The principal advantage of the DDA is that it is completely flexible
regarding the geometry of the target, being limited only by the need to
use an interdipole separation d small compared to
(1) any structural lengths in the target, and
(2) the wavelength 
.
Numerical studies (Draine & Goodman 1993; Draine & Flatau 1994; Draine 1999)
indicate that the
second criterion is adequately satisfied for calculations of
total cross sections if
where m is the complex refractive index of the target
material, and 
, where is the wavelength
in vacuo.
However, if accurate calculations of the scattering phase function
(e.g., radar or lidar cross sections)
are desired,
a more conservative criterion
will ensure that differential scattering cross sections
are accurate to within a few percent of the
average differential scattering cross section 
(see Draine 1999).
Let V be the target volume.
If the target is represented by an array of N dipoles, located on
a cubic lattice with lattice spacing d,
then
We characterize the size of the target by the ``effective radius''
the radius of an equal volume sphere.
A given scattering problem is then characterized by the
dimensionless ``size parameter''
The size parameter can be related to N and |m|kd:
Equivalently, the target size can be written
Practical considerations of CPU speed and computer memory currently
available on scientific workstations typically
limit the number
of dipoles employed to 
(see §15
for limitations on N due to available RAM);
for a given N, the limitations on |m|kd
translate into limitations on the ratio of target size to wavelength.
For calculations of total cross sections 
and 
,
we require |m|kd < 1:
For scattering phase function calculations, we require |m|kd < 0.5:
It is therefore clear that the DDA is not suitable for very large values of
the size parameter
x, or very large values of the refractive index m.
The primary utility of the DDA is for scattering by dielectric
targets with sizes comparable to the wavelength.
As discussed by Draine & Goodman (1993), Draine & Flatau (1994), and
Draine (1999),
total cross sections calculated with the DDA are
accurate to a few percent provided
dipoles are used, criterion (1) is satisfied,
and |m-1|< 2.
Examples illustrating the accuracy of the DDA are shown in Figs. 1-2 which show overall scattering and absorption efficiencies as a function of wavelength for different discrete dipole approximations to a sphere, with N ranging from 304 to 59728. The DDA calculations assumed radiation incident along the (1,1,1) direction in the ``target frame''. Figs. {3-4 show the scattering properties calculated with the DDA for x=ka=7. Additional examples can be found in Draine & Flatau (1994) and Draine (1999).
Figure 1: Scattering and absorption for a sphere with
m=1.33+0.01i. The upper panel shows the exact values of 
and 
, obtained with Mie theory, as functions of x=ka.
The middle and lower panels show fractional errors in and
, obtained using DDSCAT with polarizabilities
obtained
from the Lattice Dispersion Relation, and labelled by the number N
of dipoles in each pseudosphere.
After Fig. 1 of Draine & Flatau (1994).
Figure: Same as Fig. 1,
but for m=2+i. After Fig. 2 of Draine & Flatau (1994).
Figure 3: Differential scattering cross section for
m=1.33+0.01i pseudosphere and ka=7.
Lower panel shows fractional error compared to exact Mie theory
result.
The N=17904 pseudosphere has |m|kd=0.57, and an rms fractional
error in 
of 2.4%.
After Fig. 5 of Draine & Flatau (1994).
Figure: Same as Fig. 3
but for m=2+i.
The N=59728 pseudosphere has |m|kd=0.65, and an rms fractional
error in of 6.7%.
After Fig. 8 of Draine & Flatau (1994).