Contours of constant pseudo-Brewster angle in the complex є plane and an analytical method for the determination of optical constants

The locus of all points in the complex plane of the dielectric function є[єr + jєi = |є| exp(jθ)], that represent all possible interfaces characterized by the same pseudo-Brewster angle θpB of minimum p reflectance, is derived in the polar form: |є| = l cos(ζ/3), where l = 2(tan2ΦpB)k, ζ = arccos(- cosθ cos2ΦpB/k3), and k = (1 - 2/3 sin2ΦpB)½. Families of iso-ΦpB contours for (I) 0° ≤ ΦpB ≤ 45° and (II) 45° ≤ ΦpB ≤ 75° are presented. In range I, an iso-ΦpB contour resembles a cardioid. In range II, the contour gradually transforms toward a circle centered on the origin as ΦpB increases. However, the deviation from a circle is still substantial. Only near grazing incidence (ΦpB \u3e 80°) is the iso-ΦpB contour accurately approximated as a circle. We find that |є| \u3c 1 for ΦpB \u3c 37.23°, and |є| \u3e 1 for ΦpB \u3e 45°. The optical constants n,k (where n + jk = є½ is the complex refractive index) are determined from the normal incidence reflectance R0 and ΦpB graphically and analytically. Nomograms that consist of iso-R0 and iso-ΦpB families of contours in the nk plane are presented. Equations that permit the reader to produce his own version of the same nomogram are also given. Valid multiple solutions (n,k) for a given measurement set (R0,φpB) are possible in the domain of fractional optical constants. An analytical solution of the (R0,ΦpB) → (n,k) inversion problem is developed that involves an exact (noniterative) solution of a quartic equation in |є|. Finally, a graphic representation is developed for the determination of complex є from two pseudo-Brewster angles measured in two different media of incidence

Contours of constant pseudo-Brewster angle in the complex є plane and an analytical method for the determination of optical constants

The locus of all points in the complex plane of the dielectric function є[єr + jєi = |є| exp(jθ)], that represent all possible interfaces characterized by the same pseudo-Brewster angle θpB of minimum p reflectance, is derived in the polar form: |є| = l cos(ζ/3), where l = 2(tan2ΦpB)k, ζ = arccos(- cosθ cos2ΦpB/k3), and k = (1 - 2/3 sin2ΦpB)½. Families of iso-ΦpB contours for (I) 0° ≤ ΦpB ≤ 45° and (II) 45° ≤ ΦpB ≤ 75° are presented. In range I, an iso-ΦpB contour resembles a cardioid. In range II, the contour gradually transforms toward a circle centered on the origin as ΦpB increases. However, the deviation from a circle is still substantial. Only near grazing incidence (ΦpB \u3e 80°) is the iso-ΦpB contour accurately approximated as a circle. We find that |є| \u3c 1 for ΦpB \u3c 37.23°, and |є| \u3e 1 for ΦpB \u3e 45°. The optical constants n,k (where n + jk = є½ is the complex refractive index) are determined from the normal incidence reflectance R0 and ΦpB graphically and analytically. Nomograms that consist of iso-R0 and iso-ΦpB families of contours in the nk plane are presented. Equations that permit the reader to produce his own version of the same nomogram are also given. Valid multiple solutions (n,k) for a given measurement set (R0,φpB) are possible in the domain of fractional optical constants. An analytical solution of the (R0,ΦpB) → (n,k) inversion problem is developed that involves an exact (noniterative) solution of a quartic equation in |є|. Finally, a graphic representation is developed for the determination of complex є from two pseudo-Brewster angles measured in two different media of incidence

Constraint on the optical constants of a film-substrate system for operation as an external-reflection retarder at a given angle of incidence

Given a transparent film of refractive index n1 on an absorbing substrate of complex refractive indexn2-jk2, we examine the constraint on n1, n2, and k2 such that the film-substrate system acts as an external-reflection retarder of specified retardance Δ at a specified angle of incidence φ. The constraint, which takes the form ƒ(n1,n2,k2;φ,Δ) = 0, is portrayed graphically by equi-n1 contours in the n2,k2 plane at φ = 45, 70° and for Δ = ±90 and ±180°, corresponding to quarterwave and halfwave retarders (QWR and HWR), respectively. The required film thickness as a fraction of the film thickness period and the polarization-independent device reflectance R are also studied graphically as functions of the optical constants. It is found that as n2 → 0, R → 1, so that a metal substrate such as Ag is best suited for high-reflectance QWR (φ \u3e 45°) and HWR (φ ≤ 45°). However, films that achieve QWR at φ ≤ 45° are excellent antireflection coatings of the underlying dielectric, semiconductor, or metallic substrate

Angular range for reflection of p-polarized light at the surface of an absorbing medium with reflectance below that at normal incidence

The range of incidence angle, 0 \u3c φ \u3c φe, over which p-polarized light is reflected at interfaces between transparent and absorbing media with reflectance below that at normal incidence is determined. Contours of constant φe in the complex plane of the relative dielectric constant ε are presented. A method for determining the real and imaginary parts of the complex refractive index, ε1/2 = n + jk, which is based on measuring φe and the pseudo-Brewster angle φpB, is viable in the domain of fractional optical constants, n, k \u3c 1

Constraint on the optical constants of a film-substrate system for operation as an external-reflection retarder at a given angle of incidence

Given a transparent film of refractive index n1 on an absorbing substrate of complex refractive indexn2-jk2, we examine the constraint on n1, n2, and k2 such that the film-substrate system acts as an external-reflection retarder of specified retardance Δ at a specified angle of incidence φ. The constraint, which takes the form ƒ(n1,n2,k2;φ,Δ) = 0, is portrayed graphically by equi-n1 contours in the n2,k2 plane at φ = 45, 70° and for Δ = ±90 and ±180°, corresponding to quarterwave and halfwave retarders (QWR and HWR), respectively. The required film thickness as a fraction of the film thickness period and the polarization-independent device reflectance R are also studied graphically as functions of the optical constants. It is found that as n2 → 0, R → 1, so that a metal substrate such as Ag is best suited for high-reflectance QWR (φ \u3e 45°) and HWR (φ ≤ 45°). However, films that achieve QWR at φ ≤ 45° are excellent antireflection coatings of the underlying dielectric, semiconductor, or metallic substrate

New type of ellipsometry in infrared spectroscopy: The double-reference method

We have developed a conceptually new type of ellipsometry which allows the determination of the complex refractive index by simultaneously measuring the unpolarized normal-incidence reflectivity relative to the vacuum and to another reference media. From these two quantities the complex optical response can be directly obtained without Kramers-Kronig transformation. Due to its transparency and large refractive index over a broad range of the spectrum, from the far-infrared to the soft ultraviolet region, diamond can be ideally used as a second reference. The experimental arrangement is rather simple compared to other ellipsometric techniques.Comment: submitted to Appl. Phys. Let

Cluster analysis of multiplex ligation-dependent probe amplification data in choroidal melanoma.

PurposeTo determine underlying correlations in multiplex ligation-dependent probe amplification (MLPA) data and their significance regarding survival following treatment of choroidal melanoma (CM).MethodsMLPA data were available for 31 loci across four chromosomes (1p, 3, 6, and 8) in tumor material obtained from 602 patients with CM treated at the Liverpool Ocular Oncology Center (LOOC) between 1993 and 2012. Data representing chromosomes 3 and 8q were analyzed in depth since their association with CM patient survival is well-known. Unsupervised k-means cluster analysis was performed to detect latent structure in the data set. Principal component analysis (PCA) was also performed to determine the intrinsic dimensionality of the data. Survival analyses of the identified clusters were performed using Kaplan-Meier (KM) and log-rank statistical tests. Correlation with largest basal tumor diameter (LTD) was investigated.ResultsChromosome 3: A two-cluster (bimodal) solution was found in chromosome 3, characterized by centroids at unilaterally normal probe values and unilateral deletion. There was a large, significant difference in the survival characteristics of the two clusters (log-rank, p<0.001; 5-year survival: 80% versus 40%). Both clusters had a broad distribution in LTD, although larger tumors were characteristically in the poorer outcome group (Mann-Whitney, p<0.001). Threshold values of 0.85 for deletion and 1.15 for gain optimized the classification of the clusters. PCA showed that the first principal component (PC1) contained more than 80% of the data set variance and all of the bimodality, with uniform coefficients (0.28±0.03). Chromosome 8q: No clusters were found in chromosome 8q. Using a conventional threshold-based definition of 8q gain, and in conjunction with the chromosome 3 clusters, three prognostic groups were identified: chromosomes 3 and 8q both normal, either chromosome 3 or 8q abnormal, and both chromosomes 3 and 8q abnormal. KM analysis showed 5-year survival figures of approximately 97%, 80%, and 30% for these prognostic groups, respectively (log-rank, p<0.001). All MLPA probes within both chromosomes were significantly correlated with each other (Spearman, p<0.001).ConclusionsWithin chromosome 3, the strong correlation between the MLPA variables and the uniform coefficients from the PCA indicates a lack of evidence for a signature gene that might account for the bimodality we observed. We hypothesize that the two clusters we found correspond to binary underlying states of complete monosomy or disomy 3 and that these states are sampled by the complete ensemble of probes. Consequently, we would expect a similar pattern to emerge in higher-resolution MLPA data sets. LTD may be a significant confounding factor. Considering chromosome 8q, we found that chromosome 3 cluster membership and 8q gain as traditionally defined have an indistinguishable impact on patient outcome

Validation of a New Duplex Derived Haemodynamic Effectiveness Score, the Saphenous Treatment Score, in Quantifying Varicose Vein Treatments

AbstractObjectivesTo evaluate a duplex-derived score for varicose vein treatments using numerical values of haemodynamic effectiveness.DesignThe saphenous treatment score (STS) was developed prospectively to compare the effect of endovenous treatments on reflux within saphenous segments.PatientsSixty-six patients were randomised to endovenous laser ablation (EVLA) or ultrasound-guided foam sclerotherapy (UGFS) to the great saphenous vein (GSV).MethodsAssessments included the Aberdeen varicose vein severity score (AVVSS), the venous clinical severity score (VCSS), the venous filling index (VFI) and the STS.ResultsA mean STS of 5.70 decreased to 3.30, P < .0005, post-treatment. The median (IQR) AVVSS, VCSS and VFI (ml/sec) decreased from 21.52(15.48) to 18.86(11.27), P = .14, from 6(4) to 3(4), P < .0005 and from 7.1(6.9) to 1.9(.9) P < .0005, respectively. In 15 patients requiring additional UGFS the mean STS values decreased from 5.8 to 4.13 and then to 2.6 P < .0005, respectively. The individual above and below knee mean treatment differences in STS on 38 EVLA and 28 UGFS patients were 1.92 and .87 (EVLA) compared to 1.57and .29 (UGFS) P = .001, respectively.ConclusionsThe STS has been shown to grade the haemodynamic effects of different treatments as well as ongoing treatments on the GSV

Bearing Capacity of Defective Reinforced Concrete Pile in Sand-model Study

Concrete piles that were poorly constructed or analyzed in their soil analyses may have structural or geotechnical defects. To examine such defects, an experimental study was conducted to investigate how a defective reinforced concrete pile behaved. These piles were installed and subjected to a compression axial load in the sand that had relative densities of 30%,60%, and 80%. The tests were performed using four concrete model piles: one intact pile and the other three piles had a structural defect (necking) at three different positions of the pile at (0.25 L from the top, center, and 0.25 L bottom). Geotechnical defect (soft layer or debris) was studied using Styrofoam layer at various vertical distances under the pile toe with Y/D = (0, 0.5, 1 and 1.5) D. The test results showed that the bearing capacity of the structural defect was the most in the case of a neck at 0.25 L from the bottom, followed by a neck at the center, and finally a neck at 0.25 L from the top. In the case of a geotechnical defect, the bearing capacity of the pile decreased with the decrease of the vertical distance between the soft layer and the pile toe