This is because the beampattern synthesis is performed in radian ([theta])-space but the method based on P([phi],[theta]) cannot reflect the power distribution in radian-space because P([phi],[theta]) indeed characterizes the beampattern in steradian
Irradiance is directional; it includes UV radiation received over 2[pi] steradians
; that is, half of the possible directions from which UV rays might originate is included.
The number of the photons recorded by the detector and leaving the thin layer into the solid angle of 1 steradian
and relating to 1 electron is:
where A[OMEGA] is the throughput in square millimeter steradian
, G is the amplifier gain in volts per ampere, [tau] ([lambda]) is the spectral transmittance, [R.sub.f] ([lambda]) is the spectral flux responsivity of the detector in ampere per watt, and [L.sub.[lambda]]([lambda]) is the spectral radiance in watt per nanometer per square millimeter per steradian
For example, if the initial divergence is 30 degrees (plausible for an x-ray beam), then a beam collimated to 10 cm in diameter at 200 m (5 x 10[conjunction]-4 radian, or 2.5 x 10[conjunction]-7 steradian
) will contain about 2.5 x 10[conjunction]-7 of the source's energy and power.
Legacy Focus ($5,400) Reviewed in issue #54 by KWN, follow-up review with Steradian
processor ($888 if purchased with the Focus, $1,295 as a stand-alone unit) in Issue 79.
Say it is a tactical fighter, and we want to cover an engine signature that is 1,500 watts per steradian
in the 3- to 5-[Mu] region.
That answer, as more precisely determined by the DIRBE team, is a feeble 140-micron sky brightness of 25[+ or -]7x[10.sup.-9] watt per square meter per steradian
for each factor of 10 in wavelength.
The quantity of interest to us is the emissivity [j.sub.v] (with units of power per frequency interval per unit volume per steradian
), which we obtain from integrating the power over grain size and shape distribution [dn.sub.gr]/da (where a is meant to formally represent the characteristic size and three-dimensional shape of a grain), as well as the electric dipole distribution, f([mu]|a) convolved with the probability distribution for the angular momentum and rotational configuration f(L, [omega]|a;[mu]) (We use repeatedly the letter f to denote probability distribution functions.
Therefore the distribution of the first surface reflectance is determined by the distribution of the micro-facet normals which in turn is driven by the density function [equivalent to] ([THETA]), the relative density of micro-facet normals (per steradian
) in vector direction [THETA].
As I mentioned in that article, I did most of my listening at that time with a prototype version of what was to evolve into the Steradian
Environmental Processor in my system.