Rotation of reference frame dependent polarimetric variables for equidistant fisheye lens projections.

The effect of a linear polarizer is conventionally well defined when viewed along the axis normal to its face. However, even for ideal linear polarizers, the non-normal viewing geometries attainable with wide-angle lenses require further considerations. A method to describe the polarization state of light passed through a linear polarizer and observed with an equidistant fisheye lens is described.

Deriving consistent ocean biological and biogeochemical products from multiple satellite ocean color sensors.

A methodology is developed for deriving consistent ocean biological and biogeochemical products from multiple satellite ocean color sensors that have slightly different sensor spectral characteristics. Specifically, the required coefficients for algorithm modifications are obtained using the hyperspectral in situ optical measurements from the Marine Optical Buoy (MOBY) in the water off Hawaii. It is demonstrated that using the proposed approach for modifying ocean biological and biogeochemical algorithms, satellite-derived ocean property data over the global open ocean are consistent from multiple satellite sensors, although their corresponding sensor-measured normalized water-leaving radiance spectra nLw(λ) are different. Therefore, the proposed approach allows satellite-derived ocean biological and biogeochemical products to be consistent and can therefore be routinely merged from various satellite ocean color sensors. The proposed approach can be applied to any satellite algorithms that use the input of sensor-measured nLw(λ) spectra.

An Ocean-Colour Time Series for Use in Climate Studies: The Experience of the Ocean-Colour Climate Change Initiative (OC-CCI).

Ocean colour is recognised as an Essential Climate Variable (ECV) by the Global Climate Observing System (GCOS); and spectrally-resolved water-leaving radiances (or remote-sensing reflectances) in the visible domain, and chlorophyll-a concentration are identified as required ECV products. Time series of the products at the global scale and at high spatial resolution, derived from ocean-colour data, are key to studying the dynamics of phytoplankton at seasonal and inter-annual scales; their role in marine biogeochemistry; the global carbon cycle; the modulation of how phytoplankton distribute solar-induced heat in the upper layers of the ocean; and the response of the marine ecosystem to climate variability and change. However, generating a long time series of these products from ocean-colour data is not a trivial task: algorithms that are best suited for climate studies have to be selected from a number that are available for atmospheric correction of the satellite signal and for retrieval of chlorophyll-a concentration; since satellites have a finite life span, data from multiple sensors have to be merged to create a single time series, and any uncorrected inter-sensor biases could introduce artefacts in the series, e.g., different sensors monitor radiances at different wavebands such that producing a consistent time series of reflectances is not straightforward. Another requirement is that the products have to be validated against in situ observations. Furthermore, the uncertainties in the products have to be quantified, ideally on a pixel-by-pixel basis, to facilitate applications and interpretations that are consistent with the quality of the data. This paper outlines an approach that was adopted for generating an ocean-colour time series for climate studies, using data from the MERIS (MEdium spectral Resolution Imaging Spectrometer) sensor of the European Space Agency; the SeaWiFS (Sea-viewing Wide-Field-of-view Sensor) and MODIS-Aqua (Moderate-resolution Imaging Spectroradiometer-Aqua) sensors from the National Aeronautics and Space Administration (USA); and VIIRS (Visible and Infrared Imaging Radiometer Suite) from the National Oceanic and Atmospheric Administration (USA). The time series now covers the period from late 1997 to end of 2018. To ensure that the products meet, as well as possible, the requirements of the user community, marine-ecosystem modellers, and remote-sensing scientists were consulted at the outset on their immediate and longer-term requirements as well as on their expectations of ocean-colour data for use in climate research. Taking the user requirements into account, a series of objective criteria were established, against which available algorithms for processing ocean-colour data were evaluated and ranked. The algorithms that performed best with respect to the climate user requirements were selected to process data from the satellite sensors. Remote-sensing reflectance data from MODIS-Aqua, MERIS, and VIIRS were band-shifted to match the wavebands of SeaWiFS. Overlapping data were used to correct for mean biases between sensors at every pixel. The remote-sensing reflectance data derived from the sensors were merged, and the selected in-water algorithm was applied to the merged data to generate maps of chlorophyll concentration, inherent optical properties at SeaWiFS wavelengths, and the diffuse attenuation coefficient at 490 nm. The merged products were validated against in situ observations. The uncertainties established on the basis of comparisons with in situ data were combined with an optical classification of the remote-sensing reflectance data using a fuzzy-logic approach, and were used to generate uncertainties (root mean square difference and bias) for each product at each pixel.

New theoretical formulation for the determination of radiance transmittance at the water-air interface: comment.

We challenge a recent paper in this journal suggesting that the well-established formula governing the transmittance of radiance across a refracting interface needs revision [Optics Express, 25(22) 27086 (2017)]. We provide a simple example of radiative transfer across an interface showing that the accepted formula is correct.

Impact of spectral resolution of in situ ocean color radiometric data in satellite matchups analyses.

The spectral resolution requirements for in situ remote sensing reflectanceRRS measurements aiming at supporting satellite ocean color validation and System Vicarious Calibration (SVC) were investigated. The study, conducted using sample hyperspectral RRS from different water types, focused on the visible spectral bands of the ocean land color imager (OLCI) and of the Plankton, Aerosol, Cloud, ocean Ecosystem (PACE) satellite sensors. Allowing for a ±0.5% maximum difference between in situ and satellite derived RRS solely due to the spectral band characteristics of the in situ radiometer, a spectral resolution of 1 nm for SVC of PACE is needed in oligotrophic waters. Requirements decrease to 3 nm for SVC of OLCI. In the case of validation activities, which exhibit less stringent uncertainty requirements with respect to SVC, a maximum difference of ±1% between in situ and satellite derived data indicates the need for a spectral resolution of 3 nm for both OLCI and PACE in oligotrophic waters. Conversely, spectral resolutions of 6 nm for PACE and 9 nm for OLCI appear to satisfy validation activities in optically complex waters.

Spectral dependence of the seawater-air radiance transmission coefficient.

The transmission coefficient, TL, commonly used to propagate the upwelling nadir radiance, just below the ocean surface, to above the surface has been assumed to be a constant value of 0.543 in seawater. Because the index of refraction of seawater varies with wavelength, salinity, and temperature, the variation of TL with these parameters should be taken into account, especially if low uncertainty is required for the quantities derived using TL. In particular the wavelength dependence of this factor is important. For example at a salinity of 35 g/kg and a temperature of 26° C, TL will be 1.3% lower at 380 nm and 1.1 % higher at 700 nm than the constant value (0.543) and should be taken into account when calculating the water leaving radiance and normalized water leaving radiance from in-water measurements.

A method to extrapolate the diffuse upwelling radiance attenuation coefficient to the surface as applied to the Marine Optical Buoy (MOBY).

The upwelling radiance attenuation coefficient (KLu) in the upper 10 m of the water column can be significantly influenced by inelastic scattering processes, and thus will vary even with homogeneous water properties. The Marine Optical BuoY (MOBY), the primary vicarious calibration site for many ocean color sensors, makes measurements of the upwelling radiance (Lu) at 1 m, 5 m, and 9 m and uses these values to determine KLu and propagate the upwelling radiance directed toward the zenith, Lu, at 1 m to and through the surface. Inelastic scattering causes the KLu derived from the arm measurements to be an underestimate of the true KLu from 1 m to the surface at wavelengths greater than 575 nm, thus the derived water leaving radiance is underestimated at wavelengths longer than 575 nm. A method to correct this KLu, based on a model of the upwelling radiance including Raman scattering and chlorophyll fluorescence has been developed which corrects this bias. The model has been experimentally validated, and this technique can be applied to the MOBY data set to provide new, more accurate products at these wavelengths. When applied to a 4 month MOBY deployment, the corrected water leaving radiance, Lw, can increase by 5 % (600 nm), 10 % (650 nm) and 50 % (700 nm). This method will be used to provide additional more accurate products in the MOBY data set.

Polarization properties of FEL lamps as applied to radiometric calibration.

The polarization of the irradiance from several 1000 W FEL lamps was measured between 450 and 900 nm. These lamps are universally used as irradiance calibration standards in radiometric laboratories. The irradiance was polarized between 2.3% and 3.2%, with the polarization axis aligned with the coiled filament, nearly perpendicular to the lamp axis. We have presented a simple model of the filament that explains the degree of polarization and the plane of polarization, based on the polarized emissivity of tungsten, and gives an approximate value for this polarization. While the irradiance is polarized, this polarization does not significantly effect the polarization of the light when reflected from a Spectralon plaque (Labsphere, Inc.). The polarization of these lamps should be considered when these FEL lamps are used to characterize optical instruments, particularly grating spectrometers without polarization scrambling devices.

Neural network method to correct bidirectional effects in water-leaving radiance.

Ocean color algorithms that rely on "atmospherically corrected" nadir water-leaving radiances to infer information about marine constituents such as the chlorophyll concentration depend on a reliable method to convert the angle-dependent measured radiances from the observation direction to the nadir direction. It is also important to convert the measured radiances to the nadir direction when comparing and merging products from different satellite missions. The standard correction method developed by Morel and coworkers requires knowledge of the chlorophyll concentration. Also, the standard method was developed based on the Case 1 (open ocean) assumption, which makes it unsuitable for Case 2 situations such as turbid coastal waters. We introduce a neural network method to convert the angle-dependent water-leaving radiance (or the corresponding remote sensing reflectance) from the observation direction to the nadir direction. This method relies on neither an "atmospheric correction" nor prior knowledge of the water constituents or the inherent optical properties. It directly converts the remote sensing reflectance from an arbitrary slanted viewing direction to the nadir direction by using a trained neural network. This method is fast and accurate, and it can be easily adapted to different remote sensing instruments. Validation using NuRADS measurements in different types of water shows that this method is suitable for both Case 1 and Case 2 waters. In Case 1 or chlorophyll-dominated waters, our neural network method produces corrections similar to those of the standard method. In Case 2 waters, especially sediment-dominated waters, a significant improvement was obtained compared to the standard method.

A new instrument for measuring the high dynamic range radiance distribution in near-surface sea water.

A new instrument for measuring the full radiance distribution in the ocean interior is introduced. The system is based on CMOS technology to achieve intra-scene dynamic range of 6 decades and system dynamic range of more than 9 decades. The spatial resolution is nominally 0.5 degrees with a temporal frame rate between 1 and 15 frames per second. The general instrumentation, detailed calibration, and a characterization of the system are described. Validity of the camera systems is demonstrated by comparison of the radiance measurements with other classical oceanographic radiometers.

Detailed validation of the bidirectional effect in various Case I and Case II waters.

Simulated bidirectional reflectance distribution functions (BRDF) were compared with measurements made just beneath the water's surface. In Case I water, the set of simulations that varied the particle scattering phase function depending on chlorophyll concentration agreed more closely with the data than other models. In Case II water, however, the simulations using fixed phase functions agreed well with the data and were nearly indistinguishable from each other, on average. The results suggest that BRDF corrections in Case II water are feasible using single, average, particle scattering phase functions, but that the existing approach using variable particle scattering phase functions is still warranted in Case I water.

An instrument to measure the downwelling polarized radiance distribution in the ocean.

We have built a new camera system to measure the downwelling polarized radiance distribution in the ocean. This system uses 4 fisheye lenses and coherent fiber bundles behind each image to transmit all 4 fisheye images onto a single camera image. This allows simultaneous images to be collected with 4 unique polarization states, and thus the full Stokes vector of the rapidly changing downwelling light field.

An inherent-optical-property-centered approach to correct the angular effects in water-leaving radiance.

Remote-sensing reflectance (R(rs)), which is defined as the ratio of water-leaving radiance (L(w)) to downwelling irradiance just above the surface (E(d)(0⁺)), varies with both water constituents (including bottom properties of optically-shallow waters) and angular geometry. L(w) is commonly measured in the field or by satellite sensors at convenient angles, while E(d)(0⁺) can be measured in the field or estimated based on atmospheric properties. To isolate the variations of R(rs) (or L(w)) resulting from a change of water constituents, the angular effects of R(rs) (or L(w)) need to be removed. This is also a necessity for the calibration and validation of satellite ocean color measurements. To reach this objective, for optically-deep waters where bottom contribution is negligible, we present a system centered on water's inherent optical properties (IOPs). It can be used to derive IOPs from angular Rrs and offers an alternative to the system centered on the concentration of chlorophyll. This system is applicable to oceanic and coastal waters as well as to multiband and hyperspectral sensors. This IOP-centered system is applied to both numerically simulated data and in situ measurements to test and evaluate its performance. The good results obtained suggest that the system can be applied to angular R(rs) to retrieve IOPs and to remove the angular variation of R(rs).

Observation of non-principal plane neutral points in the in-water upwelling polarized light field.

Neutral points are specific directions in the light field where the three Stokes parameters Q, U, V, and thus the degree of polarization simultaneously go to zero. We have made the first measurement of non-principal-plane neutral points in the upwelling light field in natural waters. These neutral points are located at approximately 40°- 80° nadir angle and between 120° - 160° azimuth to the sun which is well off of the principal plane. Calculations show that the neutral point positions are very sensitive to the balance in the incident light between the partially polarized skylight and the direct solar beam.

POLRADS: polarization radiance distribution measurement system.

While the upwelling radiance distribution in the ocean can be highly polarized, there are few measurements of this parameter in the open ocean. To obtain the polarized in-water upwelling spectral radiance distribution data we have developed the POLRADS instrument. This instrument is based on the NuRADS radiance distribution camera systems in which linear polarizer's have been installed. By combining simultaneous images from three NuRADS instruments, three Stokes parameters (I, Q, U) for the water leaving radiance can be obtained for all upwelling angles simultaneously. This system measures the Stokes parameters Q/I and U/I with a 0.05-0.06 uncertainty and I with a 7-10% uncertainty.

Spectra of particulate backscattering in natural waters.

Hyperspectral profiles of downwelling irradiance and upwelling radiance in natural waters (oligotrophic and mesotrophic) are combined with inverse radiative transfer to obtain high resolution spectra of the absorption coefficient (a) and the backscattering coefficient (b(b)) of the water and its constituents. The absorption coefficient at the mesotrophic station clearly shows spectral absorption features attributable to several phytoplankton pigments (Chlorophyll a, b, c, and Carotenoids). The backscattering shows only weak spectral features and can be well represented by a power-law variation with wavelength (lambda): b(b) approximately lambda(-n), where n is a constant between 0.4 and 1.0. However, the weak spectral features in b(b)b suggest that it is depressed in spectral regions of strong particle absorption. The applicability of the present inverse radiative transfer algorithm, which omits the influence of Raman scattering, is limited to lambda < 490 nm in oligotrophic waters and lambda < 575 nm in mesotrophic waters.

Bidirectional reflectance and polarization measurements on packed surfaces of benthic sediments and spherical particles.

Laboratory bidirectional reflectance and polarization measurements were carried out on packed layers of both natural sediments and manufactured spherical particles. The results indicate that among the natural sediments showing a strong backscattering peak ("hotspot"), the rough platelets are the only sediments with a negative polarization effect. Measurements of circular and linear polarization ratios indicate that both smooth ooids and rough platelets are strongly depolarizing. Measurements of perfect spherical grains show both negative polarization and strong backscattering as a remnant of the single scattering process.

Bidirectional reflectance study on dry, wet, and submerged particulate layers: effects of pore liquid refractive index and translucent particle concentrations.

We performed extensive bidirectional reflectance measurements on dry, wet, and submerged particulate layers with various albedos to investigate the darkening effect caused by wetting with fluids. It was found that, in addition to the reduction of the refractive index contrast when there is a pore liquid (wetted), the concentration of translucent grains in a particulate layer and the surface roughness conditions of the individual grains make important contributions to the wetting-induced darkening effect. Reflectance measurements on glass-sediment mixtures confirmed that, as the concentration of translucent particles increases, the reflectance of the dry layers increases while that of the wetted layers decreases. Measurements indicate that neither the prediction made by the theory of Twomey et al. [Appl. Opt. 25, 431 (1986)] nor that of Lekner and Dorf [Appl. Opt. 27, 1278 (1988)] is sufficient.

Bidirectional reflectance of dry and submerged Labsphere Spectralon plaque.

We present the bidirectional reflectance of a Labsphere calibration plaque, both dry and submerged in water, at normal illumination. The measurements indicate that when submerged in water, the Labsphere calibration plaque has a higher reflectance value than when dry at viewing angles below 55 degrees . The results are presented in the form of a reflectance factor and are useful for calibrating underwater reflectance measurements.

Comparisons of bidirectional reflectance distribution function measurements on prepared particulate surfaces and radiative-transfer models.

To understand the connection between single-particle optics and the optics of a closely packed surface, controlled laboratory measurements of bidirectional reflectance distribution functions on layers of polymer and glass spheres are carried out. The measurements are compared with predictions from five radiative-transfer models; the Hapke's models, the Lumme-Bowell model, the BRF algorithm of Mishchenko et al., and the discrete ordinate radiative transfer. It is found that models of strict numerical radiative-transfer equations (RTEs) predict measurements well in some regions but have errors in both forward- and backward-scattering directions. The improved Hapke's model, although it has an anisotropic multiple-scattering term, still produces considerable errors compared with the strict RTE. The difference can be attributed to the exclusion of a diffraction contribution in the Hapke model.