Recipe for a Polar Map

1. Obtain the amplitudes and phases from the count rates for half a rotation, creating 9 vectors of phasors $f_j(\phi)$. These vectors will range in length from 25 up to 4000 elements.

2. Compute the Inverse FFT in $\phi$ space for each complex vector $f_j(\phi)$,and get the complex coefficients f_jk (See eq. 5).

3. Using downward recurrence relations, compute the 9 matrices $J_k(2 \pi r\ q_j)$. For the coarsest collimator, this is a $25 \times 360$array, and for the finest, it is $2000 \times 360$.

4. For each radius (r) in the map and each collimator (j), compute the vector $f_{jk} J_k(2\pi r\ q_j) \ e^{ik \pi/2},\ \ k=-N_j,...,N_j$.

5. Obtain the one-dimensional FFT, giving the $\theta$ dependence at that radius (one column of a one-collimator map).

6. Add the one-collimator maps together, weighting by the UV radius q_j. This is the natural weighting, but alternatives are possible.