The photon-scattering imaging data of Liposyn II intravenous emulsion solution samples of different
concentrations and different thicknesses is reported and analyzed. The scattering Mueller matrix
element m11 data shows that the maximum number of multi-photon scatterings is an increasing
function of concentration and sample thickness.
Analytic formulas are derived for the Jones matrix and the Mueller matrix for dipole scattering by an ellipsoid and by a
system of ellipsoids with totally random orientation. The scattering Mueller matrix by an ellipsoid as a function of
ellipsoid orientation was simulated and showed complicated structure. The average Jones matrix for an ensemble of
randomly oriented ellipsoids is proportional to the Jones matrix for a sphere. The averaging of the Mueller matrices
washes away all the complicated structures and reduces to a simple Mueller matrix only a little more complicated than
that for a sphere. The polarization of the dipole scattering by such ensemble depends on the scattering angle and the
polarizability ratio β of a single ellipsoid. Scattering in the direction perpendicular to the incident direction shows the
largest effects on both linear polarization and depolarization, although it has minimal intensity. More anisotropy (larger
β) of scattering particles results in larger depolarization.
Tissue is optically anisotropic and highly photon-scattering medium. It has long been treated as optically
diffusive medium in bio-medical applications. The diffusion equation of isotropic photon-density wave (PDW)
was widely applied to interpret the data of reflectance spectroscopy and biomedical imaging experiments. In
our recent transmission Stokes imaging experiment of the rat liver samples, the Mueller matrix elements were
measured and analyzed theoretically. The measured data of depolarization constant has shown that the optical
property is not perfectly diffusive. Based upon our recently developed theoretical model of anisotropic and
highly photon-scattering medium, the simulated results of anisotropy, photon-scattering and depolarization
property for the reflectance/backscattering experiment are reported.
Tissues are optically anisotropic and highly photon scattering media. By using a simple ellipsoid model of bio-molecules
with anisotropic distribution and using an effective mean-field theory, the principal anisotropic index of refraction nj(ω) and absorption extinction coefficient Kaj(ω), (j = x,y,z) are derived. The scattering extinction coefficient Ksj is calculated
from our scattering depolarization theory of highly scattering bio-medium. The criterion of optical isotropy and
anisotropy of a bio-medium is derived. The non-vanishing ▵n, ▵Ka and ▵Ks exist for medium with anisotropic molecules only. ▵Ks/<Ks> is larger for medium with higher density.
Polarimetric imaging of Stokes vector (I, Q, U, V) can provide 4 independent signatures showing the linear
and circular polarizations of biological tissues and cells. Using a recently developed Stokes digital imaging
system, we measured the Stokes vector images of tissue samples from sections of rat livers containing normal
portions and hematomas. The derived Mueller matrix elements can quantitatively provide multi-signature
data of the bio-sample. This polarimetric optical technology is a new option of biosensing technology to
inspect the structures of tissue samples, particularly for discriminating tumor and non-tumor biopsy. This
technology is useful for critical disease discrimination and medical diagnostics applications.
The bio-media are made of anisotropic molecules. Using a simple ellipsoid model, the scattering of bio-medium with
anisotropic bio-molecule is investigated theoretically. The scattering fields and Mueller matrices are derived from
fundamental electromagnetism theory. The bio-medium is modeled as a system of non-correlated anisotropic molecules.
Based upon a statistical model of anisotropic distribution, the scattering Mueller matrix is derived. The single and double
photon scattering models are investigated. Double scattering is more important for high density scattering medium. For
incident light with pure polarization, such as linear and circular polarizations, the results of molecular shape-dependent
differential and total scattering cross-sections are reported. This theory can provide a simulation tool for investigating the
scattering and polarization/depolarization effect in the highly scattering bio-medium.
Light depolarization due to multiple scattering in tissue is an interesting bio-medical issue. The bio-tissue is made of
anisotropic molecules. Using a simple ellipsoid model, the polarization property of single anisotropic bio-molecule has
been investigated theoretically. We extend this theory to a bio-tissue that is modeled as a system of non-correlated
anisotropic molecules. Based upon a statistical model of anisotropic distribution, the scattering depolarization effects are
investigated. The simulated molecular orientation-dependent single scattering depolarization Ds (1) and the double scattering depolarization Ds (2) are reported. Ds (2) contribution is more important for high density scattering medium. This theory has provided a simulation tool for investigating the depolarization effect in the highly scattering bio-medium.
An isotropic medium can consist of a system of spherical particles as well as anisotropic particles with perfectly random
orientation. Even though the scattering particle is spherical, the anisotropic geometry of the incident and scattering
direction can cause polarization in the scattering beam. For a system of randomly oriented anisotropic particles, both
polarization and depolarization exist. This work reports the polarization and depolarization of dipole scattering for such
an overall isotropic system whose anisotropic particles are ellipsoids by using both the Jones matrix and Mueller matrix
formulations.
The polarization of diffraction by a sawtooth reflection grating has been previously measured with fixed in and out
directions while the grating was turned. The measured polarization and depolarization can provide more information
about grating diffraction. The efficiency and polarization of diffraction by the two sawtooth facets are simulated based
on the vector formulation of the Kirchhoff diffraction theory. The simulated diffraction pattern for the two-facet model
agrees well with the measured one especially near the two specular peaks. The simulated diffraction polarization agrees
with the measured one for diffraction orders with efficiency greater than 1%. For diffraction orders with efficiency <
1%, other diffraction mechanisms also come into place.
Diffraction angles, diffraction efficiency and polarization of diffraction by a reflection grating were measured by a null ellipsometer at a wavelength of 632.8 nm. The grating is too rough to be measured by a stylus profiler or an interferometric profiler. The measured diffraction angles follow the grating equation very well and can be used to predict the period of a grating. The efficiency for different diffraction orders can be used to predict the surface profile using appropriate models. For a reflection grating with 150 grooves/mm, the measured ψ ranges from 16 to 84o and ▵ from 96 to 361o. This wide range of polarization is rarely seen for other kinds of samples. Depolarization is small when the efficiency is high and efficiency is small when the depolarization is large.
The full polarization property of a holographic volume grating sample is investigated both theoretically and experimentally. There exists strong interaction between the transmitted and diffracted beams due to the grating diffraction of orders m=-1 and 1. Based upon a volume grating mode, the diffracted fields and Mueller matrices of the interacting transmitted and diffracted beams were first analytically derived. The formalism is derived for the general case that the diffraction beam and the grating wave-vector are not in the plane of incidence, where s-waves and p-waves are not de-coupled. For a single-hologram grating sample, the Mueller matrix is measured at wavelength 632.8 nm and in good agreement with the theory. The result demonstrates a correlation between the diffraction strength and the polarization properties of the volume holographic grating. The derived algorithm has provided a simulation analysis tool for the engineering device design of real holographic beam combiner/splitter (HBCS) devices.
Polarization of both Reflection and transmission scatterings by a rough plane surface of a glass hemisphere with a smooth spherical surface were measured. Null ellipsometry was used to measure the ellipsometric parameters and depolarization. Linear polarization, circular polarization, and principal Mueller matrix were obtained from the above measured quantities. Scattering was measured at fixed incident and detection directions, and variable sample orientation. The scattering and its polarization and depolarization are symmetric with the off-specular angle (OSA). The measured linear polarization increases with increasing OSA, and may change sign for large OSA. Reflection scattering shows more depolarization than the transmission scattering and so do the deviations from the specular values for all parameters.
Principal Mueller matrices of scattering by a rough paint surface are measured. Null ellipsometry is used to measure the ellipsometric parameters and depolarization of scattering with small depolarization (< 0.2). Linear polarization, circular polarization, and principal Mueller matrix are obtained from the above measured quantities. Stokes method is used to measure the principle Mueller matrix for scattering with large depolarization (> 0.2), and all other polarization characteristics are derived from the principal Mueller matrix. Scattering is measured at fixed angle (2K) between the incident and detection directions, and variable sample orientation. The scattering and its polarization characteristics are symmetric with the off-specular angle (OSA). The measured linear polarization increases with increasing OSA, and may change sign for the cases of small K. The measured depolarization increases with increasing OSA more than linearly, and is larger for smaller K.
Surface properties and optical properties of several deformable mirror arrays (DMA) without actuators were characterized. The mirror arrays are micro-electronic- mechanical system (MEMS) devices which were fabricated by Boston University for wavefront correction in adaptive optics. The surface properties measured for the samples agree with the properties specified for the BU-MEMS-DMA structures. Scattering and diffraction by the mirror arrays were measured at a wavelength of 632.8nm. The DMA with the etching pattern generates a diffraction pattern full of special structures. The broadening is serious for a rough sample while it is negligible for a smooth continuous membrane DMA. The diffraction pattern demonstrates that the DMA with an RMS roughness of 300nm is not suitable for the adaptive optics to correct for wavefront error. The continuous membrane DMA with roughness less than 10 nm are useful for adaptive optics.
We begin with a brief review of prior work relating to optical windows for use with high power laser beams. A typical window must provide pressure separation between system segments, ultra-low loss, and small wavefront distortion of the many outgoing laser beams and signal returns despite heating by the high energy laser beam. Historically, two approaches have been examined to improve such windows.
Using conventional materials like fused silica and sapphire for critical window components in a high-power laser system can lead to intolerable thermal distortions and optical path difference effects. A new oxyfluoride glass is being developed which has the unique property of possessing a negative thermo-optic coefficient (dn/dT) in the near- and mid-wave infrared. Specifically, the refractive index (n) of oxyfluoride glass decreases as the temperature increases. The distortions caused by thermal expansion of the glass during laser irradiation are partly offset by the negative dn/dT. This paper specifically addresses optical properties and surface finishing of oxyfluoride glass compared to fused silica. Normarski micrographs and surface profiles were measured to inspect the surface quality since smooth surfaces are essential for suppressing surface scattering and absorption. The refractive index and thermo-optic coefficient were measured using null polarimetry near the Brewster angle. Low dn/dT is required for laser windows. Transmittance spectra were measured to deduce the extinction coefficient by comparing with the transmittance calculated from the refractive index and to screen for unwanted absorption from contaminants including hydrocarbon oils, polishing residue, and water or -OH groups. Total integrated scattering was measured for both surface and bulk scattering. All measurements were done on 1.0- and 1.5-inch-diameter witness samples.
Ellipsometric parameters, depolarization and directional reflectance of reflection and scattering by a rough stainless steel surface are measured. Linear and circular polarizations, and principal Mueller matrix can be obtained from the above quantities. Measurements were made at fixed incident and detection directions and variable sample's orientation. For one-dimensional rough surfaces, it was found that depolarization and circular polarization increase with the off-specular angle of scattering while linear polarization does the opposite. Measurements were also made for specular direction. The effective refractive index, extinction coefficient and rms roughness for the rough sample were derived from these data.
The nondestructive measurement of refractive index of transmissive materials using null polarimetry is simple, accurate and does not require much on sample preparation. In null polarimetry, the ellipsometric parameter (psi) for reflection from a sample is measured. (psi) for transparent material is defined by tan (psi) equals rp/rs where rp and rs are coefficients of reflection for the p- and s-polarization respectively. By choosing the angle of incidence (Theta) near the Brewster angle, refractive index can be computed from (Theta) and (psi) directly. The only requirement on the sample is that no back surface reflection is allowed to mess up the front surface reflection. Precision in the refractive index is about 0.0004. Spectra of refractive index for quartz are measured and compared with the spectra quoted from existing Handbooks.
The three independent characteristics of a polarizer are transmittance, extinction ratio, and cross-polarized scattering. Extinction ratio, depolarization, incoherent near-specular scattering (NSS), and contrasts are mutually dependent. Spectra of transmittance, extinction ratio, depolarization, and contrast for wiregrid polarizers were measured in the 3- to 5-micrometers wavelength region using the zones average method developed in this paper. Good polarizers are hard to find in this region. By putting two polarizers in a series with the polarization axes parallel to each other, the extinction ratio can be improved greatly by the ratio of total NSS to cross-polarized NSS of the rear polarizer.
Polarization characteristics of reflection and near-specular scattering by target surfaces at oblique incidence are evaluated by polarimetry in both infrared and visible wavelengths. Different materials with surfaces varying from smooth to very rough are investigated. Ellipsometry is used to measure the linear and circular polarizations for smooth to slightly rough surfaces. Polarized reflectance is measured for slightly rough to very rough surfaces. For specular reflection, dielectric surfaces show high linear polarization, and small circular polarization. Metal surfaces show high circular polarization, whereas small linear polarization and dielectric films show large linear and circular polarization. Near-specular scattering for a black anodized aluminum sample also shows polarization characteristics similar to those for specular reflection. Effective medium theory is used to model polarization for specular reflection, which shows agreement with the measured polarization for rough surfaces. Beckmann's scattering theory for random rough surfaces is used to model the near-specular scattering, which also shows agreement with the measured polarized reflectance. These data and the developed computation programs can be used to model polarization for targets of known geometric shapes.
Based upon known surface optical properties, we develop a model to calculate and analyze the linear and circular polarization signatures for targets of known geometric shapes. The linear and circular polarization radiation (emission and reflection) generated from the target surfaces are studied in two model surface structures: metallic and non-metallic substrates with/without dielectric coating. Infrared I, Q, U, and V images of a model cylindrical target with these surfaces are calculated. This paper shows that dielectric coating enhances the power of generating circular polarization radiation. In addition to the linear polarization, circular polarization imaging attributable to target surface reflection is also shown to be feasible for practical application.
Near-specular scattering (NSS) accompanying a specular beam causes errors in polarimetric measurements, especially for rough surfaces or in the short wavelength region. The Muller matrix for reflection or transmission including the NSS effect will be formulated and analyzed. NSS can cause a polarizer to have slight retardation and nonvanishing extinction ratio. NSS also can cause a retarder to be slightly diattenuated. Null ellipsometry is immune to incoherent and unpolarized NSS, but still cannot avoid partially coherent and polarized NSS. Polarimetric measurements of reflectance or transmittance pick up all types of scattering. NSS can be minimized by keeping the irradiated area and the receiving solid angle as small as possible.
In this paper we study the effects of depolarization and scattering from a rough surface over a large range of wavelengths, additional measurements are reported that have been made on a very rough black anodized aluminum sample.
Scattering pick-up from sample and environment is unavoidable in ellipsometric measurements, especially in the short wavelength region. Incoherent scattering has special properties that can simplify the analysis. The four-zone averaging in null ellipsometry can effectively cancel most of the scattering-induced errors. For rotating analyzer or rotating polarizer ellipsometry, the incoherent scattering from the sample causes the measured cos 2(Psi) and cos (Delta) to be smaller than the corresponding real cos 2(Psi) and cos (Delta) ; the incoherent scattering from the environment has similar effects for cos (Delta) as that from the sample. If the error by scattering dominates over the instrumental errors, the near-angle scattering can be estimated by comparing the results between null ellipsometry and rotating analyzer ellipsometry.
Birefringence can be obtained from the phase difference (Delta) between the ordinary and the extraordinary rays for normal transmission through a birefringent slab. Rotating analyzer ellipsometry (RAE) and null ellipsometry (NE) were used to measure (Delta) . NE gives accurate phase spectrum which shows linear dependence of phase on wave-number. The phase spectrum by RAE looks like a damped oscillatory curve. The calibration of RAE against NE shows that the extrema of RAE phase spectrum correspond to (Delta) equals m(pi) of NE spectrum, where m equals integer; the phases near m (pi) + (pi) /2 are about the same from both methods. Error caused by partially coherent interference of the multiple reflected waves within the slab consists basically of the sinusoidal functions of (Delta) and its harmonics, and is zero at (Delta) equals m(pi) . These errors can be suppressed by the least-square fit of m to a quadratic function of 1/(lambda) . The birefringence spectrum measured for a sapphire sample in the 0.4 to 0.9 micrometers wavelength region agrees with the handbook values.
New nonlinear optical polymers (NLOP) having potential utility in waveguides for the modulation and switching of optical signals are reported. A new class of chromophoric polymers which assume a folded, polar conformation of the backbone have been prepared. The polymers have a syndioregic arrangement of chromophores within the backbone (i.e., a head-to-head, tail-to-tail configuration). Polymers were synthesized by the polymerization of difunctional, precoupled pairs of chromophores and difunctional, bridging groups. Glassy, noncentrosymmetric films were prepared by electric field poling and by Langmuir-Blodgett (LB) deposition. Characterization of multilayer LB films by null ellipsometry to determine the anisotropic refractive parameters was performed at different angles of incidence and at a wavelength of 1.0 (mu).
Linearly polarized light remains linearly polarized after reflection from a transparent material at oblique incidence. The reflected polarization angle is determined from the extinction position of the analyzer. If the incident polarization angle is 45 deg, the reflected polarization angle gives the ratio of the reflected p-wave to s-wave. This value can be used to determine the index of refraction from Fresnel equations. With our instrument, the uncertainty in the deduced refractive index is +/- 0.0004. This method is fast, convenient, and versatile enough to provide accurate results on small laboratory samples. In addition to measuring the refractive index, the method is sufficiently accurate to characterize the homogeneity of transparent materials.
The reflectance and the ellipsometric parameters for two black samples were measured at
5-j.tm wavelength and at multiple incident angles using an ellipsometer. Different models
were used to reduce the ellipsometric data and to calculate the reference specular
reflectance. With the correct model, the measured reflectance and the near-angle
scattering with respect to the reference specular reflectance can agree with Beckmann's
scattering theory. The roughness reduced from reflectometry is independent of
ellipsometric models and is used to select the correct set of solutions. A three-phase model
in which the complex dielectric constant is computed from Bruggeman's effective medium
theory can provide consistent solutions between roughness from reflectometry and
effective thickness from ellipsometry. A combination of ellipsometry, reflectometry, and
scatterometry can predict accurately the complex index of refraction, roughness, and other
optical properties of black samples.
Refractive indices of transparent materials can be measured with high accuracy on small laboratory samples using null ellipsometry. Measurement precision in both n and k obtained ellipsometrically is ±0.0004 for semi- transparent samples. Systematic errors in ellipsometric characterization of optical constants for transparent materials can result from back-surface reflection as well as from front-surface scattering caused by surface roughness. An analysis of the contribution of these errors and the methods of eliminating them are discussed. We conclude that careful ellipsometric characterization can give indices of refraction to three decimal places in the infrared for materials with low k.
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