Determining the HESSI Spin Axis for Polar Maps

Before going into polar coordinates for HESSI map making, one should find the spin axis to set the origin of the maps. In principle, there is a certain arbitrainess to the selection of the origin, but a number of useful approximations can be made if the spin axis is used as the center for a polar coordinate system, and if the spin is stable.

• HESSI Point-Spread Function $\approx$ Bessel function of radius
• Map-center phase = radius * cosine(roll_angle)
• Phase factors from the nominal axis are more simply calculable. (http:
  //hesperia.gsfc.nasa.gov/ schmahl/polar_uv/node5.html)

It is noteworthy that Hurford's 7 steps to calibration never use the spin axis, and in fact it is not really needed in his formulation. You will not find it in the variable table (http://hesperia.gsfc.nasa.gov/$\sim$schmahl/hessi_variables
/node1.html), and it is not in my variable diagram (http://hesperia.gsfc.nasa
.gov/ schmahl/symbols_diagram.gif) However, for a variety of reasons it is useful to find the center of spin.

The imager axis is not necessarily the center of spin. In inertial coordinates, the image-axis position is ${\bf R^A}=(-x^A,-y^A)$ -- or in IDL notation, (-x_asp, -y_asp)--relative to sun center. In general, we expect that the track of ${\bf R^A}$ will be approximately a circle over a 4-second time interval, and its mean position during a full rotation will be the effective spin center. Alternatively, one can fit a semicircle to the data for ${\bf R^A}$ to get the spin center for half a rotation.