Specular Plane Research Articles

Batch Specular Plane Flatness Measurements Based on Phase Measuring Deflectometry.

Flatness is a critical parameter in the manufacturing industry, directly impacting the fit and overall product performance. As the efficiency of manufacturing continues to advance, there is an increasing demand for more accurate and efficient measurement techniques. Existing methods often struggle to strike a balance between precision and efficiency. In response, this article introduces a novel approach that is capable of achieving high-precision and rapid measurements concerning multiple surfaces. By enhancing the traditional phase measuring deflectometry (PMD) method, employing a matching technique based on polar lines and normal vector constraints to address discrete surface measurement challenges, and implementing a plane pre-positioning method to tackle low efficiency in binocular matching and solving, we successfully performed swift and synchronized measurements for a large batch of specular surfaces and obtained the three-dimensional surface profile of each measured surface. Through experimental validation, the method proposed in this paper can perform the batch measurement of specular planes while maintaining high measurement accuracy.

Time-series polarimetric bistatic scattering decomposition using comprehensive modified first-order radiative transfer model at C-band for vegetative terrain and validation

ABSTRACT The sensitivity of the bistatic scattered signal to both the soil and vegetation physical properties in microwave sensing of vegetation is subject to uncertainties. A multi-angular and fully polarimetric data acquisition from a bistatic system increases the number of observations. Thus, optimum bistatic system parameters for vegetation monitoring are necessary to develop an understating of microwave interactions with the surface and vegetation properties. In this study, C-band fully polarimetric bistatic scatterometer (BiSCAT) system was designed to measure the scattering response of vegetated terrain in the forward specular plane. The correlation analysis between the measured bistatic scattering coefficient () and in-situ soil/vegetation properties, such as plant water content (PWC) and soil moisture (), was used to find the optimum specular incidence angle of the BiSCAT system. The optimum parameters of the BiSCAT system were used as input to the modified first-order radiative transfer model (MRTM) for the simulation for vegetation. Kirchhoff’s approximate (KA) model for soil surface in forward specular plane was simplified for soil contribution within MRTM. Additionally, the temporal patterns of are modelled by employing the empirical formulation between the vegetation optical depth and PWC. The MRTM offers an understanding of co-polarized electromagnetic signal interaction with the temporal change in vegetation constituents and soil surface parameters. The model is limited to providing insights into co-polarized radar return from the target due to the incapability of yielding the cross-polarization factor from the KA model in the forward specular direction. The contributions of surface, vegetation, surface-vegetation, vegetation-surface and surface-vegetation-surface were quantified to better understand microwave’s interaction with the vegetation. The model is calibrated using a constrained non-linear least-square optimization algorithm. The performance indices of simulating yields good agreement with the BiSCAT measurements.

System calibration method for infrared phase measuring deflectometry

Infrared phase measuring deflectometry (IR PMD) is a kind of PMD technique, which exploits IR light as a display screen, therefore it can effectively improve the measurement accuracy by reducing the environmental noise, especially the influence of the ambient light. However, data accuracy of a deflectometric measurement system is mainly determined by calibration procedure, which establishes the relationship between phase map and depth data. In this paper, a novel using fringe projection profilometry (FPP) technology based system calibration method is proposed to obtain the geometrical parameters of the IR PMD system. A composite plane calibration board with diffused and specular surface has been designed to determine the X, Y, and Z coordinates of this specular plane at a reference position, which is located at a certain reference position parallel to the ground glass (used as the IR screen) to obtain the system parameter d. Experimental results demonstrate that 3D shape of specular objects can be effectively and accurately measured using the proposed geometrical calibration method.

Synergy in the interaction of amoxicillin and methylene blue with dipalmitoyl phosphatidyl choline (DPPC) monolayers

Understanding molecular-level mechanisms in the action of emergent pollutants is essential to correlate with their possible impact on living organisms in the environment and on human health. In this study, we investigate the interactions between two widely used compounds classified as emerging pollutants and Langmuir monolayers of 1,2-dipalmitoyl-sn-glycerol-3-phosphocholine (DPPC) that represent a simplified model of the lipidic structure of cell membranes. The pollutants studied were the antibiotic amoxicillin (AMX) and methylene blue (MB), a pharmaceutical drug also used as a dye in industry. AMX and MB were found to expand the surface pressure isotherms of DPPC, also affecting its morphology according to Brewster angle microscopy images. Significantly, when these compounds were mixed (MIX), monolayer expansion increased. The synergy in MIX activity was confirmed with in-situ polarization-modulated infrared reflection absorption spectroscopy (PM-IRRAS) measurements, which indicated that electrostatic interaction with DPPC head groups was considerably stronger than for either AMX or MB. An adduct formed between AMX and MB in MIX also caused the DPPC monolayer thickness to increase, as inferred from measurements with grazing-incidence X-ray scattering out of the specular plane (GIXOS), in contrast to the decreased thickness induced by AMX or MB. That a mixture potentiates the interaction between contaminants and cell membrane models may be relevant for cocktail effects on living organisms.

Simultaneous spatial and angular positioning of plane specular samples by a novel double beam triangulation probe with full auto-compensation

The positioning of a plane specular sample to be measured or processed is an important requirement in many fields of research and industry. Where a sample is to be processed either by electromagnetic waves or a particle beam of higher numerical aperture the irradiance or the particle number over unit area is position and angle dependent. Where optical properties of a sample are to be measured, such as in spectrophotometry, these parameters can depend on the angle of incidence and on the value of the irradiance, i.e. on the angular and spatial position of the sample. In some cases parameters of many samples have to be compared among each other or to those of a standard, this also requires the highly accurate positioning of each sample to the same position. This paper describes a method that is suitable for high accuracy alignment of specular plane samples both angularly and spatially. It applies a double beam triangulation probe, where the second beam serves not only as a reference beam to compensate for any changes of the transmitting media and that of the laser but also doubles the sensitivity of the probe. The method does not compete with interferometric methods, it is required only in special applications, but provides an absolute uncertainty for spatial positioning in the sub-micrometer range and an angular one in the 0.0003° range. Furthermore, the accuracy is tunable by the parameters of the setup.

Effects of ocean particles on the upwelling radiance and polarized radiance in the atmosphere-ocean system

Based on a vector radiative transfer model of the atmosphere-ocean system, the influence of oceanic components on radiation processes, including polarization effects, was investigated in the wavelength region ranging from 0.380 to 0.865 μm. The components considered were phytoplankton, inorganic suspended material (sediment), and colored, dissolved organic matter. Due to their important roles in oceanic radiation processes, the sensitivity of the bidirectional reflectance to the rough ocean surface, represented by the wind velocity 10 m above the ocean surface, and aerosol, were taken into account. The results demonstrated that both radiance and polarized radiance just below the ocean surface were sensitive to the change of the concentrations of the considered components, while the dependence of polarized radiance on the observation geometry was more sensitive than radiance. Significant differences in the specular plane existed between the impacts of the phytoplankton and sediment on the degree of polarization just above the ocean surface at 670 nm. At the top of the atmosphere (TOA), polarization was relatively insensitive to changing concentrations of ocean particles at longer wavelengths. Furthermore, the radiance at the TOA in the solar plane was more sensitive to the aerosol optical thickness than wind velocity. In contrast, wind velocity strongly influenced the radiance at the TOA in the sun glint region, while the polarization degree showed less dependence in that region. Finally, a nonlinear optimal inversion method was proposed to simultaneously retrieve the aerosol and wind velocity using radiance measurement.

Performance Evaluation of a Double-Glazed Box-Type Solar Oven with Reflector

This research paper describes the performance evaluation of a double-glazed box-type solar oven with reflector fabricated using locally available materials, compressed sawdust with binder; size of the box is 700&#x2009;mm&#x2009;&#xd7;&#x2009; 700&#x2009;mm &#xd7; 400&#x2009;mm and 10&#x2009;mm thickness. The experimental solar cooker consists of an aluminium absorber plate (1&#x2009;mm) painted matt black and a double-glazed lid. The bottom and sides are lagged with fibreglass wool insulator, thickness = 50&#x2009;mm, <svg style="vertical-align:-0.1638pt;width:64.612503px;" id="M1" height="12.4375" version="1.1" viewBox="0 0 64.612503 12.4375" width="64.612503" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(.017,-0,0,-.017,.062,12.162)"><path id="x1D458" d="M480 416q0 -21 -18 -41q-9 -11 -17 -7q-20 9 -42 9q-62 0 -140 -78q23 -69 88 -192q17 -31 27 -42t20 -11q16 0 62 46l17 -20q-64 -92 -119 -92q-35 0 -70 66q-41 73 -84 187q-36 -30 -62 -61q-27 -115 -35 -172q-41 -8 -78 -20l-6 6l140 612q7 28 0.5 34t-37.5 7l-34 1&#xA;l5 26q38 4 74 13.5t57 17t25 7.5q12 0 4 -32l-104 -443h2q35 38 97 93q39 35 65.5 56t62 41.5t58.5 20.5q19 0 30.5 -10t11.5 -22z" /></g><g transform="matrix(.017,-0,0,-.017,13.322,12.162)"><path id="x3D" d="M535 323h-483v50h483v-50zM535 138h-483v50h483v-50z" /></g><g transform="matrix(.017,-0,0,-.017,28.025,12.162)"><path id="x30" d="M241 635q53 0 94 -28.5t63.5 -76t33.5 -102.5t11 -116q0 -58 -11 -112.5t-34 -103.5t-63.5 -78.5t-94.5 -29.5t-95 28t-64.5 75t-34.5 102.5t-11 118.5q0 58 11.5 112.5t34.5 103t64.5 78t95.5 29.5zM238 602q-32 0 -55.5 -25t-35.5 -68t-17.5 -91t-5.5 -105&#xA;q0 -76 10 -138.5t37 -107.5t69 -45q32 0 55.5 25t35.5 68.5t17.5 91.5t5.5 105t-5.5 105.5t-18 92t-36 68t-56.5 24.5z" /></g><g transform="matrix(.017,-0,0,-.017,36.185,12.162)"><path id="x2E" d="M113 -12q-24 0 -39.5 16t-15.5 42q0 24 16 40.5t40 16.5t40 -16.5t16 -40.5q0 -26 -16 -42t-41 -16z" /></g><g transform="matrix(.017,-0,0,-.017,40.061,12.162)"><use xlink:href="#x30"/></g><g transform="matrix(.017,-0,0,-.017,48.22,12.162)"><path id="x35" d="M153 550l-26 -186q79 31 111 31q90 0 141.5 -51t51.5 -119q0 -93 -89 -166q-85 -69 -173 -71q-32 0 -61.5 11.5t-41.5 23.5q-18 17 -17 34q2 16 22 33q14 9 26 -1q61 -50 124 -50q60 0 93 43.5t33 104.5q0 69 -41.5 110t-121.5 41q-53 0 -102 -20l38 305h286l6 -8&#xA;l-26 -65h-233z" /></g><g transform="matrix(.017,-0,0,-.017,56.379,12.162)"><path id="x32" d="M412 140l28 -9q0 -2 -35 -131h-373v23q112 112 161 170q59 70 92 127t33 115q0 63 -31 98t-86 35q-75 0 -137 -93l-22 20l57 81q55 59 135 59q69 0 118.5 -46.5t49.5 -122.5q0 -62 -29.5 -114t-102.5 -130l-141 -149h186q42 0 58.5 10.5t38.5 56.5z" /></g> </svg>&#x2009;W/m&#xb0;C. The reflector consists of a wooden-framed commercially available specular plane mirror which is sized to form a cover for the box when not being in use. Its thermal performance was tested according to the ASAE International Test procedure and Bureau of Indian Standards (BIS) for testing the thermal performance of box-type solar cooker. Thermal performance experiments were conducted in order to determine the first figure of merit (<i>F</i>₁), the second figure of merit (<i>F</i>₂) and standard cooking power (<i>P</i>_<i>s</i>). The obtained test results were employed to calculate the two figures of merit (<i >F</i>₁, and <i>F</i>₂) and the standard cooking power (<i>P</i>₅₀) to be 0.11&#x2009;Km<sup >2</sup>w<sup >&#x2212;1</sup>, 0.31, and 23.95&#x2009;W, respectively. Finally, the results illustrated that the cooker has a good reliability for cooking food and boiling water.

Characterization of White Paper Sheets by BRDF Model Parameters Estimated in the Specular Reflection Plane

We characterize sheets of white paper using three bidirectional reflectance distribution function (BRDF) model parameters estimated from the BRDF in the specular reflection plane. The radiance factors of eight types of paper sheets having a wide range of material characteristics were measured for 284 geometries in the specular reflection plane. They were approximated within an average error of 4.5% using a linear combination of Torrance-Sparrow and Lambert's BRDF models. The proposed model well approximated the BRDF of samples in the specular plane. Based on the estimated BRDF model parameters, the eight measured paper sheets could be broadly classified into glossy papers and rough papers. The two glossy papers were distinguishable from each other, while the six rough papers could be classified into three groups using the BRDF model parameters. The proposed method is considered to be effective for characterizing a wide range of white paper ranging from glossy to matte paper.

Energy Transition for Depolarized Backscatter from Rough Surfaces

In this paper we study the depolarized backscatter enhancement phenomenon for electromagnetic wave scattering from rough surfaces. Some new experimental data on light scattering from rough metallic surfaces shows a phenomenon of backscattering enhancement existing in the antispecular direction under some conditions, such as the surface parameters, wave polarization and operating frequency. From a roughly random surface the backscattering enhancement is predicted due to the constructive interference of multiple surfaces scattering. The study is based upon the integral equation method modified to be able to predict the phenomenon of multiple scattering and backscattering enhancement. From the study we found the backscattering enhancement takes place on the specialized surface parameters large compared with the incident wavelength. Further we also conclude that the depolarized multiple scattering makes much contribution along the plane of incidence from random rough surfaces, but depolarized single scattering makes little contributions as our expectation. In comparison of model prediction of total multiple scattering strength with measured data along the specular plane, excellent agreement is obtained.

Depolarized Backscatter Phenomenon from Rough Surfaces

In this article, we study the depolarized backscatter enhancement phenomenon for electromagnetic wave scattering from rough surfaces. There is some new experimental data on light scattering from rough metallic surfaces that shows there is an enhancement of backscattering in the antispecular direction under certain conditions of surface parameters, wave polarization, and operating frequency. From a roughly random surface, the backscattering enhancement is predicted as the constructive interference of multiple surfaces scattering. The study is based upon the integral equation method modified to be able to predict the phenomenon of multiple scattering and backscattering enhancement. From the study, it was found that the backscattering enhancement takes place largely on the specialized surface parameters compared with the incident wavelength. Further, it is also concluded that the depolarized multiple scattering makes many contributions along the plane of incidence from random rough surfaces, but depolarized single scattering makes little contributions. In the comparison of model prediction of total multiple scattering strength with measured data along the specular plane, excellent agreement is obtained.

From Specular Reflectivity to Time-Resolved Grazing Incidence X-ray Scattering out of the Specular Plane (GISAXS): Equilibrium and Nonequilibrium States of Organic/Inorganic Monolayers at Liquid Surfaces

The grazing incidence diffuse X-ray scattering out of the specular plane technique (GISAXS) is presented, and its capabilities are compared to the more classical X-ray specular reflectivity technique (XSR). Three experimental illustrations are given to prove the efficiency of GISAXS. First, the structure of a DPPC phospholipid monolayer is analyzed. Second, the time-resolved kinetics of lipid desorption from a monolayer interacting with a mineral gel subphase is studied. Third, the structural evolution of biomembranes at extremely low temperatures is illustrated. The GISAXS technique appears to compete efficiently with neutron reflection techniques by taking advantage of remarkably short acquisition times crucial in kinetics experiments.

Grazing Incidence X-ray Scattering to Probe the Self-Assembly of Phthalocyanine Nanorods on a Liquid Surface

The structural properties of Langmuir monolayers on aqueous substrates of a metal free phthalocyanine, 2,9,16,23-tetrakis(phenylthio)-29H,31H-phthalocyanine and an Aluminum centered phthalocyanine, Aluminum 2,9,16,23-tetrakis(phenylthio)-29H,31H-phthalocyanine chloride are reported here. Their structure is investigated under progressive lateral compression by grazing incidence diffuse X-ray scattering out of the specular plane to determine specular reflectivity-like information where the phase change of the molecules from "flat-lying" on the surface to "edge-standing" perpendicular to the surface was directly observed. Furthermore grazing incident X-ray diffraction is used to investigate the in-plane ordering of the system where it has been found that at high density states the systems can be considered as monolayers consisting of arrays of side-by-side cofacially aggregated cylindrical rodlike entities.

Observation of the desorption of mineral nanoparticles from a hybrid Langmuir monolayer: an in situ grazing incidence X-ray (GIXOS) study.

The kinetics and mechanism of the desorption of mineral clay particles originally adsorbed to a phospholipid monolayer has been studied. The desorption was induced by the injection of citric acid solution into the aqueous subphase. To follow the related kinetic processes, grazing incidence diffuse X-ray scattering out of the specular plane (GIXOS) was used with a remarkable time resolution of the order of one minute. From the variations of the electron density profile normal to the surface, the Langmuir desorption isotherm and the related kinetic constants were determined.

Observation of Zinc Phthalocyanine Aggregates on a Water Surface Using Grazing Incidence X-ray Scattering

Reported here are the structural properties of a zinc 2,9,16,23-tetra-tert-butyl-29H,31H-phthalocyanine Langmuir monolayer on a water surface under progressive lateral compression investigated by grazing incidence X-ray scattering. Grazing incidence diffuse X-ray scattering out of the specular plane (GIXOS) is exploited to determine specular reflectivity-like information where the phase change of flat-lying molecules on the surface to edge-standing molecules perpendicular to the surface is directly observed. Furthermore, grazing incident X-ray diffraction (GIXD) is used to investigate the in-plane ordering of the system where it has been found that in the high-density state (approximately 0.35 nm2 per molecule) the system can be considered to be a monolayer consisting of arrays of side-by-side lying cofacially aggregated cylindrical rodlike entities.

Thermodynamic and Structural Properties of Phospholipid Langmuir Monolayers on Hydrosol Surfaces

Measurements of Langmuir pressure/area isotherms, rheology, grazing incidence X-ray diffraction (GIXD), and grazing incidence diffuse X-ray scattering out of the specular plane (GIXOS) have been used to investigate the influence of a hydrosol containing charged mineral nanoparticles on the thermodynamic and structural properties of a DPPC monolayer. The mineral adsorption layer that is formed via electrostatic interaction underneath the lipid layer alters the thermodynamic properties of the phospholipid monolayer in terms of maximal achievable compression, compressibility, and phase behavior. Modifications appear in the latter case as a coolinglike effect. Rheology measurements of the bulk viscoelastic properties revealed a stabilizing effect of the transient bulk network on the surfactant layer. The lipid chain lattice is found to be reorganized and adapted to the internal atomic structure of the mineral particles. A model for the superposition of Bragg rods from the lipid chains and the minerals is applied to separate these scattering contributions. In the vicinity of the mineral particles, the (2) reflection for DPPC on a liquid substrate was found, indicating strongly suppressed fluctuations at the surface. An estimation of the Debye-Waller factor associated with the lipid layer organization is used to quantify the damping of fluctuations within the lipid matrix due to the rigidifying and stabilizing effect of the mineral particles.

DEPOLARIZED UPWARD AND DOWNWARD MULTIPLE SCATTERING FROM A VERY ROUGH SURFACE

From a very roughly random surface the backscattering enhancement is predicted due to the constructive interference of multiple surfaces scattering. For specialized surfaces involving roughness large compared with the incident wavelength, the backscattering enhancement takes place. The phenomenon of backscatter enhancement becomes evident for both larger normalized surface height and surface rms slope. In this paper we take further study to predict the backscattering enhancement mainly comes from upward multiple scattering. On the contrary the downward multiple scattering has no contributions to the scatter strength of backscattering enhancement. The model developed in this paper is based upon the integral equation method and able to predict this phenomenon of multiple scattering and backscattering enhancement. The depolarized multiple scattering makes much contribution along the plane of incidence from random rough surfaces, but depolarized single scattering makes little contributions. The total multiple scattering strength is the summation of upward and downward multiple scattering strength. In comparison of model prediction of total multiple scattering strength with measured data along the specular plane, excellent agreement is obtained.

Nanosize Structure of Sputter-Deposited Tungsten Carbide Thin Films

The structure of thin films of tungsten-carbon, deposited onto monocrystalline silicon substrates by reactive magnetron sputtering (argon + benzene) in a wide range of preparation parameters has been investigated by GISAXS. Substrates were in a fixed position relative to the two adjacent cylindrical magnetrons. Benzene partial pressure was varied from 1% to 10% of the total working gas pressure. A series of samples were prepared, with the substrate held at room temperature and 400°C, and the substrate potential held at floating potential or biased -70 V with respect to the discharge plasma. The bulk particle contribution to the scattering was investigated outside of the specular plane, applying a two dimensional CCD detector. For higher values of benzene partial pressure, the generated films consist of densely packed tungsten carbide grains in an amorphous, carbon rich matrix, while, in some cases, the lower benzene pressure resulted in isolated carbon rich particles in tungsten carbide. From earlier work it is known that the preparation parameters influence the film’s chemical composition, the relatively complex dependence of particle sizes on benzene partial pressure can be explained as a function of the relative carbon content.

Investigation of roughness cross correlation in a Ni/C multilayer mirror by X-ray diffuse scattering method

The possibility of applying X-ray diffuse scattering for studying roughness in multilayer X-ray mirrors, including the correlation of roughnesses of neighboring interfaces (roughness cross-correlation) is considered. It is shown that the reliability and informativeness of this method can be improved by rejecting the classical experimental schemes and using alternative schemes in which not only the intensity of diffuse scattering itself, but also its dependence on certain experimental parameters (conditions), vary. Such parameters can be the spatial coherence of incident radiation, the direction of the momentum transfer relative to the specular diffraction plane, or the X-ray wavelength. In the framework of this approach, the results of comparative measurements of diffuse scattering from a Ni/C multilayer X-ray mirror prepared by laser ablation are considered for two close values of photon energy: below (8.325 keV) and above (8.350 keV) the K absorption edge for nickel. It is shown that, in view of effective screening of deep layers in the hard photoabsorption mode, this method provides more reliable (as compared to the standard diffuse scattering method) information on the evolution of interfaces between the layers. It is found that the smoothing of roughness in the experimental sample occurs over large spatial scales such as the micrometer scale. Only large-scale defects with a size exceeding 10 µm are replicated well from layer to layer. Possible physical reasons for the observed effect are considered. It is shown that effective smoothing on the micrometer and submicrometer spatial scales is of fundamental importance for preparing multilayer X-ray mirrors with high reflectances.

Design and measured performance of a plane reflector augmented box-type solar-energy cooker

The design philosophy, construction and measured performances of a plane-reflector augmented box-type solar-energy cooker are presented. The experimental solar cooker consists of an aluminum plate absorber painted matt black and a double-glazed lid. The bottom and sides are lagged with fibreglass wool insulator. The reflector consists of a wooden-framed commercially available specular plane mirror which is sized to form a cover for the box when not in use. Provision is made for four cooking vessels, each capable of holding upto 1 kg of water. Results of thermal performance tests show stagnation absorber plate temperatures of 138°C and 119°C for the cooker with and without the plane reflector in place respectively. Boiling times of 60 min (3600 s) and 70 min (4200 s) for 1 kg of water, for the cooker with and without the plane reflector in place, respectively, were recorded. The solar cooker performance has been rated using the first figure of merit (F 1) on the no-load test and the second figure of merit (F 2) on the sensible heat tests. Predicted water boiling times using the two figures of merit compared favourably with measured values. The performance of the cooker with the plane reflector in place was improved tremendously compared to that without the reflector in place.

Influence of x-ray beam spatial coherence on the diffuse scattering from multilayer mirrors

The improved spatial coherence of a synchrotron radiation beam was shown experimentally to stimulate additional diffuse scattering of x rays diffracted from x-ray multilayer mirrors. Although the large-scale (tens of microns) roughness does not affect Bragg diffraction from multilayers, its presence causes phase shifts at the wave packet front. This leads to partial decay of the coherent wave packet and creates additional diffuse scattering. Additional scattering from this mechanism was observed at angles of incidence corresponding to the Bragg and Kiessig maximum angles. The properties of this scattering caused by large-scale roughness, observed due to improved x-ray beam spatial coherence, were shown experimentally to be different from those of diffuse scattering previously reported when the incoming or outgoing angle is equal to the Bragg angle. Typical breaks in the diffuse scattering intensity due to the standing-wave effect are absent, and there is obvious asymmetry of the diffuse scattering cross section around the incoming and outgoing angles. Due to the small angle of incidence, the coherently irradiated area has very different dimensions parallel and perpendicular to the beam, which leads to the observed scattering being concentrated in the specular diffraction plane defined by the incident and reflected wave vectors.