This paper reports a technique based on spectrally differential measurement for determining the full Mueller matrix of a biological sample through an optical fiber. In this technique, two close wavelengths were used simultaneously, one for characterizing the fiber and the other for characterizing the assembly of fiber and sample. The characteristics of the fiber measured at one wavelength were used to decouple its contribution from the measurement on the assembly of fiber and sample and then to extract sample Mueller matrix at the second wavelength. The proof of concept was experimentally validated by measuring polarimetric parameters of various calibrated optical components through the optical fiber. Then, polarimetric images of histological cuts of human colon tissues were measured, and retardance, diattenuation, and orientation of the main axes of fibrillar regions were displayed. Finally, these images were successfully compared with images obtained by a free space Mueller microscope. As the reported method does not use any moving component, it offers attractive integration possibilities with an endoscopic probe.
We report the main conclusions from an interactive, multidisciplinary workshop on “Polarimetric Techniques and Technology”, held on March 24-28 2014 at the Lorentz Center in Leiden, the Netherlands. The work- shop brought together polarimetrists from different research fields. Participants had backgrounds ranging from academia to industrial RD. Here we provide an overview of polarimetric instrumentation in the optical regime geared towards a wide range of applications: atmospheric remote sensing, target detection, astronomy, biomedical applications, etc. We identify common approaches and challenges. We list novel polarimetric techniques and polarization technologies that enable promising new solutions. We conclude with recommendations to the polarimetric community at large on joint efforts for exchanging expertise.
This work is devoted to a first exploration of Mueller polarimetric imaging for the detection of residual cancer after neoadjuvant treatment for the rectum. Three samples of colorectal carcinomas treated by radiochemotherapy together with one untreated sample are analyzed ex vivo before fixation in formalin by using a multispectral Mueller polarimetric imaging system operated from 500 to 700 nm. The Mueller images, analyzed using the Lu-Chipmann decomposition, show negligible diattenuation and retardation. The nonirradiated rectum exhibits a variation of depolarization with cancer evolution stage. At all wavelengths on irradiated samples, the contrast between the footprint of the initial tumor and surrounding healthy tissue is found to be much smaller for complete tumor regression than when a residual tumor is present, even at volume fractions of the order of 5%. This high sensitivity is attributed to the modification of stromal collagen induced by the cancer. The depolarization contrast between treated cancer and healthy tissue is found to increase monotonously with the volume fraction of residual cancer in the red part of the spectrum. Polarimetric imaging is a promising technique for detecting short-time small residual cancers, which is valuable information for pathological diagnosis and patient management by clinicians.
Healthy human colon samples were analyzed ex vivo with a multispectral imaging Mueller polarimeter operating from 500 to 700 nm in a backscattering configuration with diffuse light illumination impinging on the innermost tissue layer, the mucosa. The intensity and polarimetric responses were taken on whole tissues first and after progressive exfoliation of the outer layers afterwards. Moreover, these measurements were carried out with two different substrates (one bright and the other dark) successively placed beneath each sample, allowing a reasonably accurate evaluation of the contributions to the overall backscattered light by the various layers. For the shorter investigated wavelengths (500 to 550 nm) the major contribution comes from mucosa and submucosa, while for the longer wavelengths (650 to 700 nm) muscular tissue and fat also contribute significantly. The depolarization has also been studied and is found to be stronger in the red part of the spectrum, mainly due to the highly depolarizing power of the muscular and fat layers.
The use of optical metrology techniques for process control is now widespread. These techniques are fast and nondestructive,
allowing higher throughputs than non-optical techniques like electron microscopies or AFM. We present
here new developments using complete Mueller polarimetry in the back focal plane of a microscope objective to
characterize overlay for microelectronic industry. Based on fundamental symmetries in the physics of periodic structures
and polarized light and redundancies in the angle-resolved Mueller images we define estimators which vary linearly with
the overlay. As a result, overlay measurement is sensitive to both the direction and sign of the overlay, and it does not
require any detailed modeling of the target structures, provided two independent targets with known overlay values are
available in close locations on the wafer. Realistic simulations on optimized structures suggest that accuracies in the
order of 1 or 2 nm or better should be achievable. Moreover, with high NA objectives the proposed technique can be
implemented with targets with lateral sizes as small as a few μm. Experimental results of both grating line profiles and
overlay determinations will be presented. The samples, elaborated at LETI, have been accurately characterized by optical
imaging AIM techniques and state-of-the-art AFM. The latest developments on the device itself as well as the
advantages, possibilities and limitations of this new metrology technique will be discussed.
Angle resolved Mueller polarimetry implemented as polarimetric imaging of a back focal plane of a high NA microscope objective has already demonstrated a good potential for CD metrology. Here we present the experimental and numerical results indicating that this technique may also be competitive for the measurements of overlay error δ. A series of samples of superimposed gratings with well controlled overlay errors have been manufactured and measured with the angle resolved Mueller polarimeter. The overlay targets were 20-μm wide. When the overlay error is δ is equal to 0, absolute values of elements of real 4×4 Mueller matrix M are invariant by matrix transposition. Otherwise this symmetry breaks down. Consequently, we define the following overlay estimator matrix as E = |M| − |M|t. The simulations show that matrix element E14 is the most sensitive to the overlay error. The scalar estimator of E14 was calculated by averaging the pixel values over a specifically chosen mask. This estimator is found to vary linearly with δ for overlay values up to 50 nm. Our technique allows entering small overlay marks (down to 5-μm wide). Only one target measurement is needed for each overlay direction. The actual overlay value can be determined without detailed simulation of the structure provided two calibrated overlay structures are available for each direction.
We present Monte Carlo simulations of the backscattering of polarized light by colon tissue in terms of Mueller matrix.
We validated the Monte Carlo code with measurements on aqueous suspensions of polystyrene spheres of different sizes.
In a first instance we have modeled a tissue as a monodisperse scattering medium representing the nuclei in cytoplasm;
then we included a second layer with monodisperse scatterers to represent the most superficial layers (mucosa and
submucosa) while the deeper layers (muscularis and pericolic tissue) were "lumped" into a totally depolarizing
lambertian. These simulations failed to reproduce the Rayleigh type scattering (larger depolarization for circular vs.
linear incident polarization) systematically observed on all experimentally studied tissue samples. This issue has been
solved by modelling tissues as a single layer of bimodal mixtures including large and small scatterers over a lambertian.
Angle resolved Mueller polarimetry implemented as polarimetric imaging of the back focal plane of a high NA
microscope objective has already demonstrated a good potential for CD metrology1. In this paper we present the
experimental and numerical results which indicate that this technique may also be competitive for measurements of the
overlay error δ between two gratings at different levels. Series of samples of superimposed gratings with well controlled
overlay errors have been manufactured and measured with the angle resolved Mueller polarimeter. The overlay targets
were 20 μm wide. When overlay error δ = 0 the absolute value of Mueller matrix elements is invariant by matrix
transposition. This symmetry breaks down when δ ≠ 0. As a result, we can define the following overlay estimator matrix:
Ε = |Μ | - |Μ |t. The simulations show that matrix element E14 is the most sensitive to the overlay error. In the
experiments the scalar estimator of E14 was defined by averaging the pixel values over specifically chosen mask. The
scalar estimator is found to vary essentially linearly with δ for the overlay values up to 50 nm. Our technique allows
entering quite small overlay marks (down to 5 μm wide). The only one target measurement is needed for each overlay
direction. The actual overlay value can be determined without detailed simulation of the structure provided the two
calibrated overlay structures are available for each direction.
In this paper we show the results of multi-spectral Mueller Imaging applied to the analysis of human colon cancer in a
backscattering configuration with diffuse light illumination. The analyzed sample behaves as a pure depolarizer. The
depolarization power, for both healthy and cancerous zones, is lower for linearly than for circularly polarized incident
light for all used wavelengths and increases with increasing wavelength. Based on their visual staging and polarimetric
responses, we chose specific zones which we correlated to the histology of the corresponding cuts. The histological
examination shows that we see a multilayer interaction in both healthy and abnormal zones, if the light penetration depth
is sufficient. The measured depolarization depends on several factors: the presence or absence of tumor, the microscopic
structure of cancer (ratio between cellular density and stroma), its exophytic (budding) or endophytic (penetrating)
nature, its thickness, the degree of cancer penetration in deeper layers and the nature of healthy tissue left under
abnormal layers. These results demonstrate that multi-spectral Mueller imaging can provide useful contrasts for the quick
staging of human colon cancer ex-vivo, with additional information about cancerous zones with different microscopic
structures.
We present a new optical technique using complete Mueller polarimetry in the back focal plane of a microscope
objective to characterize the overlay defects in microelectronics industry. Exploiting the fundamental symmetries in the
physics of periodic structures and polarized light and the redundancies in the angle-resolved images we prove that it is
possible to measure overlay by this fast and non-destructive technique. The simulations of the one-dimensional structures
have shown that the values of a chosen criterion exploiting the off-diagonal coefficients symmetries are proportional to
the values of overlay defects and can reach 0.25 for a 25nm defect. The accuracy of the polarimeter used for this
application becomes even more critical because it is directly linked to the overlay measurement. Beside the redundancies
in the acquired data, the angular resolution allows us also to decouple the information along X and Y directions in the
Fourier space. Due to this the overlay defect can be characterized and decomposed with respect to these two axes.
We show that the proposed new technique is sensitive to both magnitude and sign of the shift. Thus, Mueller polarimetry
in the Fourier space (MPFS) offers more parameters for the process quality control compared with conventional
spectroscopic ellipsometry (SE). It means that MPFS should be more efficient than SE for the overlay characterization
in microelectronic industry.
Subsurface polarimetric (differential polarization, degree of polarization or Mueller matrix) imaging of various targets in
turbid media shows image contrast enhancement compared with total intensity measurements. The image contrast
depends on the target immersion depth and on both target and background medium optical properties, such as scattering
coefficient, absorption coefficient and anisotropy. The differential polarization image contrast is usually not the same for
circularly and linearly polarized light. With linearly and circularly polarized light we acquired the orthogonal state
contrast (OSC) images of reflecting, scattering and absorbing targets. The targets were positioned at various depths
within the container filled with polystyrene particle suspension in water. We also performed numerical Monte Carlo
modelling of backscattering Mueller matrix images of the experimental set-up. Quite often the dimensions of container,
its shape and optical properties of container walls are not reported for similar experiments and numerical simulations.
However, we found, that depending on the photon transport mean free path in the scattering medium, the above
mentioned parameters, as well as multiple target design could all be sources of significant systematic errors in the
evaluation of polarimetric image contrast. Thus, proper design of experiment geometry is of prime importance in order to
remove the sources of possible artefacts in the image contrast evaluation and to make a correct choice between linear and
circular polarization of the light for better target detection.
In this work we report the results of the optical characterization of a periodic grating carried out with a probe spot size
larger than the sample grating "box". The measured depolarizing Mueller matrices resulting from incoherent
superposition of the optical responses of the grating and substrate were filtered by using the eigenvalues decomposition
method. The retrieved Mueller matrices of the grating alone were fitted using rigorous coupled-wave method and the
standard trapezoidal model with three parameters: the middle line-width (CD), the grating depth and the side-wall angle.
The results are shown for all measured azimuthal angles and compared with reference values taken on a similar grating
on the same wafer, in the usual conditions (beam spot inside the grating). The observed stability of the parameters very
closely coincides with the reference grating except for some azimuthal angles, where the grating contributed only 5% of
the signal. The overall dispersion of the parameters is within the few nanometers from the statistical mean value, a
performance comparable to that of standard grating characterizations with the probe beam illuminating only the grating.
In this paper we demonstrate the robustness of the Mueller matrix polarimetry used in multiple-azimuth configuration.
We first demonstrate the efficiency of the method for the characterization of small pitch gratings filling 250 μm wide
square boxes. We used a Mueller matrix polarimeter directly installed in the clean room has motorized rotating stage
allowing the access to arbitrary conical grating configurations. The projected beam spot size could be reduced to 60x25
μm, but for the measurements reported here this size was 100x100 μm. The optimal values of parameters of a trapezoidal
profile model, acquired for each azimuthal angle separately using a non-linear least-square minimization algorithm, are
shown for a typical grating. Further statistical analysis of the azimuth-dependent dimensional parameters provided
realistic estimates of the confidence interval giving direct information about the accuracy of the results. The mean values
and the standard deviations were calculated for 21 different grating boxes featuring in total 399 measured spectra and
fits. The results for all boxes are summarized in a table which compares the optical method to the 3D-AFM. The
essential conclusion of our work is that the 3D-AFM values always fall into the confidence intervals provided by the
optical method, which means that we have successfully estimated the accuracy of our results without using direct
comparison with another, non-optical, method. Moreover, this approach may provide a way to improve the accuracy of grating profile modeling by minimizing the standard deviations evaluated from multiple-azimuths results.
Light depolarization occurs whenever different polarization responses add up incoherently, as it may be the case with inhomogeneous samples. The most convenient technique to characterize such samples is Mueller matrix polarimetry, as it is the only one providing all the relevant information in presence of depolarization. We studied the case of small grating boxes surrounded by bare silicon, in conditions where both the gratings and the substrate were illuminated by the Mueller polarimeter beam. The grating optical response is modeled by using rigorous coupled-waves analysis, and added incoherently to that of the substrate by merely summing the corresponding Mueller matrices. The line width and the depth of the grating as well as the percentage of substrate in irradiated spot area were obtained by fitting the experimental data taken with controlled displacement of the light spot in the boundary region between grating and substrate. Accurate grating parameters could be obtained with the fraction of the spot area within the grating box was larger than 30%. Moreover, these parameters remained relatively constant when this fraction was further decreased to 5%.
The potential of spectroscopic Mueller polarimetry for the dimensional characterization of periodic structures has already been discussed in several instances. With respect to standard scatterometry; the added value of the technique is related to the information contained in the 16 elements of the Mueller matrix, while usual scatterometry provides only two. The additional information can prove useful to decorrelate dimensional or optical parameters, and to assess the adequacy of the model describing the profiles to be reconstructed: if the model is adequate, the optimal values of the dimensional parameters must remain stable when the measurement conditions, and thus the input data, are varied.
This issue has been addressed for a series of 1D gratings etched in bulk Si and characterized by a spectroscopic polarimeter operating in the visible (Horiba Jobin Yvon MM-16), as well as CD-SEM and state-of-the art CD-AFM. With the usual lamellar or trapezoidal models both the CD and thickness values exhibit up to 10 nm systematic variations with measurement conditions. In contrast, with an original model taking into account the non-flatness of the open areas between adjacent lines the parameters become consistent to within 2 nm, well below typical tool-to-tool offsets. The corresponding profiles are also compatible with the CD-AFM images.
Spectroscopic Mueller polarimetry may provide a useful alternative to standard spectroscopic ellipsometry (SE) for the
dimensional characterization of periodic structures, as it provides 16 quantities instead of 2 for SE. We present a detailed
experimental comparison of the results provided by conventional scatterometry (0.7 - 5 eV) spectral range), Mueller
polarimetry in the visible (450 - 825 nm), electron microscopy (top CD-SEM and cross section) and state-of-the-art CDAFM
(Veeco X3D). This last instrument was considered as the best reference currently available. The samples were 1D
gratings etched in bulk Si, with 150 and 250 nm nominal CDs and several pitches for each CD. SE spectra were taken at
zero azimuthal angles (i.e. with the grooves perpendicular to the incidence plane), as it is usually done with standard
scatterometers, while Mueller spectra were measured at all azimuths in steps of 5°, allowing significant consistency tests
by comparing the results of the corresponding fits. Both techniques provided CD values in agreement with AFM and
CD-SEM data to within 5 nm, comparable to the AFM precision. Grating thickness and sidewall angle (SWA) were best
determined by Mueller polarimetry at 90° azimuth, while in the usual zero azimuth configuration, SWA was typically
underestimated by several degrees.
Modeling of optical properties of nanogratings (sub-wavelength gratings) is of scientific and technological interests
for (i) application of nanogratings as new artificial effective materials with unusual optical properties and
(ii) application in non-destructive optical testing of nanogratings using optical spectroscopic ellipsometry and
polarimetry. This paper deals with anisotropic lamellar nanogratings described by Effective Medium Approximation
(EMA). Analytical formulae for effective medium optical parameters of nanogratings from arbitrary
anisotropic materials are derived using approximation of zero-order diffraction mode. The method is based on
Rigorous Coupled Wave Analysis (RCWA) combined with proper Fourier factorization method. Good agreement
between EMA and the rigorous model is observed, where slight differences are explained by the influence
of higher Fourier harmonics in the nanograting. Analytical spectral formulae for ordinary and extraordinary
effective optical functions are derived for nanogratings consisting of material described by Sellmeier, damped
harmonic oscillator, and Drude formulae. Spectral origin for birefringence of dielectric nanogratings and linear
dichroism for absorbing ones is discussed.
The spectroscopic Mueller polarimetry in conical diffraction was applied for the metrological characterization of
the one-dimensional (1D) holographic gratings, used for the fabrication of nanoimprint molding tool. First we
characterized the master grating that consists of patterned resist layer on chromium-covered glass and then we
studied replicated diffraction grating made of nickel. The experimental spectra of Mueller matrix of both samples
taken at different azimuthal angles were fitted with symmetric trapezoidal model. The optimal values of gratings
critical dimensions (CDs) and height were confirmed by atomic force microscopy (AFM) measurements. The
calculated profiles of corresponding master and replica gratings are found to be complementary. We showed that
Mueller polarimetry in conical diffraction, as a fast and non-contact optical characterization technique, can provide
the basis for the metrology of the molding tool fabrication step in the nanoimprint technique.
A new Mueller polarimeter based on liquid crystals and a microscope objective is presented, for the characterization of
diffraction gratings in a conical diffraction mounting. Fast measurements of complete Mueller matrices over a range of
polar angles (0-56°) and azimuthal angles (0-360°) are achieved without mechanical movements. The polarization state
generator and analyzer make use of nematic variable retarders. The angular range is achieved through focalization of
light over the measured sample with a microscope objective with a high numerical aperture and imaging of the objective
back Fourier plane on a CCD. Results on isotropic samples and diffraction gratings are shown.
We used full Mueller polarimetry in conical diffraction geometries to characterize 1D holographic optical gratings etched in bulk silica with a patterned photoresist layer. We studied four different samples corresponding to different stages of etching, with a Mueller polarimeter based on ferroelectric liquid crystals, operated in the visible. Two samples were also characterized by standard spectroscopic ellipsometry (SE) in the UV-VIS range (300-800 nm). The measured spectra were fitted with a Rigorous Coupled Wave Analysis code with different models of grating profiles. With the Mueller spectra the model adequacy could be assessed from the stability of the optimal values of the fitting parameters when the azimuthal angle was varied. The conclusions were found to be in agreement with AFM images of the sample, while the fits of the SE data were too poor to provide any information in this respect. A key issue for process control is resist-silica interface localization, a difficult task due to the low index contrast for these two materials. In fact, strong correlation occurs between resist and silica thicknesses when SE spectra, taken in the usual planar diffraction geometry, are fitted. Our approach clearly reduces such parameter correlations, leading to a reliable localization of this interface.
Spectroscopic Ellipsometry is widely used to characterize 1D gratings in the usual planar diffraction geometry, with grating grooves perpendicular to the incidence plane. The Jones matrix of the grating is then diagonal, and it can be measured properly by any conventional ellipsometer. On the other hand, if the grating is measured at different azimuthal angles, i.e. in conical diffraction geometries, its Jones matrix is no longer diagonal. As a result, additional information is available about the grating groove shape, but a generalized ellipsometer, or a Mueller polarimeter, are necessary to retrieve this information completely. We used this approach with photoresist gratings deposited on Si for nominal CDs down to 70 nm. The instrument was an original Mueller polarimeter based on ferroelectric liquid crystals, and operated in the visible. The measured spectra were fitted with a RCWA code suitable for conical diffraction, with rectangular and trapezoidal profiles. This approach proved to greatly reduce the parameter correlations observed with standard SE for very small CDs. The relevance of the trapezoidal profile can be established, and top and bottom CDs can be "disentangled" much more easily than with standard planar diffraction geometry.
We present a first evaluation of the interest of the degree of polarization (DOP) imaging technique for early detection of cervical dysplasia. A set of ten ex vivo samples of cervix have been examined, just after surgical extraction, with an DOP imaging system comprising two linear polarizers, a liquid crystal based polarization rotator, and fast CCD camera. Routine histological examination revealed that for all samples but one, dysplasia was present only in the inner part of the cervix, which cannot be imaged with our current setup. On the other hand, the only sample exhibiting dysplasia in its outer region did show nonzero DOP with, however, a somewhat loose correlation between the DOP and the histological mapping of the dysplasia.
We present a multispectral polarimetric imaging system well suited for complete Mueller matrix microscopy. The source is a spectrally filtered halogen light bulb, and the image is formed on a fast CCD camera The light polarization is modulated before the sample and analyzed after the sample by using nematic liquid crystal modulators.. The whole Mueller matrix image of the sample is typically measured over 5 seconds for a good signal-to-noise ratio. The instrument design, together with an original and easy-to-operate calibration procedure provides a high polarimetric accuracy over wide ranges of wavelengths and magnifications. Mueller polarimetry provides separate images of scalar and vector retardation and dichroism of the sample, together with its depolarizing power, while all these effects do contribute simultaneously to the contrasts observed in standard polarized microsopy. Polarimetric images of several samples, namely an unstained rabbit cornea, a picrosirius red stained hepatic biopsy, and a rat artery specifically stained for collagen III are shown and discussed
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 around 5 seconds in transmission mode. The instrument design, together with an original and easy-to-operate calibration procedure
provides a high accuracy (better than 1.5% for the normalized Mueller matrix) over a wide spectral range. The data can be processed with different algorithms. Results on hepatic biopsies with different grades of fibrosis are presented.
A very simple OCT system has been developed, based on a 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 acquisition rate with a fast CCD camera. Due to the very broad spectral width of the light source and camera response, a longitudinal resolution of 1.5 micrometers is achieved. Tomographic images of cell smears are shown.
A very simple OCT system has been developed, based on a 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 acquisition rate with a fast CCD camera. Due to the very broad spectral width of the light source and camera response, an axial resolution better than 2 micrometers is easily achieved. Tomographic images of cell smears are shown.
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