Mapmake

Mapmaking is available for computing hitmap and crosslink maps.

ScanningStrategy2map(ss::ScanningStrategy, division::Int)

This function splits the observation time specified by ScanningStrategy by the number specified by division, calculates the pointing TOD, and then creates a map using it. The reason for the split calculation is to avoid overloading the memory by calculating a huge amount of pointing TOD data at once. Inside this function, get_pointing_pixels() is being executed.

For example,

outmap = ScanningStrategy2map(ss::ScanningStrategy, 12)

Now, the pointing TOD is calculated every month and stored in the map each time.

The outmap is a matrix, the contents of which are as follows.

outmap[1]: Hitmap
outmap[2]: Crosslink map (n=1)
outmap[3]: Crosslink map (n=2)
outmap[4]: Crosslink map (n=3)
outmap[5]: Crosslink map (n=4)

The crosslink $X_n$ is represented by the following equation

Xn = \left[ \left(\frac{\sum^{N{hits}}i{\sin{(n\psii)}}}{N{hits}} \right)^2 + \left( \frac{\sum^{N{hits}}i{\cos{(n\psii)}}}{N{hits}}\right)^2 \right] = \langle \sin(n\psii) \rangle^2 + \langle \cos(n\psi_i) \rangle^2 $

The subscript $i$ indicates that this is the $i$-th time series data within a certain pixel, and $< >$ indicates that the average should be taken.

The $n$ is the spin, a measure to define the scan-derived systematic effect. It is described in detail in this paper.

Crosslink with half-wave plate

The next generation of CMB polarimetry satellites, such as LiteBIRD, will be equipped with a half-wave plate(HWP). Falcons is also possible to create a crosslink map that takes into account the optical axis of the HWP. The crosslink with HWP is calculated by the following equation $ X_n^{w/ HWP}=<\sin(4\rho-n\psi)>^2+<\cos(4\rho-n\psi)>^2 . $