Modulated scan high cadence LAT

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This post refines the work shown in High_cadence_LAT_from_Chile. We show how to modulate the scan rate to achieve maximally uniform integration depth across a maximal sky area.

Geometrical considerations

Let us assume that,

  • is the observatory latitude, measured in radians from the Equator
  • is the observing azimuth, measured in radians from North. East is at
  • is the observing elevation, measured in radians from the horizon.
  • is the declination on the celestial sphere.

Then we can write the declination as a function of the observatory latitude and observing azimuth and elevation.

Moreover, we can write for the rate at which declination changes whilst scanning at constant azimuthal rate

The time, , spent observing at a specific declination is inversely proportional to the rate at which the declination changes

If we consider the fact that the sky area at each latitude is proportional to , the integration time per unit sky area, , is