are smooth isotropic samples and perfect linear polarizers. Their optical characteristics are unambiguously determined during the calibration from the eigenvalues of the measured matrices. The ECM does not require accurate alignment of the various optical elements and does not involve any first-order approximation. The ECM also displays an efficient error control capability that can be used to improve the MME behavior. The ECM is illustrated by an experimental calibration, at two wavelengths (458 and 633 nm), of a MME consisting of a coupled phase modulator associated with a prism division-of-amplitude polarimeter.

Optimized Mueller polarimeter with liquid crystals

We demonstrate a Mueller polarimeter in which the polarization-state generator and analyzer are both composed of a linear polarizer and two liquid-crystal variable retarders. The polarimeter is designed to optimize the accuracy of the final results by minimization of the condition numbers of the modulation and analysis matrices. The polarimeter calibration, a difficult task by conventional procedures, is achieved easily by use of the eigenvalue method of Compain et al. [Appl. Opt. 38, 3490 (1999)]. The overall polarimeter performance is tested with a linear polarizer at various angles and a compensator at various retardations.

Mueller polarimetric imaging system with liquid crystals.

We present a new polarimetric imaging system based on liquid-crystal modulators, a spectrally filtered white-light source, and a CCD camera. The whole Mueller matrix image of the sample is measured in approximately 5 s in the transmission mode. The instrument design, together with an original and easy-to-operate calibration procedure, provides high accuracy over a wide spectral range (500-700 nm). This accuracy has been assessed by measurement of a linear polarizer at different orientations and a thick wedged quartz plate as an example of a partially depolarized retarder. Polarimetric images of a stained hepatic biopsy with significant fibrosis have been taken at several wavelengths. The optical properties of Picrosirius Red stained collagen (diattenuation, retardance, and polarizance) have been measured independently from each other between 500 and 700 nm.

Phase-modulated Mueller ellipsometry characterization of scattering by latex sphere suspensions

Phase-modulated Mueller ellipsometry (PMME) is used to probe scattering by suspensions of polystyrene latex spheres, with particle diameters ranging from 400 nm to 3 microm. PMME allows simultaneous measurement of the 16 coefficients of the Mueller matrix. Furthermore PMME measurements can easily be carried out owing to a calibration procedure implemented in a scattering configuration. The measurements performed on low concentrations show good agreement with Mie theory. Moreover size distribution could be obtained with a least-squares method based on a genetic fit algorithm. Experimental evidence of multiple scattering on PMME measurements is also presented.

Full-field optical coherence tomography with thermal light

A simple optical coherence tomography system has been developed based on a white-light Linnik interferometric microscope with its reference mirror mounted on a piezoelectric translator. The geometrical extension of the optics allows efficient illumination of this device with a low-power (3-W) light bulb, yielding full-field interferometric images at 50 Hz with a fast CCD camera. Owing to the very broad spectral width of the light source and of the camera response, we achieved axial resolutions equal to 1.1 microm in free space and 0.7 microm through a standard microscope cover plate. Tomographic images of an epithelial cell smear and of an hematological sample are shown.

Application of Mueller polarimetry in conical diffraction for critical dimension measurements in microelectronics.

Fast and efficient metrology tools are required in microelectronics for control of ever-decreasing feature sizes. Optical techniques such as spectroscopic ellipsometry (SE) and normal incidence reflectometry are widely used for this task. In this work we investigate the potential of spectral Mueller polarimetry in conical diffraction for the characterization of 1D gratings, with particular emphasis on small critical dimensions (CDs). Mueller matrix spectra were taken in the visible (450-700 nm) wavelength range on a photoresist grating on a Si substrate with 70/240 nm CD/period nominal values, set at nine different azimuthal angles. These spectra were fitted with a rigorous coupled-wave analysis (RCWA) algorithm by using different models for the grating profile (rectangular and trapezoidal, with or without rounded corners). A detailed study of the stability and consistency of the optimal CD values, together with the variation of the merit function (the mean square deviation D2) around these values, clearly showed that for a given wavelength range, this technique can decouple some critical parameters (e.g., top and bottom CDs, left and right sidewall projections) much more efficiently than the usual SE.

Broadband division-of-amplitude polarimeter based on uncoated prisms

A broadband division-of-amplitude polarimeter (DOAP) is presented. It can provide the real-time measurement of any state of polarization of light, described by its Stokes vector, in large spectral windows. The light is split first into two beams by a prism and then into four beams by means of any polarizer device that will separate the two linear orthogonal states of polarization. Finally, the Stokes vector is directly deduced from the four measured intensities. To avoid interference effects, the splitting of light into four beams is induced only by refractive-index contrast effects between semi-infinite media that are weakly dependent on the wavelength. An experimental setup working from 0.4 to 2 mum is described. It provides similar sensitivities for all the states of polarization, and its characteristics are constant, on a scale of a few percent, within the spectral window. Calibrations performed at 458 and 633 nm display good agreement between theoretical and experimental values. The accuracy of the prism DOAP, evaluated by measurement of the Stokes vector produced by a rotating Glan polarizer, is better than 1%. An infrared extension of this polarimeter is also presented.

Approximation of reflection coefficients for rapid real-time calculation of inhomogeneous films

Fast computer algorithms for calculating the reflection coefficients of inhomogeneous films are developed. The applications of such algorithms are aimed at real-time monitoring and control of the growth of gradient index optical coatings. Inhomogeneous films with a refractive index varying along the direction normal to the surface are generally treated by dividing the film into a large number of homogeneous layers and using an iterative or transfer-matrix method to calculate reflectivities. We develop alternative methods. We show that the elements of the transfer matrix and the reflection coefficients can be written in terms of single, double, and higher-dimensional integrals over the films. In most cases it is sufficient to include only the first term, i.e., the single integrals, and the calculation of reflection coefficients is then between 1 and 2 orders of magnitude faster than that for the transfer-matrix and iteration methods. This gives the possibility of real-time determination of optical parameters of inhomogeneous layers for growth monitoring and opens up feedback control.

Infrared ellipsometry study of the thickness-dependent vibration frequency shifts in silicon dioxide films

Spectra of thermally grown amorphous SiO2 (a-SiO2) films upon a silicon wafer with thicknesses ranging from 12 to 647 nm were measured with an infrared phase-modulated ellipsometer. The observed shifts of the transverse-optical- and longitudinal-optical-mode frequencies of the Si—O bond stretching vibration as functions of the films thickness are shown to be pure optical effects. These shifts are described in terms of the classical electromagnetic theory. The characteristic features of this optical phenomenon are discussed in detail. A method for analytical elimination of this thickness-dependent line shift is proposed.

Characterization of bidimensional gratings by spectroscopic ellipsometry and angle-resolved Mueller polarimetry.

We studied two bidimensional square gratings of square holes formed in photoresist layers deposited on silicon wafers, both by classical spectroscopic ellipsometry (1.5-4.5-eV spectral range) at a constant incidence angle (70.7 degrees) and by angle-resolved Mueller polarimetry at a constant wavelength (532 nm). The grating period was 1 microm in both directions, and the nominal hole sizes were 250 and 500 nm, respectively. The ellipsometric spectra were fitted by rigorous coupled-wave analysis simulations with two adjustable parameters, the resist layer thickness and the hole size. These parameters were found to be in good agreement with independent scanning electron microscopy measurements. The experimental angle-resolved Mueller spectra were remarkably well reproduced by the simulations, showing that angle-resolved Mueller polarimetry has a great potential for grating metrology applications.