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Backscattering properties of topographic targets in the visible, shortwave infrared, and mid-infrared spectral ranges for hard-target lidars

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Abstract

Hard-target lidars rely on the reflectivity and backscattering properties of topographic targets, which are rather difficult to evaluate, resulting in uncertainties when assessing the performance of the instrument. In this work, backscattering properties and hemispherical reflectance of topographic targets are measured in the visible, near-infrared, and mid-infrared spectral ranges. A laboratory setup mimicking a hard-target lidar is used to measure the backscattered signals at various angles of incidence, which are then fitted using a bidirectional reflectance distribution function Phong model. We show that these results are useful for optimizing active stand-off detection and hard-target lidars and for increasing their overall efficiency.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. INTRODUCTION

Active stand-off detection and hard-target lidar are common methodologies for aerosols measurements, trace gas identification, hazardous material sensing, or explosive detection, to name a few [15]. Hard-target lidars are defined as a light detection and ranging technique for measuring backscattered radiations from rigid structure targets possessing pronounced reflection properties (specular, diffuse, and retro-reflection), as opposed to regular lidars often used in atmospheric physics where the scattering medium is a volume and not a surface. Aerosols and gas exhibit weak scattering properties in comparison with hard targets. By their nature, this type of instrument heavily relies on the reflectivity or backscattering properties of distant targets. With the reduction in size of powerful lasers and detection systems, it became possible to make these instruments portable [2,6], rendering them suitable for mobile platforms such as drones, helicopters, planes, or cars. While some applications allow the use of retroreflectors or mirrors, most mobile systems require the use of actual topographic targets, such as the ground, roads, buildings, roofs, or vegetation. Thus, the overall performance of these systems depends on the optical properties of these targets. Despite previous studies [711], the lidar community keeps interest in the topic due to the large number of potential targets and possible emission wavelengths.

A relevant parameter to theoretically assess the optical properties of a solid surface is the bidirectional reflectance distribution function (BRDF) [12]. The BRDF is a function that defines the ratio between the radiance of a sample and irradiance upon that sample, for particular incident and scatter angles. The scattered light intensity depends on the position of both viewer and light source relative to the surface normal. Consequently, a BRDF is a function of four real variables, which are the azimuth and zenith angles of both incoming light and outgoing direction, taken that the surface normal is defined as the z axis. In the case of topographic targets, BRDFs are rather difficult to evaluate, since the target’s chemical compositions, roughness, and morphology are generally poorly known. Furthermore, BRDF models, such as the Ward model [13,14], generally do not take into account the wavelength of the incident light, as many of these models are developed for applications in the visible spectral range. This proves especially critical, as many targets such as sanded aluminum, will show a diffuse reflection in the visible range and a specular reflection in the mid-infrared (IR) range. In the case of hard-target lidars, the wavelength of the light source can range from UV to mid-IR [5,15,16]. The diffuse and specular properties of a target affect significantly the performance of the system, relying on backscattered light. Specular targets will result in high backscattering coefficients when the angle of incidence is close to 0° but very low signal otherwise, while diffuse targets will result in higher signals for a large angle of incidence but low signal for a small angle of incidence when compared to a specular target.

Consequently, due to the wide variety of backscattering coefficients and angular distribution [17,18], estimates of backscattering coefficients may be off by orders of magnitude. Due to the relation of proportionality between signal and backscattering coefficient, the estimated signal and signal-to-noise ratio suffer similar uncertainties of potentially orders of magnitude. With many hard-target lidars based on optical absorption spectroscopy [19], it may be difficult to compare the overall instrument performances of the system at different spectral ranges without being able to properly evaluate the signal strength. As an example, a methane detector may be operated at 1.6 μm, 3.0–3.45 μm, or 7.7 μm [2023]; while the respective absorption cross section and available laser power at the corresponding wavelength may be properly assessed, the backscattering coefficient remains difficult to evaluate.

In this contribution, we studied the optical properties of multiple common urban topographic targets using a laboratory setup mimicking a hard-target lidar in the visible, short-wave IR (SWIR) and mid-IR spectral ranges (respectively, 0.488 μm, 1.32 μm, and 7.6 μm wavelengths). The BRDF of each target is experimentally retrieved for a backscattering configuration, i.e., when azimuth angles θ and zenith angles ϕ of the incoming light and outgoing direction are equal. Then, each resulting profile has been fitted using the Phong reflectance model [24] and calibrated using a well-characterized near-Lambertian gold target. These results provide the necessary data to evaluate the expected signal from six types of targets, three spectral ranges, and angles of incidence ranging from 80° to +80°. Finally, a numerical simulation is performed to evaluate the backscattered intensity from two of the considered materials at each wavelength for two angles of incidence.

The paper is organized as follows. First, the methodology to retrieve the optical properties of topographic targets is described together with a short description of the Phong model used to fit these measurements. Then, the experimental setup is presented, followed by the last section where our experimental results are displayed and discussed.

2. METHODOLOGY

A. Experimental Methodology

In this work, an optical setup operating at three wavelengths has been designed to study the optical properties of multiple topographic targets. The system is made of interchangeable lasers emitting at 0.48 μm, 1.32 μm, and 7.6 μm wavelength. The laser beam is transmitted towards a large-area rotation stage on which can be set up multiple samples of topographic targets. The light backscattered by the target is focused on a light detector by an off-axis parabolic gold mirror, 1 m away from the target. The parabolic mirror has a hole at its center, so its optical axis and the laser beam are collinear. Signals are then recorded as the target is rotated on the rotation stage. Thus, the system mimics signals from a co-axial hard-target lidar. The optical layout of the system is displayed in Fig. 1, and specifications of each component are detailed in Section 3.

 figure: Fig. 1.

Fig. 1. Optical layout of the system used to measure the backscattered light of multiple targets at multiple angles of incidence in the visible (0.48 μm), shortwave infrared (1.32 μm), and mid-infrared (7.6 μm).

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In this configuration, the target is rotated only on its vertical axis (i.e., changing the azimuth angle θ); however, it is assumed that by symmetry, leaning the target up or down (i.e., changing the zenith angle ϕ) provides the same angular signal profile. As a result, from here after, signals are expressed only as a function of θ. Backscattered signals from the target, ST(θ), are recorded for multiple angles θ, where θ=0° is the normal angle of incidence. Due to every other variable being independent from the rotation stage position, signals are solely proportional to the backscattering coefficients β(θ), so that β(θ)=G·ST(θ), where G is a calibration constant. The latter is retrieved by using a near-Lambertian gold target as a reference target (index RT) with well-defined hemispherical reflectance RRT for each wavelength of interest and measured signal SRT(θ);G can be retrieved using Eq. (1), thus avoiding many of the difficulties of general signal calibration involved for an absolute calibration procedure [25]:

G=RRTππSRT(θ)dθ.
The hemispherical reflectance, also sometimes referred to as the integral reflectivity, is defined as the ratio between the radiant flux reflected by the surface and the radiant flux received by the surface. The hemispherical reflectance of the field target RT is retrieved by using signals SRT from the reference target and from the target ST at various azimuth angles θ. In this manner, RT is described by Eq. (2):
RT=RRTππST(θ)dθππSRT(θ)dθ=GππST(θ)dθ.

B. BRDF Model

Backscattered coefficients β(θ) are then fitted using a BRDF Phong model [23], briefly described in this section. The BRDF is defined as the ratio of surface radiance to irradiance, as described in Eq. (3), where θ and ϕ are the azimuth and zenith angles, respectively, of the incident light (index i) and reflected light (index r). Lr is the surface radiance, defined as the flux radiated by the surface per unit solid angle, per unit-foreshortened area, while E is the irradiance, defined as the light flux incident per unit area of the surface [26]:

BRDF(θi,ϕi,θr,ϕr)=dLr(θi,ϕi,θr,ϕr)dE(θi,ϕi).
The BRDF of a sample can be evaluated using different methodologies that can be classified into three groups: empirical, theoretical, and experimental [25,27]. Empirical models are based on observations of reflection and can be expressed in parametric analytical equations without any physical meaning of parameters involved. Their main objective is to provide a simple formulation specifically designed to mimic a kind of reflection. Theoretical models take into account fundamental principles to simulate light scattering. However, scattering processes on irregular and complex solids can become extremely challenging to model. Theoretical models depend on many parameters of both the incident light (wavelength or frequency) and the scattering medium (refractive index, structure, spatial configuration, or morphology), which may be hard to acquire. Various models have been developed that allow for a very wide range of materials to be classified depending on their reflection properties. Some examples of these include the Cook–Torrance model [28,29], Phong model [24], Li and Liang model [30], or Ward’s [13] model, to name a few. In general, different models are useful for modeling the reflectance characteristics of different types of materials. Ward’s model, e.g., is suitable at modeling the reflectance properties for surfaces with high anisotropy, such as brushed metal. The Cook–Torrance model is effective at simulating many types of metals, such as copper and gold [29]. It can also be used for materials such as plastics with varying degrees of roughness. In contrast to analytical models, BRDFs can be obtained through experimental measurements made with BRDF measuring devices such as a gonioreflectometer. Data produced in this way are often referred to as acquired BRDF data. This experimental methodology is particularly interesting to retrieve the BRDF of complex surface where material proprieties are rather unknown, or when no analytical model is suitable [31,32]. However, in addition to being costly, such measurements are not always an option, as some material may be inappropriate for laboratory measurements. In addition, positional variance property is observed in many materials such as wood that reflect light in a manner that produces surface detail. Both the horizontal and vertical (ringing and striping) patterns often found in wood are indications that the BRDF for wood varies with the surface spatial position.

In this contribution, experimental data are fitted using the Phong reflectance model. Due to the great variability in the retrieved backscattering coefficient profiles among targets (see Section 4), the Phong model was chosen, as it provided the highest coefficient of determination on average for all the targets and wavelengths considered in this work. The Phong lighting equation relates incoming (Iin) and outcoming (Iout) light intensity as follows:

Iout=Iin(kdL·N+ks(R·V)n),
where the vector L here stands for the direction from the light source, V is the direction to the viewer, N is the normal to the surface of the sample, and R is the direction of reflection, as shown in Fig. 2. As described by Eq. (4), the Phong model assumes that the BRDF is the sum of a diffuse contribution and specular contribution. The Phong model uses three empirical parameters: kd,ks, and n. kd,ks coefficients represent the contribution of diffuse and specular components respectively. kd=1 and ks=0 would fit a Lambertian reflectance. The n coefficient controls the width of specular contribution, the greater n is, the narrower the specular contribution is; thus kd=0 and ks=1 and n would represent a true specular reflection, i.e., mirror-like reflection.

 figure: Fig. 2.

Fig. 2. Schematic of incident and reflected light directions.

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The relationship between the Phong model and general BRDF equation is written in the following form:

BRDF(θi,ϕi,θ0,ϕ0)=kdL·N+ks(R·V)ncosθidLi.
We will use the given BRDF function to approximate reflectance properties of our set of materials. Additionally, when light interacts with a surface, different wavelengths of light may be absorbed, scattered, reflected, and transmitted to varying degrees, depending upon the physical properties of the material itself. Consequently, the wavelength dependency of the BRDF must be taken into account, especially due to the large spectral range considered in this work. The Phong model parameters have inherently no wavelength dependency; therefore, each target, irradiated at three different wavelengths, is treated as three independent targets.

3. EXPERIMENTAL SETUP

Experimental setup schematics is shown in Fig. 1 in Section 2.A. This section describes the equipment specifications and material used in this experiment.

  • • Visible: The laser source is a CW-Spectra-Physics Excelsior 488 laser emitting at 0.488 μm with average power 55 mW. The detector is an amplified switchable-gain, silicon detector 3.6×3.6mm from Thorlabs (PDA55).
  • • SWIR: The target is illuminated by a high-power Seminex diode laser emitting at 1.325 μm powered by a precision high-power 30 A current source with temperature controller. The laser is used well below its maximum power, at approximately 0.5 W average power. Return signals are measured using an InGaAs amplified photodetector with active area of 2×2mm (Thorlabs PDA20C).
  • • Mid-IR: The mid-IR laser source is a quantum cascade laser source from Alpes laser with TCU200 Temperature Controller Unit. The laser emits pulse at 7.6 μm wavelength of 300 ns duration at a 20 kHz repetition rate, resulting in an average power of 0.5 mW. The backscattered light is measured using a high sensitivity VIGO PVI-3TE thermoelectrically cooled mercury-cadmium-telluride (MCT) photovoltaic detector (1.6×1.6mm).

Each laser beam is transmitted through a 3 mm diameter hole at the center of the gold parabolic mirror. At a 1 m distance, the solid angle subtended by the 7 cm diameter parabolic mirror is equal to 3.5 msr. For actual lidars using targets further than 10 m, the solid angle of a regular-sized telescope (10cm radius) may become orders of magnitude lower. While a larger solid angle does increase the intensity of the backscattered light measured during this experiment, results presented in this paper are backscattering coefficients, which are normalized and expressed in sr1, thanks to the calibration done using the gold target. In addition, a large solid angle may reduce the intensity of sharp features in the backscattering coefficient profiles. However, this would be significant only for a backscattering coefficient profile measured with higher angular resolutions than in the presented experiment (2° maximum). Finally, a large solid angle theoretically reduces the opposition effect [33], known to enhance the intensity of the backscattered signal when the angle between illumination direction and observation direction is near 0°. However, this effect is negligible when compared to the variability due to the exact nature of the target or the positional variance.

The divergence of the laser beam is set to be around 2 mrad, so the laser beam has approximately 5mm2 area when reaching the surface of the sample. Larger surface area helps to minimize positional variance. The gold mirror is located 1 m away from the sample’s surface. Backscattered light is focused by the mirror on the detector. Each sample is installed on a rotation surface in such a way that its surface is perpendicular to the rotation plane.

The sample is rotated from approximately 80° to 80° around its vertical axis. Signals from detectors are recorded using a Spectrum Instrumentation M4i.4420-x8 acquisition system. Six samples of typical construction materials that can be find in urban environments have been considered:

  • – Maple wood plank with coating (UV-resistant epoxy-based coating)
  • – Maple wood plank without coating
  • – Red brick, composed mostly of clay, sand, and concrete materials
  • – Concrete brick
  • – Old concrete brick with dust and urban aerosol deposit on its surface
  • – Asphalt (road construction material).

4. RESULTS AND DISCUSSION

This section presents target backscattered coefficients βT(θ) and corresponding fits using the Phong model for each target at each wavelength. We present the fit parameters kd,ks, and n for each target sample, as well as the total hemispherical reflectance.

As displayed in Fig. 3, the maple wood plank sample with coating presents a specular reflection peak, as expected, as the coating gives a mirror-like reflection to the plank. The width of the specular peak is approximately 7° FWHM for each wavelength. The diffuse reflection is relatively small in the visible and SWIR, and below detection level in the mid-IR. Backscattered signals from maple wood without coating (Fig. 4) present a near-Lambertian profile, except in the mid-IR, which has a slightly stronger specular reflection. The hemispherical reflectance for both wood samples is rather similar in the visible (17% for both), SWIR (resp., 10% and 9.9%), and mid-IR (resp., 1.8% and 1.1%), indicating that the coating is rather transparent.

 figure: Fig. 3.

Fig. 3. Backscattering coefficients measured as a function of the angle of incidence (blue solid line) together with the Phong model fit (red dashed line) for a maple plank with an UV-resistant epoxy-based coating.

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 figure: Fig. 4.

Fig. 4. Backscattering coefficients measured as a function of the angle of incidence (blue solid line) together with the Phong model fit (red dashed line) for a maple plank without coating.

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Figure 5 presents the backscattered signals from the red brick. For each wavelength, measurements show diffuse reflection profiles slightly non-symmetrical, most likely due to the porosity of the material creating small holes at the surface. The absorption in the mid-IR is strong, as the hemispherical reflectance reaches down to 0.85%, while the visible and SWIR are, respectively, 6.5% and 7.2%. Figure 6 shows asphalt measurements. Asphalt exhibits low repeatability at each wavelength due to highly granular surface structure. Due to its irregular structure, large surfaces within the beam footprint may appear normal to the beam despite θ0°, creating peaks of signals at large angles. Due to their irregular shapes, these profiles have not been fit using the Phong model. It is reasonable to assume that with a larger beam footprint, the positional variance would decrease and provide a more representative profile of this type of surface. The hemispherical reflectance may slightly change due to similar reasons, however, to a much lesser extent, as they result from the integration over θ. As expected, asphalt is a highly absorbent material at every wavelength used.

 figure: Fig. 5.

Fig. 5. Backscattering coefficients measured as a function of the angle of incidence (blue solid line) together with the Phong model fit (red dashed line) for a red brick, composed mostly of clay, sand, and concrete materials.

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 figure: Fig. 6.

Fig. 6. Backscattering coefficients measured as a function of the angle of incidence for asphalt.

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Finally, Figs. 7 and 8 show measurements from the two concrete samples. Profiles at each wavelength are rather similar in both cases, showing an overall diffuse reflectance, slightly more specular in the mid-IR.

 figure: Fig. 7.

Fig. 7. Backscattering coefficients measured as a function of the angle of incidence (blue solid line) together with the Phong model fit (red dashed line) for an old concrete brick with dust and urban aerosol deposit on its surface.

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 figure: Fig. 8.

Fig. 8. Backscattering coefficients measured as a function of the angle of incidence (blue solid line) together with the Phong model fit (red dashed line) for a concrete brick.

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However, despite being made out of the same composite material, the rather small hemispherical reflectance does change between the two samples due to the deposition of dust and urban pollution on one of the samples’ surfaces. As for the red brick sample, the granular structure creates small asymmetries in the profile that vary with the laser beam position on the surface sample. Figure 9 summarizes the hemispherical reflectance for each sample at each wavelength, showing the decrease of hemispherical reflectance with increasing wavelength.

 figure: Fig. 9.

Fig. 9. Hemispherical reflectance (%) as a function of the wavelength for each target.

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To illustrate these results, a numerical model has been developed to evaluate the expected signal. The backscattered intensity I(r,θ), a function of the range r and the angle of incidence θ with unit Wm2, can be expressed as in Eq. (6):

I(r,θ)=Ω(r)I0β(θ)T,
where Ω(r) is the solid angle of the telescope or collecting optics. The initial intensity emitted by the laser source is noted I0 and is expressed in Wm2, while T is the atmospheric transmission. Using the backscattering coefficients β(θ) retrieved earlier for each target, the backscattered intensity can be evaluated as a function of the range r.

The solid angle Ω(r) is calculated for an 20 cm diameter Newtonian telescope, and the atmospheric transmission is assumed equal to 1. Figure 10 displays the backscattered intensity normalized by the initial laser power I/I0 as a function of the target range (0–200 m) for both the concrete target and the maple plank with coating target. For each of the three wavelengths considered in our experiment, two angles of incidence are plotted: θ=0° or θ=25°. As expected, signals are decreasing with the range due to the decrease of the solid angle. As it is a near-Lambertian target, the concrete target is rather unaffected by the change in angle of incidence. However, the signals returned by the maple plank decrease significantly at θ=25°, to a point where the return signal from the maple plank becomes smaller than the return signal from the concrete target in the mid-IR. When combined with the available laser power and the absorption cross section at each wavelength, such data as well as the Phong model coefficients can be used to evaluate the most appropriate spectral range for a given objective.

 figure: Fig. 10.

Fig. 10. Backscattered intensity normalized by the initial laser power I/I0 as a function of the target range for both the concrete target and the maple plank with coating target. Two angles of incidence are considered, normal and 25°, for both targets in the visible, SWIR, and mid-IR.

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5. CONCLUSION

Active stand-off detection and hard-target lidars heavily depend on the optical properties of the backscattering target. In the absence of data on these optical properties, evaluation of the signal-to-noise ratio and overall performance of a hard-target remote sensing instrument suffers great uncertainties. In this contribution, we studied experimentally the backscattering properties of multiple common building materials at three spectral ranges, visible (0.488 μm), SWIR (1.32 μm), and mid-IR (7.6 μm). The backscattering coefficients of each target is measured as a function of the angle of incidence using an optical setup designed to mimic the return signal from a hard-target lidar. The measured signals are then fitted using the bidirectional reflectance distribution function from the Phong model, and the hemispherical reflectance of the material is retrieved from measurements. Using these measurements, the simple model is presented to evaluate the backscattered intensity that can be expected from each target at different angles of incidence and for each considered wavelength. As a result, when combined with the laser power and the target gas absorption cross section, these data can provide a much more accurate estimation of the overall performance of the instrument from the visible to mid-IR spectral ranges. The choice of the emission wavelength of the light source can therefore be made adequately to minimize the detection limit and measurement uncertainties of the system.

Funding

New Jersey Institute of Technology.

REFERENCES

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References

  • View by:

  1. J. D. Spinhirne, S. Chudamani, J. F. Cavanaugh, and J. L. Bufton, “Aerosol and cloud backscatter at 1.06, 1.54, and 0.53 μm by airborne hard-target-calibrated Nd:YAG/methane Raman lidar,” Appl. Opt. 36, 3475–3490 (1997).
    [Crossref]
  2. M. B. Frish, R. T. Wainner, J. Stafford-Evans, B. D. Green, M. G. Allen, S. Chancey, J. Rutherford, G. Midgley, and P. Wehnert, “Standoff sensing of natural gas leaks: evolution of the remote methane leak detector (RMLD),” in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science and Photonic Applications, Systems and Technologies, Baltimore, Maryland (Optical Society of America, 2005).
  3. S. Kameyama, M. Imaki, Y. Hirano, S. Ueno, S. Kawakami, D. Sakaizawa, and M. Nakajima, “Development of 1.6 μm continuous-wave modulation hard-target differential absorption lidar system for CO2 sensing,” Opt. Lett. 34, 1513–1515 (2009).
    [Crossref]
  4. S. Galtier, C. Anselmo, J.-Y. Welschinger, J. F. Sivignon, J.-P. Cariou, A. Miffre, and P. Rairoux, “Remote sensing of methane with OSAS-lidar on the 2ν3 band Q-branch: experimental proof,” J. Mol. Spectrosc. 348, 130–136 (2018).
    [Crossref]
  5. T. Fujii and T. Fukuchi, Laser Remote Sensing (CRC Press, 2005).
  6. P. Corrigan, M. Lwin, R. Huntley, A. Chhabra, F. Moshary, B. Gross, and S. Ahmed, “Portable open-path chemical sensor using a quantum cascade laser,” Proc. SPIE 7312, 73120P (2009).
    [Crossref]
  7. V. Vladutescu, B. Gross, F. Moshary, and S. Ahmed, “Assessment of a QCL laser approach for the simultaneous measurement of ambient ammonia and ozone,” Proc. SPIE 6760, 676005 (2007).
    [Crossref]
  8. R. Prado and F. Ferreira, “Measurement of albedo and analysis of its influence the surface temperature of building roof materials,” Energy Build. 37, 295–300 (2005).
    [Crossref]
  9. V. Degli-Esposti, F. Fuschini, E. Vitucci, and G. Falciasecca, “Measurement and modeling of scattering from buildings,” IEEE Trans. Antennas Propag. 55, 143–153 (2007).
    [Crossref]
  10. M. Lwin, P. Corrigan, B. Gross, F. Moshary, and S. Ahmed, “Mid-infrared backscattering measurements of building materials using a quantum cascade laser,” Proc. SPIE 7660, 766043 (2010).
    [Crossref]
  11. M. J. Kavaya, R. T. Menzies, D. A. Haner, U. P. Oppenheim, and P. H. Flamant, “Target reflectance measurements for calibration of lidar atmospheric backscatter data,” Appl. Opt. 22, 2619–2628 (1983).
    [Crossref]
  12. R. Montes and C. Ureña, “An overview of BRDF models,” (2012).
  13. G. J. Ward, “Measuring and modeling anisotropic reflection,” in SIGGRAPH (1992), pp. 265–272.
  14. A. Dür, “An improved normalization for the ward reflectance model,” J. Graph. Tools 11, 51–59 (2011).
    [Crossref]
  15. C. Weitkamp, Lidar Range-Resolved Optical Remote Sensing of the Atmosphere (Springer, 2005).
  16. S. Bergin, J. Hodgkinson, D. Francis, and R. P. Tatam, “Integrating cavity based gas cells: a multibeam compensation scheme for pathlength variation,” Opt. Express 24, 13647–13664 (2016).
    [Crossref]
  17. D. A. Haner and R. T. Menzies, “Reflectance characteristics of reference materials used in lidar hard target calibration,” Appl. Opt. 28, 857–864 (1989).
    [Crossref]
  18. H. Henshall and J. Cruickshank, “Reflectance characteristics of selected materials for reference targets for 10.6 μm laser radars,” Appl. Opt. 27, 2748–2755 (1988).
    [Crossref]
  19. U. Platt and J. Stutz, Differential Optical Absorption Spectroscopy (Springer, 2008).
  20. A. Diaz, B. Thomas, P. Castillo, B. Gross, and F. Moshary, “Active standoff detection of CH4 and N2O leaks using hard-target backscattered light using an open-path quantum cascade laser sensor,” Appl. Phys. B 122, 121 (2016).
    [Crossref]
  21. B. Thomas, A. Miffre, G. David, J.-P. Cariou, and P. Rairoux, “Remote sensing of trace gases with optical correlation spectroscopy and lidar: theoretical and numerical approach,” Appl. Phys. B 108, 689–702 (2012).
    [Crossref]
  22. B. Thomas, G. David, C. Anselmo, E. Coillet, K. Rieth, A. Miffre, J.-P. Cariou, and P. Rairoux, “Remote sensing of methane with broadband laser and optical correlation spectroscopy on the Q-branch of the 2ν3 band,” J. Mol. Spectrosc. 291, 3–8 (2013).
    [Crossref]
  23. S. Veerabuthiran, A. K. Razdan, M. K. Jindal, R. K. Sharma, and V. Sagar, “Development of 3.0-3.45 μm OPO laser based range resolved and hard-target differential absorption lidar for sensing of atmospheric methane,” Opt. Laser Technol. 73, 1–5 (2015).
    [Crossref]
  24. B. T. Phong, “Illumination for computer generated pictures,” Commun. ACM 18, 311–317 (1975).
    [Crossref]
  25. F. O. Bartell, E. L. Dereniak, and W. L. Wolfe, “The theory and measurement of bidirectional reflectance distribution functions (BRDF) and bidirectional transmittance distribution function (BTDF),” Proc. SPIE 257, 154–160 (1980).
    [Crossref]
  26. R. McCluney, Introduction to Radiometry and Photometry, 2nd ed. (Artech House, 2014).
  27. S. H. Westin, H. Li, and K. E. Torrance, “A comparison of four BRDF models,” in Eurographics Symposium on Rendering (2004), pp. 1–10.
  28. E. Heitz, “Understanding the masking-shadowing function in microfacet-based BRDFs,” (2014).
  29. R. L. Cook and K. E. Torrance, “A reflectance model for computer graphics,” ACM Trans. Graph. 1, 7–24 (1982).
    [Crossref]
  30. X. Li and Y. Liang, “Surface characteristics modeling and performance evaluation of urban building materials using LiDAR data,” Appl. Opt. 54, 4750–4759 (2015).
    [Crossref]
  31. A. Ngan, F. Durand, and W. Matusik, “Experimental analysis of BRDF models,” in Eurographics Symposium on Rendering (2005).
  32. A. Earp, G. B. Smith, and J. Franklin, “Simplified BRDF of a non-Lambertian diffuse surface,” Lighting Res. Technol. 39, 265–281 (2007).
    [Crossref]
  33. F. M. Bréon, F. Maignan, M. Leroy, and I. Grant, “Analysis of hot spot directional signatures measured from space,” J. Geophys. Res.107, AAC1-1–AAC1-15 (2002).
    [Crossref]

2018 (1)

S. Galtier, C. Anselmo, J.-Y. Welschinger, J. F. Sivignon, J.-P. Cariou, A. Miffre, and P. Rairoux, “Remote sensing of methane with OSAS-lidar on the 2ν3 band Q-branch: experimental proof,” J. Mol. Spectrosc. 348, 130–136 (2018).
[Crossref]

2016 (2)

S. Bergin, J. Hodgkinson, D. Francis, and R. P. Tatam, “Integrating cavity based gas cells: a multibeam compensation scheme for pathlength variation,” Opt. Express 24, 13647–13664 (2016).
[Crossref]

A. Diaz, B. Thomas, P. Castillo, B. Gross, and F. Moshary, “Active standoff detection of CH4 and N2O leaks using hard-target backscattered light using an open-path quantum cascade laser sensor,” Appl. Phys. B 122, 121 (2016).
[Crossref]

2015 (2)

S. Veerabuthiran, A. K. Razdan, M. K. Jindal, R. K. Sharma, and V. Sagar, “Development of 3.0-3.45 μm OPO laser based range resolved and hard-target differential absorption lidar for sensing of atmospheric methane,” Opt. Laser Technol. 73, 1–5 (2015).
[Crossref]

X. Li and Y. Liang, “Surface characteristics modeling and performance evaluation of urban building materials using LiDAR data,” Appl. Opt. 54, 4750–4759 (2015).
[Crossref]

2013 (1)

B. Thomas, G. David, C. Anselmo, E. Coillet, K. Rieth, A. Miffre, J.-P. Cariou, and P. Rairoux, “Remote sensing of methane with broadband laser and optical correlation spectroscopy on the Q-branch of the 2ν3 band,” J. Mol. Spectrosc. 291, 3–8 (2013).
[Crossref]

2012 (1)

B. Thomas, A. Miffre, G. David, J.-P. Cariou, and P. Rairoux, “Remote sensing of trace gases with optical correlation spectroscopy and lidar: theoretical and numerical approach,” Appl. Phys. B 108, 689–702 (2012).
[Crossref]

2011 (1)

A. Dür, “An improved normalization for the ward reflectance model,” J. Graph. Tools 11, 51–59 (2011).
[Crossref]

2010 (1)

M. Lwin, P. Corrigan, B. Gross, F. Moshary, and S. Ahmed, “Mid-infrared backscattering measurements of building materials using a quantum cascade laser,” Proc. SPIE 7660, 766043 (2010).
[Crossref]

2009 (2)

S. Kameyama, M. Imaki, Y. Hirano, S. Ueno, S. Kawakami, D. Sakaizawa, and M. Nakajima, “Development of 1.6 μm continuous-wave modulation hard-target differential absorption lidar system for CO2 sensing,” Opt. Lett. 34, 1513–1515 (2009).
[Crossref]

P. Corrigan, M. Lwin, R. Huntley, A. Chhabra, F. Moshary, B. Gross, and S. Ahmed, “Portable open-path chemical sensor using a quantum cascade laser,” Proc. SPIE 7312, 73120P (2009).
[Crossref]

2007 (3)

V. Vladutescu, B. Gross, F. Moshary, and S. Ahmed, “Assessment of a QCL laser approach for the simultaneous measurement of ambient ammonia and ozone,” Proc. SPIE 6760, 676005 (2007).
[Crossref]

V. Degli-Esposti, F. Fuschini, E. Vitucci, and G. Falciasecca, “Measurement and modeling of scattering from buildings,” IEEE Trans. Antennas Propag. 55, 143–153 (2007).
[Crossref]

A. Earp, G. B. Smith, and J. Franklin, “Simplified BRDF of a non-Lambertian diffuse surface,” Lighting Res. Technol. 39, 265–281 (2007).
[Crossref]

2005 (1)

R. Prado and F. Ferreira, “Measurement of albedo and analysis of its influence the surface temperature of building roof materials,” Energy Build. 37, 295–300 (2005).
[Crossref]

1997 (1)

1989 (1)

1988 (1)

1983 (1)

1982 (1)

R. L. Cook and K. E. Torrance, “A reflectance model for computer graphics,” ACM Trans. Graph. 1, 7–24 (1982).
[Crossref]

1980 (1)

F. O. Bartell, E. L. Dereniak, and W. L. Wolfe, “The theory and measurement of bidirectional reflectance distribution functions (BRDF) and bidirectional transmittance distribution function (BTDF),” Proc. SPIE 257, 154–160 (1980).
[Crossref]

1975 (1)

B. T. Phong, “Illumination for computer generated pictures,” Commun. ACM 18, 311–317 (1975).
[Crossref]

Ahmed, S.

M. Lwin, P. Corrigan, B. Gross, F. Moshary, and S. Ahmed, “Mid-infrared backscattering measurements of building materials using a quantum cascade laser,” Proc. SPIE 7660, 766043 (2010).
[Crossref]

P. Corrigan, M. Lwin, R. Huntley, A. Chhabra, F. Moshary, B. Gross, and S. Ahmed, “Portable open-path chemical sensor using a quantum cascade laser,” Proc. SPIE 7312, 73120P (2009).
[Crossref]

V. Vladutescu, B. Gross, F. Moshary, and S. Ahmed, “Assessment of a QCL laser approach for the simultaneous measurement of ambient ammonia and ozone,” Proc. SPIE 6760, 676005 (2007).
[Crossref]

Allen, M. G.

M. B. Frish, R. T. Wainner, J. Stafford-Evans, B. D. Green, M. G. Allen, S. Chancey, J. Rutherford, G. Midgley, and P. Wehnert, “Standoff sensing of natural gas leaks: evolution of the remote methane leak detector (RMLD),” in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science and Photonic Applications, Systems and Technologies, Baltimore, Maryland (Optical Society of America, 2005).

Anselmo, C.

S. Galtier, C. Anselmo, J.-Y. Welschinger, J. F. Sivignon, J.-P. Cariou, A. Miffre, and P. Rairoux, “Remote sensing of methane with OSAS-lidar on the 2ν3 band Q-branch: experimental proof,” J. Mol. Spectrosc. 348, 130–136 (2018).
[Crossref]

B. Thomas, G. David, C. Anselmo, E. Coillet, K. Rieth, A. Miffre, J.-P. Cariou, and P. Rairoux, “Remote sensing of methane with broadband laser and optical correlation spectroscopy on the Q-branch of the 2ν3 band,” J. Mol. Spectrosc. 291, 3–8 (2013).
[Crossref]

Bartell, F. O.

F. O. Bartell, E. L. Dereniak, and W. L. Wolfe, “The theory and measurement of bidirectional reflectance distribution functions (BRDF) and bidirectional transmittance distribution function (BTDF),” Proc. SPIE 257, 154–160 (1980).
[Crossref]

Bergin, S.

Bréon, F. M.

F. M. Bréon, F. Maignan, M. Leroy, and I. Grant, “Analysis of hot spot directional signatures measured from space,” J. Geophys. Res.107, AAC1-1–AAC1-15 (2002).
[Crossref]

Bufton, J. L.

Cariou, J.-P.

S. Galtier, C. Anselmo, J.-Y. Welschinger, J. F. Sivignon, J.-P. Cariou, A. Miffre, and P. Rairoux, “Remote sensing of methane with OSAS-lidar on the 2ν3 band Q-branch: experimental proof,” J. Mol. Spectrosc. 348, 130–136 (2018).
[Crossref]

B. Thomas, G. David, C. Anselmo, E. Coillet, K. Rieth, A. Miffre, J.-P. Cariou, and P. Rairoux, “Remote sensing of methane with broadband laser and optical correlation spectroscopy on the Q-branch of the 2ν3 band,” J. Mol. Spectrosc. 291, 3–8 (2013).
[Crossref]

B. Thomas, A. Miffre, G. David, J.-P. Cariou, and P. Rairoux, “Remote sensing of trace gases with optical correlation spectroscopy and lidar: theoretical and numerical approach,” Appl. Phys. B 108, 689–702 (2012).
[Crossref]

Castillo, P.

A. Diaz, B. Thomas, P. Castillo, B. Gross, and F. Moshary, “Active standoff detection of CH4 and N2O leaks using hard-target backscattered light using an open-path quantum cascade laser sensor,” Appl. Phys. B 122, 121 (2016).
[Crossref]

Cavanaugh, J. F.

Chancey, S.

M. B. Frish, R. T. Wainner, J. Stafford-Evans, B. D. Green, M. G. Allen, S. Chancey, J. Rutherford, G. Midgley, and P. Wehnert, “Standoff sensing of natural gas leaks: evolution of the remote methane leak detector (RMLD),” in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science and Photonic Applications, Systems and Technologies, Baltimore, Maryland (Optical Society of America, 2005).

Chhabra, A.

P. Corrigan, M. Lwin, R. Huntley, A. Chhabra, F. Moshary, B. Gross, and S. Ahmed, “Portable open-path chemical sensor using a quantum cascade laser,” Proc. SPIE 7312, 73120P (2009).
[Crossref]

Chudamani, S.

Coillet, E.

B. Thomas, G. David, C. Anselmo, E. Coillet, K. Rieth, A. Miffre, J.-P. Cariou, and P. Rairoux, “Remote sensing of methane with broadband laser and optical correlation spectroscopy on the Q-branch of the 2ν3 band,” J. Mol. Spectrosc. 291, 3–8 (2013).
[Crossref]

Cook, R. L.

R. L. Cook and K. E. Torrance, “A reflectance model for computer graphics,” ACM Trans. Graph. 1, 7–24 (1982).
[Crossref]

Corrigan, P.

M. Lwin, P. Corrigan, B. Gross, F. Moshary, and S. Ahmed, “Mid-infrared backscattering measurements of building materials using a quantum cascade laser,” Proc. SPIE 7660, 766043 (2010).
[Crossref]

P. Corrigan, M. Lwin, R. Huntley, A. Chhabra, F. Moshary, B. Gross, and S. Ahmed, “Portable open-path chemical sensor using a quantum cascade laser,” Proc. SPIE 7312, 73120P (2009).
[Crossref]

Cruickshank, J.

David, G.

B. Thomas, G. David, C. Anselmo, E. Coillet, K. Rieth, A. Miffre, J.-P. Cariou, and P. Rairoux, “Remote sensing of methane with broadband laser and optical correlation spectroscopy on the Q-branch of the 2ν3 band,” J. Mol. Spectrosc. 291, 3–8 (2013).
[Crossref]

B. Thomas, A. Miffre, G. David, J.-P. Cariou, and P. Rairoux, “Remote sensing of trace gases with optical correlation spectroscopy and lidar: theoretical and numerical approach,” Appl. Phys. B 108, 689–702 (2012).
[Crossref]

Degli-Esposti, V.

V. Degli-Esposti, F. Fuschini, E. Vitucci, and G. Falciasecca, “Measurement and modeling of scattering from buildings,” IEEE Trans. Antennas Propag. 55, 143–153 (2007).
[Crossref]

Dereniak, E. L.

F. O. Bartell, E. L. Dereniak, and W. L. Wolfe, “The theory and measurement of bidirectional reflectance distribution functions (BRDF) and bidirectional transmittance distribution function (BTDF),” Proc. SPIE 257, 154–160 (1980).
[Crossref]

Diaz, A.

A. Diaz, B. Thomas, P. Castillo, B. Gross, and F. Moshary, “Active standoff detection of CH4 and N2O leaks using hard-target backscattered light using an open-path quantum cascade laser sensor,” Appl. Phys. B 122, 121 (2016).
[Crossref]

Dür, A.

A. Dür, “An improved normalization for the ward reflectance model,” J. Graph. Tools 11, 51–59 (2011).
[Crossref]

Durand, F.

A. Ngan, F. Durand, and W. Matusik, “Experimental analysis of BRDF models,” in Eurographics Symposium on Rendering (2005).

Earp, A.

A. Earp, G. B. Smith, and J. Franklin, “Simplified BRDF of a non-Lambertian diffuse surface,” Lighting Res. Technol. 39, 265–281 (2007).
[Crossref]

Falciasecca, G.

V. Degli-Esposti, F. Fuschini, E. Vitucci, and G. Falciasecca, “Measurement and modeling of scattering from buildings,” IEEE Trans. Antennas Propag. 55, 143–153 (2007).
[Crossref]

Ferreira, F.

R. Prado and F. Ferreira, “Measurement of albedo and analysis of its influence the surface temperature of building roof materials,” Energy Build. 37, 295–300 (2005).
[Crossref]

Flamant, P. H.

Francis, D.

Franklin, J.

A. Earp, G. B. Smith, and J. Franklin, “Simplified BRDF of a non-Lambertian diffuse surface,” Lighting Res. Technol. 39, 265–281 (2007).
[Crossref]

Frish, M. B.

M. B. Frish, R. T. Wainner, J. Stafford-Evans, B. D. Green, M. G. Allen, S. Chancey, J. Rutherford, G. Midgley, and P. Wehnert, “Standoff sensing of natural gas leaks: evolution of the remote methane leak detector (RMLD),” in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science and Photonic Applications, Systems and Technologies, Baltimore, Maryland (Optical Society of America, 2005).

Fujii, T.

T. Fujii and T. Fukuchi, Laser Remote Sensing (CRC Press, 2005).

Fukuchi, T.

T. Fujii and T. Fukuchi, Laser Remote Sensing (CRC Press, 2005).

Fuschini, F.

V. Degli-Esposti, F. Fuschini, E. Vitucci, and G. Falciasecca, “Measurement and modeling of scattering from buildings,” IEEE Trans. Antennas Propag. 55, 143–153 (2007).
[Crossref]

Galtier, S.

S. Galtier, C. Anselmo, J.-Y. Welschinger, J. F. Sivignon, J.-P. Cariou, A. Miffre, and P. Rairoux, “Remote sensing of methane with OSAS-lidar on the 2ν3 band Q-branch: experimental proof,” J. Mol. Spectrosc. 348, 130–136 (2018).
[Crossref]

Grant, I.

F. M. Bréon, F. Maignan, M. Leroy, and I. Grant, “Analysis of hot spot directional signatures measured from space,” J. Geophys. Res.107, AAC1-1–AAC1-15 (2002).
[Crossref]

Green, B. D.

M. B. Frish, R. T. Wainner, J. Stafford-Evans, B. D. Green, M. G. Allen, S. Chancey, J. Rutherford, G. Midgley, and P. Wehnert, “Standoff sensing of natural gas leaks: evolution of the remote methane leak detector (RMLD),” in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science and Photonic Applications, Systems and Technologies, Baltimore, Maryland (Optical Society of America, 2005).

Gross, B.

A. Diaz, B. Thomas, P. Castillo, B. Gross, and F. Moshary, “Active standoff detection of CH4 and N2O leaks using hard-target backscattered light using an open-path quantum cascade laser sensor,” Appl. Phys. B 122, 121 (2016).
[Crossref]

M. Lwin, P. Corrigan, B. Gross, F. Moshary, and S. Ahmed, “Mid-infrared backscattering measurements of building materials using a quantum cascade laser,” Proc. SPIE 7660, 766043 (2010).
[Crossref]

P. Corrigan, M. Lwin, R. Huntley, A. Chhabra, F. Moshary, B. Gross, and S. Ahmed, “Portable open-path chemical sensor using a quantum cascade laser,” Proc. SPIE 7312, 73120P (2009).
[Crossref]

V. Vladutescu, B. Gross, F. Moshary, and S. Ahmed, “Assessment of a QCL laser approach for the simultaneous measurement of ambient ammonia and ozone,” Proc. SPIE 6760, 676005 (2007).
[Crossref]

Haner, D. A.

Heitz, E.

E. Heitz, “Understanding the masking-shadowing function in microfacet-based BRDFs,” (2014).

Henshall, H.

Hirano, Y.

Hodgkinson, J.

Huntley, R.

P. Corrigan, M. Lwin, R. Huntley, A. Chhabra, F. Moshary, B. Gross, and S. Ahmed, “Portable open-path chemical sensor using a quantum cascade laser,” Proc. SPIE 7312, 73120P (2009).
[Crossref]

Imaki, M.

Jindal, M. K.

S. Veerabuthiran, A. K. Razdan, M. K. Jindal, R. K. Sharma, and V. Sagar, “Development of 3.0-3.45 μm OPO laser based range resolved and hard-target differential absorption lidar for sensing of atmospheric methane,” Opt. Laser Technol. 73, 1–5 (2015).
[Crossref]

Kameyama, S.

Kavaya, M. J.

Kawakami, S.

Leroy, M.

F. M. Bréon, F. Maignan, M. Leroy, and I. Grant, “Analysis of hot spot directional signatures measured from space,” J. Geophys. Res.107, AAC1-1–AAC1-15 (2002).
[Crossref]

Li, H.

S. H. Westin, H. Li, and K. E. Torrance, “A comparison of four BRDF models,” in Eurographics Symposium on Rendering (2004), pp. 1–10.

Li, X.

Liang, Y.

Lwin, M.

M. Lwin, P. Corrigan, B. Gross, F. Moshary, and S. Ahmed, “Mid-infrared backscattering measurements of building materials using a quantum cascade laser,” Proc. SPIE 7660, 766043 (2010).
[Crossref]

P. Corrigan, M. Lwin, R. Huntley, A. Chhabra, F. Moshary, B. Gross, and S. Ahmed, “Portable open-path chemical sensor using a quantum cascade laser,” Proc. SPIE 7312, 73120P (2009).
[Crossref]

Maignan, F.

F. M. Bréon, F. Maignan, M. Leroy, and I. Grant, “Analysis of hot spot directional signatures measured from space,” J. Geophys. Res.107, AAC1-1–AAC1-15 (2002).
[Crossref]

Matusik, W.

A. Ngan, F. Durand, and W. Matusik, “Experimental analysis of BRDF models,” in Eurographics Symposium on Rendering (2005).

McCluney, R.

R. McCluney, Introduction to Radiometry and Photometry, 2nd ed. (Artech House, 2014).

Menzies, R. T.

Midgley, G.

M. B. Frish, R. T. Wainner, J. Stafford-Evans, B. D. Green, M. G. Allen, S. Chancey, J. Rutherford, G. Midgley, and P. Wehnert, “Standoff sensing of natural gas leaks: evolution of the remote methane leak detector (RMLD),” in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science and Photonic Applications, Systems and Technologies, Baltimore, Maryland (Optical Society of America, 2005).

Miffre, A.

S. Galtier, C. Anselmo, J.-Y. Welschinger, J. F. Sivignon, J.-P. Cariou, A. Miffre, and P. Rairoux, “Remote sensing of methane with OSAS-lidar on the 2ν3 band Q-branch: experimental proof,” J. Mol. Spectrosc. 348, 130–136 (2018).
[Crossref]

B. Thomas, G. David, C. Anselmo, E. Coillet, K. Rieth, A. Miffre, J.-P. Cariou, and P. Rairoux, “Remote sensing of methane with broadband laser and optical correlation spectroscopy on the Q-branch of the 2ν3 band,” J. Mol. Spectrosc. 291, 3–8 (2013).
[Crossref]

B. Thomas, A. Miffre, G. David, J.-P. Cariou, and P. Rairoux, “Remote sensing of trace gases with optical correlation spectroscopy and lidar: theoretical and numerical approach,” Appl. Phys. B 108, 689–702 (2012).
[Crossref]

Montes, R.

R. Montes and C. Ureña, “An overview of BRDF models,” (2012).

Moshary, F.

A. Diaz, B. Thomas, P. Castillo, B. Gross, and F. Moshary, “Active standoff detection of CH4 and N2O leaks using hard-target backscattered light using an open-path quantum cascade laser sensor,” Appl. Phys. B 122, 121 (2016).
[Crossref]

M. Lwin, P. Corrigan, B. Gross, F. Moshary, and S. Ahmed, “Mid-infrared backscattering measurements of building materials using a quantum cascade laser,” Proc. SPIE 7660, 766043 (2010).
[Crossref]

P. Corrigan, M. Lwin, R. Huntley, A. Chhabra, F. Moshary, B. Gross, and S. Ahmed, “Portable open-path chemical sensor using a quantum cascade laser,” Proc. SPIE 7312, 73120P (2009).
[Crossref]

V. Vladutescu, B. Gross, F. Moshary, and S. Ahmed, “Assessment of a QCL laser approach for the simultaneous measurement of ambient ammonia and ozone,” Proc. SPIE 6760, 676005 (2007).
[Crossref]

Nakajima, M.

Ngan, A.

A. Ngan, F. Durand, and W. Matusik, “Experimental analysis of BRDF models,” in Eurographics Symposium on Rendering (2005).

Oppenheim, U. P.

Phong, B. T.

B. T. Phong, “Illumination for computer generated pictures,” Commun. ACM 18, 311–317 (1975).
[Crossref]

Platt, U.

U. Platt and J. Stutz, Differential Optical Absorption Spectroscopy (Springer, 2008).

Prado, R.

R. Prado and F. Ferreira, “Measurement of albedo and analysis of its influence the surface temperature of building roof materials,” Energy Build. 37, 295–300 (2005).
[Crossref]

Rairoux, P.

S. Galtier, C. Anselmo, J.-Y. Welschinger, J. F. Sivignon, J.-P. Cariou, A. Miffre, and P. Rairoux, “Remote sensing of methane with OSAS-lidar on the 2ν3 band Q-branch: experimental proof,” J. Mol. Spectrosc. 348, 130–136 (2018).
[Crossref]

B. Thomas, G. David, C. Anselmo, E. Coillet, K. Rieth, A. Miffre, J.-P. Cariou, and P. Rairoux, “Remote sensing of methane with broadband laser and optical correlation spectroscopy on the Q-branch of the 2ν3 band,” J. Mol. Spectrosc. 291, 3–8 (2013).
[Crossref]

B. Thomas, A. Miffre, G. David, J.-P. Cariou, and P. Rairoux, “Remote sensing of trace gases with optical correlation spectroscopy and lidar: theoretical and numerical approach,” Appl. Phys. B 108, 689–702 (2012).
[Crossref]

Razdan, A. K.

S. Veerabuthiran, A. K. Razdan, M. K. Jindal, R. K. Sharma, and V. Sagar, “Development of 3.0-3.45 μm OPO laser based range resolved and hard-target differential absorption lidar for sensing of atmospheric methane,” Opt. Laser Technol. 73, 1–5 (2015).
[Crossref]

Rieth, K.

B. Thomas, G. David, C. Anselmo, E. Coillet, K. Rieth, A. Miffre, J.-P. Cariou, and P. Rairoux, “Remote sensing of methane with broadband laser and optical correlation spectroscopy on the Q-branch of the 2ν3 band,” J. Mol. Spectrosc. 291, 3–8 (2013).
[Crossref]

Rutherford, J.

M. B. Frish, R. T. Wainner, J. Stafford-Evans, B. D. Green, M. G. Allen, S. Chancey, J. Rutherford, G. Midgley, and P. Wehnert, “Standoff sensing of natural gas leaks: evolution of the remote methane leak detector (RMLD),” in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science and Photonic Applications, Systems and Technologies, Baltimore, Maryland (Optical Society of America, 2005).

Sagar, V.

S. Veerabuthiran, A. K. Razdan, M. K. Jindal, R. K. Sharma, and V. Sagar, “Development of 3.0-3.45 μm OPO laser based range resolved and hard-target differential absorption lidar for sensing of atmospheric methane,” Opt. Laser Technol. 73, 1–5 (2015).
[Crossref]

Sakaizawa, D.

Sharma, R. K.

S. Veerabuthiran, A. K. Razdan, M. K. Jindal, R. K. Sharma, and V. Sagar, “Development of 3.0-3.45 μm OPO laser based range resolved and hard-target differential absorption lidar for sensing of atmospheric methane,” Opt. Laser Technol. 73, 1–5 (2015).
[Crossref]

Sivignon, J. F.

S. Galtier, C. Anselmo, J.-Y. Welschinger, J. F. Sivignon, J.-P. Cariou, A. Miffre, and P. Rairoux, “Remote sensing of methane with OSAS-lidar on the 2ν3 band Q-branch: experimental proof,” J. Mol. Spectrosc. 348, 130–136 (2018).
[Crossref]

Smith, G. B.

A. Earp, G. B. Smith, and J. Franklin, “Simplified BRDF of a non-Lambertian diffuse surface,” Lighting Res. Technol. 39, 265–281 (2007).
[Crossref]

Spinhirne, J. D.

Stafford-Evans, J.

M. B. Frish, R. T. Wainner, J. Stafford-Evans, B. D. Green, M. G. Allen, S. Chancey, J. Rutherford, G. Midgley, and P. Wehnert, “Standoff sensing of natural gas leaks: evolution of the remote methane leak detector (RMLD),” in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science and Photonic Applications, Systems and Technologies, Baltimore, Maryland (Optical Society of America, 2005).

Stutz, J.

U. Platt and J. Stutz, Differential Optical Absorption Spectroscopy (Springer, 2008).

Tatam, R. P.

Thomas, B.

A. Diaz, B. Thomas, P. Castillo, B. Gross, and F. Moshary, “Active standoff detection of CH4 and N2O leaks using hard-target backscattered light using an open-path quantum cascade laser sensor,” Appl. Phys. B 122, 121 (2016).
[Crossref]

B. Thomas, G. David, C. Anselmo, E. Coillet, K. Rieth, A. Miffre, J.-P. Cariou, and P. Rairoux, “Remote sensing of methane with broadband laser and optical correlation spectroscopy on the Q-branch of the 2ν3 band,” J. Mol. Spectrosc. 291, 3–8 (2013).
[Crossref]

B. Thomas, A. Miffre, G. David, J.-P. Cariou, and P. Rairoux, “Remote sensing of trace gases with optical correlation spectroscopy and lidar: theoretical and numerical approach,” Appl. Phys. B 108, 689–702 (2012).
[Crossref]

Torrance, K. E.

R. L. Cook and K. E. Torrance, “A reflectance model for computer graphics,” ACM Trans. Graph. 1, 7–24 (1982).
[Crossref]

S. H. Westin, H. Li, and K. E. Torrance, “A comparison of four BRDF models,” in Eurographics Symposium on Rendering (2004), pp. 1–10.

Ueno, S.

Ureña, C.

R. Montes and C. Ureña, “An overview of BRDF models,” (2012).

Veerabuthiran, S.

S. Veerabuthiran, A. K. Razdan, M. K. Jindal, R. K. Sharma, and V. Sagar, “Development of 3.0-3.45 μm OPO laser based range resolved and hard-target differential absorption lidar for sensing of atmospheric methane,” Opt. Laser Technol. 73, 1–5 (2015).
[Crossref]

Vitucci, E.

V. Degli-Esposti, F. Fuschini, E. Vitucci, and G. Falciasecca, “Measurement and modeling of scattering from buildings,” IEEE Trans. Antennas Propag. 55, 143–153 (2007).
[Crossref]

Vladutescu, V.

V. Vladutescu, B. Gross, F. Moshary, and S. Ahmed, “Assessment of a QCL laser approach for the simultaneous measurement of ambient ammonia and ozone,” Proc. SPIE 6760, 676005 (2007).
[Crossref]

Wainner, R. T.

M. B. Frish, R. T. Wainner, J. Stafford-Evans, B. D. Green, M. G. Allen, S. Chancey, J. Rutherford, G. Midgley, and P. Wehnert, “Standoff sensing of natural gas leaks: evolution of the remote methane leak detector (RMLD),” in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science and Photonic Applications, Systems and Technologies, Baltimore, Maryland (Optical Society of America, 2005).

Ward, G. J.

G. J. Ward, “Measuring and modeling anisotropic reflection,” in SIGGRAPH (1992), pp. 265–272.

Wehnert, P.

M. B. Frish, R. T. Wainner, J. Stafford-Evans, B. D. Green, M. G. Allen, S. Chancey, J. Rutherford, G. Midgley, and P. Wehnert, “Standoff sensing of natural gas leaks: evolution of the remote methane leak detector (RMLD),” in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science and Photonic Applications, Systems and Technologies, Baltimore, Maryland (Optical Society of America, 2005).

Weitkamp, C.

C. Weitkamp, Lidar Range-Resolved Optical Remote Sensing of the Atmosphere (Springer, 2005).

Welschinger, J.-Y.

S. Galtier, C. Anselmo, J.-Y. Welschinger, J. F. Sivignon, J.-P. Cariou, A. Miffre, and P. Rairoux, “Remote sensing of methane with OSAS-lidar on the 2ν3 band Q-branch: experimental proof,” J. Mol. Spectrosc. 348, 130–136 (2018).
[Crossref]

Westin, S. H.

S. H. Westin, H. Li, and K. E. Torrance, “A comparison of four BRDF models,” in Eurographics Symposium on Rendering (2004), pp. 1–10.

Wolfe, W. L.

F. O. Bartell, E. L. Dereniak, and W. L. Wolfe, “The theory and measurement of bidirectional reflectance distribution functions (BRDF) and bidirectional transmittance distribution function (BTDF),” Proc. SPIE 257, 154–160 (1980).
[Crossref]

ACM Trans. Graph. (1)

R. L. Cook and K. E. Torrance, “A reflectance model for computer graphics,” ACM Trans. Graph. 1, 7–24 (1982).
[Crossref]

Appl. Opt. (5)

Appl. Phys. B (2)

A. Diaz, B. Thomas, P. Castillo, B. Gross, and F. Moshary, “Active standoff detection of CH4 and N2O leaks using hard-target backscattered light using an open-path quantum cascade laser sensor,” Appl. Phys. B 122, 121 (2016).
[Crossref]

B. Thomas, A. Miffre, G. David, J.-P. Cariou, and P. Rairoux, “Remote sensing of trace gases with optical correlation spectroscopy and lidar: theoretical and numerical approach,” Appl. Phys. B 108, 689–702 (2012).
[Crossref]

Commun. ACM (1)

B. T. Phong, “Illumination for computer generated pictures,” Commun. ACM 18, 311–317 (1975).
[Crossref]

Energy Build. (1)

R. Prado and F. Ferreira, “Measurement of albedo and analysis of its influence the surface temperature of building roof materials,” Energy Build. 37, 295–300 (2005).
[Crossref]

IEEE Trans. Antennas Propag. (1)

V. Degli-Esposti, F. Fuschini, E. Vitucci, and G. Falciasecca, “Measurement and modeling of scattering from buildings,” IEEE Trans. Antennas Propag. 55, 143–153 (2007).
[Crossref]

J. Graph. Tools (1)

A. Dür, “An improved normalization for the ward reflectance model,” J. Graph. Tools 11, 51–59 (2011).
[Crossref]

J. Mol. Spectrosc. (2)

S. Galtier, C. Anselmo, J.-Y. Welschinger, J. F. Sivignon, J.-P. Cariou, A. Miffre, and P. Rairoux, “Remote sensing of methane with OSAS-lidar on the 2ν3 band Q-branch: experimental proof,” J. Mol. Spectrosc. 348, 130–136 (2018).
[Crossref]

B. Thomas, G. David, C. Anselmo, E. Coillet, K. Rieth, A. Miffre, J.-P. Cariou, and P. Rairoux, “Remote sensing of methane with broadband laser and optical correlation spectroscopy on the Q-branch of the 2ν3 band,” J. Mol. Spectrosc. 291, 3–8 (2013).
[Crossref]

Lighting Res. Technol. (1)

A. Earp, G. B. Smith, and J. Franklin, “Simplified BRDF of a non-Lambertian diffuse surface,” Lighting Res. Technol. 39, 265–281 (2007).
[Crossref]

Opt. Express (1)

Opt. Laser Technol. (1)

S. Veerabuthiran, A. K. Razdan, M. K. Jindal, R. K. Sharma, and V. Sagar, “Development of 3.0-3.45 μm OPO laser based range resolved and hard-target differential absorption lidar for sensing of atmospheric methane,” Opt. Laser Technol. 73, 1–5 (2015).
[Crossref]

Opt. Lett. (1)

Proc. SPIE (4)

M. Lwin, P. Corrigan, B. Gross, F. Moshary, and S. Ahmed, “Mid-infrared backscattering measurements of building materials using a quantum cascade laser,” Proc. SPIE 7660, 766043 (2010).
[Crossref]

P. Corrigan, M. Lwin, R. Huntley, A. Chhabra, F. Moshary, B. Gross, and S. Ahmed, “Portable open-path chemical sensor using a quantum cascade laser,” Proc. SPIE 7312, 73120P (2009).
[Crossref]

V. Vladutescu, B. Gross, F. Moshary, and S. Ahmed, “Assessment of a QCL laser approach for the simultaneous measurement of ambient ammonia and ozone,” Proc. SPIE 6760, 676005 (2007).
[Crossref]

F. O. Bartell, E. L. Dereniak, and W. L. Wolfe, “The theory and measurement of bidirectional reflectance distribution functions (BRDF) and bidirectional transmittance distribution function (BTDF),” Proc. SPIE 257, 154–160 (1980).
[Crossref]

Other (11)

R. McCluney, Introduction to Radiometry and Photometry, 2nd ed. (Artech House, 2014).

S. H. Westin, H. Li, and K. E. Torrance, “A comparison of four BRDF models,” in Eurographics Symposium on Rendering (2004), pp. 1–10.

E. Heitz, “Understanding the masking-shadowing function in microfacet-based BRDFs,” (2014).

F. M. Bréon, F. Maignan, M. Leroy, and I. Grant, “Analysis of hot spot directional signatures measured from space,” J. Geophys. Res.107, AAC1-1–AAC1-15 (2002).
[Crossref]

A. Ngan, F. Durand, and W. Matusik, “Experimental analysis of BRDF models,” in Eurographics Symposium on Rendering (2005).

T. Fujii and T. Fukuchi, Laser Remote Sensing (CRC Press, 2005).

M. B. Frish, R. T. Wainner, J. Stafford-Evans, B. D. Green, M. G. Allen, S. Chancey, J. Rutherford, G. Midgley, and P. Wehnert, “Standoff sensing of natural gas leaks: evolution of the remote methane leak detector (RMLD),” in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science and Photonic Applications, Systems and Technologies, Baltimore, Maryland (Optical Society of America, 2005).

U. Platt and J. Stutz, Differential Optical Absorption Spectroscopy (Springer, 2008).

C. Weitkamp, Lidar Range-Resolved Optical Remote Sensing of the Atmosphere (Springer, 2005).

R. Montes and C. Ureña, “An overview of BRDF models,” (2012).

G. J. Ward, “Measuring and modeling anisotropic reflection,” in SIGGRAPH (1992), pp. 265–272.

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Figures (10)

Fig. 1.
Fig. 1. Optical layout of the system used to measure the backscattered light of multiple targets at multiple angles of incidence in the visible (0.48 μm), shortwave infrared (1.32 μm), and mid-infrared (7.6 μm).
Fig. 2.
Fig. 2. Schematic of incident and reflected light directions.
Fig. 3.
Fig. 3. Backscattering coefficients measured as a function of the angle of incidence (blue solid line) together with the Phong model fit (red dashed line) for a maple plank with an UV-resistant epoxy-based coating.
Fig. 4.
Fig. 4. Backscattering coefficients measured as a function of the angle of incidence (blue solid line) together with the Phong model fit (red dashed line) for a maple plank without coating.
Fig. 5.
Fig. 5. Backscattering coefficients measured as a function of the angle of incidence (blue solid line) together with the Phong model fit (red dashed line) for a red brick, composed mostly of clay, sand, and concrete materials.
Fig. 6.
Fig. 6. Backscattering coefficients measured as a function of the angle of incidence for asphalt.
Fig. 7.
Fig. 7. Backscattering coefficients measured as a function of the angle of incidence (blue solid line) together with the Phong model fit (red dashed line) for an old concrete brick with dust and urban aerosol deposit on its surface.
Fig. 8.
Fig. 8. Backscattering coefficients measured as a function of the angle of incidence (blue solid line) together with the Phong model fit (red dashed line) for a concrete brick.
Fig. 9.
Fig. 9. Hemispherical reflectance (%) as a function of the wavelength for each target.
Fig. 10.
Fig. 10. Backscattered intensity normalized by the initial laser power I / I 0 as a function of the target range for both the concrete target and the maple plank with coating target. Two angles of incidence are considered, normal and 25°, for both targets in the visible, SWIR, and mid-IR.

Equations (6)

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G = R RT π π S RT ( θ ) d θ .
R T = R R T π π S T ( θ ) d θ π π S RT ( θ ) d θ = G π π S T ( θ ) d θ .
BRDF ( θ i , ϕ i , θ r , ϕ r ) = d L r ( θ i , ϕ i , θ r , ϕ r ) d E ( θ i , ϕ i ) .
I out = I in ( k d L · N + k s ( R · V ) n ) ,
BRDF ( θ i , ϕ i , θ 0 , ϕ 0 ) = k d L · N + k s ( R · V ) n cos θ i d L i .
I ( r , θ ) = Ω ( r ) I 0 β ( θ ) T ,

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