Geometrical Optics Model Research Articles

Optical Trapping and Manipulation of Superparamagnetic Beads Using Annular-Shaped Beams

We propose an optical tweezers setup based on an annular-shaped laser beam that is efficient to trap 2.8 m-diameter superparamagnetic particles. The optical trapping of such particles was fully characterized, and a direct absolute comparison with a geometrical optics model was performed. With this comparison, we were able to show that light absorption by the superparamagnetic particles is negligible for our annular beam tweezers, differing from the case of conventional Gaussian beam tweezers, in which laser absorption by the beads makes stable trapping difficult. In addition, the trap stiffness of the annular beam tweezers increases with the laser power and with the bead distance from the coverslip surface. While this first result is expected and similar to that achieved for conventional Gaussian tweezers, which use ordinary dielectric beads, the second result is quite surprising and different from the ordinary case, suggesting that spherical aberration is much less important in our annular beam geometry. The results obtained here provide new insights into the development of hybrid optomagnetic tweezers, which can apply simultaneously optical and magnetic forces on the same particles.

From Geometric-Optical Remote Sensing Modeling to Quantitative Remote Sensing Science—In Memory of Academician Xiaowen Li

The academician Xiaowen Li devoted much of his life to pursuing fundamental research in remote sensing. A pioneer in the geometric-optical modeling of vegetation canopies, his work is held in high regard by the international remote sensing community. He codeveloped the Li–Strahler geometric-optic model, and this paper was selected by a member of the International Society for Optical Engineering (SPIE) milestone series. As a chief scientist, Xiaowen Li led a scientific team that made outstanding advances in bidirectional reflectance distribution modeling, directional thermal emission modeling, comprehensive experiments, and the understanding of spatial and temporal scale effects in remote sensing information, and of quantitative inversions utilizing remote sensing data. In addition to his broad research activities, he was noted for his humility and his dedication in making science more accessible for the general public. Here, the life and academic contributions of Xiaowen Li to the field of quantitative remote sensing science are briefly reviewed.

Shrub biomass estimation in semi-arid sandland ecosystem based on remote sensing technology

Global land degradation and sustainable development has become a serious challenge for the terrestrial ecosystems. Shrub plays a crucial role in global ecosystem protection, ecological reconstruction, which is especially important in arid and semi-arid sandland ecosystem. Shrub above ground biomass (AGB) is a proxy of carbon sequestration capacity. Shrub AGB in Mu Us Sandland was estimated using different methods based on Landsat Thematic Mapper (TM) data, topography data, combined with in situ survey data. Linear regression model, multiple stepwise regression model, machine learning model and geometric optical model were used to estimate shrub biomass in combination with in situ data, respectively and their effects were validated and compared. Results showed that shrub AGB predicted from one multiple stepwise regression model with Ratio Vegetation Index (RVI) and Brightness from K-T transformation as input variables reached highest accuracy. For both high and low shrub coverage regions, shrub AGB distribution maps derived from this multiple stepwise regression model achieved higher precision. All these findings will provide a scientific support for ecological sustainable development in eco-vulnerable ecosystems.

An Optical Fiber Refractive Index Sensor Based on the Hybrid Mode of Tamm and Surface Plasmon Polaritons.

A novel high performance optical fiber refractive index (RI) sensor based on the hybrid transverse magnetic (TM) mode of Tamm plasmon polariton (TPP) and surface plasmon polariton (SPP) is proposed. The structure of the sensor is a multi-mode optical fiber with a one dimensional photonic crystal (1 DPC)/metal multi-films outer coated on its fiber core. A simulation study of the proposed sensor is carried out with the geometrical optical model to investigate the performance of the designed sensor with respect to the center wavelength, bilayer period and the thickness of silver layer. Because the lights transmitted in the fiber sensor have much larger incident angles than those in the prism based sensors, the center wavelength of the 1 DPC should shift to longer wavelength. When the coupling between TM-TPP and SPP is stronger, the sensor exhibits better performance because the electromagnetic field of the TPP-SPP hybrid mode is enhanced more in the analyte. Compared to most conventional fiber surface plasmon resonance sensors, the figure of merit of the proposed sensor is much higher while the sensitivity is comparable. The idea of utilizing TPP-SPP hybrid mode for RI sensing in the solid-core optical fiber structure presented in this paper could contribute to the study of the fiber RI sensor based on TPP.

On the structure of the drifton phase space and its relation to the Rayleigh–Kuo criterion of the zonal-flow stability

The phase space of driftons (drift-wave quanta) is studied within the generalized Hasegawa–Mima collisionless-plasma model in the presence of zonal flows. This phase space is made intricate by the corrections to the drifton ray equations that were recently proposed by Parker [J. Plasma Phys. 82, 595820602 (2016)] and Ruiz et al. [Phys. Plasmas 23, 122304 (2016)]. Contrary to the traditional geometrical-optics (GO) model of the drifton dynamics, it is found that driftons can not only be trapped or passing but also accumulate spatially while experiencing indefinite growth of their momenta. In particular, it is found that the Rayleigh–Kuo threshold known from geophysics corresponds to the regime when such “runaway” trajectories are the only ones possible. On one hand, this analysis helps to visualize the development of the zonostrophic instability, particularly its nonlinear stage, which is studied here both analytically and through wave-kinetic simulations. On the other hand, the GO theory predicts that zonal flows above the Rayleigh–Kuo threshold can only grow; hence, the deterioration of intense zonal flows cannot be captured within a GO model. In particular, this means that the so-called tertiary instability of intense zonal flows cannot be adequately described within the quasilinear wave kinetic equation, contrary to some previous studies.

Moisture content estimation of forest litter based on remote sensing data.

As a fine fuel, forest litter plays an important role in fire danger rating systems, so forest litter moisture data are necessary and meaningful for fire risk management and prevention. An optical remote sensing technique can provide continuous and regional data for litter moisture estimates, but such an approach is restricted in separating the background reflectance of the forest floor from pixel reflectance because the litter moisture information is included only in background reflectance while pixel reflectance in the forest area consists of both canopy reflectance and background reflectance. Therefore, we present a geometrical-optical model to estimate forest litter moisture by separating contributions of background reflectance from the remote sensing image and use a statistical model to estimate the forest litter moisture content based on the calculated background reflectance. The results show that the model had an R2, root mean square error (RMSE), and average precision of 0.595, 0.372, and 69.654%, respectively. This approach provides a new way of estimating forest litter moisture content from an optical remote sensing image, and it can potentially be applied in large-scale forest litter moisture content mapping.

PROCEDURE ENABLING SIMULATION AND IN-DEPTH ANALYSIS OF OPTICAL EFFECTS IN CAMERA-BASED TIME-OF-FLIGHT SENSORS

Abstract. This paper presents a simulation approach for Time-of-Flight cameras to estimate sensor performance and accuracy, as well as to help understanding experimentally discovered effects. The main scope is the detailed simulation of the optical signals. We use a raytracing-based approach and use the optical path length as the master parameter for depth calculations. The procedure is described in detail with references to our implementation in Zemax OpticStudio and Python. Our simulation approach supports multiple and extended light sources and allows accounting for all effects within the geometrical optics model. Especially multi-object reflection/scattering ray-paths, translucent objects, and aberration effects (e.g. distortion caused by the ToF lens) are supported. The optical path length approach also enables the implementation of different ToF senor types and transient imaging evaluations. The main features are demonstrated on a simple 3D test scene.

Topographic Correction of Forest Image Data Based on the Canopy Reflectance Model for Sloping Terrains in Multiple Forward Mode

Topographic correction methods rarely consider the canopy parameter effects directly and explicitly for sloping canopies. In order to address this problem, the topographic correction method MFM-GOST2 was developed by implementing the second version of the Geometric-Optical model for Sloping Terrains (the GOST2 model) in the multiple forward mode (MFM) inversion framework. First, a look up table (LUT) was constructed by multiple forward modeling of the GOST2 model; second, the radiance of a remotely sensed image and its corresponding topographic data were used for searching potential canopy parameter combinations from the LUT; and third, the corrected radiance was determined by averaging potential radiances of horizontal canopies from the LUT according to the canopy parameter combinations. The MFM-GOST2 and twelve generally used topographic correction methods were evaluated via a case study by visual analysis, linear relationship analysis, and the rose diagram analysis. The result showed that the MFM-GOST2 method successfully removed most of the topographic effects of a subset image of the Landsat-8 image in a case study. The case study also illustrates that the rose diagram analysis is a good way to evaluate topographic corrections, but the linear relationship analysis cannot be used independently for the evaluations because the decorrelation is not a sufficient condition to determine a successful topographic correction.

Individual tree crown detection in sub-meter satellite imagery using Marked Point Processes and a geometrical-optical model

This article describes a new algorithm for the detection and delineation of tree crowns using optical sub-meter resolution satellite images. The algorithm focuses on detecting individual semi-isolated trees in a variety of environments defined as trees outside forests (TOF). The concept of Marked Point Processes (MPPs), which alternates phases of “birth” and “death” iterations to satisfy a density factor was used as a theoretical basis. The “mark” in the MPP represents the object being sought. Unlike most applications of MPP to object recognition, the mark used in our algorithm is computed from a 3D geometrical optical model artificially lit using the same illumination parameters as the image itself. Because trees differ in size, the process also incorporates a tree crown radius variable. The algorithm is tested on four sub-meter satellite images, each in a different environment. Validation was performed on both detection and delineation. The detection was based on tree crown counting and yielded an accuracy ranging from 0.81 to 0.95 for the four images. The delineation accuracy was estimated based on the crown pixel count and yielded an accuracy of ≈ 0.63 (0.57–0.72).

Estimation of forest LAI by inverting canopy reflectance models and multi-angle imagery

Computer simulation models have seldom been applied for estimating the structural and biophysical variables of forest canopy. In this study, an approach for the estimation of leaf area index (LAI) using the information contained in hyperspectral, multi-angle images and the inversion of a computer simulation model are explored. For this purpose, L-systems combined with forest growth model ZELIG were applied to render 3-D forest architectural scenarios. The Radiosity-graphics combined model (RGM) was used to estimate forest LAI from the Compact High-Resolution Imaging Spectrometer/Project for On-Board Autonomy (CHRIS/PROBA) data. LAI inversion was performed using the look-up table (LUT) method. The estimated LAI was evaluated against in situ LAI measurement and compared against the LAI predictions from CHRIS data obtained using the Li-Strahler geometric-optical canopy reflectance model (GOMS). The results indicated that the method used in this study can be efficient strategy to estimate LAI by RGM model inversion.

Target response in a focused, modulated sound field: Modeling and experiment

In a previous work, we had shown that low frequency flexural modes of circular plates and cylinders could be excited using modulated radiation pressure generated by focused ultrasound [ J. Acoust. Soc. Am. 139, 2053 (2016)]. We recently conducted experiments probing how the response of these targets varied as a function of position in the focused ultrasound field. Surprisingly, the response of the circular plate was found to change sign as it was moved away from the source. Two different models were developed to analyze the target response and understand this sign change. A purely geometric model based on ray optics and a semi-physical optics model that uses the incident intensity calculated for the focused source, using a Rayleigh-Sommerfeld integral. Both geometric and semi-physical optics models predict a sign change for the plate response at approximately the correct distance from the source. The sign change is due to a factor in a mode projection that more strongly weights points farther from the center of the plate. The physical optics model was also applied to cylindrical targets. [Work supported by ONR.]In a previous work, we had shown that low frequency flexural modes of circular plates and cylinders could be excited using modulated radiation pressure generated by focused ultrasound [ J. Acoust. Soc. Am. 139, 2053 (2016)]. We recently conducted experiments probing how the response of these targets varied as a function of position in the focused ultrasound field. Surprisingly, the response of the circular plate was found to change sign as it was moved away from the source. Two different models were developed to analyze the target response and understand this sign change. A purely geometric model based on ray optics and a semi-physical optics model that uses the incident intensity calculated for the focused source, using a Rayleigh-Sommerfeld integral. Both geometric and semi-physical optics models predict a sign change for the plate response at approximately the correct distance from the source. The sign change is due to a factor in a mode projection that more strongly weights points farther from the cen...

Predicting forest height using the GOST, Landsat 7 ETM+, and airborne LiDAR for sloping terrains in the Greater Khingan Mountains of China

Sloping terrain of forests is an overlooked factor in many models simulating the canopy bidirectional reflectance distribution function, which limits the estimation accuracy of forest vertical structure parameters (e.g., forest height). The primary objective of this study was to predict forest height on sloping terrain over large areas with the Geometric-Optical Model for Sloping Terrains (GOST) using airborne Light Detection and Ranging (LiDAR) data and Landsat 7 imagery in the western Greater Khingan Mountains of China. The Sequential Maximum Angle Convex Cone (SMACC) algorithm was used to generate image endmembers and corresponding abundances in Landsat imagery. Then, LiDAR-derived forest metrics, topographical factors and SMACC abundances were used to calibrate and validate the GOST, which aimed to accurately decompose the SMACC mixed forest pixels into sunlit crown, sunlit background and shade components. Finally, the forest height of the study area was retrieved based on a back-propagation neural network and a look-up table. Results showed good performance for coniferous forests on all slopes and at all aspects, with significant coefficients of determination above 0.70 and root mean square errors (RMSEs) between 0.50 m and 1.00 m based on ground observed validation data. Higher RMSEs were found in areas with forest heights below 5 m and above 17 m. For 90% of the forested area, the average RMSE was 3.58 m. Our study demonstrates the tremendous potential of the GOST for quantitative mapping of forest height on sloping terrains with multispectral and LiDAR inputs.

Advances in the studies on topographic effects of vegetation indices.

Vegetation index is a key indicator for qualitative and quantitative assessment of green vegetation, which has been widely used in vegetation monitoring. Forests are often distributed in mountainous areas with complex topography, which is one of the main factors of accurate retrieval of forest vegetation information. Here, we analyzed the topographic effects on canopy reflectance using a geometric optical model. The responses of complete ratio vegetation indices [simple ratio index (SR), normalized difference vegetation index (NDVI) and moisture adjusted vegetation index (MAVI)], incomplete ratio vegetation indices [enhanced vegetation index (EVI) and soil adjusted vegetation index (SAVI)], non-ratio vegetation indices [reduced simple ratio (RSR), modified normalized difference vegetation index (MNDVI), greenness vegetation index (GVI)] and, topography adjusted vegetation index [topography adjusted vegetation index (TAVI)] to topography were discussed in detail, with the aim to provide reference for selecting vegetation index in complex terrain mountainous area. The shortcomings of current literatures about the topographic effects on vegetation indices were analyzed and the future research directions were prospected.

Conversion of sparsely-captured light field into alias-free full-parallax multiview content

We propose shearlet decomposition based light field (LF) reconstruction and filtering techniques for mitigating artifacts in the visualized contents of 3D multiview displays. Using the LF reconstruction capability, we first obtain the densely sampled light field (DSLF) of the scene from a sparse set of view images. We design the filter via tiling the Fourier domain of epipolar image by shearlet atoms that are directionally and spatially localized versions of the desired display passband. In this way, it becomes possible to process the DSLF in a depth-dependent manner. That is, the problematic areas in the 3D scene that are outside of the display depth of field (DoF) can be selectively filtered without sacrificing high details in the areas near the display, i.e. inside the DoF. The proposed approach is tested on a synthetic scene and the improvements achieved by means of the quality of the visualized content are verified, where the visualization process is simulated using a geometrical optics model of the human eye.

Study of sea-surface slope distribution and its effect on radar backscatter based on Global Precipitation Measurement Ku-band precipitation radar measurements

The collocated normalized radar backscattering cross-section measurements from the Global Precipitation Measurement (GPM) Ku-band precipitation radar (KuPR) and the winds from the moored buoys are used to study the effect of different sea-surface slope probability density functions (PDFs), including the Gaussian PDF, the Gram–Charlier PDF, and the Liu PDF, on the geometrical optics (GO) model predictions of the radar backscatter at low incidence angles (0 deg to 18 deg) at different sea states. First, the peakedness coefficient in the Liu distribution is determined using the collocations at the normal incidence angle, and the results indicate that the peakedness coefficient is a nonlinear function of the wind speed. Then, the performance of the modified Liu distribution, i.e., Liu distribution using the obtained peakedness coefficient estimate; the Gaussian distribution; and the Gram–Charlier distribution is analyzed. The results show that the GO model predictions with the modified Liu distribution agree best with the KuPR measurements, followed by the predictions with the Gaussian distribution, while the predictions with the Gram–Charlier distribution have larger differences as the total or the slick filtered, not the radar filtered, probability density is included in the distribution. The best-performing distribution changes with incidence angle and changes with wind speed.

Satellite-derived LAI products exhibit large discrepancies and can lead to substantial uncertainty in simulated carbon and water fluxes

Understanding the terrestrial carbon and water cycles is crucial for mitigation and adaptation for climate change. Leaf area index (LAI) is a key biophysical parameter in process-based ecosystem models for simulating gross primary productivity (GPP) and evapotranspiration (ET). The uncertainty in satellite-derived LAI products and their effects on the simulation of carbon and water fluxes at regional scales remain unclear. We evaluated three satellite-derived LAI products - MODIS (MCD15), GLASS, and Four-Scale Geometric Optical Model based LAI (FSGOM) over the period 2003–2012 using fine-resolution (30m) LAI data and field LAI measurements. GLASS had higher accuracy than FSGOM and MCD15 for forests, while FSGOM had higher accuracy than MCD15 and GLASS for grasslands. The three LAI products differed in magnitude, spatial patterns, and trends in LAI. We then examined the resulting discrepancies in simulated annual GPP and ET over China using a process-based, diagnostic terrestrial biosphere model. Mean annual total GPP for China's terrestrial ecosystems based on GLASS (6.32PgCyr−1) and FSGOM (6.15PgCyr−1) was 22.5% and 19.2% higher than that based on MCD15 (5.16PgCyr−1), respectively. Annual GPP based on GLASS and MCD15 increased over larger fractions of China's vegetated area (15.9% and 17.3%, respectively) than that based on FSGOM (12.6%). National annual ET based on GLASS (379.9mmyr−1) and FSGOM (374.4mmyr−1) was 7.9% and 6.3% higher than that based on MCD15 (352.1mmyr−1), respectively. Simulated ET increased in larger fractions of the vegetated area for GLASS (5.7%) and MCD15 (5.8%) than for FSGOM (3.9%). Our study shows that there were large discrepancies in LAI among satellite-derived LAI products and the biases of the LAI products could lead to substantial uncertainties in simulated carbon and water fluxes.

Influence of Surface Roughness Sample Size for C-Band SAR Backscatter Applications on Agricultural Soils

Soil surface roughness determines the backscatter coefficient observed by radar sensors. The objective of this letter was to determine the surface roughness sample size required in synthetic aperture radar applications and to provide some guidelines on roughness characterization in agricultural soils for these applications. With this aim, a data set consisting of ten ENVISAT/ASAR observations acquired coinciding with soil moisture and surface roughness surveys has been processed. The analysis consisted of: 1) assessing the accuracies of roughness parameters $s$ and ${l}$ depending on the number of 1-m-long profiles measured per field; 2) computing the correlation of field average roughness parameters with backscatter observations; and 3) evaluating the goodness of fit of three widely used backscatter models, i.e., integral equation model (IEM), geometrical optics model (GOM), and Oh model. The results obtained illustrate a different behavior of the two roughness parameters. A minimum of 10–15 profiles can be considered sufficient for an accurate determination of $s$ , while 20 profiles might still be not enough for accurately estimating ${l}$ . The correlation analysis revealed a clear sensitivity of backscatter to surface roughness. For sample sizes >15 profiles, ${R}$ values were as high as 0.6 for ${s}$ and ~0.35 for ${l}$ , while for smaller sample sizes ${R}$ values dropped significantly. Similar results were obtained when applying the backscatter models, with enhanced model precision for larger sample sizes. However, IEM and GOM results were poorer than those obtained with the Oh model and more affected by lower sample sizes, probably due to larger uncertainly of ${l}$ .

Volumetric integration model of the Stiles-Crawford effect of the first kind and its experimental verification.

The integrated Stiles-Crawford function is commonly used as apodization model for vision through the natural eye pupil. However, this method does not account for possible effects related to the retinal thickness, the large length-to-diameter aspect ratio of the photoreceptors, or the use of nonMaxwellian illumination. Here, we introduce a geometrical optics model to calculate the fraction of overlap between light at the retina and the photoreceptor outer segments where absorption triggers vision. The model, which does not account for photoreceptor waveguiding, is discussed for both Maxwellian and nonMaxwellian illumination. The integrated Stiles-Crawford effect is analyzed experimentally with a uniaxial pupil-size flicker methodology and we find that the psychophysical measurements match better to the geometrical optics predictions than direct integration of a Stiles-Crawford function.

GOFP: A Geometric-Optical Model for Forest Plantations

Geometric-optical (GO) model suitable for forest plantation (GOFP) is a GO model for forest plantations at the stand level developed in this study based on a four-scale GO model a Geometric-Optical Model for Sloping Terrains-II (GOST2), which simulates the bidirectional reflectance distribution function (BRDF) for natural forest canopies. In most previous GO models, tree distributions are often assumed to meet the Poisson or Neyman model in a forest; therefore, these models are suitable for simulating BRDF for natural forest canopies. However, in forest plantations, tree distributions are proven to meet the hypergeometric model rather than the Poisson or Neyman model at the stand level. GOFP, in which the tree distributions are described using the hypergeometric model, is proposed to simulate the bidirectional reflectance factor (BRF) of forest plantations at the stand level. The area ratios of the four scene components (sunlit foliage, sunlit ground, shaded foliage, and shaded ground) of GOFP compare well with those simulated by a 3-D canopy visualization technique. A comparison is also made against discrete anisotropic radiative transfer, showing that GOFP has the ability to simulate BRF of forest plantations. Another comparison is made against operational land imager and Moderate Resolution Imaging Spectroradiometer surface reflectance, showing that GOFP with the hypergeometric model outperforms GOST2 with the Poisson and Neyman models. The results further show that the differences in BRFs between GOFP and GOST2 pronouncedly increase with the difference between the reflectance of sunlit foliage ( $R_{T}$ ) and the reflectance of sunlit ground ( $R_{G}$ ), as well as the distances among trees and the number of crowns in a forest plantation, suggesting that GOFP significantly outperforms GOST2 for simulating BRF of forest plantations.

Estimation of coniferous forest aboveground biomass with aggregated airborne small-footprint LiDAR full-waveforms.

Forest aboveground biomass (AGB) is critical for assessing forest productivity and evaluating carbon sequestration rates. Discrete-return LiDAR has been widely used to estimate forest AGB, however, fewer studies have estimated the coniferous forest AGB using airborne small-footprint full-waveform LiDAR data. The objective of this study was to extract a suite of newly proposed metrics from airborne small-footprint full-waveform LiDAR data and to evaluate the ability of these metrics in estimating coniferous forest AGB. To achieve this goal, each waveform was first preprocessed, including de-noising, smoothing, and normalization. Next, all the waveforms within each plot were aggregated into a large pseudo waveform and the return energy profile was generated. Then, the foliage profile was retrieved from the return energy profile based on the Geometric Optical and Radiative Transfer (GORT) model. Finally, a series of new return energy profile metrics and foliage profile metrics were extracted to estimate forest AGB. Simple linear regression was conducted to assess the correlation between each LiDAR metric and forest AGB. Stepwise multiple regression analysis was then carried out to select important prediction metrics and establish the optimal forest AGB estimation model. Results indicated that both return energy profile and foliage profile based height-related metrics were strongly correlated to forest AGB. The energy weighted canopy height (HEweight) (R = 0.88) and foliage area weighted height (HFweight) (R = 0.89) all had the highest correlation coefficients with forest AGB in return energy profile metrics and foliage profile metrics respectively. Energy height percentiles and foliage height percentiles also had the ability to explain AGB variation. The energy-related metrics, foliage area-related metrics, and bounding volume-related metrics derived from the return energy profile and foliage profile were not all sensitive to forest AGB. This study also concluded that combining return energy profile metrics and foliage profile metrics could improve the accuracy of forest AGB estimation, and the optimal model contained the metrics of HFweight, HEweight, and VolumemaxHE, which is the product of the maximum canopy return energy profile amplitude (maxCE) and the maximum height of return energy profile (maxHE).