## 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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### Equations (20)

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(1)
$$dF={\beta}_{\text{eff}}\mathrm{\Omega}{EA}_{o}\hspace{0.17em}\text{exp}[-c(L+z+R)]dz,$$
(2)
$${\beta}_{\text{eff}}=\frac{{\int}_{{w}_{m}}^{{w}_{M}}\beta ({\mathrm{\Theta}}^{\prime})d{\mathrm{\Omega}}^{\prime}(w)}{{\int}_{{w}_{m}}^{{w}_{M}}d{\mathrm{\Omega}}^{\prime}(w)},$$
(3)
$${\mathrm{\Theta}}^{\prime}=\mathrm{\Theta}+\frac{z\hspace{0.17em}\text{sin}\mathrm{\Theta}-w}{R-z\hspace{0.17em}\text{cos}\mathrm{\Theta}+nD}.$$
(4)
$$d{\mathrm{\Omega}}^{\prime}=\frac{dwh}{{(L+nD)}^{2}},$$
(5)
$$h=2\sqrt{[{r}_{c}^{2}-{(w-{x}_{c})}^{2}]},$$
(6)
$${r}_{c}={r}_{d}\left(1+\frac{nD}{R-z\hspace{0.17em}\text{cos}\mathrm{\Theta}}\right),$$
(7)
$${x}_{c}=-nD\frac{\text{sin}\mathrm{\Theta}}{R-z\hspace{0.17em}\text{cos}\mathrm{\Theta}},$$
(8)
$${x}_{s}=\frac{{x}_{c}^{2}-{r}_{c}^{2}+{r}_{d}^{2}}{2{x}_{c}}.$$
(9)
$$h=2\sqrt{({r}_{d}^{2}-{w}^{2})}.$$
(10)
$${z}_{1}=-\frac{{r}_{d}(2R+nD)}{nD\hspace{0.17em}\text{sin}\mathrm{\Theta}-2{r}_{d}\hspace{0.17em}\text{cos}\mathrm{\Theta}},$$
(11)
$${z}_{2}=-\frac{{r}_{d}}{\text{sin}\mathrm{\Theta}},$$
(12)
$${z}_{3}=-{z}_{2},$$
(13)
$${z}_{4}=\frac{{r}_{d}(2R+nD)}{nD\hspace{0.17em}\text{sin}\mathrm{\Theta}+2{r}_{d}\hspace{0.17em}\text{cos}\mathrm{\Theta}},$$
(14)
$$dF={EA}_{0}{\int}_{{w}_{m}}^{{w}_{M}}[\beta ({\mathrm{\Theta}}^{\prime})d{\mathrm{\Omega}}^{\prime}]\hspace{0.17em}\text{exp}[-c(L+z+R)]dz.$$
(15)
$$L\cong \sqrt{({z}^{2}+{R}^{2}-2zR\hspace{0.17em}\text{cos}\mathrm{\Theta})},$$
(16)
$$F={\int}_{{z}_{1}}^{{z}_{4}}dF(z).$$
(17)
$$F={\beta}_{\text{av}}E\hspace{0.17em}\text{exp}(-2cR)V\mathrm{\Omega},$$
(18)
$$V\mathrm{\Omega}={A}_{0}{\int}_{{z}_{1}}^{{z}_{4}}{\int}_{{w}_{m}}^{{w}_{M}}d{\mathrm{\Omega}}^{\prime}(w,z)dz.$$
(19)
$${\beta}_{\text{av}}=\frac{{\int}_{{z}_{1}}^{{z}_{4}}{\int}_{{w}_{m}}^{{w}_{M}}[\beta ({\mathrm{\Theta}}^{\prime})d{\mathrm{\Omega}}^{\prime}(w,z)]\hspace{0.17em}\text{exp}[-c(L+z-R)]dz}{{\int}_{{z}_{1}}^{{z}_{4}}{\int}_{{w}_{m}}^{{w}_{M}}d{\mathrm{\Omega}}^{\prime}(w,z)dz}.$$
(20)
$$\u220a=({\beta}_{\text{av}}-{\beta}_{\text{true}})/{\beta}_{\text{true}},$$