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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Editor: Franco Gori
  • Vol. 30, Iss. 11 — Nov. 1, 2013
  • pp: 2244–2252
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Monte Carlo simulation of light scattering in the atmosphere and effect of atmospheric aerosols on the point spread function

Joshua Colombi and Karim Louedec  »View Author Affiliations


JOSA A, Vol. 30, Issue 11, pp. 2244-2252 (2013)
http://dx.doi.org/10.1364/JOSAA.30.002244


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Abstract

We present a Monte Carlo simulation for the scattering of light in the case of an isotropic light source. The scattering phase functions are studied particularly in detail to understand how they can affect the multiple light scattering in the atmosphere. We show that, although aerosols are usually in lower density than molecules in the atmosphere, they can have a non-negligible effect on the atmospheric point spread function. This effect is especially expected for ground-based detectors when large aerosols are present in the atmosphere.

© 2013 Optical Society of America

1. INTRODUCTION

Light coming from an isotropic source is scattered and/or absorbed by molecules and/or aerosols in the atmosphere. In the case of fog or rain, the single light scattering approximation—when scattered light cannot be dispersed again to the detector and only direct light is recorded—is no longer valid. Thus, the multiple light scattering—when photons are scattered several times before being detected—has to be taken into account in the total signal recorded. Whereas the first phenomenon reduces the amount of light arriving at the detector, the latter increases the spatial blurring of the isotropic light source. Atmospheric blur occurs especially for long distances and total optical depths greater than unity. This effect is well known for light propagation in the atmosphere and has been studied by many authors. A nice review of relevant findings in this research field can be read in [1

1. N. S. Kopeika, I. Dror, and D. Sadot, “Causes of atmospheric blur: comment on atmospheric scattering effect on spatial resolution of imaging systems,” J. Opt. Soc. Am A 15, 3097–3106 (1998).

]. Originally, these studies began with satellites imaging Earth where aerosol blur is considered as the main source of atmospheric blur [2

2. J. V. Dave, “Effect of atmospheric conditions on remote sensing of a surface non-homogeneity,” Photogramm. Eng. Remote Sens. 46, 1173–1180 (1980).

5

5. I. Dror and N. S. Kopeika, “Experimental comparison of turbulence modulation transfer function and aerosol modulation transfer function through the open atmosphere,” J. Opt. Soc. Am. A 12, 970–980 (1995). [CrossRef]

]. This effect is usually called the adjacency effect [6

6. J. Otterman and R. S. Fraser, “Adjacency effects on imaging by surface reflection and atmospheric scattering: cross radiance to zenith,” Appl. Opt. 18, 2852–2860 (1979). [CrossRef]

8

8. P. N. Reinersman and K. L. Carder, “Monte Carlo simulation of the atmospheric point-spread function with an application to correction for the adjacency effect,” Appl. Opt. 34, 4453–4471 (1995). [CrossRef]

] since photons scattered by aerosols are recorded in pixels adjacent to where they should be.

The problem of light scattering in the atmosphere does not have analytical solutions. Even if analytical approximation solutions can be used in some cases [4

4. D. Sadot and N. S. Kopeika, “Imaging through the atmosphere: practical instrumentation-based theory and verification of aerosol modulation transfer function,” J. Opt. Soc. Am. A 10, 172–179 (1993). [CrossRef]

,9

9. A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, 1978).

], Monte Carlo simulations are usually used to study light propagation in the atmosphere. A multitude of Monte Carlo simulations have been developed in the past years, all yielding a similar conclusion: aerosol scattering is the main contribution to atmospheric blur, atmospheric turbulence being much less important. An especially significant source of atmospheric blur is aerosol scatter of light at near-forward angles [1

1. N. S. Kopeika, I. Dror, and D. Sadot, “Causes of atmospheric blur: comment on atmospheric scattering effect on spatial resolution of imaging systems,” J. Opt. Soc. Am A 15, 3097–3106 (1998).

,8

8. P. N. Reinersman and K. L. Carder, “Monte Carlo simulation of the atmospheric point-spread function with an application to correction for the adjacency effect,” Appl. Opt. 34, 4453–4471 (1995). [CrossRef]

]. The multiple scattering of light is affected by the optical thickness of the atmosphere, the aerosol size distribution, and the aerosol vertical profile. Whereas many works have studied the effect of the optical thickness, the aerosol blur is also very dependent on the aerosol size distribution, and especially on the corresponding asymmetry parameter of the aerosol scattering phase function. The purpose of this work is to better explain the dependence of the aerosol blur on the aerosol size, and its corresponding effect on the atmospheric point spread function. Indeed, as explained previously, aerosol scattering at very forward angles is a significant source of blur and this phenomenon is strongly governed by the asymmetry parameter. Section 2 is a brief introduction of some quantities concerning light scattering, before describing in detail the Monte Carlo simulation developed for this work. Section 3 gives a general overview of how scattered photons disperse across space for different atmospheric conditions. Then, in Section 4, we explain how different atmospheric conditions affect the multiple scattering contribution to the total light arriving at detectors within a given integration time across all space. This result is finally applied to the point spread function for a ground-based detector in Section 5.

2. MODELING AND SIMULATION OF SCATTERING IN THE ATMOSPHERE

Throughout this paper, the scatterers in the atmosphere will be modeled as nonabsorbing spherical particles of different sizes [10

10. H. C. Van De Hulst, Light Scattering by Small Particles (Dover, 1981).

,11

11. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1998).

]. Scatterers in the atmosphere are usually divided into two main types, aerosols and molecules.

A. Density of Scatterers in the Atmosphere

B. Different Scattering Phase Functions

A scattering phase function is used to describe the angular distribution of scattered photons. It is typically written as a normalized probability density function expressed in units of probability per unit of solid angle. When integrated over a given solid angle Ω, a scattering phase function gives the probability of a photon being scattered with a direction that is within this solid angle range. Since scattering is always uniform in azimuthal angle ϕ for both aerosols and molecules, the scattering phase function is always written simply as a function of polar scattering angle ψ.

Molecules are governed by Rayleigh scattering, which can be derived analytically via the approximation that the electromagnetic field of incident light is constant across the small size of the particle [12

12. A. Bucholtz, “Rayleigh-scattering calculations for the terrestrial atmosphere,” Appl. Opt. 34, 2765–2773 (1995). [CrossRef]

]. The molecular phase function is written as
Pmol(ψ)=316π(1+cos2ψ),
(2)
where ψ is the polar scattering angle and Pmol is the probability per unit solid angle. The function Pmol is symmetric about the point π/2 and so the probability of a photon scattering in forward or backward directions is always equal for molecules.

Atmospheric aerosols typically come in the form of small particles of dust or droplets found in suspension in the atmosphere. The angular dependence of scattering by these particles is less easily described as the electromagnetic field of incident light can no longer be approximated as constant over the volume of the particle. Mie scattering theory [15

15. G. Mie, “Beiträge zur Optik Trüber-Medien, speziell Kolloidaler Metallösungen,” Ann. Physik 25, 377–452 (1908).

] offers a solution in the form of an infinite series for the scattering of nonabsorbing spherical objects of any size. The number of terms required in this infinite series to calculate the scattering phase function is given in [16

16. W. J. Wiscombe, “Improved Mie scattering algorithms,” Appl. Opt. 19, 1505–1509 (1980). [CrossRef]

]; it is far too time consuming for the Monte Carlo simulations. As such, a parameterization named the Double–Henyey Greenstein (DHG) phase function [14

14. K. Louedec and R. Losno, for the Pierre Auger Collaboration, “Atmospheric aerosols at the Pierre Auger Observatory and environmental implications,” Eur. Phys. J. Plus 127, 97 (2012).

,17

17. L. C. Henyey and J. L. Greenstein, “Diffuse radiation in the galaxy,” Astrophys. J. 93, 70–83 (1941). [CrossRef]

] is usually used. It is a parameterization valid for various particle types and different media [18

18. D. Toublanc, “Henyey-Greenstein and Mie phase functions in Monte Carlo radiative transfer computations,” Appl. Opt. 35, 3270–3274 (1996). [CrossRef]

20

20. T. Binzoni, T. S. Leung, A. H. Gandjbakhche, D. Rüfenacht, and D. T. Delpy, “The use of the Henyey-Greenstein phase function in Monte Carlo simulations in biomedical optics,” Phys. Med. Biol. 51, N313–N322 (2006). [CrossRef]

]. It is written as
Paer(ψ|g,f)=1g24π[1(1+g22gcosψ)32+f(3cos2ψ12(1+g2)32)],
(3)
where g is the asymmetry parameter given by cosψ and f is the backward scattering correction parameter. g and f vary in the intervals [1,1] and [0, 1], respectively. Most of the atmospheric conditions can be probed by varying the value of the asymmetry parameter g: aerosols (0.2g0.7), haze (0.7g0.8), mist (0.8g0.85), fog (0.85g0.9), or rain (0.9g1.0) [21

21. S. Metari and F. Deschênes, “A new convolution kernel for atmospheric point spread function applied to computer vision,” In Proceedings of the IEEE 11th International Conference on Computer Vision (ICCV) (IEEE, 2007), pp 1–8.

]. Changing g from 0.2 to 1.0 increases greatly the probability of scattering in the very forward direction as can be observed in Fig. 1 (left). The reader is referred to [22

22. K. Louedec, S. Dagoret-Campagne, and M. Urban, “Ramsauer approach to Mie scattering of light on spherical particles,” Phys. Scr. 80, 035403 (2009). [CrossRef]

,23

23. K. Louedec and M. Urban, “Ramsauer approach for light scattering on non absorbing spherical particles and application to the Henyey-Greenstein phase function,” Appl. Opt 51, 7842–7852 (2012). [CrossRef]

] to see the recently published work on the relation between g and the mean radius of an aerosol: a physical interpretation of the asymmetry parameter g in the DHG phase function is the mean aerosol size. The parameter f is an extra parameter acting as a fine tune for the amount of backward scattering. It will be fixed at 0.4 for the rest of this work.

Fig. 1. Scattering phase function per unit of polar angle ψ, and its dependence on atmospheric conditions. Scattering phase functions are in units of probability per solid angle Ω as opposed to probability per unit of ψ as necessary to get the probability density function of the polar angle ψ. Thus, the scattering phase functions Pmol(ψ) and Paer(ψ) have to be multiplied by 2πsinψ to remove the solid angle weighting. (Left) Paer(ψ) plotted for different values of g and fixed f=0.4 used in the DHG phase function and Pmol(ψ) for the molecular phase function. (Right) The joint probability phase function weighted by 2πsin(ψ), with different ratios of Λaer/Λmol (g is kept equal to 0.6).

A joint scattering phase function, weighting the aerosol and molecular phase functions by the corresponding densities of aerosols and molecules at a given position in space, gives the scattering phase function associated with any random scattering event. This joint scattering phase function can be written as
Pjpf(ψ)=Paer(ψ)1+(ΛaerΛmol)+Pmol(ψ)1+(ΛmolΛaer).
(4)
The use of this joint scattering phase function is relevant in understanding to what degree aerosols and molecules change the overall angular distribution of scattering at a given point in space. Figure 1 (right) displays the joint scattering phase function for different ratios of density of aerosols and molecules, all for a value of g=0.6 (typical value for aerosols in the atmosphere). It shows the probability of generating a scattering angle ψ for different ratios of concentration of aerosols and molecules for a random scattering event that could be either caused by a molecule or aerosol. It is seen that as Λaer/Λmol decreases (i.e., the density of aerosols increases), the high forward scattering peak associated with the aerosols becomes increasingly prominent.

C. Monte Carlo Code Description

3. DISTRIBUTION OF SCATTERED PHOTONS FROM AN ISOTROPIC SOURCE IN THE ATMOSPHERE

The Monte Carlo simulation is used to study the distribution of scattered photons across space for an isotropic light source. The variable ε is introduced as the fraction of total energy of the isotropic source in a given histogram bin. In this simulation, which is for a fixed wavelength (λ=350nm), this is given by the number of photons in a bin divided by the total number of photons N. Then, the density per unit volume of the fraction of initial energy dε/dV(rrel,θrel) is calculated by dividing by the elemental volume of each bin. The elemental volume dV of each bin is equal to dV=2πrrel2sin(θrel)drreldθrel, where drrel and dθrel are the widths of each bin in rrel and θrel, respectively. The quantity dε/dV(rrel,θrel) is such that the total fraction of energy in a given volume εtotal is given by
εtotal=dεdVrrel2sin(θrel)drreldθreldϕrel,
(5)
where limits of the integral are chosen to represent this volume. Figure 2 displays the density of indirect photons (scattered photons) for an isotropic light source at an initial height of 20 km after a distance of propagation of 20 km. On each plot, a black semi-circle with radius rdir is drawn to represent the position of direct (unscattered) photons. At θrel=0° (i.e., positive vertical axis), rrel extends in a direction directly above the initial source’s position and at θrel=180° (i.e., negative vertical axis) directly to the ground. Aerosols are less dense than molecules in a real atmosphere and the object of this section is to show that this difference in density means aerosols have a very small effect on the overall distribution of scattered photons across space. The multiplicative scale factor for aerosols is set to Λaer0=10km to represent a density of aerosols that is higher than likely to be found in a real atmosphere. Simulations are run independently for atmospheres of only molecules (left), only aerosols (middle), and both being simultaneously present (right). It is directly evident by eye from the striking similarity between Fig. 2 (left) and Fig. 2 (right) that the overall distribution of indirect photons in the atmosphere is governed by molecules. In spite of the negligible effect of aerosols on the overall distribution of indirect photons, their presence should not be forgotten, in particular near to ground level where the ground-based detectors are located.

Fig. 2. Relative effect on the density distribution of indirect photons for aerosols and molecules in a real atmosphere, illustrated by simulations with aerosols and molecules independently and simultaneously present. (Left) An atmosphere consisting of molecules only. (Middle) An atmosphere consisting of only aerosols with parameters {g=0.6, Λaer0=10km, and Haer0=1.5km}. (Right) An atmosphere consisting simultaneously of both aerosols and molecules with the same atmospheric conditions.

Fig. 3. Effect of changing the g value on the density distribution of photons propagating from an isotropic source. Simulations are for atmospheres of only aerosols with Λaer0=14.2km and Haer0=8km, i.e., an aerosol density distribution similar to molecules. Results are presented for three different values of g={0.3,0.6,0.9}, left, middle, and right, respectively.

4. GLOBAL VIEW OF INDIRECT PHOTON CONTRIBUTION TO THE TOTAL LIGHT DETECTED

This section aims to observe how different aerosol conditions, and especially different scattering phase functions, affect the ratio of indirect to direct light arriving at detectors within a given time interval (or integration time) tdet across all space. The simulation is used to propagate photons from an isotropic source for a given distance D, at which point, values of position are stored for direct photons only. Indirect photons are then simulated to propagate for a further amount of time tdet. Any of these indirect photons crossing the sphere of direct photons with radius D within the time tdet are considered detected. With respect to the position in space that each histogram bin holds data for, the histograms presented in this section have the same format as in Section 3. However, in this section, each histogram bin now represents the ratio of indirect to direct photons Nindirect/Ndirect detected at the point {rrel,θrel} within the interval of time starting when direct photons reach the point and finishing within a time tdet later.

Simulations here are run separately for atmospheres of only molecules or aerosols. Density parameters of {Λaer0=25.0km,Haer0=1.5km} for the aerosol population are deliberately chosen such that the effects observed can not be simply accredited to an overestimated density of aerosols in the atmosphere. Figure 4 (top) shows results for a detection time of tdet=100ns for atmospheres of molecules only (left) and aerosols only with values of g={0.3,0.9} (middle and right, respectively). For all configurations, there is an increasing ratio of indirect to direct photons observed toward ground level. This is expected as the amount of direct photons decreases and indirect photons increases for the increasing concentration of scatterers at lower heights. Of much greater interest is the fact that at ground level, Nindirect/Ndirect for aerosols with a high g value is much greater than Nindirect/Ndirect for molecules (in spite of a much lower concentration). This directly demonstrates that, for low detection times, a high value of g has an influence on the ratio Nindirect/Ndirect that outweighs the fact that aerosols are at a lower density than molecules. It can be explained by referring back to Fig. 3, where an increasing value of g leads to an increasing accumulation of indirect photons just before the direct photon ring. However, this amount of scattering by aerosols begins to become significant enough only at low heights above ground level. This is an important fact for ground-based detectors.

Fig. 4. Effect of the scattering phase function and the detection time. Simulations are run for sources of initial height hinit=10km and a detection time of tdet=100ns for the top panel and tdet=1000ns for the bottom panel, individually for atmospheres of (left) molecules only or aerosols only, (left) g=0.3 or (right) g=0.9. Aerosol density parameters are {Λaer0=25.0km,Haer0=1.5km}. Ray structures are related to a lack of statistics for simulation of scattered photons.

5. ATMOSPHERIC POINT SPREAD FUNCTION FOR A GROUND-BASED DETECTOR

The quantity of multiple scattered light recorded by an imaging system or telescope is of principal interest, and especially this contribution as a function of the integration angle ζ. The angle ζ is defined as the angular deviation in the entry of indirect photons at the detector aperture with respect to direct photons. For direct photons from an isotropic source, the angle of entry is usually approximated to be constant as the entry aperture of the detector is always very small relative to the distance of the isotropic sources. In contrast, multiply scattered photons can enter the aperture of the detector at any deviated angle ζ from the direct light between 0° and 90°. The value ζ for each indirect photon entering the detector is calculated by considering its deviation from direct light in elevation and azimuthal angle noted Δθ and Δϕ, respectively: ζ=cos1[cosΔθcosΔϕ]. A Taylor expansion of this equation, keeping all terms up to second-order, means that ζ can approximately be written as ζΔθ2+Δϕ2.

The main problem in simulating indirect light contribution at detectors is obtaining reasonable statistics within reasonable simulation running times. The root of the problem is the very small surface area of the detector relative to the large distances where isotropic sources are created. The amount of direct photons is calculated analytically by modeling the detector as a point relative to the initial position of the isotropic source. Thus, all direct photons are considered to follow the same path and the infinitesimal change in the number of direct photons dNdirect for an infinitesimal step length dl is then written as dNdirect=[Ndirectdl/Λmol(l)+Ndirectdl/Λaer(l)]. The same approach as explained in [24

24. M. D. Roberts, “The role of atmospheric multiple scattering in the transmission of fluorescence light from extensive air showers,” J. Phys. G 31, 1291–1301 (2005).

] is used to cut running times of the simulation for indirect photons. The symmetry in the distribution of scatterers in azimuthal angle, as explained in Section 2.B, is once again applied here. This symmetry means that so long as the detector has the same height and distance from the source, the azimuthal angle relative to it is unimportant. As such, the surface area of the detector is increased in the simulation by extending it through an azimuthal angle of 2π so that a greater amount of indirect photons is detected and better statistics are obtained. The setup of the extended detector is drawn in Fig. 5, where the strip of the sphere has a width corresponding to the diameter of the detector. Also, stopping the tracking of all photons that can no longer be detected further reduces the simulation time.

Fig. 5. Diagram showing how the detector is simulated to have an extent of 2π in azimuthal angle to increase the amount of statistics retrieved for indirect photons.

This part aims to look at the effect of changing aerosol size (via the asymmetry parameter g) on the amount of indirect light recorded at the detector for an isotropic source at different positions. The integration time of the detector is set to tdet=100ns and the aerosol attenuation length is fixed at Λaer0=25km. The percentage of light due to indirect photons against integration angle ζ is given by the ratio (indirect light) over (direct light+indirect light), where the direct or indirect light signals are the number of photons collected within the given integration angle ζ. Figure 6 (left) shows the results for an isotropic source placed at a distance of D=1km and at a very low inclination angle of θinc=3° [θinc=sin1(hsource/D), where hsource is the height of the source above ground level]. As expected, the amount of signal due to indirect light increases consistently with integration angle ζ as all direct light arrived at ζ=0°. These curves are directly linked to the point spread function since only a differentiation with respect to ζ is needed. These curves are similar to measurements done, for instance, by Bissonnette and co-workers [25

25. L. R. Bissonnette, “Imaging through fog and rain,” Opt. Eng. 31, 1045–1052 (1992). [CrossRef]

,26

26. B. Ben Dor, A. D. Devir, G. Shaviv, P. Bruscaglioni, P. Donelli, and A. Ismaelli, “Atmospheric scattering effect on spatial resolution of imaging systems,” J. Opt. Soc. Am. A 14, 1329–1337 (1997). [CrossRef]

]. A more interesting feature is the increased contribution from indirect light for increasing aerosol size (i.e., a higher value of the asymmetry parameter g). Comparing the situation of an atmosphere with no aerosols to one with aerosols, atmospheric aerosols have a non-negligible effect on the percentage of indirect light received at a ground-based detector. The explanation of this observation lies once again in the anisotropy associated with the scattering phase function. The percentage of indirect photons last scattered at a given distance relative to the detector is plotted in Fig. 6 (right). In the case of an atmosphere with only molecules, most of scattered photons recorded within the integration time of 100 ns originate from the position of the isotropic source. Indeed, there is an increased density of photons at this distance where the source is initiated. For the case of larger aerosol sizes, corresponding to larger g values, the peak at the source’s initial position is now greatly diminished. This is a result of detection of photons scattered more uniformly across all distances. This occurs because aerosols with higher values of g have a higher probability of scattered photons in a very forward direction.

Fig. 6. Plots for an isotropic source placed at θinc=3°, D=1km for atmospheres where aerosols and molecules are simultaneously present. The aerosol concentration and the detection time are kept constant at Λaer0=25km and tdet=100ns, respectively. (Left) Percentage of signal due to indirect light for different integration angles ζ and different g values. The black line is an exclusive case where only molecules are present. (Right) Percentage of the detected indirect photons that were last scattered at different distances from the detector for the three same cases.

Figure 7 (left) displays results of simulations run for the same geometrical configuration and aerosol parameters but different integration times. The distance to the detector is set to be D=15km, inclination angle θinc=15°, g=0.6, and Λaer0=25km. It is observed that for an increasing time, the total amount of signal due to indirect light also increases. For the 900 ns interval between tdet=100ns and tdet=1000ns, the amount of signal due to indirect light increases greatly, meaning that there are still a lot of indirect photons yet to arrive after the integration time of 100 ns. However, this observation is not true anymore after a large time delay, typically greater than 4000 ns in our case. The bar chart displayed in Fig. 7 (right) shows the percentage of detected indirect photons having undergone one or two or more scatterings by aerosols or molecules. The most notable feature of this chart is the increasing amount of molecularly scattered photons detected for increasing integration times. As previously explained in Section 4, aerosols begin to play a lesser role for longer detection times. This is because photons that were scattered at positions that are not necessarily close to the path of direct light now have enough time to travel and reach the detector within this longer integration time. This idea is confirmed by an increased uniformity across space in the distance from the last scattering event for increasing integration times (plot not shown here).

Fig. 7. Plots to demonstrate the effect of increasing integration time tdet. The inclination angle is θinc=15° and the distance D=30km. Λaer0=25km and g=0.6. (Left) Percentage of signal due to indirect light for different integration angles ζ and different integration times tdet. (Right) Percentage of detected indirect photons that have undergone either one or two or more scatterings by aerosols or molecules.

6. CONCLUSION

A new Monte Carlo simulation for the scattering of light has been created and used to observe atmospheric aerosol effects on the percentage of indirect light collected by detectors. The study began with a general description of the dispersion of scattered photons in different atmospheric conditions. It was found that for an increased value of the asymmetry parameter g (i.e., a larger aerosol size), a greater accumulation of scattered photons close to the direct photons is found. The principal argument presented in this work is that, even for a low density of aerosols in the atmosphere, the ratios of indirect to direct photons detected can be comparable or greater to those caused by molecules. In particular, the value of detection time tdet is proved to play an important role on the relative effects of molecules and aerosols on the ratio. This phenomenon is also used to estimate the aerosol size distribution, especially for very large aerosols. The technique is described in detail in [27

27. G. Zaccanti and P. Bruscaglioni, “Method of measuring the phase function of a turbid medium in the small scattering angle range,” Appl. Opt. 28, 2156–2164 (1989). [CrossRef]

29

29. E. Trakhovsky and U. P. Oppenheim, “Determination of aerosol size distribution from observation of the aureole around a point source. 2: experimental,” Appl. Opt. 23, 1848–1852 (1984). [CrossRef]

].

In addition, this aerosol size effect could still solve some unsolved experimental observations, such as the measurement done at the Pierre Auger Observatory [30

30. J. Abraham, for the Pierre Auger Collaboration, “The fluorescence detector of the Pierre Auger Observatory,” Nucl. Instrum. Methods Phys. Res. A 620, 227–251 (2010). [CrossRef]

,31

31. K. Louedec, for the Pierre Auger Collaboration, “Atmospheric monitoring at the Pierre Auger Observatory—Status and Update,” in Proceedings of the 32nd ICRC, Beijing, (2011), Vol. 2, pp. 63–66.

] a few years ago. Indeed, part of the point spread function measured by ground-based telescopes is still not fully understood, i.e., cannot be reproduced in simulations [32

32. J. Baüml, for the Pierre Auger Collaboration, “Measurement of the optical properties of the Auger fluorescence telescopes,” in Proceedings of the 33rd ICRC, Rio de Janeiro, (2013), pp. 15–18. arxiv:astro-ph/1307.5059.

,33

33. P. Assis, R. Conceiçao, P. Gonçalves, M. Pimenta, and B. Tomé, for the Pierre Auger Collaboration, “Multiple scattering measurement with laser events,” Astrophys. Space Sci. Trans. 7, 383–386 (2011).

]. One of possible explanations could be an additional contribution coming from a large population of aerosols present in the atmosphere.

ACKNOWLEDGMENTS

K. L. thanks Marcel Urban for having provided the stimulus to begin this study. Also, the authors thank their colleagues from the Pierre Auger Collaboration for fruitful discussions and for their comments on this work.

REFERENCES

1.

N. S. Kopeika, I. Dror, and D. Sadot, “Causes of atmospheric blur: comment on atmospheric scattering effect on spatial resolution of imaging systems,” J. Opt. Soc. Am A 15, 3097–3106 (1998).

2.

J. V. Dave, “Effect of atmospheric conditions on remote sensing of a surface non-homogeneity,” Photogramm. Eng. Remote Sens. 46, 1173–1180 (1980).

3.

W. A. Pearce, “Monte Carlo study of the atmospheric spread function,” Appl. Opt. 25, 438–447 (1986). [CrossRef]

4.

D. Sadot and N. S. Kopeika, “Imaging through the atmosphere: practical instrumentation-based theory and verification of aerosol modulation transfer function,” J. Opt. Soc. Am. A 10, 172–179 (1993). [CrossRef]

5.

I. Dror and N. S. Kopeika, “Experimental comparison of turbulence modulation transfer function and aerosol modulation transfer function through the open atmosphere,” J. Opt. Soc. Am. A 12, 970–980 (1995). [CrossRef]

6.

J. Otterman and R. S. Fraser, “Adjacency effects on imaging by surface reflection and atmospheric scattering: cross radiance to zenith,” Appl. Opt. 18, 2852–2860 (1979). [CrossRef]

7.

D. Tanre, P. Y. Deschamps, P. Duhaut, and M. Herman, “Adjacency effect produced by the atmospheric scattering in thematic mapper data,” J. Geophys. Res. 92, 12000–12006 (1987). [CrossRef]

8.

P. N. Reinersman and K. L. Carder, “Monte Carlo simulation of the atmospheric point-spread function with an application to correction for the adjacency effect,” Appl. Opt. 34, 4453–4471 (1995). [CrossRef]

9.

A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, 1978).

10.

H. C. Van De Hulst, Light Scattering by Small Particles (Dover, 1981).

11.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1998).

12.

A. Bucholtz, “Rayleigh-scattering calculations for the terrestrial atmosphere,” Appl. Opt. 34, 2765–2773 (1995). [CrossRef]

13.

B. Keilhauer and M. Will, for the Pierre Auger Collaboration, “Description of atmospheric conditions at the Pierre Auger Observatory using meteorological measurements and models,” Eur. Phys. J. Plus 127, 96 (2012).

14.

K. Louedec and R. Losno, for the Pierre Auger Collaboration, “Atmospheric aerosols at the Pierre Auger Observatory and environmental implications,” Eur. Phys. J. Plus 127, 97 (2012).

15.

G. Mie, “Beiträge zur Optik Trüber-Medien, speziell Kolloidaler Metallösungen,” Ann. Physik 25, 377–452 (1908).

16.

W. J. Wiscombe, “Improved Mie scattering algorithms,” Appl. Opt. 19, 1505–1509 (1980). [CrossRef]

17.

L. C. Henyey and J. L. Greenstein, “Diffuse radiation in the galaxy,” Astrophys. J. 93, 70–83 (1941). [CrossRef]

18.

D. Toublanc, “Henyey-Greenstein and Mie phase functions in Monte Carlo radiative transfer computations,” Appl. Opt. 35, 3270–3274 (1996). [CrossRef]

19.

O. Boucher, “On aerosol shortwave forcing and the Henyey-Greenstein phase function,” J. Atmos. Sci. 55, 128–134 (1998). [CrossRef]

20.

T. Binzoni, T. S. Leung, A. H. Gandjbakhche, D. Rüfenacht, and D. T. Delpy, “The use of the Henyey-Greenstein phase function in Monte Carlo simulations in biomedical optics,” Phys. Med. Biol. 51, N313–N322 (2006). [CrossRef]

21.

S. Metari and F. Deschênes, “A new convolution kernel for atmospheric point spread function applied to computer vision,” In Proceedings of the IEEE 11th International Conference on Computer Vision (ICCV) (IEEE, 2007), pp 1–8.

22.

K. Louedec, S. Dagoret-Campagne, and M. Urban, “Ramsauer approach to Mie scattering of light on spherical particles,” Phys. Scr. 80, 035403 (2009). [CrossRef]

23.

K. Louedec and M. Urban, “Ramsauer approach for light scattering on non absorbing spherical particles and application to the Henyey-Greenstein phase function,” Appl. Opt 51, 7842–7852 (2012). [CrossRef]

24.

M. D. Roberts, “The role of atmospheric multiple scattering in the transmission of fluorescence light from extensive air showers,” J. Phys. G 31, 1291–1301 (2005).

25.

L. R. Bissonnette, “Imaging through fog and rain,” Opt. Eng. 31, 1045–1052 (1992). [CrossRef]

26.

B. Ben Dor, A. D. Devir, G. Shaviv, P. Bruscaglioni, P. Donelli, and A. Ismaelli, “Atmospheric scattering effect on spatial resolution of imaging systems,” J. Opt. Soc. Am. A 14, 1329–1337 (1997). [CrossRef]

27.

G. Zaccanti and P. Bruscaglioni, “Method of measuring the phase function of a turbid medium in the small scattering angle range,” Appl. Opt. 28, 2156–2164 (1989). [CrossRef]

28.

E. Trakhovsky and U. P. Oppenheim, “Determination of aerosol size distribution from observation of the aureole around a point source. 1: theoretical,” Appl. Opt. 23, 1003–1008 (1984). [CrossRef]

29.

E. Trakhovsky and U. P. Oppenheim, “Determination of aerosol size distribution from observation of the aureole around a point source. 2: experimental,” Appl. Opt. 23, 1848–1852 (1984). [CrossRef]

30.

J. Abraham, for the Pierre Auger Collaboration, “The fluorescence detector of the Pierre Auger Observatory,” Nucl. Instrum. Methods Phys. Res. A 620, 227–251 (2010). [CrossRef]

31.

K. Louedec, for the Pierre Auger Collaboration, “Atmospheric monitoring at the Pierre Auger Observatory—Status and Update,” in Proceedings of the 32nd ICRC, Beijing, (2011), Vol. 2, pp. 63–66.

32.

J. Baüml, for the Pierre Auger Collaboration, “Measurement of the optical properties of the Auger fluorescence telescopes,” in Proceedings of the 33rd ICRC, Rio de Janeiro, (2013), pp. 15–18. arxiv:astro-ph/1307.5059.

33.

P. Assis, R. Conceiçao, P. Gonçalves, M. Pimenta, and B. Tomé, for the Pierre Auger Collaboration, “Multiple scattering measurement with laser events,” Astrophys. Space Sci. Trans. 7, 383–386 (2011).

OCIS Codes
(010.1300) Atmospheric and oceanic optics : Atmospheric propagation
(280.1100) Remote sensing and sensors : Aerosol detection
(280.1310) Remote sensing and sensors : Atmospheric scattering
(290.1090) Scattering : Aerosol and cloud effects
(290.4210) Scattering : Multiple scattering
(290.5820) Scattering : Scattering measurements

ToC Category:
Atmospheric and Oceanic Optics

History
Original Manuscript: August 5, 2013
Revised Manuscript: September 10, 2013
Manuscript Accepted: September 11, 2013
Published: October 11, 2013

Virtual Issues
Vol. 9, Iss. 1 Virtual Journal for Biomedical Optics

Citation
Joshua Colombi and Karim Louedec, "Monte Carlo simulation of light scattering in the atmosphere and effect of atmospheric aerosols on the point spread function," J. Opt. Soc. Am. A 30, 2244-2252 (2013)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-30-11-2244


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References

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  20. T. Binzoni, T. S. Leung, A. H. Gandjbakhche, D. Rüfenacht, and D. T. Delpy, “The use of the Henyey-Greenstein phase function in Monte Carlo simulations in biomedical optics,” Phys. Med. Biol. 51, N313–N322 (2006). [CrossRef]
  21. S. Metari and F. Deschênes, “A new convolution kernel for atmospheric point spread function applied to computer vision,” In Proceedings of the IEEE 11th International Conference on Computer Vision (ICCV) (IEEE, 2007), pp 1–8.
  22. K. Louedec, S. Dagoret-Campagne, and M. Urban, “Ramsauer approach to Mie scattering of light on spherical particles,” Phys. Scr. 80, 035403 (2009). [CrossRef]
  23. K. Louedec and M. Urban, “Ramsauer approach for light scattering on non absorbing spherical particles and application to the Henyey-Greenstein phase function,” Appl. Opt 51, 7842–7852 (2012). [CrossRef]
  24. M. D. Roberts, “The role of atmospheric multiple scattering in the transmission of fluorescence light from extensive air showers,” J. Phys. G 31, 1291–1301 (2005).
  25. L. R. Bissonnette, “Imaging through fog and rain,” Opt. Eng. 31, 1045–1052 (1992). [CrossRef]
  26. B. Ben Dor, A. D. Devir, G. Shaviv, P. Bruscaglioni, P. Donelli, and A. Ismaelli, “Atmospheric scattering effect on spatial resolution of imaging systems,” J. Opt. Soc. Am. A 14, 1329–1337 (1997). [CrossRef]
  27. G. Zaccanti and P. Bruscaglioni, “Method of measuring the phase function of a turbid medium in the small scattering angle range,” Appl. Opt. 28, 2156–2164 (1989). [CrossRef]
  28. E. Trakhovsky and U. P. Oppenheim, “Determination of aerosol size distribution from observation of the aureole around a point source. 1: theoretical,” Appl. Opt. 23, 1003–1008 (1984). [CrossRef]
  29. E. Trakhovsky and U. P. Oppenheim, “Determination of aerosol size distribution from observation of the aureole around a point source. 2: experimental,” Appl. Opt. 23, 1848–1852 (1984). [CrossRef]
  30. J. Abraham, for the Pierre Auger Collaboration, “The fluorescence detector of the Pierre Auger Observatory,” Nucl. Instrum. Methods Phys. Res. A 620, 227–251 (2010). [CrossRef]
  31. K. Louedec, for the Pierre Auger Collaboration, “Atmospheric monitoring at the Pierre Auger Observatory—Status and Update,” in Proceedings of the 32nd ICRC, Beijing, (2011), Vol. 2, pp. 63–66.
  32. J. Baüml, for the Pierre Auger Collaboration, “Measurement of the optical properties of the Auger fluorescence telescopes,” in Proceedings of the 33rd ICRC, Rio de Janeiro, (2013), pp. 15–18. arxiv:astro-ph/1307.5059.
  33. P. Assis, R. Conceiçao, P. Gonçalves, M. Pimenta, and B. Tomé, for the Pierre Auger Collaboration, “Multiple scattering measurement with laser events,” Astrophys. Space Sci. Trans. 7, 383–386 (2011).

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