Rainbow Region Research Articles

Optimized strategies of cloud droplet distribution retrieval using satellite multi-directional polarimetric optical measurements: information content approach

Multi-directional polarized optical sensors are increasingly vital in passive remote sensing, deepening our understanding of global cloud properties. Nevertheless, uncertainty lingers on how these observations can contribute to our knowledge of cloud diversity. The variability in cloud PSD (Particle Size Distribution) significantly influences a wide array of cloud characteristics, while unidentified factors in RT (Radiative Transfer) may introduce errors into the cloud PSD retrieval algorithm. Therefore, establishing unified evaluation criteria for both optical device configuration and inversion methods is crucial. Our study, based on Bayesian theory and RT, assesses the information content of both cloud effective radius and effective variance retrieval, along with the key factors affecting their retrieval in multi-directional polarized observations, using the calculation of DFS (Degree of Freedom for Signals).We consider the process of solar incidence, cloud scattering, and sensor reception, and discuss the impact of various sensor configurations, cloud characteristics, and other components on the retrieval of cloud PSD. Correspondingly, we observed a 48% improvement in the information content of cloud PSD with the incorporation of multi-directional polarized measurements in the rainbow region. Cloud droplet concentration significantly influences inversion, but its PSD does not cause monotonic linear interference on information content. The blending of particle mixtures with different PSD has a significant negative impact on DFS. In cases where the AOD (Aerosol Optical Depth) is less than 0.5 and the COT (Cloud Optical Thickness) exceeds 5, the influence of aerosol and surface contributions on inversion can be neglected. Our findings would serve as a foundation for future instrument design improvements and enhancements to retrieval algorithms.

A method for scattering angle calibration in the rainbow region using a droplet stream.

Accurate quantification of scattering angle versus detector pixel strongly determines the measurement accuracy of rainbow refractometry. This is an emerging measurement technique operating at backscatter angles and characterizing droplets or complex droplets in terms of size and refractive index. A novel method for calibration of the rainbow scattering angle using a monodisperse droplet stream is introduced and the achievable accuracy is estimated. The assumption of a linear pixel-to-angle relation is derived, and a calibration procedure is proposed based on global fit of calibration data to the theoretically known rainbow signal. The accuracy of this method was examined by simulations and experiments, where the uncertainties of a priori parameters of droplets were also considered and validated using shadowgraphy as a ground truth. The results confirm the feasibility of this method with a maximum absolute error of 0.032°and 3.9E-5°/pixel respectively for the intercept and slope of the linear relationship. These values translate into maximum uncertainties in diameter and refractive index of approx. 0.67% and 2.8 × 10-4.

Scattering by relatively small oblate spheroidal drops of water in the rainbow region: T-matrix results and geometric interpretation

Late in 1999 Michael Mishchenko carried out T-matrix calculations of light scattered by oblate spheroidal drops of water at Marston's request. The purpose of the investigation was to determine if the caustic features, known by that time to be visible in the far-field scattering near the primary rainbow region for horizontally illuminated relatively large drops, would also be present in T-matrix calculations of the scattering by small drops. The axis of rotational symmetry of the drop was taken to be vertical, and the illumination was taken to be horizontal. Scattering into the relevant angular region was evaluated for drop aspect ratios D/H = 1, 1.23, 1.311, and 1.37 where D denotes the equatorial diameter and H the vertical diameter. The results are limited to polarized monochromatic illumination with ka = 140 where a = D/2 and k = 2π/λ with λ being the wavelength of the illumination. As expected from geometrical analysis, a horizontal “V” shaped caustic is visible for D/H = 1.311. The T-matrix results, gray-tone intensity displays provided by Mishchenko, remain instructive.

Data inversion algorithms for droplet characterization based on simulated rainbows

In characterizing droplets, the rainbow reveals information about the size of individual drops, their refractive index, temperature, and in some instances composition. Previous experience in exploiting rainbow scattering for this purpose has led to classical rainbow refractometry, but also to the global rainbow technique. To improve on these existing techniques, a highly focused Gaussian illumination beam offers some advantages for achieving higher spatial resolution in dense spray situations. This is explored in the present study, using simulations of rainbow scattering from a spherical droplet in the primary and secondary rainbow regions. These simulations are performed using the generalized Lorenz-Mie theory (GLMT), allowing for a focused Gaussian beam illumination. For droplet characterization, three inversion algorithms are investigated, designated as the peak-trough method, inflection-inflection method and trough-trough method. The effect of the incident position of the beam on the droplet characterization is considered, as are effects of white noise superimposed on the rainbow. For a spherical water droplet in the size range 50–200 μm, an accuracy of the measured relative refractive index up to 4 decimal places and a relative error in size smaller than 5% can be achieved in most cases.

Droplet Characterization Based on the Simulated Secondary Rainbows

The droplet size, size distribution, refractive index, and temperature can be measured simultaneously by the rainbow technique. In the present work, the rainbow scattering diagram for a spherical droplet in the secondary rainbow region is simulated by the use of the generalized Lorenz-Mie theory. For achieving high spatial resolution in denser droplet sprays, a focused Gaussian beam is used. For droplet characterization, different inversion algorithms are investigated, which includes trough-trough (θmin1 and θmin2) method and inflection-inflection (θinf1 and θinf2) method. For the trough-trough algorithm, the absolute error of the refractive index is between −6.4 × 10−4 and 1.7 × 10−4, and the error of the droplet radius is only between −0.55% and 1.77%. For the inflection-inflection algorithm, the maximum absolute error of the inverted refractive index is less than −1.1 × 10−3. The error of the droplet radius is between −0.75% and 5.67%.

Characterization of refractive index and size of a spherical drop by using Gaussian beam scattering in the secondary rainbow region

In the present study the structure of the secondary rainbow is examined for the case of a spherical drop illuminated by a Gaussian beam with its waist radius comparable to the drop radius. Computations are performed using the generalized Lorenz-Mie theory (GLMT) and Debye series. The influence of beam waist radius on the secondary rainbow pattern is investigated. The possibility of extracting size and refractive index from the secondary rainbow pattern is then evaluated by examining the achievable accuracy. The influence of incident position of the beam on extracting drop information is also investigated. For a Gaussian beam centered on the impact parameter associated with the Descartes ray, the absolute error of the refractive index is smaller than 6.8 × 10−4 and the value of relative error for drop radius is smaller than 4.0% for water drops with a radius between 50 and 200 μm.

Unusual area-law violation in random inhomogeneous systems

The discovery of novel entanglement patterns in quantum many-body systems is a prominent research direction in contemporary physics. Here we provide the example of a spin chain with random and inhomogeneous couplings that in the ground state exhibits a very unusual area-law violation. In the clean limit, i.e. without disorder, the model is the rainbow chain and has volume law entanglement. We show that, in the presence of disorder, the entanglement entropy exhibits a power-law growth with the subsystem size, with an exponent 1/2. By employing the strong disorder renormalization group (SDRG) framework, we show that this exponent is related to the survival probability of certain random walks. The ground state of the model exhibits extended regions of short-range singlets (that we term ‘bubble’ regions) as well as rare long range singlet (‘rainbow’ regions). Crucially, while the probability of extended rainbow regions decays exponentially with their size, that of the bubble regions is power law. We provide strong numerical evidence for the correctness of SDRG results by exploiting the free-fermion solution of the model. Finally, we investigate the role of interactions by considering the random inhomogeneous XXZ spin chain. Within the SDRG framework and in the strong inhomogeneous limit, we show that the above area-law violation takes place only at the free-fermion point of phase diagram. This point divides two extended regions, which exhibit volume-law and area-law entanglement, respectively.

基于一阶彩虹区域高斯光散射的液滴测量

基于一阶彩虹区域高斯光散射的液滴测量

Measurements of refractive index and size of a spherical drop from Gaussian beam scattering in the primary rainbow region

The primary rainbow observed when light is scattered by a spherical drop has been exploited in the past to measure drop size and relative refractive index. However, if higher spatial resolution is required in denser drop ensembles/sprays, and to avoid then multiple drops simultaneously appearing in the measurement volume, a highly focused beam is desirable, inevitably with a Gaussian intensity profile. The present study examines the primary rainbow pattern resulting when a Gaussian beam is scattered by a spherical drop and estimates the attainable accuracy when extracting size and refractive index. The scattering is computed using generalized Lorenz–Mie theory (GLMT) and Debye series decomposition of the Gaussian beam scattering. The results of these simulations show that the measurement accuracy is dependent on both the beam waist radius and the position of the drop in the beam waist.

Hyperbolic umbilic caustics from oblate water drops with tilted illumination: Observations

Various groups have reported observations of hyperbolic umbilic diffraction catastrophe patterns in the far-field scattering by oblate acoustically levitated drops with symmetric illumination. In observations of that type the drop's symmetry axis is vertical and the illuminating light beam (typically an expanded laser beam) travels horizontally. In the research summarized here, scattering patterns in the primary rainbow region and drop measurements were recorded with vertically tilted laser beam illumination having a grazing angle as large as 4 degrees. The findings from these observations may be summarized as follows: (a) It remains possible to adjust the drop aspect ratio (diameter/height) = D/H so as to produce a V-shaped hyperbolic umbilic focal section (HUFS) in the far-field scattering. (b) The shift in the required D/H was typically an increase of less than 1% and was quadratic in the tilt. (c) The apex of the V-shaped HUFS was shifted vertically by an amount proportional to the tilt with a coefficient close to unity. The levitated drops had negligible up-down asymmetry. Our method of investigation should be useful for other generalized rainbows with tilted illumination.

Simulation of optical caustics associated with the tertiary rainbow of oblate droplets.

In this paper, a vector ray tracing (VRT) model is used to simulate optical caustic structures, including rainbow and hyperbolic umbilic (HU) fringes, in the tertiary rainbow region of light scattering from oblate spheroidal droplets. In order to apply the optical caustic structures to particle diagnostics, the evolution of rainbow and HU fringes with an increase in the aspect ratio of oblate spheroidal droplets is investigated in detail, and the curvature of rainbow fringes are calculated. Next, on the basis of the VRT model, the location of cusp caustics is calculated and compared with theoretical prediction.

Impact of cloud horizontal inhomogeneity and directional sampling on the retrieval of cloud droplet size by the POLDER instrument

Abstract. The principles of cloud droplet size retrieval via Polarization and Directionality of the Earth's Reflectance (POLDER) requires that clouds be horizontally homogeneous. The retrieval is performed by combining all measurements from an area of 150 km × 150 km to compensate for POLDER's insufficient directional sampling. Using POLDER-like data simulated with the RT3 model, we investigate the impact of cloud horizontal inhomogeneity and directional sampling on the retrieval and analyze which spatial resolution is potentially accessible from the measurements. Case studies show that the sub-grid-scale variability in droplet effective radius (CDR) can significantly reduce valid retrievals and introduce small biases to the CDR (~ 1.5 μm) and effective variance (EV) estimates. Nevertheless, the sub-grid-scale variations in EV and cloud optical thickness (COT) only influence the EV retrievals and not the CDR estimate. In the directional sampling cases studied, the retrieval using limited observations is accurate and is largely free of random noise. Several improvements have been made to the original POLDER droplet size retrieval. For example, measurements in the primary rainbow region (137–145°) are used to ensure retrievals of large droplet (> 15 μm) and to reduce the uncertainties caused by cloud heterogeneity. We apply the improved method using the POLDER global L1B data from June 2008, and the new CDR results are compared with the operational CDRs. The comparison shows that the operational CDRs tend to be underestimated for large droplets because the cloudbow oscillations in the scattering angle region of 145–165° are weak for cloud fields with CDR > 15 μm. Finally, a sub-grid-scale retrieval case demonstrates that a higher resolution, e.g., 42 km × 42 km, can be used when inverting cloud droplet size distribution parameters from POLDER measurements.

Sensitivity analysis of polarimetric O<sub>2</sub> A-band spectra for potential cloud retrievals using OCO-2/GOSAT measurements

Abstract. Clouds play a crucial role in Earth's radiative budget, yet their climate feedbacks are poorly understood. The advent of space-borne high resolution spectrometers probing the O2 A band, like GOSAT and OCO-2, could make it possible to simultaneously retrieve vertically resolved cloud parameters that play a vital role in Earth's radiative budget, thereby allowing a reduction of the corresponding uncertainty due to clouds. Such retrievals would also facilitate air mass bias reduction in corresponding measurements of CO2 columns. In this work, the hyperspectral, polarimetric response of the O2 A band to mainly three important cloud parameters, viz., optical thickness, top height and droplet size has been studied, revealing a different sensitivity to each for the varying atmospheric absorption strength within the A band. Cloud optical thickness finds greatest sensitivity in intensity measurements, the sensitivity of other Stokes parameters being limited to low cloud optical thicknesses. Cloud height had a negligible effect on intensity measurements at non-absorbing wavelengths but finds maximum sensitivity at an intermediate absorption strength, which increases with cloud height. The same is found to hold for cloud geometric thickness. The geometry-dependent sensitivity to droplet size is maximum at non-absorbing wavelengths and diminishes with increasing absorption strength. It has been shown that significantly more information on droplet size can be drawn from multi-angle measurements. We find that, in the absence of sunglint, the backscatter hemisphere (scattering angle larger than 90°) is richer in information on droplet size, especially in the glory and rainbow regions. It has been shown that I and Q generally have differing sensitivities to all cloud parameters. Thus, accurate measurements of two orthogonal components IP andIS (as in GOSAT) are expected to contain more information than measurements of only I, Ih or Iv (as in the case of OCO-2).

Experimental validation of the vectorial complex ray model on the inter-caustics scattering of oblate droplets.

We report the first experimental validation of the Vectorial Complex Ray Model (VCRM) using the scattering patterns of large oblate droplets trapped in an acoustic field. The two principal radii and refractive index of the droplets are retrieved with a minimization method that involves VCRM predictions and experimental light scattering patterns. The latter are recorded in the droplet equatorial plane between the primary rainbow region and the associated hyperbolic-umbilic diffraction catastrophe. The results demonstrate that the VCRM can predict the fine and coarse stuctures of scattering patterns with good precision, opening up perspectives for the characterization of large non-spherical particles.

Realizing high photovoltaic efficiency with parallel multijunction solar cells based on spectrum-splitting and -concentrating diffractive optical element**Project supported by the National Natural Science Foundation of China (Grant Nos. 91233202, 21173260, and 51072221) and the National Basic Research Program of China (Grant No. 2012CB932903).

Based on the facts that multijunction solar cells can increase the efficiency and concentration can reduce the cost dramatically, a special design of parallel multijunction solar cells was presented. The design employed a diffractive optical element (DOE) to split and concentrate the sunlight. A rainbow region and a zero-order diffraction region were generated on the output plane where solar cells with corresponding band gaps were placed. An analytical expression of the light intensity distribution on the output plane of the special DOE was deduced, and the limiting photovoltaic efficiency of such parallel multijunction solar cells was obtained based on Shockley–Queisser’s theory. An efficiency exceeding the Shockley–Queisser limit (33%) can be expected using multijunction solar cells consisting of separately fabricated subcells. The results provide an important alternative approach to realize high photovoltaic efficiency without the need for expensive epitaxial technology widely used in tandem solar cells, thus stimulating the research and application of high efficiency and low cost solar cells.

Negotiating Off-Grid

This paper explores the practices of illicit, low-tech shelter construction that proliferated during the 1960s and 1970s back-to-the-land movement. More specifically, it considers the conflict over unauthorised rural settlements in Australia's Rainbow Region during the 1970s and the related production of the Low Cost Country Home Building manual by the University of Sydney's Department of Architecture. The rudimentary, off-grid architecture of the settlements was at the heart of conflicts over ways of living, property regimes and sites of institutional recognition. Ventures in “dropping out” across the Rainbow Region involved creative negotiation, the formation of new social and political collectivities, and the exploitation of contingency in the forming of state controls. The interactions of progressive architectural practitioners, educators and students, self-builders, politicians, planners and building inspectors, will be investigated in relation to their shaping of legislation to afford the settlements' extralegal living arrangements and non-pedigreed architecture. The paper's exploration of this historical episode contributes to a growing historical scholarship on Australian countercultural architecture, and situates the Australian experience within an international context.

Counterculture

Counterculture

Aquarius and Beyond: Thinking through the Counterculture

Aquarius and Beyond: Thinking through the Counterculture

Counterculture and Alternative Media in Utopian Contexts: A Slice of Life from the Rainbow Region

Counterculture and Alternative Media in Utopian Contexts: A Slice of Life from the Rainbow Region

Black Fellas and Rainbow Fellas: Convergence of Cultures at the Aquarius Arts and Lifestyle Festival, Nimbin, 1973

Black Fellas and Rainbow Fellas: Convergence of Cultures at the Aquarius Arts and Lifestyle Festival, Nimbin, 1973