## Light scattering and absorption by randomly-oriented cylinders: dependence on aspect ratio for refractive indices applicable for marine particles |

Optics Express, Vol. 19, Issue 5, pp. 4673-4691 (2011)

http://dx.doi.org/10.1364/OE.19.004673

Acrobat PDF (1273 KB)

### Abstract

Typically, explanation/interpretation of observed light scattering and absorption properties of marine particles is based on assuming a spherical shape and homogeneous composition. We examine the influence of shape and homogeneity by comparing the optics of randomly-oriented cylindrically-shaped particles with those of equal-volume spheres, in particular the influence of aspect ratio (*AR* = length/diameter) on extinction and backscattering. Our principal finding is that the when *AR* > ~3–5 and the diameter is of the order of the wavelength, the extinction efficiency and the backscattering probability are close to those of an infinite cylinder. In addition, we show the spherical-based interpretation of extinction and absorption can lead to large error in predicted backscattering.

© 2011 OSA

## 1. Introduction

1. S. G. Ackleson, “Optical determinations of suspended sediment dynamics in western Long Island Sound and the Connecticut River plume,” J. Geophys. Res. **111**(C7), C07009 (2006), doi:. [CrossRef]

2. N. Hoepffner and S. Sathyendranath, “Determination of major groups of phytoplankton pigments from absorption spectra of total particulate matter,” J. Geophys. Res. **98**(C12), 22789–22803 (1993). [CrossRef]

*a*), the scattering coefficient (

*b*), the extinction coefficient

*c*=

*a + b*, the volume scattering function

*β*(Θ) (Θ is the scattering angle), and the backscattering coefficient (

*b*). The extinction coefficient is particularly important in sediment studies, the spectral absorption coefficient in photosynthesis, and the backscattering coefficient in remote sensing (water-leaving radiance ∝

_{b}*b*/

_{b}*a*).

4. D. Stramski, E. Boss, D. Bogucki, and K. J. Voss, “The role of seawater constituents in light backscattering in the ocean,” Prog. Oceanogr. **61**(1), 27–56 (2004). [CrossRef]

5. H. R. Gordon and T. Du, “Light scattering by nonspherical particles: application to coccoliths detached from *Emiliania huxleyi*,” Limnol. Oceanogr. **46**(6), 1438–1454 (2001). [CrossRef]

7. W. R. Clavano, E. Boss, and L. Karp-Boss, “Inherent Optical Properties of Non-Spherical Marine-Like Particles - From Theory to Observations,” Oceanogr. Mar. Biol. **45**, 1–38 (2007). [CrossRef]

5. H. R. Gordon and T. Du, “Light scattering by nonspherical particles: application to coccoliths detached from *Emiliania huxleyi*,” Limnol. Oceanogr. **46**(6), 1438–1454 (2001). [CrossRef]

8. H. R. Gordon, T. J. Smyth, W. M. Balch, G. C. Boynton, and G. A. Tarran, “Light scattering by coccoliths detached from *Emiliania huxleyi*,” Appl. Opt. **48**(31), 6059–6073 (2009). [CrossRef] [PubMed]

*E. huxleyi*. Gordon [9

9. H. R. Gordon, “Backscattering of light from disklike particles: is fine-scale structure or gross morphology more important?” Appl. Opt. **45**(27), 7166–7173 (2006). [CrossRef] [PubMed]

10. H. R. Gordon, “Backscattering of light from disk-like particles with aperiodic angular fine structure,” Opt. Express **15**(25), 16424–16430 (2007). [CrossRef] [PubMed]

*λ*/4) had little influence on the backscattering of disk-like particles. Clavano et al. [7

7. W. R. Clavano, E. Boss, and L. Karp-Boss, “Inherent Optical Properties of Non-Spherical Marine-Like Particles - From Theory to Observations,” Oceanogr. Mar. Biol. **45**, 1–38 (2007). [CrossRef]

11. L.-X. Zhang, J.-Z. Lin, and T. L. Chan, “Orientation distribution of cylindrical particles suspended in turbulent pipe flow,” Phys. Fluids **17**(9), 093105 (2005). [CrossRef]

12. L. Karp-Boss and P. A. Jumars, “Motion of diatom chains in steady shear flow,” Limnol. Oceanogr. **43**(8), 1767–1773 (1998). [CrossRef]

*β*(Θ)/

*b*, and the backscattering probability,

*b*/

_{b}*b*, become nearly independent of the aspect ratio (length/diameter) when it becomes greater than ~3−5. This implies that the IOPs of longer cylindrical particles can be inferred from those of particles with aspect ratios in this range.

## 2. Review of light scattering and absorption concepts

### 2.1. Finite cylinders

*dA*with it’s normal parallel to

*r*is the distance from the detector to the particle, this gives the conventional definition of the differential scattering cross section:Far from the scattering center the scattered fields are ∝ 1/

*r*, so the scattered Poynting vector is

*r*. The total scattering cross section is defined bythe backscattering cross section byand the scattering phase function byNow, if we average over all orientations of the particle (to represent a collection of identical, randomly-oriented, particles) these relationships are replaced by where

*i*referencing one of

*N*appropriately chosen orientations of the particle. Note that the resulting

*b*, of a collection of such (randomly-oriented) particles are given bywhere

*n*is the number of such particles per unit volume. The backscattering coefficient isand the backscattering probability is

*Q*is defined by

_{b}*σ*[13]:where

_{a}*plus*scattered. Similarly, performing the orientational averaging,

*a*, is defined by

*c*is usually referred to as the beam attenuation coefficient).

### 2.2 Infinite cylinders

*r*from the origin of coordinates (located somewhere on the axis of the cylinder), for a given orientation of the cylinder the quantities defined in Eqs. (1)–(4) can be formally computed in a straightforward manner. If

*r*is sufficiently large, the scattered fields are ∝ √

*r*, so both the differential and the total cross sections are ∝

*r*; however, the scattering phase function is independent of

*r*. Thus, the cross sections defined in this way lose their meaning as characteristics of the particle (they depend on how they are measured, i.e.,

*r*). Nevertheless, by constructing a large-diameter coaxial cylindrical surface of some length around the cylindrical particle, one can show that the scattering, absorption, and extinction cross sections

*per unit length*are finite [13], so one can define scattering, absorption, and extinction efficiencies such that the cross sections of a given length of particle are finite, e.g.,

*ς*is the angle between the cylinder axis and the direction of the incident beam (

*A*for the length

_{p}*L*of the cylindrical particle).

*r*is made, there will be some orientations for which the detector is not in the far-field zone (or scattered field zone). Thus, the notion of the scattered field (fields ∝ √

*r*) is not applicable for all orientations and a fixed

*r*. In contrast, quantities that are independent of

*r*, i.e., the

*Q*’s, can be averaged over orientation in a straightforward manner [15

15. G. R. Fournier and B. T. Evans, “Approximations to extinction from randomly oriented circular and elliptical cylinders,” Appl. Opt. **35**(21), 4271–4282 (1996). [CrossRef] [PubMed]

*L*of cylinder,

*r*, and one can formally define the its orientational average through

## 3. Cylinders examined in the present work

*m*−

_{r}*im*, relative to water. The lower cylinder (coated) has the same outer diameter (

_{i}*D*) as the homogeneous cylinder, however the core diameter is

*D*/2 and the core index is

*m*− 4

_{r}*im*. The index of the outer layer is

_{i}*m*− 0

_{r}*i*, so this simulates a situation in which the mass of absorbing material (or the number of absorbing molecules) is the same in the upper and lower cylinder, and allows simulation of the influence of the distribution of absorbing pigments in cylindrically shaped particles. In marine optics, there are two phenomena that are referred to as the “package effect.” The first is the difference in absorption between equal quantities of absorbing material in solution or in particles suspended in the same volume [16

16. L. N. M. Duysens, “The flattening of the absorption spectrum of suspensions, as compared to that of solutions,” Biochim. Biophys. Acta **19**(1), 1–12 (1956). [CrossRef] [PubMed]

18. A. Bricaud and A. Morel, “Light attenuation and scattering by phytoplanktonic cells: a theoretical modeling,” Appl. Opt. **25**(4), 571–580 (1986). [CrossRef] [PubMed]

6. A. Quirantes and S. Bernard, “Light scattering methods for modeling algal particles as a collection of coated and/or nonspherical scatterers,” J. Quant. Spectrosc. Radiat. Transf. **100**(1-3), 315–324 (2006). [CrossRef]

19. J. R. V. Zaneveld and J. C. Kitchen, “The variation of inherent optical properties of phytoplankton near an absorption peak as determined by various models of cell structure,” J. Geophys. Res. **100**(C7), 13,309–13,320 (1995). [CrossRef]

*D*= 0.5, 1.0, 1.5, 2.0 μm,

*L*= 0.5, 1.0, 3.0, 5.0, 7.0, 10.0, 15.0, and 20 μm,

*λ*= 400, 500, 600, and 700 nm (in vacuum), and

*m*−

_{r}*im*= 1.02, 1.05, 1.05 – 0.002

_{i}*i*, 1.05 – 0.008

*i*, 1.05 – 0.010

*i*, 1.05 – 0.040

*i*, 1.10, 1.15, and 1.20, relative to water. The discrete-dipole approximation code [20

20. B. T. Draine, “The discrete-dipole approximation and its application to interstellar graphite grains,” Astrophys. J. **333**, 848–872 (1988). [CrossRef]

21. B. T. Draine and P. Flatau, “Discrete dipole approximation for scattering calculations,” J. Opt. Soc. Am. A **11**(4), 1491–1499 (1994). [CrossRef]

22. R. D. Haracz, L. D. Cohen, and A. Cohen, “Scattering of linearly polarized light from randomly oriented cylinders and spheroids,” J. Appl. Phys. **58**(9), 3322–3327 (1985). [CrossRef]

*λ*/18 at 400 nm and ~

*λ*/31 at 700 nm. This insured that the backscattering cross section could be computed with an error < about 5%. Even with the multi-processor cluster, the computations were very time consuming for the larger particles: ~10 days were required to compute the scattering (at 4 wavelengths) by a cylinder with

*D*= 1.5 μm,

*L*= 15 μm and

*m*= 1.20.

## 4. Extinction and absorption efficiencies

*AR*≡

*L*/

*D*) and diameter of the cylinders?; (2) how do the efficiencies compare with those for an infinite cylinder with the same diameter?; and (3) how do the efficiencies depend on the distribution of absorbing material within the cylinders (Fig. 1)?

*Q*for a coated cylinder with indices

_{a}*m*= 1.05−0.040

_{inside}*i*and

*m*1.05−0.000

_{outside}*i*(

*Q*(Packaged)) to that of a homogeneous cylinder

_{a}*m*=

_{inside}*m*= 1.05−0.010

_{outside}*i*(

*Q*(Homo)). Note that both cylinders contain the same number of absorbing molecules. The figure shows that the effect of the absorbing pigment packaging is greatest in the blue region of the spectrum and for larger-diameter cylinders. The maximum decrease in

_{a}*Q*due to the packaging is about 25%. Although the symbols do not differentiate between cylinder lengths, for a given diameter the packaging effect is smallest in the shortest cylinder and depends very little on the length once

_{a}*AR*exceeds unity. In the case with less overall absorption, i.e.,

*m*= 1.05−0.008

_{inside}*i*and

*m*= 1.05−0.000

_{outside}*i*compared to that of a homogeneous cylinder

*m*=

_{inside}*m*= 1.05−0.002

_{outside}*i*, similar results are obtained; however, the maximum decrease in

*Q*due to the packaging is only about 10% (Fig. 2.).

_{a}*ρ*are compared with those of infinite cylinders in Fig. 4 . In this case the refractive index is 1.20 and since there is no absorption

*Q*=

_{b}*Q*. The figure clearly shows that for

_{c}*AR*≥ 3, the extinction efficiency is again close to that of an infinite cylinder, with all cases except two differing by less than ± 10% (RMS difference ~5%).

*Q*(

_{c}*D*,

*m*,

*AR*) ≈

*Q*(

_{c}*D*,

*m*,∞). This implies that

*AR*and

*AR*′ (both > about 3),Similar expressions hold for the orientationally averaged absorption and scattering efficiencies. Although

## 5. Phase function and backscattering probability of cylinders

*AR*≥ 3. Is this the case for the phase function and backscattering probability? I mentioned earlier that the default orientational-averaging scheme used in DDSCAT 7.0 was employed in the present computations. Is this default sufficient to provide orientational averaging for long cylinders? To examine this question, I computed the orientationally-averaged phase function (and

*AR*. To achieve the very large variation in

*AR*, I used

*D*= 0.25 μm. The results of this computation are shown in Fig. 5 . One sees that with the exception of small scattering angles (Θ ≤ 8°), as

*AR*increases the computed phase function simply becomes “noisier.” This is what would be expected, as the scattering pattern (for a given orientation) degenerates into an infinitely thin cone as

*L*→ ∞. Careful examination shows that there is a high correlation between the “noise” at

*AR*= 100 and 200, etc., as would be expected as the scattering cone thins. Since the thickness of the scattering cone depends mostly on

*λ / L*(the thickness decreases as

*L*increases), I conclude that for the values of

*L*examined in this work (≤ 25 μm) the averaging procedure in DDSCAT is sufficiently accurate to yield reliable phase functions and backscattering probabilities.

*AR*= 20 and

*AR*= 3 are the enhanced scattering near zero degrees and the deeper minima near 30°, 50°, 80°, and 130° for

*AR*= 20. This weak dependence on aspect ratios as long as

*AR*≥ 5 is also displayed by the backscattering probability as shown in Fig. 7 for a wide range of refractive indices and particle diameters.

*AR >*about 3–5,

*AR*′ >

*AR*≈3-5 (Figs. 7 and 13 ). I used Eq. (14) to compute the orientationally averaged backscattering cross section for cylinders with

*D*= 1 μm and

*AR*′ ≥ 5 from

*AR*= 3 and for

*AR*′ ≥ 7 from

*AR*= 5 with

*m =*1.05 – 0.010

*i*. The rms error was 2.5% for

*AR*= 3 and 1.2% for

*AR*= 5. Similar computations with

*m*= 1.20 – 0.000

*i*resulted in rms errors of 8.1% and 2.6% for

*AR*= 3, and 5, respectively.

## 6. Cylinders compared to equal-volume spheres

18. A. Bricaud and A. Morel, “Light attenuation and scattering by phytoplanktonic cells: a theoretical modeling,” Appl. Opt. **25**(4), 571–580 (1986). [CrossRef] [PubMed]

*Q*and

_{c}*Q*for spheres, it is much simpler to use the analytical formulas of the van de Hulst anomalous diffraction approximation for the scattering and absorption efficiencies of a homogeneous sphere. These are [14]andwhere

_{a}*ρ*= 2

*α*(

*m*−1),

_{r}*ρ′*= 4

*α m*, tan

_{i}*β*=

*m*/(

_{i}*m*−1), and

_{r}*α =*π

*d*/

*λ*, with

*d*the sphere’s diameter and

*λ*the wavelength of light

*in*the water. In this analysis, we take

*d*to be the diameter of a sphere with the same volume as the cylinder, i.e., the

*equal-volume sphere.*Fig. 8 provides the extinction and absorption efficiencies computed assuming the spherical shape, e.g.,

*Q*and

_{c}*Q*computed with the Van de Hulst anomalous diffraction theory (VdH), and with exact the Mie theory (MIE). There are three important observations to be made from Fig. 8: (1) the volume-equivalent sphere assumption is not very good in the case of

_{a}*Q*(left figure) even if full Mie theory is used; (2) the volume-equivalent sphere assumption is better in the case of

_{c}*Q*(right figure), especially if full Mie theory is used; and (3) the package effect, while relatively unimportant for

_{a}*Q*, is important in

_{c}*Q*(right figure) for the case with stronger absorption, but not for the case with weaker absorption.

_{a}*Q*and

_{c}*Q*from Eqs. (18) and (19) make in estimating the refractive index? Given the volume of the particle, and assuming a spherical shape,

_{a}*d*and

*α*are determined. Calculations of the beam attenuation coefficient and absorption coefficients for coated cylinders were inserted into Eqs. (15) and (16) to find

*m*and

_{r}*m*. Figure 9 provides the resulting computations for a coated cylinder with indices

_{i}*m*= 1.05−0.040

_{inside}*i*and

*m*= 1.05−0.000

_{outside}*i*, and all combinations of diameter and length. Recall that the package effect is larger for this case. Ideally one should derive an index of 1.05−0.010

*i*, based on the concentration of absorbing material. Clearly,

*m*is retrieved to within ± 20% with an average (over all sizes) close to 0.010, and the retrieved

_{i}*m*appears to be too low in almost all cases, but averages ~1.044. One notes that if the exact Mie theory were used in the retrieval of

_{r}*m*(Fig. 8) the retrieved values would be about 10% larger than shown in Fig. 9 due to the inaccuracy of the Van de Hulst approximation to

_{i}*Q*[Eq. (15)]. However, the exact Mie results cannot actually be used because

_{a}*m*is required, and as we see in the figure, it is strongly dependent on

_{r}*AR*. Thus, it is clear that measuring particle volume and the extinction and absorption cross sections, assuming the particles are spherical, then applying Eqs. (15) and (16) does yield meaningful results for

*m*even for particles with large aspect ratios; however, the retrieved values of

_{i}*m*depend strongly on the aspect ratio. It is interesting to note that if one employed the homogeneous infinite-cylinder assumption in the analysis of the cross sections (Fig. 2) for this example, the error in the retrieved

_{r}*m*would actually be larger than for the equivalent-volume sphere approach: accurate retrieval would require consideration of the package effect, probably by using a coated infinite-cylinder retrieval model.

_{i}*Q*for cylinders determined from the cross-sectional area of the equal-volume sphere (in a manner identical to that in Fig. 8), and

_{c}*ρ*evaluated using the diameter of the equal-volume sphere. The thick solid line in the figure is the Van de Hulst approximation to

*Q*. Note that for

_{c}*ρ*> about 3, for most cases shown, there is no refractive index value for equal-volume spheres that can produce the associated extinction efficiency. Thus, this method often fails to provide

*any*value for

*m*.

*m*and

_{r}*m*derived from measurements of the absorption and extinction efficiencies, the particle volume, and the assumption of sphericity (using the methodology described above, when it works, i.e., for low-index cylinders), how well does the predicted backscattering cross section reproduce the actual backscattering cross section of cylindrical particles? To shed light on this question, I used the retrieved refractive indices shown in Fig. 9 and Mie theory to compute

_{i}*R*over the visible spectrum for each size. Figure 11 (black points/lines) shows the resulting

*R*for particles with diameters ~1-3 times the wavelength as a function of the aspect ratio. The red points/lines on the figure provide

*R*values when the true value of the cylinder’s refractive index is used to compute the backscattering the sphere, rather than that determined from particle extinction, absorption, and volume. We note that for cylinders in this size range,

*R*is greater than 1 and increases approximately linearly with aspect ratio. The large values of

*R*when the index is retrieved from extinction, etc., is due to the increased error in the derived values of

*m*as the aspect ratio increases (the retrieved

_{r}*m*becomes smaller as the aspect ratio increases, and

_{r}*m*). Thus, the extinction, absorption, volume, and sphericity-assumption methodology cannot yield reliable values of the backscattering cross section of cylindrically shaped particles with even moderate (>5) aspect ratios; however, if the correct refractive index is known and used in the computation, the backscattering of the equal-volume sphere is much closer to that of the cylinder.

_{r}*R*for the higher index (1.20 – 0.000

*i*) is shown in Fig. 12 . Note that in this case

*m*= 1.05. Note that when the absorption is weak (

_{r}*m*= 0.002 with a homogeneous distribution of absorbing molecules, ■, or

_{i}*m*= 0.008 with the absorbing molecules confined to the inner cylinder of Fig. 1, ▲) there is little difference in the backscattering probability and that of a non-absorbing cylinder (♦). In contrast, for the more strongly absorbing, homogeneous (◊) or packaged (□), cylinders, absorption clearly influences the backscattering probability with larger values for the packaged case.

_{i}## 7. Comparison with spheroids

23. G. R. Fournier and B. T. Evans, “Approximation to extinction efficiency for randomly oriented spheroids,” Appl. Opt. **30**(15), 2042–2048 (1991). [CrossRef] [PubMed]

*Q*for spheroids. If one uses their relationships for a spheroid with minor axes

_{c}*D*and major axis

*L*(

*AR = L*/

*D*), it is seen that

*Q*becomes almost independent of

_{c}*AR*for

*AR*> about 3. I have carried out computations (using DDSCAT) for spheroids with

*D =*0.5, 1.0, and 1.5 μm, and

*AR*= 3, 5, and 10, for

*m*= 1.05 – 0.010

*i*and

*m*= 1.20 – 0.000

*i*. The resulting values of

*Q*(and

_{c}*Q*) are virtually independent of

_{a}*AR*and agree well with the Fournier and Evans [23

23. G. R. Fournier and B. T. Evans, “Approximation to extinction efficiency for randomly oriented spheroids,” Appl. Opt. **30**(15), 2042–2048 (1991). [CrossRef] [PubMed]

*AR*(e.g.,

*AR*= 100).

*AR*for

*AR*

*AR*> about 5. Thus, our conclusions regarding the dependenceof light scattering properties on

*AR*for cylinders appear to apply equally well to spheroids.

*D*and

*L*are <<

*λ*, and the polarizabilities are determined in the electrostatic approximation (Rayleigh approximation [13,14]), the total scattering for spheroids is proportional to the square of the volume times a factor that is dependent on

*AR*. This latter factor becomes nearly independent of

*AR*for

*AR*>

*~*3 for the refractive indices of interest here. In this case,

*AR*, a similar expression replaces Eq. (14). Again, similar expressions also apply to cylinders.

## 8. Concluding remarks

*AR >*~3-5, for refractive indices characteristic of marine particles (organic and inorganic). This applies to cylinders with diameters in the range 0.25 to 1.5 μm when illuminated with visible light (wavelength, 400-700 nm). Some long-chain phytoplankton, e.g.,

*Prochlorotrix hollandica*, fall in this size range [24]. It should also apply to much larger cylindrically-shaped particles, i.e., in sizes for which geometrical optics is applicable. Computational schemes for intermediate sized cylinders with high aspect ratios are not available; however, as the validity of the observation does not appear to depend on the actual diameter of the cylinders (Figs. 7 and 13) in the size ranges examined, one would expect that it would apply to intermediate sized particles as well. A limited number of computations for prolate spheroids suggest that the observations apply equally well to particles with this shape. This should simplify the inclusion of

*AR*-distributions in the characterization of scattering by marine particles.

18. A. Bricaud and A. Morel, “Light attenuation and scattering by phytoplanktonic cells: a theoretical modeling,” Appl. Opt. **25**(4), 571–580 (1986). [CrossRef] [PubMed]

*m*) can be determined with reasonable accuracy, i.e., ~ ± 20%, when

_{i}*m*is low as it usually is for phytoplankton [24]. Remarkably, this approximation is actually better in retrieving

_{r}*m*than using a homogeneous cylinder to model (incorrectly) a coated cylinder (Fig. 2). This suggests that in the absence of shape information, the equivalent-volume-sphere approximation is capable of yielding realistic estimates of

_{i}*m*for low-

_{i}*m*particles that deviate significantly from spheres. When

_{r}*m*is high, the method fails completely (Fig. 10), and a more appropriate shape is required to interpret the observed cross sections.

_{r}*σ*for the equal-volume sphere, can lead to an underestimation (

_{bb}*m*; however, if the correct value of the refractive index is known, the error is significantly decreased. For the high-index case (for which the equal-volume-sphere analysis fails), given the correct value of the refractive index, the equal-volume sphere backscatters more than the cylinder, i.e.,

_{r}4. D. Stramski, E. Boss, D. Bogucki, and K. J. Voss, “The role of seawater constituents in light backscattering in the ocean,” Prog. Oceanogr. **61**(1), 27–56 (2004). [CrossRef]

*λ*.

## Acknowledgments

## References and links

1. | S. G. Ackleson, “Optical determinations of suspended sediment dynamics in western Long Island Sound and the Connecticut River plume,” J. Geophys. Res. |

2. | N. Hoepffner and S. Sathyendranath, “Determination of major groups of phytoplankton pigments from absorption spectra of total particulate matter,” J. Geophys. Res. |

3. | H. R. Gordon, and A. Y. Morel, |

4. | D. Stramski, E. Boss, D. Bogucki, and K. J. Voss, “The role of seawater constituents in light backscattering in the ocean,” Prog. Oceanogr. |

5. | H. R. Gordon and T. Du, “Light scattering by nonspherical particles: application to coccoliths detached from |

6. | A. Quirantes and S. Bernard, “Light scattering methods for modeling algal particles as a collection of coated and/or nonspherical scatterers,” J. Quant. Spectrosc. Radiat. Transf. |

7. | W. R. Clavano, E. Boss, and L. Karp-Boss, “Inherent Optical Properties of Non-Spherical Marine-Like Particles - From Theory to Observations,” Oceanogr. Mar. Biol. |

8. | H. R. Gordon, T. J. Smyth, W. M. Balch, G. C. Boynton, and G. A. Tarran, “Light scattering by coccoliths detached from |

9. | H. R. Gordon, “Backscattering of light from disklike particles: is fine-scale structure or gross morphology more important?” Appl. Opt. |

10. | H. R. Gordon, “Backscattering of light from disk-like particles with aperiodic angular fine structure,” Opt. Express |

11. | L.-X. Zhang, J.-Z. Lin, and T. L. Chan, “Orientation distribution of cylindrical particles suspended in turbulent pipe flow,” Phys. Fluids |

12. | L. Karp-Boss and P. A. Jumars, “Motion of diatom chains in steady shear flow,” Limnol. Oceanogr. |

13. | C. F. Bohren, and D. R. Huffman, |

14. | H. C. Van de Hulst, |

15. | G. R. Fournier and B. T. Evans, “Approximations to extinction from randomly oriented circular and elliptical cylinders,” Appl. Opt. |

16. | L. N. M. Duysens, “The flattening of the absorption spectrum of suspensions, as compared to that of solutions,” Biochim. Biophys. Acta |

17. | A. Morel and A. Bricaud, “Theoretical results concerning light absorption in a discrete medium, and application to specific absorption of phytoplankton,” Deep-Sea Res. |

18. | A. Bricaud and A. Morel, “Light attenuation and scattering by phytoplanktonic cells: a theoretical modeling,” Appl. Opt. |

19. | J. R. V. Zaneveld and J. C. Kitchen, “The variation of inherent optical properties of phytoplankton near an absorption peak as determined by various models of cell structure,” J. Geophys. Res. |

20. | B. T. Draine, “The discrete-dipole approximation and its application to interstellar graphite grains,” Astrophys. J. |

21. | B. T. Draine and P. Flatau, “Discrete dipole approximation for scattering calculations,” J. Opt. Soc. Am. A |

22. | R. D. Haracz, L. D. Cohen, and A. Cohen, “Scattering of linearly polarized light from randomly oriented cylinders and spheroids,” J. Appl. Phys. |

23. | G. R. Fournier and B. T. Evans, “Approximation to extinction efficiency for randomly oriented spheroids,” Appl. Opt. |

24. | M. Jonasz, and G. R. Fournier, |

**OCIS Codes**

(010.4450) Atmospheric and oceanic optics : Oceanic optics

(010.1030) Atmospheric and oceanic optics : Absorption

**ToC Category:**

Atmospheric and Oceanic Optics

**History**

Original Manuscript: December 21, 2010

Revised Manuscript: February 13, 2011

Manuscript Accepted: February 18, 2011

Published: February 24, 2011

**Virtual Issues**

Vol. 6, Iss. 3 *Virtual Journal for Biomedical Optics*

**Citation**

Howard R. Gordon, "Light scattering and absorption by randomly-oriented cylinders: dependence on aspect ratio for refractive indices applicable for marine particles," Opt. Express **19**, 4673-4691 (2011)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-5-4673

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### References

- S. G. Ackleson, “Optical determinations of suspended sediment dynamics in western Long Island Sound and the Connecticut River plume,” J. Geophys. Res. 111(C7), C07009 (2006), doi:. [CrossRef]
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