FIGURE 8. Definition of User Angle
When in position angle mode, the rotator remains at a fixed orientation on the sky. This orientation is indicated to the DCS by the "user angle" (ROTDEST), which is the angle, measured North through East, between North and the pointing origin Y (YIM) axis. See See Definition of User Angle .
FIGURE 8. Definition of User Angle
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An astronomer will think of the "position angle" (PA) as the angle, measured North through East, between North and some vector of interest to him or her. This vector of interest may be a column or slit on a science detector, or it may be the line joining a science star to a guide star. In the example above, we see that if the vector of interest is the YIM axis, then the DCS' user angle (UA) is the same as the astronomer's position angle.
Consider the case where the vector of interest is at a fixed direction on the science detector (e.g. a column or a slit). Usually the instrument coordinate system will be defined so that its Y (INSTY) axis is parallel with this vector of interest (both NIRC and LRIS define INSTANGL so that the INSTY axis is parallel with their columns).
See Definition of Position Angle (instrument column mode) , which is modified from See Telescope coordinate systems looking towards sky (excludes Nasmyth foci) (which applies to both NIRC and LRIS), shows that the user angle (ROTDEST) to achieve the desired orientation is "PA + INSTANGL".
FIGURE 9. Definition of Position Angle (instrument column mode)
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The sky and facsum programs collaborate to operate in this mode for LRIS and HIRES. sky subtracts (LRIS) or adds (HIRES) 90 deg from the astronomer's PA when calculating ROTDEST and facsum restores what the user input. By the above, this is consistent with the (Keck II) LRIS INSTANGL of -90 deg (the HIRES INSTANGL hasn't been set).
Consider the case where the position angle of a guide star relative to a science star has been specified (this is a common mode with the f/25 offset guider where guide stars are likely to be scarce and where the rotational degree of freedom will often have to be sacrificed in the interests of guiding).
FIGURE 10. Definition of Position Angle (guide star mode)
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See Definition of Position Angle (guide star mode) illustrates the relationship between the position angle (PA), the orientation of the science star to guide star vector (in the pointing origin coordinate system) j and the resultant user angle (UA).
j is simply calculated from a knowledge of the pointing origins. Taking NIRC as an example ( See f/25 IR Frame (KI) (looking toward the sky) ), the NIRC pointing origin is (-2.4, 58.8) and the REF (guider) pointing origin is (-366.4,-10.2). Therefore, j is atan2(-10.2-58.8,-366.4+2.4) = atan2(-69.0,-364.0) = 190.73 deg. Thus, for NIRC, UA = 90 + PA - 190.73, or UA = PA - 100.73. U = PA - 100 is fine for practical purposes. If the resulting UA will cause the rotator to drive into a limit, 360 deg must be added to it or subtracted from it as appropriate.