Abstract

The finite angular resolution of nephelometers causes systematic measurement error of the volume scattering function. For scattering angles <90° this error depends mainly on the angular resolution of the nephelometer. For scattering angles >90° the error also depends on the attenuation of light in seawater and the instrument size. For nephelometers with angular resolution of ~2°, in clean ocean waters the error may assume a negative value of the order of −20% at scattering angles smaller than ~5°, i.e., the scattering function may be underestimated. The error may then increase to as much as +15% at ~10°, i.e., the scattering function may be overestimated. For greater scattering angles the error decreases to a few percent until, in turbid coastal waters, it may reach a negative peak of the order of −3% at ~170°, followed by an increase to about +15% for scattering angles in the vicinity of 175°.

© 1990 Optical Society of America

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References

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  1. N. G. Jerlov, Marine Optics (Elsevier, Amsterdam, 1976).
  2. T. J. Petzold, “Volume Scattering Functions for Selected Ocean Waters,” Scripps Institution of Oceanography, San Diego Ref. 72–78 (1978).
  3. M. Jonasz, H. Prandke, “Comparison of Measured and Computed Light Scattering in the Baltic,” Tellus 38B, 144–157 (1986).
    [CrossRef]
  4. L. C. Chow, C. L. Tien, “Inversion Techniques for Determining the Droplet Size Distribution in Clouds: Numerical Examinations,” Appl. Opt. 15, 378–383 (1976).
    [CrossRef] [PubMed]
  5. G. Kullenberg, “Scattering of Light by Sargasso Sea Water,” Deep-Sea Res. 15, 423–432 (1968).
  6. B. S. Pritchard, W. G. Elliot, “Two Instruments for Atmospheric Optics Measurements,” J. Opt. Soc. Am. 50, 191–202 (1960).
    [CrossRef]
  7. E. Fry, “Absolute Calibration of a Scatterance Meter,” in Suspended Solids in Water, R. J. Gibbs, Ed. (Plenum, New York, 1974) pp. 101–109.
    [CrossRef]

1986

M. Jonasz, H. Prandke, “Comparison of Measured and Computed Light Scattering in the Baltic,” Tellus 38B, 144–157 (1986).
[CrossRef]

1976

1968

G. Kullenberg, “Scattering of Light by Sargasso Sea Water,” Deep-Sea Res. 15, 423–432 (1968).

1960

Chow, L. C.

Elliot, W. G.

Fry, E.

E. Fry, “Absolute Calibration of a Scatterance Meter,” in Suspended Solids in Water, R. J. Gibbs, Ed. (Plenum, New York, 1974) pp. 101–109.
[CrossRef]

Jerlov, N. G.

N. G. Jerlov, Marine Optics (Elsevier, Amsterdam, 1976).

Jonasz, M.

M. Jonasz, H. Prandke, “Comparison of Measured and Computed Light Scattering in the Baltic,” Tellus 38B, 144–157 (1986).
[CrossRef]

Kullenberg, G.

G. Kullenberg, “Scattering of Light by Sargasso Sea Water,” Deep-Sea Res. 15, 423–432 (1968).

Petzold, T. J.

T. J. Petzold, “Volume Scattering Functions for Selected Ocean Waters,” Scripps Institution of Oceanography, San Diego Ref. 72–78 (1978).

Prandke, H.

M. Jonasz, H. Prandke, “Comparison of Measured and Computed Light Scattering in the Baltic,” Tellus 38B, 144–157 (1986).
[CrossRef]

Pritchard, B. S.

Tien, C. L.

Appl. Opt.

Deep-Sea Res.

G. Kullenberg, “Scattering of Light by Sargasso Sea Water,” Deep-Sea Res. 15, 423–432 (1968).

J. Opt. Soc. Am.

Tellus

M. Jonasz, H. Prandke, “Comparison of Measured and Computed Light Scattering in the Baltic,” Tellus 38B, 144–157 (1986).
[CrossRef]

Other

E. Fry, “Absolute Calibration of a Scatterance Meter,” in Suspended Solids in Water, R. J. Gibbs, Ed. (Plenum, New York, 1974) pp. 101–109.
[CrossRef]

N. G. Jerlov, Marine Optics (Elsevier, Amsterdam, 1976).

T. J. Petzold, “Volume Scattering Functions for Selected Ocean Waters,” Scripps Institution of Oceanography, San Diego Ref. 72–78 (1978).

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Figures (8)

Fig. 1
Fig. 1

Optical schematic of a light scattering meter. Notation: 1, container with water sample; 2, incident beam; 3, window; 4, air-filled detector housing; 5, detector; and 6, entrance aperture.

Fig. 2
Fig. 2

Detector plane: 5, detector aperture; 6′, image of the entrance aperture cast by the scattered light originating from dV; 7, locus of the rays scattered from dV at angle Θ′ and 8, strip used in the integration leading to βeff. The origin of the reference frame is at the center of 5, i.e., w and xc are positive and xs is negative in this figure. The dotted area denotes part of the detector aperture which is not vignetted by the entrance aperture (6).

Fig. 3
Fig. 3

No vignetting of the detector (5) by the entrance aperture (6) occurs when dV is at z2zz3. Partial vignetting occurs for z1 < z < z2 and for z3 < z < z4. Full vignetting occurs otherwise.

Fig. 4
Fig. 4

Values of βeff sampled by the detector in a low angular resolution nephelometer (1, Table I) viewing scattering volume elements dV at various locations z within its field of view. The ranges of sampled values are shown for two nominal scattering angles Θ indicated by the curves. The scattering function values characteristic of the volume element dV at z = 0 for each of the scattering angles are normalized to unity.

Fig. 5
Fig. 5

Ratio, exp[−c(L + zR)], of the transmission of light scattered by a scattering volume element dV located at z in the low angular resolution nephelometer (1, Table I) to that of the light scattered by the element at z = 0. The attenuation coefficient is c = 2 m−1. The nominal scattering angle Θ is shown by the curves.

Fig. 6
Fig. 6

Acceptance solid angle Ω(z) subtended by the detector at an element dV of the scattering volume at z. The results for a nephelometer having low angular resolution (2.2°, nephelometer 1, thin lines) are compared with those for a nephelometer having high angular resolution (1.0°, nephelometer 2, thick lines). The nominal scattering angle Θ is shown by the curves.

Fig. 7
Fig. 7

Relative systematic error of the volume scattering function β1. The thin solid and broken lines represent the error characteristic of the nephelometer with a low angular resolution of 2.2° used in waters with the attenuation coefficient c of 2 and 0.2 m−1, respectively. The solid thick line represents the error characteristic of a nephelometer with a high angular resolution of 1° used in waters with attenuation coefficient of 2 m−1. The curve for the low attenuation coefficient value is not shown for clarity as it overlaps the former for most of the scattering angles except those from the range 175–177° where the error stays within the limits of a few percent.

Fig. 8
Fig. 8

Same as Fig. 7 except for the different volume scattering function data β2.

Tables (1)

Tables Icon

Table I Characteristics of the Model Nephelometers

Equations (20)

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d F = β eff Ω E A o exp [ - c ( L + z + R ) ] d z ,
β eff = w m w M β ( Θ ) d Ω ( w ) w m w M d Ω ( w ) ,
Θ = Θ + z sin Θ - w R - z cos Θ + n D .
d Ω = d w h ( L + n D ) 2 ,
h = 2 [ r c 2 - ( w - x c ) 2 ] ,
r c = r d ( 1 + n D R - z cos Θ ) ,
x c = - n D sin Θ R - z cos Θ ,
x s = x c 2 - r c 2 + r d 2 2 x c .
h = 2 ( r d 2 - w 2 ) .
z 1 = - r d ( 2 R + n D ) n D sin Θ - 2 r d cos Θ ,
z 2 = - r d sin Θ ,
z 3 = - z 2 ,
z 4 = r d ( 2 R + n D ) n D sin Θ + 2 r d cos Θ ,
d F = E A 0 w m w M [ β ( Θ ) d Ω ] exp [ - c ( L + z + R ) ] d z .
L ( z 2 + R 2 - 2 z R cos Θ ) ,
F = z 1 z 4 d F ( z ) .
F = β av E exp ( - 2 c R ) V Ω ,
V Ω = A 0 z 1 z 4 w m w M d Ω ( w , z ) d z .
β av = z 1 z 4 w m w M [ β ( Θ ) d Ω ( w , z ) ] exp [ - c ( L + z - R ) ] d z z 1 z 4 w m w M d Ω ( w , z ) d z .
= ( β av - β true ) / β true ,

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