Geometrical Optics Model Research Articles

Simulating the Effects of the Airborne Lidar Scanning Angle, Flying Altitude, and Pulse Density for Forest Foliage Profile Retrieval

Foliage profile is a key biophysical parameter for forests. Airborne Light Detection and Ranging is an effective tool for vegetation parameter retrieval. Data acquisition conditions influence the estimation of biophysical parameters. To acquire accurate foliage profiles at the lowest cost, we used simulations to explore the effects of data acquisition conditions on forest foliage profile retrieval. First, a 3-D forest scene and the airborne small-footprint full-waveform LiDAR data were simulated by the DART model. Second, the foliage profile was estimated from LiDAR data based on a Geometric Optical and Radiative Transfer model. Lastly, the effects of the airborne LiDAR scanning angle, flying altitude, and pulse density on foliage profile retrieval were explored. The results indicated that the scanning angle was an important factor in the foliage profile retrieval, and the optimal scanning angle was 20°. The optimal scanning angle was independent of flying altitude and pulse density, and combinations of multiple scanning angles could improve the accuracy of the foliage profile estimation. The flying altitude and pulse density had little influence on foliage profile retrieval at plot level and could be ignored. In general, our study provides reliable information for selecting the optimal instrument operational parameters to acquire more accurate foliage profiles and minimize data acquisition costs.

Interpreting lunar polarimetric anomalies at large phase angles

This work was inspired by the paper “Polarimetry of moonlight: A new method for determining the refractive index of the lunar regolith”, by Fearnside et al. [Icarus 2016, 268, 156–171], in which the authors show that the parameter of polarimetric anomaly describing the deviation from the Umov law solely is a function of the real part of the refractive index. Within their model, this parameter does not depend on the average particle size. We consider that the geometrical optics (GO) model by Fearnside et al. (2016) is oversimplified and, therefore, it is not applicable for the lunar regolith. In particular, this model is similar to other GO models that do not produce the negative polarization branch of the Moon. Most critically, experimental measurements of the lunar regolith and lunar simulants demonstrate that the parameter of polarimetric anomaly does depend on particle size. We show that the applications of the Fearnside et al. (2016) model in lunar optics (e.g., their lunar maps of the real part of the refractive index) must be considered with caution.

Second-harmonic imaging in random media

We consider the problem of optical imaging of small nonlinear scatterers in random media. We propose an extension of coherent interferometric imaging (CINT) that applies to scatterers that emit second-harmonic light. We compare this method to a nonlinear version of migration imaging and find that the images obtained by CINT are more robust to statistical fluctuations. This finding is supported by a resolution analysis that is carried out in the setting of geometrical optics in random media. It is also consistent with numerical simulations for which the assumptions of the geometrical optics model do not hold.

Improving the ability of the photochemical reflectance index to track canopy light use efficiency through differentiating sunlit and shaded leaves

Accurate estimation of light use efficiency (LUE) of plant canopies is essential for calculating gross primary productivity (GPP) using LUE models and is also useful for calibrating process-based models for regional and global applications. A promising method for estimating LUE is through remote sensing of the photochemical reflectance index (PRI). However, there are internal (e.g. pigment concentrations) and external factors (e.g. environmental conditions and sun-target-view geometry) that affect PRI signals. Considering the reflectance difference between sunlit and shaded leaves, the ratio of observed canopy reflectance to leaf reflectance is used to represent the observed fraction of sunlit leaves, and the observed fraction of shaded leaves is calculated with a geometrical optical model. Thus, a canopy-level PRI observation is separated into sunlit and shaded PRI values, and a two-leaf canopy PRI (PRIt) is calculated as sum of these two values weighted by their respective sunlit and shaded leaf area indices. The usefulness of PRIt in assessing the canopy-level LUE is evaluated with automated multi-angle PRI observations acquired on a flux tower from April to September 2013 over a sub-tropical coniferous forest in southern China. In each 15-minute observation cycle, PRI is observed at four view zenith angles fixed at (37°, 47°, 57°) or (42°, 52°, 62°) and the instantaneous solar zenith angle in the azimuth angle range from 45° to 325° (from the geodetic north). In both the half-hourly and daily time steps, PRIt can effectively improve (>50% and >35% increases in R2, respectively) the ability as a proxy of LUE derived from the tower flux measurements over the big-leaf PRI taken as the arithmetic average of the multi-angle measurements in a given time interval. In the dry season from July to September, correlations of PRI with LUE at daily time steps are much stronger in the two-leaf case than in the big-leaf case. The correlation between PRIt and LUE is the strongest (R2=0.785, p<0.001) in July. PRIt is very effective in detecting the light and low-moderate drought stress on LUE at half-hourly time steps, while ineffective in detecting severe atmospheric water and heat stress, which is probably due to alternative radiative energy sink, i.e. photorespiration. Overall, the two-leaf approach well overcomes some external effects (e.g. sun-target-view geometry) that interfere with PRI signals.

Thermal Diffusivities Studied by Single-Particle Photothermal Deflection Microscopy

Using a fixed pump beam and a steerable probe beam, we image the thermal lens generated by a harmonically heated gold nanoparticle using photothermal deflection. In combination with a simple geometric optics model, we extract thermal diffusivities. The measurement technique is applied to reveal the anisotropic thermal conductivity of a nematic liquid crystal. As the measurement is highly local, it paves the way for applications in heterogeneous and anisotropic nanoscale thermal transport studies in complex biological systems.

Distance measurement based on light field geometry and ray tracing.

In this paper, we propose a geometric optical model to measure the distances of object planes in a light field image. The proposed geometric optical model is composed of two sub-models based on ray tracing: object space model and image space model. The two theoretic sub-models are derived on account of on-axis point light sources. In object space model, light rays propagate into the main lens and refract inside it following the refraction theorem. In image space model, light rays exit from emission positions on the main lens and subsequently impinge on the image sensor with different imaging diameters. The relationships between imaging diameters of objects and their corresponding emission positions on the main lens are investigated through utilizing refocusing and similar triangle principle. By combining the two sub-models together and tracing light rays back to the object space, the relationships between objects' imaging diameters and corresponding distances of object planes are figured out. The performance of the proposed geometric optical model is compared with existing approaches using different configurations of hand-held plenoptic 1.0 cameras and real experiments are conducted using a preliminary imaging system. Results demonstrate that the proposed model can outperform existing approaches in terms of accuracy and exhibits good performance at general imaging range.

Estimation of forest aboveground biomass from HJ1B imagery using a canopy reflectance model and a forest growth model

Accurately estimating the spatial distribution of forest aboveground biomass (AGB) is important because of its carbon budget forms part of the global carbon cycle. This paper presented three methods for obtaining forest AGB based on a forest growth model, a Multiple-Forward-Mode (MFM) method and a stochastic gradient boosting (SGB) model. A Li-Strahler geometric-optical canopy reflectance model (GOMS) with the ZELIG forest growth model was run using HJ1B imagery to derive forest AGB. GOMS-ZELIG simulated data were used to train the SGB model and AGB estimation. The GOMS-ZELIG AGB estimation was evaluated for 24 field-measured data and compared against the GOMS-SGB model and GOMS-MFM biomass predictions from multispectral HJ1B data. The results show that the estimation accuracy of the GOMS-MFM model is slightly higher than that of the GOMS-SGB model. The GOMS-ZELIG and GOMS-MFM models are considerably more accurate at estimating forest AGB in arid and semiarid regions.

Light scattering by irregular particles much larger than the wavelength with wavelength-scale surface roughness.

We simulate light scattering by random irregular particles that have dimensions much larger than the wavelength of incident light at the size parameter of X=200 using the discontinuous Galerkin time domain method. A comparison of the DGTD solution for smoothly faceted particles with that obtained with a geometric optics model shows good agreement for the scattering angle curves of intensity and polarization. If a wavelength-scale surface roughness is introduced, diffuse scattering at rough interface results in smooth and featureless curves for all scattering matrix elements which is consistent with the laboratory measurements of real samples.

Design of periodic nano- and macro-scale textures for high-performance thin-film multi-junction solar cells

Surface textures in thin-film silicon multi-junction solar cells play an important role in gaining the photocurrent of the devices. In this paper, a design of the textures is carried out for the case of amorphous silicon/micro-crystalline silicon (a-Si:H/μc-Si:H) solar cells, employing advanced modelling to determine the textures for defect-free silicon layer growth and to increase the photocurrent. A model of non-conformal layer growth and a hybrid optical modelling approach are used to perform realistic 3D simulations of the structures. The hybrid optical modelling includes rigorous modelling based on the finite element method and geometrical optics models. This enables us to examine the surface texture scaling from nano- to macro-sized (several tens or hundreds of micrometers) texturisation features. First, selected random and periodic nanotextures are examined with respect to critical positions of defect-region formation in Si layers. We show that despite careful selection of a well-suited semi-ellipsoidal periodic texture for defect-free layer growth, defective regions in Si layers of a-Si:H/μc-Si:H cell cannot be avoided if the lateral and vertical dimensions of the nano features are optimised only for high gain in photocurrent. Macro features are favourable for defect-free layer growth, but do not render the photocurrent gains as achieved with light-scattering properties of the optimised nanotextures. Simulation results show that from the optical point of view the semi-ellipsoidal periodic nanotextures with lateral features smaller than 0.4 μm and vertical peak-to-peak heights around or above 0.3 μm are required to achieve a gain in short-circuit current of the top cell with respect to the state-of-the-art random texture (>16% increase), whereas lateral dimensions around 0.8 μm and heights around 0.6 μm lead to a >6% gain in short-circuit current of the bottom cell.

Single camera volumetric shadowgraphy system for simultaneous droplet sizing and depth location, including empirical determination of the effective optical aperture

This work proposes an improvement of the shadowgraphy technique by allowing for 3-D droplet/particle location and sizing in a volumetric measurement with a single camera.The shadowgraphy technique implemented in this work uses a diffuse backward illuminated screen as background stage. Using this setup, the shadow image of droplets or particles is recorded on a camera. As particles get out of focus, apparent shape, size and visibility of the gray level profiles registered from the particle images change. Based on these effects, this work proposes an improved methodology to extract out-of-plane location information. Thus, the mentioned camera is enough for obtaining the 3D location of the shadow images of the particles/droplets in a control volume, and no additional hardware is needed.A simple geometrical optics model links the defocused particle image to the sizes of the circle of confusion and the particle itself. Based on this connection, a robust practical procedure is proposed to determine the circle of confusion size from the gray scale gradients of the particle image profile and from image contrast considerations. This knowledge of the circle of confusion size provides the particle depth location.The proposed approach is tested on real opaque images of a calibrated target. The proposal includes a practical procedure to double-check relevant optical parameters like the effective aperture of the lens setup. The empirical determination of the effective optical aperture is essential as it may significantly deviate from the nominal expected value, depending on the optical setup. Results obtained are satisfactory, allowing for an accurate volumetric measurement with displacements up to 30 particle diameters away in the out of focus direction (less than 20% error in particle sizing and 2mm in particle depth location). Extension of these results to the measurement of transparent water droplets generated by an injector is also proposed and the coherence of results is checked. In this case, the size of the background stage and its location are important issues. Following the indications detailed in the paper, satisfactory results are obtained for measurements of transparent water droplets with displacements up to 10 particle diameters away in the out of focus direction.

A geometrical optics model based on the non-Gaussian probability density distribution of sea surface slopes for wind speed retrieval at low incidence angles

ABSTRACTIn this study, a large amount of data from precipitation radar (PR) and National Data Buoy Center (NDBC) buoys are collocated for the development and validation of a Geometrical Optics Model, in order to retrieve wind speed at small incidence angles. The omni-directional model is developed based on the combination of the quasi-specular scattering theory and non-Gaussian probability density distribution of ocean surface slope, and can be applied at incidence angles as high as 15°. There are four parameters included in the proposed model: the effective Fresnel reflection coefficient, the mean square slope, and the two coefficients associated with the kurtosis of the sea surface slope distribution. Using one half of the collocated data, the dependence of the four parameters on the in situ wind speed is acquired. The results show that the effective Fresnel reflection coefficient has a decrease relative to that obtained in previous studies. We combine the proposed model with the maximum-likelihood estimation (MLE) technique to retrieve the ocean surface wind speed at the 10 m height. The retrieved wind speeds are then validated against those measured by the NDBC buoys. The comparison shows that the root mean square error (RMSE) and bias between the model retrievals and buoy observations are 1.54 m s–1 and 0.1 m s–1, respectively, revealing high agreements in the wind speed estimations. The results of this study indicate that the proposed model and the PR measurements at low incidence angles can provide reasonably accurate estimates of the surface wind speeds within the range of 0–20 m s–1.

Modelling spectral reflectance of open cork oak woodland: a simulation analysis of the effects of vegetation structure and background

ABSTRACTThis study analyses the influence of vegetation structure (i.e. leaf area index and canopy cover) and seasonal background changes on moderate-resolution imaging spectrometer (MODIS)-simulated reflectance data in open woodland. Approximately monthly spectral reflectance and transmittance field measurements (May 2011 to October 2013) of cork oak tree leaves (Quercus suber) and of the herbaceous understorey were recorded in the region of Ribatejo, Portugal. The geometric-optical and radiative transfer (GORT) model was used to simulate MODIS response (red, near-infrared) and to calculate vegetation indices, investigating their response to changes in the structure of the overstorey vegetation and to seasonal changes in the understorey using scenarios corresponding to contrasting phenological status (dry season vs. wet season). The performance of normalized difference vegetation index (NDVI), soil-adjusted vegetation index (SAVI), and enhanced vegetation index (EVI) is discussed. Results showed that SAVI and EVI were very sensitive to the emergence of background vegetation in the wet season compared to NDVI and that shading effects lead to an opposing trend in the vegetation indices. The information provided by this research can be useful to improve our understanding of the temporal dynamic of vegetation, monitored by vegetation indices.

热红外与被动微波遥感协同反演地表温度研究进展

作为地表与大气界面的关键参量，地表温度是全球与区域气候变化的指示因子。本文首先分别阐述了热红外与被动微波的优劣势，指出将两者协同反演地表温度的必要性。在此基础上着重归纳阐述热红外与被动微波遥感协同反演地表温度的研究进展。随后讲述了热红外与被动微波遥感的三种协同机制即空间尺度匹配、有效温度与肤面温度转换和空间分辨率提升。其中空间尺度匹配问题可利用几何光学模型加以解决。根据热传导方程计算出地表一定深度下地表辐射对有效温度的贡献量，得到地表有效温度，可提高地表温度的反演精确，使地表温度的反演研究更具有实际意义。同时对低分辨率被动微波遥感数据的空间分辨率提升提出了构想。最后归纳总结了目前的进展和面临的问题，并就目前形势提出了未来研究的方向。 As a key parameter of surface and atmosphere, the land surface temperature (LST) is the indicator of global and regional climate change. Firstly, the advantages and disadvantages of thermal infrared and passive microwave remote sensing are expounded in this paper, and the necessity of combining passive microwave with thermal infrared remote sensing to retrieve LST is pointed out. On this basis, the research progress of combining thermal infrared with passive microwave to retrieve LST is focused on. Then this paper describes three kinds of coordination mechanisms of thermal infrared and passive microwave remote sensing, including spatial scale matching, effective temperature and LST conversion and spatial resolution enhancing. Among these, the spatial scale matching problem can be solved by using the geometrical optics model. Calculating the contribution of surface radiation at a certain depth to the effective temperature based on the heat conduction equation to obtain effective temperature of the surface can improve the inversion accuracy of LST, so that the LST inversion research will make more practical significance. At the same time, the conception to improve the spatial resolution of passive microwave is put forward. In the end, the author summarizes the current progress and problems, and puts forward the direction of future research.

Extracting Leaf Area Index by Sunlit Foliage Component from Downward-Looking Digital Photography under Clear-Sky Conditions

The development of near-surface remote sensing requires the accurate extraction of leaf area index (LAI) from networked digital cameras under all illumination conditions. The widely used directional gap fraction model is more suitable for overcast conditions due to the difficulty to discriminate the shaded foliage from the shadowed parts of images acquired on sunny days. In this study, a new LAI extraction method by the sunlit foliage component from downward-looking digital photography under clear-sky conditions is proposed. In this method, the sunlit foliage component was extracted by an automated image classification algorithm named LAB2, the clumping index was estimated by a path length distribution-based method, the LAD and G function were quantified by leveled digital images and, eventually, the LAI was obtained by introducing a geometric-optical (GO) model which can quantify the sunlit foliage proportion. The proposed method was evaluated at the YJP site, Canada, by the 3D realistic structural scene constructed based on the field measurements. Results suggest that the LAB2 algorithm makes it possible for the automated image processing and the accurate sunlit foliage extraction with the minimum overall accuracy of 91.4%. The widely-used finite-length method tends to underestimate the clumping index, while the path length distribution-based method can reduce the relative error (RE) from 7.8% to 6.6%. Using the directional gap fraction model under sunny conditions can lead to an underestimation of LAI by (1.61; 55.9%), which was significantly outside the accuracy requirement (0.5; 20%) by the Global Climate Observation System (GCOS). The proposed LAI extraction method has an RMSE of 0.35 and an RE of 11.4% under sunny conditions, which can meet the accuracy requirement of the GCOS. This method relaxes the required diffuse illumination conditions for the digital photography, and can be applied to extract LAI from downward-looking webcam images, which is expected for the regional to continental scale monitoring of vegetation dynamics and validation of satellite remote sensing products.

Multi-scale crown closure retrieval for moso bamboo forest using multi-source remotely sensed imagery based on geometric-optical and Erf-BP neural network models

This article focuses on retrieving the multi-scale crown closure (CC) of Moso bamboo forest using Système Pour l’Observation de la Terre (SPOT5) and Landsat Thematic Mapper (TM) satellite remotely sensed imagery based on the geometric-optical model and the artificial neural network (ANN) model. CC at local scale was first retrieved using the Li-Strahler geometric-optical model (LSGM) and images from an unmanned aerial vehicle (UAV). Then, multi-scale CC was retrieved using the Erf-BP model (a kind of back-propagation (BP) feed-forward neural network, which takes a Gaussian error function (Erf) as an activation function of the hidden layer) based on a combination of SPOT5 and Landsat TM images. The results show that by combining multi-source remotely sensed data, the CC of Moso bamboo forest can be retrieved at the local region, township area, and county scale with high accuracy using the Erf-BP model. Estimated values have a linear relationship with the observed values at a significance level of 0.05. The highest accuracy of the retrieval of CC (referred to as LSGM-UAV-CC) was observed at the local region based on LSGM and UAV, with the coefficient of determination (R2) of 0.63, followed by that at the township area with an R2 of 0.0.55 based on LSGM-UAV-CC and SPOT5 data using the Erf-BP model (Erf-BP-SPOT5-CC), and that at the county scale with an R2 of 0.54 based on Erf-BP-SPOT5-CC and Landsat TM data using the Erf-BP model (Erf-BP-TM-CC).

A white–cyan-red LED system for low correlated colour temperature lighting

A white LED complemented by cyan and red LEDs is a good candidate for achieving high colour rendering at low correlated colour temperatures. This is usually very difficult with commercially available white LEDs. In addition, the system is able to replace incandescent lighting in many applications; for example, the lighting for museum display cases. To investigate and optimize the colour and light distribution properties, both spectral and geometrical modelling are used. Mapping of the possible combinations of LEDs is used to locate the optimal solutions within the colour gamut, with emphasis on chromaticity and colour rendering indices. A geometric optical model is used to design and optimize the homogeneity of the colour and light intensity distribution as a function of angle. The resulting system produces diffused homogeneous white light with a tunable correlated colour temperature from 2000 K to 2400 K. Within this range the white light is characterized by a high general colour rendering index (Ra &gt; 90), special colour rendering indices for saturated red objects (R9 &gt; 85), and low chromaticity distance (Duv) from the Planckian locus (Duv &lt; 2 × 10−3).

The GO4 Model in Near-Nadir Microwave Scattering From the Sea Surface

We introduce a practical and accurate model, referred to as “GO4,” to describe near-nadir microwave scattering from the sea surface, and at the same time, we address the issue of the filtered mean square slope (mss) conventionally used in the geometrical optics model. GO4 is a simple correction of this last model, taking into account the diffraction correction induced by the rough surface through what we call an effective mean square curvature (msc). We evaluate the effective msc as a function of the surface wavenumber spectrum and the radar frequency and show that GO4 reaches the same accuracy as the physical optics model in a wide range of incidence and frequency bands with the sole knowledge of the mss and msc parameters. The key point is that the mss entering in GO4 is not the filtered but the total slope. We provide estimation of the effective msc on the basis of classical sea spectrum models. We also evaluate the effective msc from near-nadir satellite data in various bands and show that it is consistent with model predictions. Non-Gaussian effects are discussed and shown to be incorporated in the effective msc. We give some applications of the method, namely, the estimation of the total sea surface mss and the recalibration of relative radar cross sections.

Uma atividade experimental sobre sombras inspirada em um cartum

Um desenho de Gervasio Troche, representando um pai e uma filha caminhando, com a sombra da menina sendo maior que a projetada pelo pai, foi utilizado em uma proposta de reconceitualização de atividades experimentais, conforme conceituada por Hodson. A imagem foi apresentada a estudantes de óptica no ensino médio, que deveriam discutir sua possibilidade física, além de construir e testar um modelo experimental baseado na figura. Uma recriação dos modelos é apresentada nesse artigo, além da sua formulação algébrica e da descrição das atividades pedagógicas desenvolvidas. A atividade foi considerada motivadora para os estudantes, por permitir uma maior compreensão sobre os modelos da óptica geométrica e também sobre as práticas científicas.

Controlling local temperature in water using femtosecond optical tweezer.

A novel method of directly observing the effect of temperature rise in water at the vicinity of optical trap center is presented. Our approach relies on changed values of corner frequency of the optical trap that, in turn, is realized from its power spectra. Our two color experiment is a unique combination of a non-heating femtosecond trapping laser at 780 nm, coupled to a femtosecond infrared heating laser at 1560 nm, which precisely controls temperature at focal volume of the trap center using low powers (100-800 µW) at high repetition rate. The geometric ray optics model quantitatively supports our experimental data.

Error analysis and liquid film thickness measurement in gas–liquid annular flow

The parameters measurement of liquid film in gas–liquid two-phase annular flow is of great significance for the study of heat and mass transfer and flow characteristics. The paper focuses on the thickness measurement and flow evolution analysis of the liquid film in downward gas–liquid two-phase annular flow. Compared with the traditional measurement methods, the method combined the laser-induced fluorescence (LIF) technique with the high-speed photography is developed to measure the liquid film thickness and analyze the flow distribution. Firstly, the geometric optical path model of the organic glass pipeline was established based on the Gauss optics to recognize the real and virtual film images and quantitatively estimate the measurement linearity. And then the digital image processing technology was developed to achieve non-intrusive measurement of liquid film thickness. Finally, the film thickness distribution in downward gas–liquid two-phase annular flow was further analyzed. The method can avoid the interference with the flow field. Meanwhile, the measurement results by experiment show that the film thickness manifests stochastic distribution, which corresponds to the features of randomness and small flow in the process of liquid film flow.