(1) The expression (See Hurford et al 2002) 

c = F0 G (1 + A1 M1 cos(Phi) +...)   (1)

is a convolution in Fourier space of the collimator transmission function
T(phi) with the source profile (point source) delta(phi).

(2) The form of (1) for a source with coefficients a0,a1,a2,... may be written

c(phi) = F0 (g0 a0 + (1/2)a1 m1 cos(phi) + (1/2)a2 m2 cos(2 Phi) +... (2)

where g0 is the gridtran value at the given roll angle, a0 is the source's
DC value, m1 is proportional to the modamp term, and a1 is the
fundamental amplitude.

The reader may ask, "Why are there no (1/2) terms in equation (1)?"

(3)  For a point source of flux F0, the Fourier coefficients are:

a = F0 * {1,2,2,2,2,...}   (3)

Thus the (1/2) terms are cancelled out in (2):

c(phi) = F0 (g0 + m1 cos(Phi) + m2 cos(2 Phi) + ...  (4)


(4) The relative amplitude of a point source is 2.  For any other kind
of source, |a1/a0| < 2.

a_n = 2 a_0 {\intgrl F(x) cos(x) dx / \intgrl F(x) dx}  (5)

The magnitude of the fraction in curly brackets is always <= 2

(5) For a triangle of base 2*a and height 1/a the DC value is 1:

T(x) = (1/a)*|1-x/a|, |x| < a and 0 o.w.

a0 = intgrl{T(x) dx} = 1

a1 = (2/a) intgrl T(x) cos x dx = (2/a) \ingrl_0^a (1-x/a) cos x dx 
   = (4/a) {4 sin(a) -4/a \intgrl_0^a [d/dx(x sin x) - sin x] dx
   = (4/a^2) (1 - cos(a))

a1(0) = 2, a1 decreases monotonically to 8/!pi^2 at x=!pi
a1(!pi) = 8/!pi^2
a1(2.784) = 1.0