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| Mie theory: Linear regressions for the lowest dominant frequency in frequency spectra of M11(x) | Click the browser's "Back" button to return to topic Parent topic |
| Table 1. Linear regression coefficients for the central frequency, fx(θ) = af + bf θ, of the lowest dominant component of the frequency spectrum of the element M11(x, θ) of the scattering matrix for a microsphere according to Mie theory at several values of the real refractive index, m, of the microsphere. The spectra have been obtained for the relative particle size, x, in a range of 99 to 201.4. This range is located well beyond the first maximum of M11 as a function of x. Parameter θ is the scattering angle. There is no descending branch for a refractive index of 1.02. See also Fig. 3a and Fig. 3b. The goodness-of-fit parameter r 2 is about 0.999 in all cases. A single SD is given in the parentheses in each second row, following the value of a coefficient. By using the above equation, for example, at m = 1.05 for θ = 90° one obtains fx = ~0.491. Hence, the period (1 / fx ) of the dominant oscillation of M11(x) at that scattering angle is ~2.04. |
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| ascending branch | descending branch | |||||
| m | af | bf | θ range | af | bf | θ range |
| 1.02 | 0.012878 (0.005119) |
0.005079 (0.000091) |
0° to 90° | n/a | n/a | n/a |
| 1.05 | 0.008044 (0.002604) |
0.005369 (0.000046) |
0° to 90° | 1.02965 (0.00489) |
-0.005709 (0.000037) |
80° to 170° |
| 1.19a | 0.038152 (0.012105) |
0.00526 (0.000164) |
0° to 90° | 1.11889 (0.00944) |
-0.006234 (0.00008) |
40° to 170° |
| 1.33b | 0.061117 (0.005883) |
0.005244 (0.000105) |
0° to 90° | 1.179117 (0.017436) |
-0.006521 (0.000154) |
30° to 170° |
a - for example, polystyrene in water b - for example, water in air |
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| CITATION: Jonasz M. 2006. Mie theory: Fourier analysis of particle size-dependent patterns (www.tpdsci.com/Tpc/MiePtnSzFT.php). In: Top. Part. Disp. Sci. (www.tpdsci.com). |
HISTORY: Published: 03-Mar-2006 Modified: 02-May-2007 Peer-reviewed: PENDING |
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