Linearizing the vertical scale of an interferometric microscope and its effect on step-height measurement.

The vertical scale calibration of an interferometric microscope is important for establishing traceability of surface topography measurements to the International System of Units (SI) unit of length, the meter. Building on the calibration procedure for the amplification coefficient developed by de Groot and Beverage [Proc. SPIE 9526, 952610 (2015)], this paper describes a calibration procedure that yields the response curve for the entire vertical scan motion of a coherent scanning interferometric microscope. The method requires only a flat mirror as an artifact, a narrow band spectral filter, an aperture to reduce the effective numerical aperture, and the ability to raise and lower the microscope head so that the center of the interferogram can be varied within the scan range. The local frequency of the interferogram is determined by fitting sections of the interferogram to a sinusoidal function. The nonlinearity determined from the local frequency data can be used to estimate the uncertainty in uncorrected vertical height measurements. We describe how optical profile data can be corrected for nonlinearity due to dynamic effects in the scan motion and show that the correction improves the reproducibility of step height measurements by at least a factor of three and close to that of the repeatability.

Spatial frequency domain Mueller matrix imaging.

Significance: Mueller matrix polarimetry (MMP) and spatial frequency domain imaging (SFDI) are wide-field optical imaging modalities that differentiate tissue primarily by structure alignment and photon transport coefficient, respectively. Because these effects can be related, combining MMP and SFDI may enhance tissue differentiation beyond the capability of each modality alone. Aim: An instrument was developed to combine MMP and SFDI with the goal of testing whether it enhances contrast of features in reflection mode. Approach: The instrument was constructed using liquid crystal elements for polarization control, a digital light processing projector for generating sinusoidal illumination patterns, and a digital camera for imaging. A theoretical analysis shows that the SFD Mueller matrix is complex-valued and does not follow the same behavior as a regular Mueller matrix. Images were acquired from an anisotropic tissue phantom, an optical fiber bundle, and cerebellum, thalamus, and cerebrum tissues. Results: The measurement results suggest that singly scattered, few scattered, and diffusely scattered photon paths can be distinguished in some of the samples investigated. The combined imaging modality yields additional spatial frequency phase information, which highlights paths having only a few scattering events. Conclusions: The combination of MMP and SFDI offers contrast mechanisms inaccessible by each modality used alone.

Bidirectional reflectance capabilities of the NIST Robotic Optical Scattering Instrument.

The National Institute of Standards and Technology (NIST) Robotic Optical Scattering Instrument (ROSI) serves as the national reference instrument for specular and diffuse bidirectional reflectance measurements in the ultraviolet to short-wave infrared wavelength regions. This paper gives a comprehensive overview of the design, operation, and capabilities of ROSI. We describe measurement methods for diffuse and specular reflectance, identify and quantify the elements of the uncertainty budget, and validate the reflectance scale through comparison with NIST's previous reference instrument, the Spectral Tri-function Automated Reference Reflectometer. Examples of the range of ROSI's capabilities, including the limits for low-reflectance measurements and a research application using out-of-plane measurements of bidirectional reflectance for remote sensing reference reflectors, are also covered.

Spectropolarimetry of Primitive Phototrophs as Global Surface Biosignatures.

Photosynthesis is an ancient metabolic process that began on early Earth and offers plentiful energy to organisms that can utilize it such that that they achieve global significance. The potential exists for similar processes to operate on habitable exoplanets and result in observable biosignatures. Before the advent of oxygenic photosynthesis, the most primitive phototrophs, anoxygenic phototrophs, dominated surface environments on the planet. Here, we characterize surface polarization biosignatures associated with a diverse sample of anoxygenic phototrophs and cyanobacteria, examining both pure cultures and microbial communities from the natural environment. Polarimetry is a tool that can be used to measure the chiral signature of biomolecules. Chirality is considered a universal, agnostic biosignature that is independent of a planet's biochemistry, receiving considerable interest as a target biosignature for life-detection missions. In contrast to preliminary indications from earlier work, we show that there is a diversity of distinctive circular polarization signatures, including the magnitude of the polarization, associated with the variety of chiral photosynthetic pigments and pigment complexes of anoxygenic and oxygenic phototrophs. We also show that the apparent death and release of pigments from one of the phototrophs is accompanied by an elevation of the reflectance polarization signal by an order of magnitude, which may be significant for remotely detectable environmental signatures. This work and others suggest that circular polarization signals up to ∼1% may occur, significantly stronger than previously anticipated circular polarization levels. We conclude that global surface polarization biosignatures may arise from anoxygenic and oxygenic phototrophs, which have dominated nearly 80% of the history of our rocky, inhabited planet.

Scattering mechanism for quadratic evolution of depolarization.

It was recently demonstrated theoretically, when the polarimetric properties of a material depend only upon the direction transverse to that of propagation (long coherence length regime), depolarization in transmission evolves quadratically with material thickness. This behavior was observed in several experimental studies. However, some of these studies unlikely satisfy the long coherence length condition under which the theory applies. Here, we demonstrate that abandoning a unidirectional approach to the propagation of light through a medium, i.e., introducing scatter, causes quadratic depolarization to occur in the short coherence length regime.

Evolution of transmitted depolarization in diffusely scattering media.

We performed Mueller matrix Monte Carlo simulations of the propagation of optical radiation in diffusely scattering media for collimated incidence and report the results as a function of thickness and the angle subtended by the detector. For sufficiently small thickness, a fraction of the radiation does not undergo any scattering events and is emitted at zero angle. Thus, for a very small detector angle, the measured signal will indicate mostly the attenuation of the coherent contribution, while for larger angles, the diffuse scattering radiation will contribute significantly more. The degree to which the radiation is depolarized thus depends on the angle subtended by the detector. A three-stream model-where the coherent radiation, the forward diffusely scattered radiation, and the backward scattered radiation are propagated according to the differential Mueller matrix formalism-is introduced and describes the results from the Monte Carlo simulations and the results of measurements well. This scatter-based model for depolarization in diffusely scattering media is an alternative to that based upon elementary fluctuation theory applied to a single propagation stream. Results for average photon path length, determined from the Monte Carlo simulations, suggest that applying fluctuation theory to photon path length may unify the two approaches.

Modelling photovoltaic soiling losses through optical characterization.

The accumulation of soiling on photovoltaic (PV) modules affects PV systems worldwide. Soiling consists of mineral dust, soot particles, aerosols, pollen, fungi and/or other contaminants that deposit on the surface of PV modules. Soiling absorbs, scatters, and reflects a fraction of the incoming sunlight, reducing the intensity that reaches the active part of the solar cell. Here, we report on the comparison of naturally accumulated soiling on coupons of PV glass soiled at seven locations worldwide. The spectral hemispherical transmittance was measured. It was found that natural soiling disproportionately impacts the blue and ultraviolet (UV) portions of the spectrum compared to the visible and infrared (IR). Also, the general shape of the transmittance spectra was similar at all the studied sites and could adequately be described by a modified form of the Ångström turbidity equation. In addition, the distribution of particles sizes was found to follow the IEST-STD-CC 1246E cleanliness standard. The fractional coverage of the glass surface by particles could be determined directly or indirectly and, as expected, has a linear correlation with the transmittance. It thus becomes feasible to estimate the optical consequences of the soiling of PV modules from the particle size distribution and the cleanliness value.

Classical polarimetry with a twist: a compact, geometric approach.

We present an approach to classical polarimetry that requires no moving parts, is compact and robust, and that encodes the complete polarization information on a single data frame, accomplished by replacing the rotation of components such as wave plates with position along a spatial axis. We demonstrate the concept with a polarimeter having a quarter wave plate whose fast axis direction changes with location along one axis of a 2D data frame in conjunction with a fixed-direction polarization analyzer, analogous to a classical rotating quarter wave plate polarimeter. The full set of Stokes parameters is obtained, with maximal sensitivity to circular polarization Stokes V if a quarter wave retarder is used. Linear and circular polarization terms are encoded with spatial carrier frequencies that differ by a factor two, which minimizes cross-talk. Other rotating component polarimeters lend themselves to the approach. Since the polarization modulation spatial frequencies do not change greatly, if at all, with wavelength such devices are close to achromatic, simplifying instrument design. Since the polarimetric information is acquired in a single observation, rapidly varying, transient and moving targets are accessible, loss of precision due to sequential data acquisition is avoided, and moving parts are not required.

Structured illumination Mueller matrix imaging.

We perform Mueller matrix imaging (MMI) of diffusely scattering phantoms under sinusoidal irradiance of varying spatial frequency. Quantitative polarimetric sensing via MMI completely characterizes a sample's polarimetric properties, while structured illumination (SI) allows for the control of photon path length. Intralipid phantoms were measured with varying absorption and with varying depth to demonstrate photon path length control for Mueller matrix elements. We observe unpolarized intensity, linear polarization, and circular polarization to depend upon spatial frequency differently. Finally, we measured an ex vivo chicken skin sample over a bright and dark substrate to further demonstrate the sensitivity of SI-MMI to depth.

Uncertainty in global downwelling plane irradiance estimates from sintered polytetrafluoroethylene plaque radiance measurements.

Global downwelling plane irradiance is a necessary variable to normalize water-leaving radiance measurements, reducing the magnitude and spectral variabilities introduced by the incident light field. As a result, the normalized measurements, known as remote sensing reflectance, have higher correlation with the inherent optical properties of the water body and so to the composition of optically active water components. For in situ measurements, the global downwelling plane irradiance can be estimated from the exitant radiance of sintered polytetrafluoroethylene plaques or other diffuse reflectance standards. This allows use of a single spectrometer to measure all necessary variables to estimate the remote sensing reflectance, reducing cost in acquisition and maintenance of instrumentation. However, despite being in use for more than 30 years, the uncertainty associated with the method has been only partially evaluated. In this study, we use a suite of sky radiance distributions for 24 atmospheres and nine solar zenith angles in combination with full bidirectional reflectance distribution function determinations of white and gray plaques to evaluate the uncertainties. The isolated and interactive effects of bidirectional reflectance distribution, shadowing, and tilt error sources are evaluated. We find that under the best-performing geometries of each plaque, and with appropriate estimation functions, average standard uncertainty ranges from 1% to 6.5%. The simulated errors are found to explain both previous empirical uncertainty estimates and new data collected during this study. Those errors are of the same magnitude as uncertainties of plane irradiance sensors (e.g., cosine collectors) and overlap with uncertainty requirements for different uses of in situ data, which supports the continued use of the plaque method in hydrologic optics research and monitoring. Recommendations are provided to improve the quality of measurements and assure that uncertainties will be in the range of those calculated here.

Imaging linear and circular polarization features in leaves with complete Mueller matrix polarimetry.

Spectropolarimetry of intact plant leaves allows to probe the molecular architecture of vegetation photosynthesis in a non-invasive and non-destructive way and, as such, can offer a wealth of physiological information. In addition to the molecular signals due to the photosynthetic machinery, the cell structure and its arrangement within a leaf can create and modify polarization signals. Using Mueller matrix polarimetry with rotating retarder modulation, we have visualized spatial variations in polarization in transmission around the chlorophyll a absorbance band from 650 nm to 710 nm. We show linear and circular polarization measurements of maple leaves and cultivated maize leaves and discuss the corresponding Mueller matrices and the Mueller matrix decompositions, which show distinct features in diattenuation, polarizance, retardance and depolarization. Importantly, while normal leaf tissue shows a typical split signal with both a negative and a positive peak in the induced fractional circular polarization and circular dichroism, the signals close to the veins only display a negative band. The results are similar to the negative band as reported earlier for single macrodomains. We discuss the possible role of the chloroplast orientation around the veins as a cause of this phenomenon. Systematic artefacts are ruled out as three independent measurements by different instruments gave similar results. These results provide better insight into circular polarization measurements on whole leaves and options for vegetation remote sensing using circular polarization.

Waveguide coupling via magnetic gratings with effective strips.

Gratings with complex multilayer strips are studied under inclined incident light. Great interest in these gratings is due to applications as input/output tools for waveguides and as subwavelength metafilms. The structured strips introduce anisotropy in the effective parameters, providing additional flexibility in polarization and angular dependences of optical responses. Their characterization is challenging in the intermediate regime between subwavelength and diffractive modes. The transition between modes occurs at the Wood's anomaly wavelength, which is different at different angle of incidence. The usual characterization with an effective film using permittivity ε and permeability µ has limited effectiveness at normal incidence but does not apply at inclined illumination, due to the effect of periodicity. The optical properties are better characterized with effective medium strips instead of an effective medium layer to account for the multilayer strips and the underlying periodic nature of the grating. This approach is convenient for describing such intermediate gratings for two types of applications: both metafilms and the coupling of incident waves to waveguide modes or diffraction orders. The parameters of the effective strips are retrieved by matching the spectral-angular map at different incident angles.

Plasma nanotexturing of silicon surfaces for photovoltaics applications: influence of initial surface finish on the evolution of topographical and optical properties.

Using a plasma to generate a surface texture with feature sizes on the order of tens to hundreds of nanometers ("nanotexturing") is a promising technique being considered to improve efficiency in thin, high-efficiency crystalline silicon solar cells. This study investigates the evolution of the optical properties of silicon samples with various initial surface finishes (from mirror polish to various states of micron-scale roughness) during a plasma nanotexturing process. It is shown that during said process, the appearance and growth of nanocone-like structures are essentially independent of the initial surface finish, as quantified by the auto-correlation function of the surface morphology. During the first stage of the process (2 min to 15 min etching), the reflectance and light-trapping abilities of the nanotextured surfaces are strongly influenced by the initial surface roughness; however, the differences tend to diminish as the nanostructures become larger. For the longest etching times (15 min or more), the effective reflectance is less than 5% and a strong anisotropic scattering behavior is also observed for all samples, leading to very elevated levels of light-trapping.

Full four-dimensional and reciprocal Mueller matrix bidirectional reflectance distribution function of sintered polytetrafluoroethylene.

We measured the Mueller matrix bidirectional reflectance distribution function (BRDF) of a sintered polytetrafluoroethylene (PTFE) sample over the scattering hemisphere for six incident angles (0°-75° in 15° steps) and for four wavelengths (351 nm, 532 nm, 633 nm, and 1064 nm). The data for each wavelength were fit to a phenomenological description for the Mueller matrix BRDF, which is an extension of the bidirectional surface scattering modes developed by Koenderink and van Doorn [J. Opt. Soc. Am. A.15, 2903 (1998)JOAOD60740-323210.1364/JOSAA.15.002903] for unpolarized BRDF. This description is designed to be complete, to obey the appropriate reciprocity conditions, and to provide a full description of the Mueller matrix BRDF as a function of incident and scattering directions for each wavelength. The description was further extended by linearizing the surface scattering mode coefficients with wavelength. This data set and its parameterization provides a comprehensive on-demand description of the reflectance properties for this commonly used diffuse reflectance reference material over a wide range of wavelengths.

Polarized optical scattering by inhomogeneities and surface roughness in an anisotropic thin film.

We extend the theory of Kassam et al. [J. Opt. Soc. Am. A12, 2009 (1995)JOAOD60740-323210.1364/JOSAA.12.002009] for scattering by oblique columnar structure thin films to include the induced form birefringence and the propagation of radiation in those films. We generalize the 4×4 matrix theory of Berreman [J. Opt. Soc. Am.62, 502 (1972)JOSAAH0030-394110.1364/JOSA.62.000502] to include arbitrary sources in the layer, which are necessary to determine the Green function for the inhomogeneous wave equation. We further extend first-order vector perturbation theory for scattering by roughness in the smooth surface limit, when the layer is anisotropic. Scattering by an inhomogeneous medium is approximated by a distorted Born approximation, where effective medium theory is used to determine the effective properties of the medium, and strong fluctuation theory is used to determine the inhomogeneous sources. In this manner, we develop a model for scattering by inhomogeneous films, with anisotropic correlation functions. The results are compared with Mueller matrix bidirectional scattering distribution function measurements for a glancing-angle deposition (GLAD) film. While the results are applied to the GLAD film example, the development of the theory is general enough that it can guide simulations for scattering in other anisotropic thin films.

Modeling the polarized X-ray scattering from periodic nanostructures with molecular anisotropy.

There is a need to characterize nanoscale molecular orientation in soft materials, and polarized scattering is a powerful means to measure this property. However, few approaches have been demonstrated that quantitatively relate orientation to scattering. Here, a modeling framework to relate the molecular orientation of nanostructures to polarized resonant soft X-ray scattering measurements is developed. A variable-angle transmission measurement called critical-dimension X-ray scattering enables the characterization of the three-dimensional shape of periodic nanostructures. When this measurement is conducted at resonant soft X-ray energies with different polarizations to measure soft material nanostructures, the scattering contains convolved information about the nanostructure shape and the preferred molecular orientation as a function of position, which is extracted by fitting using inverse iterative algorithms. A computationally efficient Born approximation simulation of the scattering has been developed, with a full tensor treatment of the electric field that takes into account biaxial molecular orientation, and this approach is validated by comparing it with a rigorous coupled wave simulation. The ability of various sample models to generate unique best fit solutions is then analyzed by generating simulated scattering pattern sets and fitting them with an inverse iterative algorithm. The interaction of the measurement geometry and the change in orientation across a periodic repeat unit leads to distinct asymmetry in the scattering pattern which must be considered for an accurate fit of the scattering.

Bidirectional scattering distribution function measurements from volume diffusers: correction factors and associated uncertainties.

We consider the effect of volume diffusion on measurements of the bidirectional scattering distribution function when a finite distance is used for the solid angle defining aperture. We derive expressions for correction factors that can be used when the reduced scattering coefficients and the index of refraction are known. When these quantities are not known, the expressions can be used to guide the assessment of measurement uncertainty. We find that some measurement geometries reduce the effect of volume diffusion compared to their reciprocal geometries.

Optical reflectance of pyrheliometer absorption cavities: progress toward SI-traceable measurements of solar irradiance.

We have accurately determined the absorptance of three pyrheliometer cavities at 532 nm by measuring the residual reflectance using an angle-resolved bidirectional reflectometer. Measurements were performed at a normal incidence as a function of the viewing angle and position on the cavity cone. By numerically integrating the measured angle-resolved scatter over both the direction and position and accounting for an obstructed view of the cavity, we determined that the effective cavity reflectance was between 8×10-4 and 9×10-4. Thus, the absorptance of the three cavities ranged from 0.99909±0.00014 to 0.99922±0.00012 (k=2 combined expanded uncertainties). These measurements, when extended over the spectral range of operation of the pyrheliometer, are required to establish SI traceability for absolute solar irradiance measurements.

Goniometric and hemispherical reflectance and transmittance measurements of fused silica diffusers.

Fused silica diffusers, made by forming scattering centers inside fused silica glass, can exhibit desirable optical properties, such as reflectance or transmittance independent of viewing angle, spectrally flat response into the ultraviolet wavelength range, and good spatial uniformity. The diffusers are of interest for terrestrial and space borne remote sensing instruments, which use light diffusers in reflective and transmissive applications. In this work, we report exploratory measurements of two samples of fused silica diffusers. We will present goniometric bidirectional scattering distribution function (BSDF) measurements under normal illumination provided by the National Institute of Standards and Technology (NIST)'s Goniometric Optical Scatter Instrument (GOSI), by NIST's Infrared reference integrating sphere (IRIS) and by the National Aeronautics and Space Administration (NASA)'s Diffuser Calibration Laboratory. We also present hemispherical diffuse transmittance and reflectance measurements provided by NIST's Double integrating sphere Optical Scattering Instrument (DOSI). The data from the DOSI is analyzed by Prahl's inverse adding-doubling algorithm to obtain the absorption and reduced scattering coefficient of the samples. Implications of fused silica diffusers for remote sensing applications are discussed.

Anisotropic, hierarchical surface patterns via surface wrinkling of nanopatterned polymer films.

By combining surface wrinkling and nanopatterned polymer films, we create anisotropic, hierarchical surfaces whose larger length-scale (wrinkling wavelength) depends intimately on the geometry and orientation of the smaller length-scale (nanopattern). We systematically vary the pattern pitch, pattern height, and residual layer thickness to ascertain the dependence of the wrinkling wavelength on the nanopattern geometry. We apply a composite mechanics model to gain a quantitative understanding of the relationship between the geometric parameters and the anisotropy in wrinkling wavelength. Additionally, these results shed light on the effect of surface roughness, as represented by the nanopattern, on the metrology of thin films via surface wrinkling.