Benchmark results for spheroids
[This page will contain a number of tables like given ones.]
In the following tables we present
the normalized cross-sections tabulated for
prolate and oblate spheroids having
the refractive index m = 1.3, 2.5, 1.7 +0.7i, 2.5 +1.5i, 3.0 +4.0i;
the semiaxis ratio a/b = 1.1, 2, 4, 10;
the incidence angle alpha = 0 and 90 (TE and TM modes), and
different diffraction parameter
xV=2 pi rV/lambda, where
rV is the radius of an equal volume sphere and
lambda the wavelength of incident radiation.
The results were obtained by at least two different methods,
and all given digits were the same.
Some more benchmarks can be found in papers ...
Extinction and scattering cross-sections
Table 1. Normalized extinction (scattering) cross-sections
Cext/pi rV2
for spheroids with m = 1.3
| | | | | prolate |
| | | oblate | |
|---|
| a/b | xV | | alpha = 0 |
alpha = 90 (TM) | alpha = 90 (TE) | |
alpha = 0 | alpha = 90 (TM) | alpha = 90 (TE) |
|---|
| 1.1 | 0.1 | | 9.182080E-06 | 9.584544E-06 |
9.185689E-06 | | 9.453529E-06 | 9.049059E-06 |
9.450043E-06 |
| | 0.3 | | 7.353049E-04 | 7.711279E-04 |
7.378481E-04 | | 7.608544E-04 | 7.250718E-04 |
7.583891E-04 |
| | 1.0 | | 7.447337E-02 | 8.134987E-02 |
7.649733E-02 | | 8.037420E-02 | 7.362975E-02 |
7.832033E-02 |
| | 3.0 | | 1.540311E-00 | 1.437064E-00 |
1.395298E-00 | | 1.380468E-00 | 1.472662E-00 |
1.519971E-00 |
| | 10.0 | | 2.230447E-00 | 2.822134E-00 |
2.867127E-00 | | 3.034794E-00 | 2.416342E-00 |
2.441388E-00 |
| | 30.0 | | 2.006623E+00 | 2.572447E+00 |
| | | |
|
|
| 2.0 | 0.1 | | 8.497336E-06 | 1.125232E-05 |
8.529378E-06 | | 1.042893E-05 | 7.558188E-06 |
1.040419E-05 |
| | 0.3 | | 6.605367E-04 | 9.119126E-04 |
6.825033E-04 | | 8.450193E-04 | 5.950242E-04 |
8.275387E-04 |
| | 1.0 | | 5.447619E-02 | 1.025111E-01 |
6.691507E-02 | | 9.418041E-02 | 5.141485E-02 |
7.960716E-02 |
| | 3.0 | | 1.968352E-00 | 1.333052E-00 |
1.083852E-00 | | 1.024408E-00 | 1.427102E-00 |
1.865927E-00 |
| | 10.0 | | 1.538734E-00 | 4.353976E-00 |
4.273941E-00 | | 5.229347E-00 | 1.270176E-00 |
1.336617E-00 |
|
| 4.0 | 0.1 | | 7.979755E-06 | 1.273937E-05 |
8.074529E-06 | | 1.160638E-05 | 6.345801E-06 |
1.155186E-05 |
| | 0.3 | | 5.722482E-04 | 1.026860E-03 |
6.318278E-04 | | 9.361833E-04 | 4.847639E-04 |
8.983728E-04 |
| | 1.0 | | 3.647086E-02 | 1.085455E-01 |
4.947725E-02 | | 9.776480E-02 | 3.277807E-02 |
7.254568E-02 |
| | 3.0 | | 2.208284E-00 | 1.168012E-00 |
7.362909E-01 | | 7.018565E-01 | 1.055080E-00 |
1.967821E-00 |
| | 10.0 | | 1.812869E+00 | 5.680530E+00 |
5.416727E+00 | | 5.183390E-00 | 1.225550E-00 |
1.425348E-00 |
|
| 10.0 | 0.1 | | 7.436218E-06 | 1.363190E-05 |
7.751983E-06 | | 1.280422E-05 | 5.467201E-06 |
1.268771E-05 |
| | 0.3 | | 4.111163E-04 | 1.049295E-03 |
5.521820E-04 | | 1.010622E-03 | 3.922034E-04 |
9.341944E-04 |
| | 1.0 | | 2.210801E-02 | 8.074041E-02 |
2.516490E-02 | | 8.226629E-02 | 1.862260E-02 |
5.558987E-02 |
| | 3.0 | | 1.704760E-00 | 9.341732E-01 |
4.068989E-01 | | 5.908465E-01 | 5.660661E-01 |
1.610737E-00 |
Note:
The values printed by italics were obtained using only
our Separation of Variables code.
Since in these cases we got the same extinction and scattering
cross-sections with (much) more than seven significant digits,
the numbers were believed to be correct.
Table 2. Normalized extinction (scattering) cross-sections
Cext/pi rV2
for spheroids with m = 1.3
| | | | | prolate |
| | | oblate | |
|---|
| a/b | xV | | alpha = 0 |
alpha = 90 (TM) | alpha = 90 (TE) | |
alpha = 0 | alpha = 90 (TM) | alpha = 90 (TE) |
|---|
| 1.1 | 0.1 | | 1.035794E-04 | 1.199431E-04 | 1.036199E-04 |
| 1.142661E-04 | 9.863955E-05 | 1.142242E-04 |
| | 0.3 | | 8.770520E-03 | 1.027102E-02 | 8.799159E-03 |
| 9.764975E-03 | 8.338921E-03 | 9.735097E-03 |
| | 1.0 | | 1.803740E-00 | 2.086949E-00 | 1.688006E-00 |
| 1.905530E-00 | 1.634429E-00 | 2.042280E-00 |
| | 3.0 | | 3.619850E-00 | 2.702825E-00 | 1.617508E-00 |
| 1.483010E-00 | 2.695134E-00 | 4.391523E-00 |
| | 10.0 | | 2.069972E-00 | 2.534723E-00 | 2.552629E-00 |
| 2.244362E-00 | 2.500382E-00 | 2.485442E-00 |
|
| 2.0 | 0.1 | | 8.132300E-05 | 2.262901E-04 | 8.162806E-05 |
| 1.641502E-04 | 5.756336E-05 | 1.637629E-04 |
| | 0.3 | | 6.610480E-03 | 2.018734E-02 | 6.819180E-03 |
| 1.433111E-02 | 4.685330E-03 | 1.404947E-02 |
| | 1.0 | | 1.299951E-00 | 3.736834E-00 | 9.854978E-01 |
| 2.464760E-00 | 6.647633E-01 | 3.680223E-00 |
| | 3.0 | | 2.756951E-00 | 2.423317E-00 | 1.456577E-00 |
| 4.484763E-00 | 1.777398E-00 | 3.846601E-00 |
|
| 4.0 | 0.1 | | 6.871662E-05 | 4.258699E-04 | 6.952952E-05 |
| 2.612223E-04 | 3.688507E-05 | 2.600006E-04 |
| | 0.3 | | 5.105309E-03 | 3.919277E-02 | 5.615168E-03 |
| 2.307084E-02 | 2.874841E-03 | 2.217663E-02 |
| | 1.0 | | 7.055768E-01 | 5.493155E-00 | 5.426740E-01 |
| 3.362340E-00 | 2.595873E-01 | 5.360019E-00 |
| | 3.0 | | 1.673046E-00 | 5.755844E-00 | 4.730299E-00 |
| 7.392485E-00 | 2.580128E-00 | 3.791884E-00 |
| | 10.0 | | | | |
| 6.174717E-00 | | |
|
| 10.0 | 0.1 | | 6.058991E-05 | 6.745045E-04 | 6.315583E-05 |
| 4.423506E-04 | 2.643817E-05 | 4.383382E-04 |
| | 0.3 | | 3.446015E-03 | 5.950350E-02 | 4.588377E-03 |
| 3.852378E-02 | 1.918230E-03 | 3.569470E-02 |
| | 1.0 | | 3.088317E-01 | 6.153316E-00 | 2.283901E-01 |
| 3.605985E-00 | 1.053865E-01 | 5.126838E-00 |
| | 3.0 | | 4.612520E-01 | 9.781859E-00 | 7.081355E-00 |
| 7.766600E-00 | 7.497780E-00 | 4.701476E-00 |
| | 10.0 | | | | |
| 8.892024E-00 | | |
Note:
The values printed by italics were obtained using only
our Separation of Variables code.
Since in these cases we got the same extinction and scattering
cross-sections with (much) more than seven significant digits,
the numbers were believed to be correct.
Table 3a. Normalized extinction and scattering cross-sections
for prolate spheroids with m = 1.7 + 0.7i.
| a/b |
xV |
|
Cext/pi rV (alpha=0) |
Csca/pi rV (alpha=0) |
|
Cext/pi rV (alpha=90; TM) |
Csca/pi rV (alpha=90; TM) |
Cext/pi rV (alpha=90; TE) |
Csca/pi rV (alpha=90; TE) |
| 1.1 | 0.1 | | 1.112202E-01 | 7.864300E-05 | | 1.237998E-01 | 8.760800E-05 | 1.112025E-01 | 7.867500E-05 |
| | 0.3 | | 3.606976E-01 | 6.456163E-03 | | 4.013411E-01 | 7.232842E-03 | 3.602422E-01 | 6.478287E-03 |
| | 1.0 | | 1.905984E-00 | 5.355063E-01 | | 2.032662E-00 | 5.973659E-01 | 1.887403E-00 | 5.471636E-01 |
| | 3.0 | | 2.701331E-00 | 1.231402E-00 | | 2.806987E-00 | 1.315163E-00 | 2.786968E-00 | 1.278780E-00 |
| | 10.0 | | 2.291426E-00 | 1.219106E-00 | | 2.446885E-00 | 1.312233E-00 | 2.452426E-00 | 1.289792E-00 |
|
| 2.0 | 0.1 | | 9.260996E-02 | 6.520100E-05 | | 1.867292E-01 | 1.323250E-04 | 9.250492E-02 | 6.544660E-05 |
| | 0.3 | | 3.001614E-01 | 5.177635E-03 | | 6.027228E-01 | 1.099226E-02 | 2.974687E-01 | 5.348186E-03 |
| | 1.0 | | 1.697352E-00 | 3.846683E-01 | | 2.477888E-00 | 7.841288E-01 | 1.556310E-00 | 4.492447E-01 |
| | 3.0 | | 2.481402E-00 | 1.039641E-00 | | 3.195685E-00 | 1.600695E-00 | 3.021085E-00 | 1.360101E-00 |
| | 10.0 | | 1.804330E-00 | 9.737252E-01 | | 2.874307E-00 | 1.607439E-00 | 2.908106E-00 | 1.453882E-00 |
|
| 4.0 | 0.1 | | 8.155853E-02 | 5.681280E-05 | | 2.550670E-01 | 1.807060E-04 | 8.141510E-02 | 5.748690E-05 |
| | 0.3 | | 2.621134E-01 | 4.141768E-03 | | 8.113704E-01 | 1.476105E-02 | 2.585912E-01 | 4.568657E-03 |
| | 1.0 | | 1.501459E-00 | 2.669788E-01 | | 2.713089E-00 | 8.506337E-01 | 1.243460E-00 | 3.192207E-01 |
| | 3.0 | | 2.580295E-00 | 9.865859E-01 | | 3.848184E-00 | 1.966160E-00 | 3.409582E-00 | 1.515164E-00 |
| | 10.0 | | 1.506484E-00 | 8.354435E-01 | | 3.584853E-00 | 2.355147E-00 | 3.677056E-00 | 1.920250E-00 |
|
| 10.0 | 0.1 | | 7.602801E-02 | 5.084200E-05 | | 3.011971E-01 | 2.122690E-04 | 7.589427E-02 | 5.299880E-05 |
| | 0.3 | | 2.398816E-01 | 2.843924E-03 | | 9.378379E-01 | 1.631801E-02 | 2.368506E-01 | 3.807946E-03 |
| | 1.0 | | 1.262913E-00 | 1.653620E-01 | | 2.963340E-00 | 7.538500E-01 | 9.994957E-01 | 1.659754E-01 |
| | 3.0 | | 3.124793E-00 | 1.400933E-00 | | 4.859030E-00 | 2.372744E-00 | 3.342797E-00 | 1.749225E-00 |
Table 3b. Normalized extinction and scattering cross-sections
for prolate spheroids with m = 1.7 + 0.7i.
| a/b |
xV |
|
Cext/pi rV (alpha=0) |
Csca/pi rV (alpha=0) |
|
Cext/pi rV (alpha=90; TM) |
Csca/pi rV (alpha=90; TM) |
Cext/pi rV (alpha=90; TE) |
Csca/pi rV (alpha=90; TE) |
| 1.1 | 0.1 | | 1.195146E-01 | 8.458200E-05 | | 1.071869E-01 | 7.580000E-05 | 1.195327E-01 | 8.455100E-05 |
| | 0.3 | | 3.872282E-01 | 6.983265E-03 | | 3.473992E-01 | 6.223923E-03 | 3.876931E-01 | 6.960843E-03 |
| | 1.0 | | 1.979097E-00 | 5.846022E-01 | | 1.849906E-00 | 5.229885E-01 | 1.997317E-00 | 5.725476E-01 |
| | 3.0 | | 2.830111E-00 | 1.319935E-00 | | 2.722550E-00 | 1.234025E-00 | 2.742786E-00 | 1.271537E-00 |
| | 10.0 | | 2.505115E-00 | 1.330005E-00 | | 2.345806E-00 | 1.234293E-00 | 2.340025E-00 | 1.256973E-00 |
|
| 2.0 | 0.1 | | 1.533476E-01 | 1.086960E-04 | | 6.964599E-02 | 4.913110E-05 | 1.534705E-01 | 1.084390E-04 |
| | 0.3 | | 4.941085E-01 | 9.029149E-03 | | 2.246184E-01 | 3.938983E-03 | 4.971749E-01 | 8.843852E-03 |
| | 1.0 | | 2.198062E-00 | 7.105949E-01 | | 1.291186E-00 | 3.151001E-01 | 2.326983E-00 | 6.221156E-01 |
| | 3.0 | | 3.378955E-00 | 1.672422E-00 | | 2.603296E-00 | 1.040019E-00 | 2.768031E-00 | 1.330862E-00 |
| | 10.0 | | 3.424418E-00 | 1.823962E-00 | | 2.102060E-00 | 1.075898E-00 | 2.078338E-00 | 1.254424E-00 |
|
| 4.0 | 0.1 | | 2.021662E-01 | 1.432990E-04 | | 4.737106E-02 | 3.331120E-05 | 2.023435E-01 | 1.426270E-04 |
| | 0.3 | | 6.442415E-01 | 1.176912E-02 | | 1.509486E-01 | 2.574738E-03 | 6.483922E-01 | 1.129677E-02 |
| | 1.0 | | 2.394211E-00 | 7.756880E-01 | | 8.254487E-01 | 1.707659E-01 | 2.658211E-00 | 6.204606E-01 |
| | 3.0 | | 4.160786E-00 | 2.063017E-00 | | 2.908122E-00 | 1.093205E-00 | 3.118426E-00 | 1.527032E-00 |
|
| 10.0 | 0.1 | | 2.592012E-01 | 1.833420E-04 | | 3.519341E-02 | 2.458170E-05 | 2.593550E-01 | 1.816740E-04 |
| | 0.3 | | 8.101747E-01 | 1.452893E-02 | | 1.102168E-01 | 1.774836E-03 | 8.134503E-01 | 1.343542E-02 |
| | 1.0 | | 2.582792E-00 | 7.310081E-01 | | 5.183328E-01 | 8.548927E-02 | 2.994641E-00 | 5.616921E-01 |
| | 3.0 | | 5.071606E-00 | 2.388579E-00 | | 3.466482E-00 | 1.457912E-00 | 4.053009E-00 | 1.871199E-00 |
Table 4a. Normalized extinction and scattering cross-sections
for prolate spheroids with m = 2.5 + 1.5i.
| a/b |
xV |
|
Cext/pi rV (alpha=0) |
Csca/pi rV (alpha=0) |
|
Cext/pi rV (alpha=90; TM) |
Csca/pi rV (alpha=90; TM) |
Cext/pi rV (alpha=90; TE) |
Csca/pi rV (alpha=90; TE) |
| 1.1 | 0.1 | | 4.857457E-02 | 2.662824E-04 | | 6.075554E-02 | 3.380031E-04 | 4.829951E-02 | 2.663845E-04 |
| | 0.3 | | 2.500260E-01 | 2.355979E-02 | | 3.008235E-01 | 3.052714E-02 | 2.440823E-01 | 2.363001E-02 |
| | 1.0 | | 3.010733E-00 | 1.943640E-00 | | 3.660982E-00 | 2.472199E-00 | 3.107353E-00 | 2.043307E-00 |
| | 3.0 | | 2.712810E-00 | 1.952128E-00 | | 2.884653E-00 | 2.137721E-00 | 2.780978E-00 | 2.018383E-00 |
| | 10.0 | | 2.353277E-00 | 1.773023E-00 | | 2.497087E-00 | 1.920239E-00 | | |
|
| 2.0 | 0.1 | | 3.459049E-02 | 1.836889E-04 | | 1.929191E-01 | 1.115412E-03 | 3.339258E-02 | 1.843746E-04 |
| | 0.3 | | 1.944302E-01 | 1.537309E-02 | | 9.098178E-01 | 1.129382E-01 | 1.661101E-01 | 1.585916E-02 |
| | 1.0 | | 1.894857E-00 | 9.206887E-01 | | 5.495079E-00 | 3.970900E-00 | 2.283547E-00 | 1.438695E-00 |
| | 3.0 | | 2.388466E-00 | 1.478325E-00 | | 3.453263E-00 | 2.702600E-00 | 2.762240E-00 | 1.941164E-00 |
|
| 4.0 | 0.1 | | 2.730303E-02 | 1.441102E-04 | | 9.964447E-01 | 5.837496E-03 | 2.615886E-02 | 1.458221E-04 |
| | 0.3 | | 1.519406E-01 | 1.085174E-02 | | 4.991269E-00 | 6.624600E-01 | 1.226751E-01 | 1.200416E-02 |
| | 1.0 | | 1.463283E-00 | 3.937427E-01 | | 5.398163E-00 | 3.832019E-00 | 1.604720E-00 | 9.183725E-01 |
| | 3.0 | | 2.300718E-00 | 1.086833E-00 | | 4.265932E-00 | 3.396000E-00 | 3.006776E-00 | 2.056315E-00 |
|
| 10.0 | 0.1 | | 2.346226E-02 | 1.225093E-04 | | 3.457393E-00 | 2.017965E-02 | 2.275013E-02 | 1.277193E-04 |
| | 0.3 | | 1.133338E-01 | 6.935209E-03 | | 8.769814E-00 | 1.125691E-00 | 9.556359E-02 | 9.380992E-03 |
| | 1.0 | | 1.386188E-00 | 2.456454E-01 | | 7.150973E-00 | 4.383860E-00 | 1.036091E-00 | 4.588306E-01 |
Table 4b. Normalized extinction and scattering cross-sections
for oblate spheroids with m = 2.5 + 1.5i.
| a/b |
xV |
|
Cext/pi rV (alpha=0) |
Csca/pi rV (alpha=0) |
|
Cext/pi rV (alpha=90; TM) |
Csca/pi rV (alpha=90; TM) |
Cext/pi rV (alpha=90; TE) |
Csca/pi rV (alpha=90; TE) |
| 1.1 | 0.1 | | 1.063091E-01 | 2.027530E-04 | | 8.850409E-02 | 1.684017E-04 | 1.063972E-01 | 2.026790E-04 |
| | 0.3 | | 3.884586E-01 | 1.754138E-02 | | 3.248624E-01 | 1.439400E-02 | 3.909319E-01 | 1.748734E-02 |
| | 1.0 | | 3.299242E-00 | 1.519356E-00 | | 2.960052E-00 | 1.285217E-00 | 3.294445E-00 | 1.481333E-00 |
| | 3.0 | | 2.915360E-00 | 1.616238E-00 | | 2.779851E-00 | 1.487376E-00 | 2.832633E-00 | 1.561297E-00 |
|
| 2.0 | 0.1 | | 1.683208E-01 | 3.228280E-04 | | 4.590543E-02 | 8.685830E-05 | 1.690525E-01 | 3.220660E-04 |
| | 0.3 | | 6.046926E-01 | 2.854920E-02 | | 1.682741E-01 | 7.112129E-03 | 6.246817E-01 | 2.798368E-02 |
| | 1.0 | | 4.007697E-00 | 2.005398E-00 | | 1.852325E-00 | 6.182319E-01 | 3.928646E-00 | 1.726163E-00 |
| | 3.0 | | 3.644115E-00 | 2.139153E-00 | | 2.436512E-00 | 1.057701E-00 | 2.916411E-00 | 1.654727E-00 |
|
| 4.0 | 0.1 | | 3.072162E-01 | 5.903690E-04 | | 2.714797E-02 | 5.130230E-05 | 3.085216E-01 | 5.876060E-04 |
| | 0.3 | | 1.089947E-00 | 5.221910E-02 | | 9.612426E-02 | 4.009507E-03 | 1.123093E-00 | 5.017062E-02 |
| | 1.0 | | 4.550598E-00 | 2.313767E-00 | | 1.043029E-00 | 2.876447E-01 | 4.684036E-00 | 1.847488E-00 |
| | 3.0 | | 5.233787E-00 | 3.234486E-00 | | 2.370631E-00 | 7.777997E-01 | 3.251025E-00 | 1.885156E-00 |
|
| 10.0 | 0.1 | | 5.869667E-01 | 1.126115E-03 | | 1.854663E-02 | 3.498488E-05 | 5.756589E-01 | 1.114894E-03 |
| | 0.3 | | 1.984941E-00 | 9.372724E-02 | | 6.193207E-02 | 2.540922E-03 | 2.042807E-00 | 8.672525E-02 |
| | 1.0 | | 5.252690E-00 | 2.480982E-00 | | 4.762698E-01 | 1.301479E-01 | 6.089094E-00 | 2.016472E-00 |
| | 3.0 | | 7.991256E-00 | 4.978289E-00 | | 3.318379E-00 | 1.142783E-00 | 4.196434E-00 | 2.432267E-00 |
Table 5a. Normalized extinction and scattering cross-sections
for prolate spheroids with m = 3 + 4i.
| a/b |
xV |
|
Cext/pi rV (alpha=0) |
Csca/pi rV (alpha=0) |
|
Cext/pi rV (alpha=90; TM) |
Csca/pi rV (alpha=90; TM) |
Cext/pi rV (alpha=90; TE) |
Csca/pi rV (alpha=90; TE) |
| 1.1 | 0.1 | | 4.857457E-02 | 2.662824E-04 | | 6.075554E-02 | 3.380031E-04 | 4.829951E-02 | 2.663845E-04 |
| | 0.3 | | 2.500260E-01 | 2.355979E-02 | | 3.008235E-01 | 3.052714E-02 | 2.440823E-01 | 2.363001E-02 |
| | 1.0 | | 3.010733E-00 | 1.943640E-00 | | 3.660982E-00 | 2.472199E-00 | 3.107353E-00 | 2.043307E-00 |
| | 3.0 | | 2.712810E-00 | 1.952128E-00 | | 2.884653E-00 | 2.137721E-00 | 2.780978E-00 | 2.018383E-00 |
| | 10.0 | | 2.353277E-00 | 1.773023E-00 | | 2.497087E-00 | 1.920239E-00 | | |
|
| 2.0 | 0.1 | | 3.459049E-02 | 1.836889E-04 | | 1.929191E-01 | 1.115412E-03 | 3.339258E-02 | 1.843746E-04 |
| | 0.3 | | 1.944302E-01 | 1.537309E-02 | | 9.098178E-01 | 1.129382E-01 | 1.661101E-01 | 1.585916E-02 |
| | 1.0 | | 1.894857E-00 | 9.206887E-01 | | 5.495079E-00 | 3.970900E-00 | 2.283547E-00 | 1.438695E-00 |
| | 3.0 | | 2.388466E-00 | 1.478325E-00 | | 3.453263E-00 | 2.702600E-00 | 2.762240E-00 | 1.941164E-00 |
|
| 4.0 | 0.1 | | 2.730303E-02 | 1.441102E-04 | | 9.964447E-01 | 5.837496E-03 | 2.615886E-02 | 1.458221E-04 |
| | 0.3 | | 1.519406E-01 | 1.085174E-02 | | 4.991269E-00 | 6.624600E-01 | 1.226751E-01 | 1.200416E-02 |
| | 1.0 | | 1.463283E-00 | 3.937427E-01 | | 5.398163E-00 | 3.832019E-00 | 1.604720E-00 | 9.183725E-01 |
| | 3.0 | | 2.300718E-00 | 1.086833E-00 | | 4.265932E-00 | 3.396000E-00 | 3.006776E-00 | 2.056315E-00 |
|
| 10.0 | 0.1 | | 2.346226E-02 | 1.225093E-04 | | 3.457393E-00 | 2.017965E-02 | 2.275013E-02 | 1.277193E-04 |
| | 0.3 | | 1.133338E-01 | 6.935209E-03 | | 8.769814E-00 | 1.125691E-00 | 9.556359E-02 | 9.380992E-03 |
| | 1.0 | | 1.386188E-00 | 2.456454E-01 | | 7.150973E-00 | 4.383860E-00 | 1.036091E-00 | 4.588306E-01 |
Table 5b. Normalized extinction and scattering cross-sections
for oblate spheroids with m = 3 + 4i.
| a/b |
xV |
|
Cext/pi rV (alpha=0) |
Csca/pi rV (alpha=0) |
|
Cext/pi rV (alpha=90; TM) |
Csca/pi rV (alpha=90; TM) |
Cext/pi rV (alpha=90; TE) |
Csca/pi rV (alpha=90; TE) |
| 1.1 | 0.1 | | 5.612657E-02 | 3.119622E-04 | | 4.500012E-02 | 2.464553E-04 | 5.643647E-02 | 3.118502E-04 |
| | 0.3 | | 2.780221E-01 | 2.801834E-02 | | 2.319978E-01 | 2.170902E-02 | 2.845873E-01 | 2.794121E-02 |
| | 1.0 | | 3.509895E-00 | 2.361293E-00 | | 2.873149E-00 | 1.847522E-00 | 3.399752E-00 | 2.253059E-00 |
| | 3.0 | | 2.878324E-00 | 2.124266E-00 | | 2.694723E-00 | 1.929101E-00 | 2.805930E-00 | 2.055328E-00 |
| | 10.0 | | 2.541936E-00 | 1.943805E-00 | | | | | |
|
| 2.0 | 0.1 | | 1.017897E-01 | 5.864570E-04 | | 2.106561E-02 | 1.116025E-04 | 1.046258E-01 | 5.850970E-04 |
| | 0.3 | | 4.583023E-01 | 5.527781E-02 | | 1.197910E-01 | 9.258967E-03 | 5.167953E-01 | 5.426552E-02 |
| | 1.0 | | 5.236749E-00 | 3.731015E-00 | | 1.404715E-00 | 6.821323E-01 | 4.215200E-00 | 2.800509E-00 |
| | 3.0 | | 3.647681E-00 | 2.814034E-00 | | 2.014876E-00 | 1.173930E-00 | 3.039072E-00 | 2.239774E-00 |
|
| 4.0 | 0.1 | | 2.631899E-01 | 1.539965E-03 | | 1.151162E-02 | 6.162460E-05 | 2.692782E-01 | 1.532804E-03 |
| | 0.3 | | 1.177409E-00 | 1.544476E-01 | | 6.279030E-02 | 4.840135E-03 | 1.295292E-00 | 1.484126E-01 |
| | 1.0 | | 6.852812E-00 | 4.898007E-00 | | 8.678566E-01 | 2.635941E-01 | 5.134813E-00 | 3.146706E-00 |
| | 3.0 | | 5.352621E-00 | 4.207347E-00 | | 1.567910E-00 | 6.070681E-01 | 3.573088E-00 | 2.544887E-00 |
|
| 10.0 | 0.1 | | 1.128218E-00 | 6.607310E-03 | | 7.300898E-03 | 4.054916E-05 | 1.134808E-00 | 6.547190E-03 |
| | 0.3 | | 4.937262E-00 | 6.479088E-01 | | 3.253295E-02 | 2.950166E-03 | 4.945121E-00 | 5.975757E-01 |
| | 1.0 | | 8.641034E-00 | 5.952626E-00 | | 4.895687E-01 | 1.239376E-01 | 7.872300E-00 | 4.088165E-00 |
| | 3.0 | | 8.980463E-00 | 7.079498E-00 | | 1.952602E-00 | 5.393900E-01 | 4.617530E-00 | 3.219906E-00 |
Backscattering cross-section
Table 6. Normalized backscattering cross-sections
Cbk/pi rV2
for spheroids with m = 1.3
...
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Created by V.I.
Last modified:
04/10/00, V.I.