,
etc.
DDSCAT automatically carries out numerical integration of various
scattering properties. In particular, it calculates the mean value
for the scattered intensity for each
incident polarization state.
This is accomplished by evaluating the scattered intensity for
ICTHM different values of 
(including 
and 
), and taking a weighted sum.
For each value of except 0 and 
, the scattering
intensity is evaluated for IPHM different values of the scattering
angle 
.
The angular integration over is accomplished using Simpson's
rule (with uniform intervals in 
),
so ICTHM should be an odd number.
The angular integration over is accomplished by sampling
uniformly in with uniform weighting; IPHM can be either
even or odd.
The following quantities are evaluated by this angular integration:
It is important that the user recognize that accurate evaluation of these angular averages requires adequate sampling over scattering angles. For small values of the size parameter
,
the angular distribution of scattered radiation has a dipolar character
and the sampling in and does not need to be very fine,
so ICTHM and IPHM need not be large.
For larger values of the size parameter x, however, higher multipoles
in the scattered radiation field become important, and finer sampling
in and is required.
We do not have any foolproof prescription to offer, since the scattering
pattern will depend upon the target geometry and dielectric constant
in addition to overall size parameter.
However, as a very rough guide, we suggest that the user specify
values of ICTHM and IPHM satisfying
and
; the above criteria would suggest that this would
be suitable for x<5.
The cpu time required for evaluation of these angular averages
is proportional to 
.
Since the computational time spent in evaluating these angular
integrals can be a significant part of the total, it is important
to choose values of ICTHM and IPHM which will provide
a suitable balance between accuracy (in this part of the overall calculation)
and cpu time.
Within one scattering plane, the scattered intensity tends to
have approximately (1+x) peaks for 
, so that
the above prescription for ICTHM would have at least 5 sampling
points per maximum.
The angular distribution over is usually not as
structured as that over so we suggest that IPHM need not
be as large as ICTHM.
We have refrained from ``hard-wiring'' the values of ICTHM
and IPHM because we are not confident of the reliability of the
recommended criteria (23,24) - it is up to
the user to specify appropriate values of ICTHM and IPHM
according to the requirements of the problem being addressed.
(see §
(see §