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An exact expression of the outgoing boundary intensities in the case of a gray nonscattering semitransparent medium (STM) confined in a plane parallel slab with a refractive index linearly depending on the position is proposed. It is shown that directly using the diffuse reflection law gives in a much easier way exactly the same result as the one obtained with the pseudosource method.

Optical trapping combined with Mie spectroscopy is a new technique used to record the refractive index of insoluble organic material extracted from atmospheric aerosol samples over a wide wavelength range. The refractive index of the insoluble organic extracts was shown to follow a Cauchy equation between 460 and 700 nm for organic aerosol extracts collected from urban (London) and remote (Antarctica) locations. Cauchy coefficients for the remote sample were for the Austral summer and gave the Cauchy coefficients of A = 1.467 and B = 1000 nm2 with a real refractive index of 1.489 at a wavelength of 589 nm. Cauchy coefficients for the urban samples varied with season, with extracts collected during summer having Cauchy coefficients of A = 1.465 ± 0.005 and B = 4625 ± 1200 nm2 with a representative real refractive index of 1.478 at a wavelength of 589 nm, whilst samples extracted during autumn had larger Cauchy coefficients of A = 1.505 and B = 600 nm2 with a representative real refractive index of 1.522 at a wavelength of 589 nm. The refractive index of absorbing aerosol was also recorded. The absorption Ångström exponent was determined for woodsmoke and humic acid aerosol extract. Typical values of the Cauchy coefficient for the woodsmoke aerosol extract were A = 1.541 ± 0.03 and B = 14 800 ± 2900 nm2, resulting in a real refractive index of 1.584 ± 0.007 at a wavelength of 589 nm and an absorption Ångström exponent of 8.0. The measured values of refractive index compare well with previous monochromatic or very small wavelength range measurements of refractive index. In general, the real component of the refractive index increases from remote to urban to woodsmoke. A one-dimensional radiative-transfer calculation of the top-of-the-atmosphere albedo was applied to model an atmosphere containing a 3 km thick layer of aerosol comprising pure water, pure insoluble organic aerosol, or an aerosol consisting of an aqueous core with an insoluble organic shell. The calculation demonstrated that the top-of-the-atmosphere albedo increases by 0.01 to 0.04 for pure organic particles relative to water particles of the same size and that the top-of-the-atmosphere albedo increases by 0.03 for aqueous core-shell particles as volume fraction of the shell material increases to 25 %.

The aerosol single scattering albedo (SSA) is the dominant intensive particle parameter determining aerosols direct radiative forcing. For homogeneous spherical particles and a complex refractive index independent of wavelength, the SSA is solely dependent on size parameter (ratio of particle circumference and wavelength) and complex refractive index of the particle. Here, we explore this dependency for the small and large particle limits with size parameters much smaller and much larger than one. We show that in the small particle limit of Rayleigh scattering, a novel, generalized size parameter can be introduced that unifies the SSA dependence on particle size parameter independent of complex refractive index. In the large particle limit, SSA decreases with increasing product of imaginary part of the refractive index and size parameter, another generalized parameter, until this product becomes about one, then stays fairly constant until the imaginary part of the refractive index becomes comparable with the real part minus one. Beyond this point, particles start to acquire metallic character and SSA quickly increases with the imaginary part of the refractive index and approaches one.

To correctly determine the relative contribution of aerosol to the scattering properties of a gas–aerosol medium in the continuum, we propose a method that allows more reliable values of the imaginary part of the refractive index n i to be obtained for Jupiter’s atmosphere in the short-wavelength spectral range. We considered the measurement data on the spectral values of the geometric albedo of Jupiter acquired in 1993 and used the model of homogeneous spherical aerosol particles. The obtained values of n i are 0.00378, 0.00309, 0.00254, 0.00175, 0.00123, 0.00084, 0.00064, 0.00045, 0.00031, 0.00033, 0.00013, and 0.00008 at wavelengths λ = 320, 350, 375, 400, 420, 450, 470, 500, 520, 550, 606, and 631 nm, respectively.

Measurements of Raman backscattering spectra between -15 C-omicron and 22 C-omicron in liquid water (including its supercooled state) and in polycrystalline ice (-35 C-omicron to 0 C-omicron) at two excitation wavelengths (407 and 532 nm) are presented. It is found that the spectrum-integrated backscattering cross-section of the 3400 cm(-1) band is about 1.2 times larger for ice in comparison to liquid water. The excitation-wavelength dependence of the cross-section in ice is very close to that in water. A discontinuous change of the spectrum is observed upon phase transition at 0 C-omicron. The results are applicable to preliminary calibration of lidar systems designed for water content surveys in the atmosphere. (C) 2017 Elsevier Ltd. All rights reserved.

An ice crystal single-scattering property database is developed in the microwave spectral region (1 to 874 GHz) to provide the scattering, absorption, and polarization properties of 12 ice crystal habits (10-plate aggregate, 5-plate aggregate, 8-column aggregate, solid hexagonal column, hollow hexagonal column, hexagonal plate, solid bullet rosette, hollow bullet rosette, droxtal, oblate spheroid, prolate spheroid, and sphere) with particle maximum dimensions from 2 µm to 10 mm. For each habit, four temperatures (160, 200, 230, and 270 K) are selected to account for temperature dependence of the ice refractive index. The microphysical and scattering properties include projected area, volume, extinction efficiency, single-scattering albedo, asymmetry factor, and six independent nonzero phase matrix elements (i.e. P11, P12, P22, P33, P43 and P44). The scattering properties are computed by the Invariant Imbedding T-Matrix (II-TM) method and the Improved Geometric Optics Method (IGOM). The computation results show that the temperature dependence of the ice single-scattering properties in the microwave region is significant, particularly at high frequencies. Potential active and passive remote sensing applications of the database are illustrated through radar reflectivity and radiative transfer calculations. For cloud radar applications, ignoring temperature dependence has little effect on ice water content measurements. For passive microwave remote sensing, ignoring temperature dependence may lead to brightness temperature biases up to 5 K in the case of a large ice water path.

To derive the bulk radiative properties of ice clouds, aircraft contrails and snow grains, which are fundamental to atmospheric radiative transfer calculations in downstream applications, it is necessary to accurately simulate the scattering of light by individual ice particles. An ice particle optical property database reported in 2013 (hereafter, TAMUice2013) is updated (hereafter, TAMUice2016) to incorporate recent advances in computation of the optical properties of nonspherical particles. Specifically, we employ the invariant imbedding T-matrix (II-TM) method to compute the optical properties of particles with small to moderate size parameters. Both versions use the Improved Geometric Optics Method (IGOM) to compute the optical properties of large ice crystals, but TAMUice2016 improves the treatment of inhomogeneous waves inside the scattering particles in the case where ice is absorptive such as at infrared wavelengths. To bridge the gap between the extinction efficiencies computed from the II-TM and the IGOM, TAMUice2016 includes spectrally dependent higher order terms of the edge effect in addition to the first order counterpart considered in TAMUice2013. Furthermore, the differences between TAMUice2013 and TAMUice2016 are quantified with respect to the computation of the bulk optical properties of ice clouds.

We suggest the method for determining the imaginary part ni of the complex refractive index of aerosol particles forming a cloud layer at a specified altitude in the atmosphere of a giant planet. From the data of spectral measurements of the geometric albedo of Jupiter (carried out in 1993), the value of ni was calculated for the whole atmospheric column and the pressure range of 0.52 to 0.78 bar in the cloud layer presumably composed of ammonium hydrosulfides. The values of ni obtained for the cloud layer and the whole atmospheric column substantially differ and amount to 0.00098 and 0.00012, respectively.

Cirrus clouds are distributed globally and present at all latitudes. These clouds have a large influence to climate and weather processes on all scales and have a great effect on the radiative budget of earth and atmosphere system. They cover about 30–40% globally and they are composed of non-spherical ice crystals with various shapes and sizes. The ice crystals shapes can be defined by the incident coordinate systems and appropriate geometric models [1]. The shapes include: the complex bullet rosettes, hollow columns, aggregates, dendrites, capped columns and hexagonal and plates. However, the exact solution for scattering by non-spherical ice crystals in the infrared's part of the spectrum is a complex problem. However, there are classical methods that have been employed to solve scattering problems such as Rayleigh, Mie and T-matrix theories. These methods cannot readily be applied at infrared wavelength because of the size parameters, typically of order 100 or more, which lead to very long computation time. Given an incident wave to a facet of the crystal, part of it is transmitted through the ice and part is reflected. The transmitted part will again meet a boundary where part of it will be reflected inside the ice. For a dielectric scatterer, the scattered field can in principle be evaluated as a volume interval of the interval polarization. This can also be converted into an equivalent surface current distribution. It suffices to be able to evaluate the total internal field on the crystal facets. Considering only the portion of the wave that is reflected inside the ice, a set of functions representing the wave inside can be found and the functions can be separated into functions that are orthogonal to each other. The solution is made up of summation of possible solutions. Then, the combination of possible solutions that meets the boundary condition can be found [2, 3]. In this work, a new physical optics approach is introduced and numerical modeling is proposed to evaluate the scattered field.

In this study, we present a theoretical description of the experimental spectra of the optical reflection and transmission in a composite layer (PMMA+Ag) with silver nanoparticles. This layer is considered to have a quasi-zero refractive index with a random value. Therefore, there are inhomogeneous boundaries in the layer, and non-Fresnel modes of reflection and refraction are created in the layer due to the random distribution of the refractive index of the layer near its zero value. The formulae for the reflectivity and transparency of a layer with a quasi-zero refractive index are recovered by considering its unique optical properties.

Based on airborne spectral imaging observations, three-dimensional (3-D) radiative effects between Arctic boundary layer clouds and highly variable Arctic surfaces were identified and quantified. A method is presented to discriminate between sea ice and open water under cloudy conditions based on airborne nadir reflectivity γλ measurements in the visible spectral range. In cloudy cases the transition of γλ from open water to sea ice is not instantaneous but horizontally smoothed. In general, clouds reduce γλ above bright surfaces in the vicinity of open water, while γλ above open sea is enhanced. With the help of observations and 3-D radiative transfer simulations, this effect was quantified to range between 0 and 2200 m distance to the sea ice edge (for a dark-ocean albedo of αwater = 0.042 and a sea-ice albedo of αice = 0.91 at 645 nm wavelength). The affected distance Δ L was found to depend on both cloud and sea ice properties. For a low-level cloud at 0–200 m altitude, as observed during the Arctic field campaign VERtical Distribution of Ice in Arctic clouds (VERDI) in 2012, an increase in the cloud optical thickness τ from 1 to 10 leads to a decrease in Δ L from 600 to 250 m. An increase in the cloud base altitude or cloud geometrical thickness results in an increase in Δ L; for τ = 1/10 Δ L = 2200 m/1250 m in case of a cloud at 500–1000 m altitude. To quantify the effect for different shapes and sizes of ice floes, radiative transfer simulations were performed with various albedo fields (infinitely long straight ice edge, circular ice floes, squares, realistic ice floe field). The simulations show that Δ L increases with increasing radius of the ice floe and reaches maximum values for ice floes with radii larger than 6 km (500–1000 m cloud altitude), which matches the results found for an infinitely long, straight ice edge. Furthermore, the influence of these 3-D radiative effects on the retrieved cloud optical properties was investigated. The enhanced brightness of a dark pixel next to an ice edge results in uncertainties of up to 90 and 30 % in retrievals of τ and effective radius reff, respectively. With the help of Δ L, an estimate of the distance to the ice edge is given, where the retrieval uncertainties due to 3-D radiative effects are negligible.

A new method for retrieving the refractive index, horizontally and vertically polarized emissivities (eH, eV), and temperature of sea ice has been developed by using the “combined Fresnel equation,” which combines two Fresnel-polarized reflectivity equations into one. By using low-frequency 6.9 GHz brightness temperature measurements, the full microwave radiative transfer equation was simplified so that the atmospheric influence on the horizontally and vertically polarized brightness temperatures (TH, TV) can be ignored, and thus eH/eV = TH/TV. Since eH can be expressed by eV according to the combined Fresnel equation (or vice versa), eH and eV can directly be retrieved from TH/TV. The Advanced Microwave Scanning Radiometer–Earth Observing System (AMSR-E) measurements based on the developed method indicate that retrieved eV is close to 1, regardless of region and season, which is consistent with the theoretically expected value of eV near the Brewster angle (close to AMSR-E viewing angle of 55°). This finding strongly suggests that eH and eV hold the same degree of accuracy because eH/eV = TH/TV. Such expected accuracy can also be applied to associated sea ice temperature and refractive index retrievals. Likewise, the close agreement of retrieved sea ice temperature with in situ measurement at the ice surface suggests that emissivity and refractive index retrievals are also sound. Some caveats of this approach for the surface temperature over the area including open water are discussed.

The atmospheric refractive index consists of both real and imaginary parts. The intensity of refractive index fluctuations is generally expressed as the refractive index structure parameter, with the real part reflecting the strength of atmospheric turbulence and the imaginary part reflecting absorption in the light path. A large aperture scintillometer (LAS) is often used to measure the structure parameter of the real part of the atmospheric refractive index, from which the sensible and latent heat fluxes can further be obtained, whereas the influence of the imaginary part is ignored or considered noise. In this theoretical analysis study, the relationship between logarithmic light intensity variance and the atmospheric refractive index structure parameter (ARISP), as well as that between the logarithmic light intensity structure function and the ARISP, is derived. Additionally, a simple expression for the imaginary part of the ARISP is obtained which can be conveniently used to determine the imaginary part of the ARISP from LAS measurements. Moreover, these relationships provide a new method for estimating the outer scale of turbulence. Light propagation experiments were performed in the urban surface layer, from which the imaginary part of the ARISP was calculated. The experimental results showed good agreement with the presented theory. The results also suggest that the imaginary part of the ARISP exhibits a different diurnal variation from that of the real part. For the wavelength of light used (0.62 μm), the variation of the imaginary part of the ARISP is related to both the turbulent transport process and the spatial distribution characteristics of aerosols.

A new parameterization of the solar and infrared optical properties of ice clouds that considers the multiple habits of ice particles was developed on the basis of a prescribed dataset. First, the fitting formulae of the bulk extinction coefficient, single-scatter albedo, asymmetry factor, and δ-function forward-peak factor at the given 65 wavelengths as a function of effective radius were created for common scenarios, which consider a greater number of wavelengths and are more accurate than those used previously. Then, the band-averaged volume extinction and absorption coefficients, asymmetry factor and forward-peak factor of ice cloud were derived for the BCC-RAD (Beijing Climate Center radiative transfer model) using a parameter reference table. Finally, the newly developed and the original schemes in the BCC-RAD and the commonly used Fu Scheme of ice cloud were all applied to the BCC-RAD. Their influences on radiation calculations were compared using the mid-latitude summer atmospheric profile with ice clouds under no-aerosol conditions, and produced a maximum difference of approximately 30.0 W/m2 for the radiative flux, and 4.0 K/d for the heating rate. Additionally, a sensitivity test was performed to investigate the impact of the ice crystal density on radiation calculations using the three schemes. The results showed that the maximum difference was 68.1 W/m2 for the shortwave downward radiative flux (for the case of perpendicular solar insolation), and 4.2 K/d for the longwave heating rate, indicating that the ice crystal density exerts a significant effect on radiation calculations for a cloudy atmosphere.

Calculations of aerosol radiative forcing require knowledge of wavelength-dependent aerosol optical properties, such as single-scattering albedo. These aerosol optical properties can be calculated using Mie theory from knowledge of the key microphysical properties of particle size and refractive index, assuming that atmospheric particles are well-approximated to be spherical and homogeneous. We provide refractive index determinations for aqueous aerosol particles containing the key atmospherically relevant inorganic solutes of NaCl, NaNO3, (NH4)2SO4, NH4HSO4 and Na2SO4, reporting the refractive index variation with both wavelength (400–650 nm) and relative humidity (from 100 % to the efflorescence value of the salt). The accurate and precise retrieval of refractive index is performed using single-particle cavity ring-down spectroscopy. This approach involves probing a single aerosol particle confined in a Bessel laser beam optical trap through a combination of extinction measurements using cavity ring-down spectroscopy and elastic light-scattering measurements. Further, we assess the accuracy of these refractive index measurements, comparing our data with previously reported data sets from different measurement techniques but at a single wavelength. Finally, we provide a Cauchy dispersion model that parameterises refractive index measurements in terms of both wavelength and relative humidity. Our parameterisations should provide useful information to researchers requiring an accurate and comprehensive treatment of the wavelength and relative humidity dependence of refractive index for the inorganic component of atmospheric aerosol.

The Hong approximation, an approximation between the vertically and horizontally polarized reflectivities of specular surfaces has been useful for estimating the changes and characteristics produced in sea ice surfaces by climate change. Recently, the direct relationship (Azzam relationship) and the analytical (Azzam–Sohn–Hong (ASH)) approximation were derived and validated between two polarized reflectivities. In this study, the small-scale roughness and refractive index over sea ice are estimated using the ASH and Hong approximations with observations from the Advanced Microwave Scanning Radiometer for the Earth Observing System (AMSR-E). The ASH approximation is useful to monitor the properties of ice or snow, because those materials have a small value of the imaginary part of the refractive index ( ). Meanwhile, the Hong approximation is effective for estimating the melting of sea ice, because the melting of ice or snow indicates the increase in the imaginary part of the refractive index. Consequently...

Certain characteristics of a material such as the surface reflectivities can be determined even without knowledge of its internal properties. In this letter, a direct relationship (Azzam relationship) and an analytical approximation (Azzam-Sohn-Hong (ASH) approximation) between the vertically and horizontally polarized reflectivities of specular surfaces are derived and validated using the refractive indices of water and metal in a variety of spectral regions. For the purpose of practical remote applications, land, sea water, sea ice, and oil surfaces are considered and compared using the Hong and ASH approximations. Consequently, ASH approximation has an advantage in a variety of spectral bands for materials with a small imaginary part of refractive index, while the Hong approximation does well in the microwave spectral region, or when the imaginary part of the reflective index is not neglected. Thus, a combination of the Hong and ASH approximations is suggested to improve upon previous studies that used only the Hong approximation in a variety of applications.

We report a systematic study based on the random laser behaviors of comparable systems in which the refractive indices are varied. Threshold and spectra features have been obtained. The experimental results indicate that the threshold (Eth) of the random laser depends on the refractive index of the scatterers and surrounding solvents. The larger the refractive index of scatters or smaller the refractive index of solvents is, the smaller the Eth will be. The theoretical explanation based on Mie scattering theory for this phenomenon is made. We introduce refractive index contrast-ratio w. The thresholds variation is attributed to the alteration of w which influences the scattering strength and the transport mean free path. As for the spectra, typical emission evolution spectra have been observed. The peak positions vary with the change of scatterers and solvents, the reason of the variation is the absorption of the samples.

In this work, a novel technique is used to estimate the aerosol complex index of refraction of in situ collected samples. Samples of atmospheric particulate matter were collected in El Arenosillo, southern Spain, on polycarbonate filters during summer 2004 as part of an aerosol characterization campaign. These samples were analyzed for the volumetric absorption coefficient in the 320-800 nm spectral region and an estimation of the effective imaginary refractive index was made. The values of the imaginary part of the complex refractive index ranged between 0.0009-0.0215 at 800 nm and 0.0015-0.0114 at 320 nm. Little dependence on the wavelength was observed. Several intense and long lasting desert outbreaks were registered during the campaign and the complex refractive index almost doubles its value during these dust events. Finally, we present a comparison of data obtained in situ with columnar data obtained from the AERONET network. A correlation factor of 0.64 was obtained between both data, which gives an idea of how accurately the in situ ground data represent the total column.

Random fluctuation of turbulence brings random fluctuation of refractive index, which makes atmosphere become a random fluctuation medium and destroys the coherence of light wave especially laser tranferring in it. Exploration of atmospheric turbulence is essentially investigation of atmospheric refractive index. The atmospheric structure constant of refractive index is a basic parameter of expressing atmospheric turbulence, and is measured using HTP-2 micro-thermal meter at different areas from inland to ocean. It is analysed that the relation of atmospheric structure constant of refractive index with corresponding temperature and wind speed. The conclusion of developing law of turbulence and main influencing factors is to deepen the research in atmospheric optical transmission, and to provide data support for the siting of ship board photoelectric systems.

It is always a challenge to realize extreme and unusual values of refractive index for a broad range of frequencies. We show that when water is covered by a thick, rigid and unmovable plate, it behaves like a medium with zero refractive index for water waves at any frequency. Hence, by covering water with a plate of a concave or rectangular shape, water waves can be focused or collimated in a broad range of frequencies. Experiments were conducted to demonstrate these effects and results are in excellent agreement with numerical simulations.

The present work uses the Community Radiative Transfer Model to assess the influence of complex particle shapes, including snowflakes, in hyper-spectral calculations. Also considered will be the temperature-dependence of the refractive-index of ice.

For a spectrum from ultraviolet to microwave and a temperature range from 160 to 270 K, the optical constants of water ice are compiled on the basis of the Kramers–Kronig relation in conjunction with existing datasets reported in literature. Significant temperature dependence is observed in both the mid-infrared and longer wavelengths. A sensitivity study at wavelengths in the infrared split window region indicates that the temperature dependence of the single-scattering properties of ice crystals is not negligible. Thus, it is necessary to take into account the temperature dependence of ice optical constants when simulating the radiative properties of cirrus clouds for various applications to remote sensing under cirrus cloud conditions.

A radiative transfer model for coupled atmosphere-snow-ice-ocean systems (CASIO-DISORT) is used to develop accurate and efficient tools for computing the bidirectional reflectance distribution function (BRDF) of sea ice for a wide range of situations occurring in nature. These tools include a method to generate sea ice inherent optical properties (IOPs: single-scattering albedo, extinction optical depth, and scattering asymmetry parameter) for any wavelength between 300 and 4000 nm as a function of sea ice physical parameters including real and imaginary parts of the sea ice refractive index, brine pocket concentration and effective brine pocket size, air bubble concentration and effective air bubble size, volume fraction of ice impurities and impurity absorption coefficient, and sea ice thickness. The CASIO-DISORT code was used to compute look-up tables (LUTs) of the Fourier expansion coefficients of the BRDF as a function of angles of illumination and observation, sea ice IOPs, and ocean albedo. By interpolation in the LUTs one efficiently obtains accurate BRDF values. To include snow on the ice we modified DISORT2 to accept Fourier expansion coefficients for the BDRF as input instead of the BRDF itself, thereby reducing the computation time by a factor of about 60. The BRDF computed by CASIO-DISORT or retrieved from the LUTs applies to diffuse light only. To remedy this shortcoming we added a specular Gaussian beam component to the new BRDF tool and verified that it works well for BRDFs for bare and snow-covered sea ice.

Sea ice is one of the most important parameters in the global climate system, specifically the exchange of energy and momentum between the ocean and the atmosphere. In previous studies, a steady decline in Arctic sea ice has been observed over recent decades. The aim of this study is to estimate and analyze the spatial and temporal characteristics of the averaged sea ice extent, surface roughness, and refractive index from March 2003 to September 2009. A unique inversion algorithm is used for deriving the surface roughness and refractive index from Advanced Microwave Scanning Radiometer for Earth Observing System (AMSR-E) daily observations. Surface roughness significantly affects the microwave emission of the sea ice/snow surface. The sea ice, snow, and water show the dielectric contrast in the microwave frequencies. Consequently, the averaged roughness as well as the sea ice extent shows a downward trend, while the averaged refractive index shows the opposite signature. The increased trend of the refractive index in summer on both poles supports more sea ice melting in summer because of the increased temperature. This research can be applied to the climate change studies and supports the previous approaches based on the sea ice concentration in passive microwave remote sensing by the physical explanations.

Polar ice masses and sheets are sensitive indicators of climate change. Small-scale surface roughness significantly impacts the microwave emission of the sea ice/snow surface; however, published results of surface roughness measurements of sea ice are rare. Knowing the refractive index is important to discriminate between objects. In this study, the small-scale roughness and refractive index over sea ice are estimated with AMSR-E observations and a unique method. Consequently, the small-scale surface roughness of 0.25 cm to 0.5 cm at AMSR-E 6.9 GHz shows reasonable agreement with the results of known observations, ranging from 0.2 cm to 0.6 cm for the sea ice in the Antarctic and Arctic regions. The refractive indexes are retrieved from 1.6 to 1.8 for winter, from 1.2 to 1.4 for summer in the Arctic and the Antarctic, which are similar to those of the sea ice and results from previous studies. This research shows the physical characteristics of the sea ice edges and melting process. Accordingly, this investigation provides an effective procedure for retrieving the small-scale roughness and refractive index of sea ice and snow. Another advantage of this study is the ability to distinguish sea ice from the sea surface by their relative small-scale roughness.

Optical constants in a broad temperature and wavelength range are important input parameters in radiative transfer models used in studies of planetary atmospheres. In the laboratory, the refractive index values of ices at the HeNe laser wavelength (632.8 nm) are often used to monitor the growth rate and thickness of ice films. In this report we present laboratory measurements determining the refractive index at 632.8 nm of ammonia and hydrocarbon ices in the temperature range 80–100 K. Thin ice films are vapor-deposited on a cryogenically cooled mirror located inside a high-vacuum apparatus. The real component of the refractive index of these ice films is determined by a two-angle interferometric technique. Optical modeling calculations of the transmittance and reflectance through the thin ice films assist in the interpretation of the experimental results. We discuss our results and compare them with other measurements available in the literature. The results reported here are relevant to the spectroscopy of icy objects in the solar system; they are needed to perform laboratory characterization of ices, derive optical constants, and model spectra.

The results of the analysis of the spectral observations of Mars carried out with the OMEGA spectrometer onboard the Mars Express spacecraft are presented. The data from one of the spectrometer’s channels working in the near-IR spectral range (0.93–2.69 µm) were analyzed. This range includes the characteristic absorption bands of both condensed water phases (ice and frost) and bound water contained in hydrated minerals of the Martial soil. From the 1.93-µm band indicating the presence of these minerals, global maps of the bound-water index have been made. They show a noticeable latitude dependence of the index: the largest values refer to high latitudes (>60°), while they gradually diminish toward the equator. Seasonal variations of the spectral index obtained by the 1.93-µm band are connected with the hydration-dehydration processes occurring in hydrogenous minerals when the temperature of the soil and the relative humidity in the near-surface atmospheric layer are changing. The evolution of the spectral absorption bands of water ice (1.2 and 1.5 µm) dependent on the season testifies to the changes in the microstructure of the surface layer in the North ploar cap caused by the sublimate re-crystallization processes in the ice sheet. The spatial pattern of the location of the areas where the microstructure most quickly grows could be formed under the influence of the stationary atmospheric waves.

We study the influence of material absorption on light scattering by agglomerated debris particles whose sizes are comparable with the wavelength. We find that the angular profile of linear polarization is extremely sensitive to the imaginary part of refractive index, and there are some unique features that may assist in the retrieval of physical properties of particles using remote-sensing techniques. Most notably, the position of the positive polarization maximum αmax changes monotonically with the imaginary part of refractive index, allowing it to be used to characterize this property. In addition, the amplitude of the negative polarization branch (NPB) is significantly greater for dielectric particles than for non-dielectric particles. It disappears in the transition region between dielectric and conducting particles before reappearing as the imaginary part of the refractive index is increased further. Further increasing the imaginary part of the refractive index may see the NPB disappearing and reappearing in quasi-periodic fashion. This recurrent NPB has a much smaller amplitude than that of dielectric particles. This suggests that the cometary circumnuclear haloes, which have significant NPBs, cannot contain significant quantities of absorbing particles. In addition, combined observations suggest that the polarization maximum of circumnuclear haloes are relatively small Pmax∼12%, and occur at relatively small phase angles αmax∼60°, which is also consistent with dielectric particles.

The ray-tracing technique can be employed to simulate the scattering of light by a dielectric particle whose characteristic dimension is much larger than the incident wavelength. When a scattering particle is absorptive, a localized electromagnetic wave refracted into the scatterer is inhomogeneous, which requires the use of an effective refractive index to determine the propagation direction of the refracted ray. The effective refractive index for the first-order reflection–refraction event (i.e., the case for the ray-transmission from air into a particle) has been previously derived by the authors. In this study, we further develop recurrence formulae for the effective refractive indices associated with higher-order reflection–refraction events when the ray-transmission is from a particle to air. It is shown from the new formulae that effective refractive indices in this case depend upon ray history. Numerical results indicate that the real and imaginary parts of the effective refractive index are larger and smaller, respectively, than the real and imaginary parts of the inherent complex refractive index of an absorbing particle. Furthermore, if the particle faces associated with two sequential internal reflections are parallel to each other, the corresponding effective refractive indices are the same.

Arctic boundary-layer clouds were investigated with remote sensing and in situ instruments during the Arctic Study of Tropospheric Aerosol, Clouds and Radiation (ASTAR) campaign in March and April 2007. The clouds formed in a cold air outbreak over the open Greenland Sea. Beside the predominant mixed-phase clouds pure liquid water and ice clouds were observed. Utilizing measurements of solar radiation reflected by the clouds three methods to retrieve the thermodynamic phase of the cloud are introduced and compared. Two ice indices IS and IP were obtained by analyzing the spectral pattern of the cloud top reflectance in the near infrared (1500–1800 nm wavelength) spectral range which is characterized by ice and water absorption. While IS analyzes the spectral slope of the reflectance in this wavelength range, IS utilizes a principle component analysis (PCA) of the spectral reflectance. A third ice index IA is based on the different side scattering of spherical liquid water particles and nonspherical ice crystals which was recorded in simultaneous measurements of spectral cloud albedo and reflectance. Radiative transfer simulations show that IS, IP and IA range between 5 to 80, 0 to 8 and 1 to 1.25 respectively with lowest values indicating pure liquid water clouds and highest values pure ice clouds. The spectral slope ice index IS and the PCA ice index IP are found to be strongly sensitive to the effective diameter of the ice crystals present in the cloud. Therefore, the identification of mixed-phase clouds requires a priori knowledge of the ice crystal dimension. The reflectance-albedo ice index IA is mainly dominated by the uppermost cloud layer (τ

The single-scattering properties of four types of ice crystals (pure ice crystals, ice crystals with an internal mixture of ice and black carbon, ice crystals coated with black carbon, and soot coated with ice) in young contrails are investigated at wavelengths 0.65 and 2.13mm using Mie codes for coated spheres. The four types of ice crystals show differences in their single-scattering properties because of the embedded black carbon whose volume ratio is assumed to be 5%. The bulk-scattering properties of young contrails consisting of the four types of ice crystals are further investigated by averaging their single-scattering properties over a typical ice particle size distribution found in young contrails. The effect of the radiative properties of the four types of ice particles on the Stokes parameters I, Q, U, and V is also investigated for different viewing zenith angles and relative azimuth angles with a solar zenith angle of 301 using a vector radiative transfer model based on the adding-doubling technique. The Stokes parameters at a wavelength of 0.65 mm show pronounced differences for the four types of ice crystals, whereas the counterparts at a wavelength of 2.13mm show similar variations with the viewing zenith angle and relative azimuth angle. However, the values of the results for the two wavelengths are noticeably different.

Applying Fourier series expansion and a discrete ordinates method, we obtain accurate solutions of azimuthally dependent radiative transfer in an anisotropically scattering slab with variable refractive index and oblique irradiation. It is found that in a slab with a positive gradient of refractive index the optical distance traveled by incident rays decreases, and thus the value of transmittance increases. Besides, the increase of gradient of refractive index enhances the above effect. Influence of the optical thickness, scattering albedo and phase function of the medium, the incident angle of irradiation and the spatial variation of refractive index on the angular distribution of bidirectional reflectance is also investigated.

It is shown that the translucence of a substrate strongly influences light transmission by glass articles modified by sol-gel coatings. In contrast to glass, where light scattering is proportional to the refractive index, an inverse proportionality has been found in the films studied, which can be explained by the influence of porosity on the decrease of the refractive index of the coating.

Theoretical calculations of emissivity difference, Δe, with changing of water temperature from 301 to 279 K are performed at 820 cm−1 using the temperature-dependent refractive index of sea water recently proposed by Newman and co-workers. The results are compared with the calculations using the temperature-dependent refractive index presented in 1977 by Pinkley and co-workers. The difference in Δe between the two models is as small as ∼0.0003 for emission angles less than 30° . At larger emission angles, the discrepancy in Δe between the two models is notable. For example, Δe are ∼ − 0.0055 and ∼ − 0.0070 for the Newman and Pinkley models, respectively, at an emission angle of 55° . This discrepancy is mainly caused by the fact that the temperature dependence of the imaginary part of the refractive index of the Pinkley model is ∼1.5 times larger than that of the Newman model and the sea surface emissivity is significantly sensitive to the change of imaginary refractive index at this wavenumber. It is important that accurate values of the imaginary part of the refractive index be obtained. Copyright © 2008 Royal Meteorological Society

We have used the T-matrix method and the discrete dipole approximation to compute the midinfrared extinction cross-sections (4500-800 cm(-1)) of randomly oriented circular ice cylinders for aspect ratios extending up to 10 for oblate and down to 1/6 for prolate particle shapes. Equal-volume sphere diameters ranged from 0.1 to 10 microm for both particle classes. A high degree of particle asphericity provokes a strong distortion of the spectral habitus compared to the extinction spectrum of compactly shaped ice crystals with an aspect ratio around 1. The magnitude and the sign (increase or diminution) of the shape-related changes in both the absorption and the scattering cross-sections crucially depend on the particle size and the values for the real and imaginary part of the complex refractive index. When increasing the particle asphericity for a given equal-volume sphere diameter, the values for the overall extinction cross-sections may change in opposite directions for different parts of the spectrum. We have applied our calculations to the analysis of recent expansion cooling experiments on the formation of cirrus clouds, performed in the large coolable aerosol and cloud chamber AIDA of Forschungszentrum Karlsruhe at a temperature of 210 K. Depending on the nature of the seed particles and the temperature and relative humidity characteristics during the expansion, ice crystals of various shapes and aspect ratios could be produced. For a particular expansion experiment, using Illite mineral dust particles coated with a layer of secondary organic matter as seed aerosol, we have clearly detected the spectral signatures characteristic of strongly aspherical ice crystal habits in the recorded infrared extinction spectra. We demonstrate that the number size distributions and total number concentrations of the ice particles that were generated in this expansion run can only be accurately derived from the recorded infrared spectra when employing aspect ratios as high as 10 in the retrieval approach. Remarkably, the measured spectra could also be accurately fitted when employing an aspect ratio of 1 in the retrieval. The so-deduced ice particle number concentrations, however, exceeded the true values, determined with an optical particle counter, by more than 1 order of magnitude. Thus, the shape-induced spectral changes between the extinction spectra of platelike ice crystals of aspect ratio 10 and compactly shaped particles of aspect ratio 1 can be efficiently balanced by deforming the true number size distribution of the ice cloud. As a result of this severe size/shape ambiguity in the spectral analysis, we consider it indispensable to cross-check the infrared retrieval results of wavelength-sized ice particles with independent reference measurements of either the number size distribution or the particle morphology.

We derive some empirical relations describing the refractive index changes in the dry and moist atmosphere. The seasonal variation harmonics are calculated for the atmospheric correction.

The nonlinear optical response of a material is conventionally assumed to be very much smaller than its linear response. Here we report that the nonlinear contribution to the refractive index of a sample of indium-tin oxide can be much larger than the linear contribution when the optical wavelength is close to the material’s bulk plasma wavelength, where the material exhibits epsilon-near-zero behavior. In particular, we demonstrate that a change in refractive index as large as 0.7 can be obtained in an ultra-thin indium-tin oxide film using an optical intensity of 140 GW/cm2.

Transient heat transfer of coupled radiation and conduction within a semitransparent parallel plane slab of absorbing-emitting-scattering gray medium with graded index is investigated. The refractive index of the medium varies continuously along the slab thickness, and both boundary surfaces are specular and semitransparent. The medium is discretized into a number of sublayers with a constant refractive index in each, in which the radiative transfer is numerically simulated using a multilayer radiative transfer model. The multilayer model is developed using a ray-tracing method based on a zonal method. Comparison of present results with previous research shows excellent agreement, which helps to verify the validity of the multilayer radiative transfer model of a medium with a graded refractive index. Effects of optical thickness, scattering albedo, and gradient of refractive index on transient thermal behavior are examined for a medium with nonlinear refractive index distributions. It is found that temperature peaks also appear in the inner regions of a graded refractive index medium with two semitransparent surfaces subjected to external radiation even though there is no convection cooling on the surfaces and the absorbing coefficient (or extinction coefficient) is spatially uniform in the medium.

Cloud microphysical and optical properties are inferred from the bidirectional reflectances simulated for a single-layered cloud consisting of an external mixture of ice particles and liquid droplets. The reflectances are calculated with a rigorous discrete ordinates radiative transfer model and are functions of the cloud effective particle size, the cloud optical thickness, and the values of the ice fraction in the cloud (i.e., the ratio of ice water content to total water content). In the present light scattering and radiative transfer simulations, the ice fraction is assumed to be vertically homogeneous; the habit (shape) percentage as a function of ice particle size is consistent with that used for the Moderate Resolution Imaging Spectroradiometer (MODIS) operational (Collection 4 and earlier) cloud products; and the surface is assumed to be Lambertian with an albedo of 0.03. Furthermore, error analyses are performed that pertain to the inference of the mixed-phase cloud effective particle size and optical thickness. Errors are calculated with respect to the assumption of a cloud containing solely liquid or ice phase particles. The analyses suggest that the effective particle size inferred for a mixed-phase cloud can be underestimated (or overestimated) if pure liquid phase (or pure ice phase) is assumed for the cloud, whereas the corresponding cloud optical thickness can be overestimated (or underestimated)

The analysis of the brightness temperature differences (BTD) between 11 µm and 12 µm channels of Moderate Resolution Imaging Spectroradiometer (MODIS) aboard Aqua/NASA satellite for a Yellow Sand event on 8 April 2006 reveals that the BTD on this event cannot be explained by the theoretical simulation using the complex refractive index of ‘Sahara’ or ‘Afghan’ dust. The refractive indexes at 11 µm and 12 µm so determined as to fit the observed BTD are similar to those of quartz. In a visible wavelength, the observed reflectance of 0.65 µm channel of MODIS over the most dense portion of Yellow Sand on this day is much higher than that expected by the conventional complex refractive index of mineral dust. The weaker absorption, like the quartz refractive index, is required to explain the observed reflectance. The optical thickness at infrared and visible wavelengths using a small value of imaginary part of refractive index in visible wavelength show a smooth and monotonic relationship between them.

This study develops numerical models for thermal emission in a two-dimensional semitransparent graded-index medium. Two piecewise continuous refractive index models, the bar model and the slab model, are presented. The formal is a combination of rectangular bars each having its own unique refractive index. The latter is a combination of slabs, each of which has a linear refractive index distribution. Two interface hypotheses are discussed: the reflection/refraction hypothesis and the refraction/total reflection hypothesis. The backward ray tracing method and the backward Monte Carlo method are employed for calculation. The apparent directional emissivity of a semitransparent medium with linear and nonlinear refractive index distributions is calculated. The results show that piecewise continuous refractive index can be used for modeling semitransparent media with continuously variable refractive index. Emission from the medium is complex and quite different from a medium with a constant refractive index, when the absorption coefficient is small and/or the refractive index varies greatly in the medium. The refractive/totally reflective inner interface in the bar model gives a more precise emission distribution and can be extended to simulate emission from a medium with a complex three-dimensional refractive index distribution.

Light refraction in a medium results from energy exchange between the medium and the magnetic field of the light. Formulas of refractive index, that is, the ratio of light speed in vacuum to light speed in the medium, were derived with the inductor model of electron cloud and the law of energy conservation. Refractive indices of several media were calculated using the formulas derived and the calculated results are in agreement with the results measured. The anisotropy and the nonlinearity of the refractive index are explained with the theory described in this work.

We present a novel method for the determination of the index of refraction of single droplets by light scattering measurements in the region of the first and second order rainbow. An inversion algorithm is proposed which allows to extract the refractive index with high precision from the position and width of both rainbow peaks. The method is applied to determine the index of refraction of supercooled levitated water droplets in the temperature region between 237 K and 273 K.

Two models describing the single-scattering properties of cirrus cloud are tested for physical consistency at solar and thermal wavelengths using airborne high-resolution radiance data. The data were obtained from a case of semi-transparent cirrus cloud, which occurred north of Scotland during October 2000. The single-scattering models tested are randomly oriented hexagonal ice columns and randomly oriented ice aggregates. High-spectral resolution radiances were measured from above the cirrus at a number of wavelengths between 0.3 and 16.7 µm, thereby covering a large range of ice crystal size parameter space and complex refractive index. It is shown that consistency between retrieved optical thickness and ice crystal effective radius at both solar and infrared wavelengths could only be achieved if the ice aggregate model was assumed. Moreover, differences between the ice aggregate model and spectrally resolved brightness temperature measurements were generally well within ±1 K between the wavelengths of 3.3 and 16.0 µm in the clean atmospheric window regions. The paper shows that it is important to have simultaneous radiance measurements from both the solar and thermal spectral regions so that ice crystal scattering models and cirrus retrievals can be rigorously tested. © Crown copyright 2004.

This paper is devoted to the calculation of ice content-dependent, refractive index of mixed ice–water particles in clouds and precipitation from Debye's, Maxwell Garnet's and other models and the effects of differently structured particles upon microwave absorption, scattering and backscattering cross-sections. Evidence suggests that while both the real and imaginary parts of the refractive index diminish with increased ice content of such a sphere, the radiation intensity variation differs from one model to another. The results from the commonly used Debye's algorithm go to an extreme. Mie's theoretical calculations show that for a fixed sized mixture its absorption cross-section may exceed that of a pure water particle of the same size. At a small physical parameter |2 πmr / λ |, the scattering cross-section decreases with increased ice content f , and at a bigger value of the parameter, the cross-section may be greater at a certain f range than that of a pure water sphere of the same volume. The absorption, scattering and backscattering cross-sections of a mixture change with f in an oscillatory manner. However, differing algorithms of the refractive index give different oscillation's features. Since these algorithms are based on particular assumptions of the physical properties of these mixtures, our conclusions achieved here can be utilized as a reference in the study of microwave transfer and atmospheric remote sensing.

The aim of this review is to consider optical characteristics of terrestrial clouds. Both single and multiple light-scattering properties of water clouds are studied. The numerous results discussed can be used for solutions to both inverse and direct problems of cloud optics. An introduction to main microphysical characteristics of water and ice clouds, including the effective size, the liquid water content and path, the concentration of particles, is given. The refractive index of water and ice, which is of importance for optical waves propagation in clouds, is also considered. We consider extinction and absorption coefficients, phase functions, and asymmetry parameters of water and ice clouds and their relationships with the size, shape, and concentration of water droplets and ice crystals. Simple analytical results for absorption, reflection, and transmission characteristics of cloudy media are given. They are valid for optically thick clouds with optical thickness larger than 5. We have reviewed studies of polarization of solar light reflected from clouds. Image transfer problems have been considered as well. Modern methods of passive remote sensing of water and ice clouds are discussed. The review is finished by the discussion of optical properties of inhomogeneous clouds, which is a main topic of modern cloud optics research. D 2003 Elsevier B.V. All rights reserved.