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Advanced Camera for Surveys Instrument Handbook for Cycle 22 > Chapter 7: Observing Techniques > 7.8 Specifying Orientation on the Sky

7.8
Determining the orientation of an image requires knowledge of the telescope roll and the angle of the aperture relative to the HST coordinate frame. A target may need to be oriented in a preferred direction on a detector, particularly when spectroscopy is to be performed.
To specify an ORIENT in Phase II, note that this parameter is just the usual Position Angle (PA) of the HST U3 axis (= V3, see below); see Figure 3.1 and Figure 7.9 in this Handbook, as well as the Phase II Proposal Instructions. APT provides a convenient interactive display of the aperture and orientations in your field. The ORIENT parameter is related to the following discussion of ACS geometry.
All HST aperture positions and orientations are defined within an orthogonal coordinate system labeled V1,V2,V3, in which V1 is nominally along the telescope roll axis. Apertures are therefore in the V2,V3 plane. For more information about HST instrument aperture locations and axes in the HST FOV, please visit the Observatory Support webpage section on apertures at:
http://www.stsci.edu/hst/observatory/apertures.
The V3 position angle p is defined as the angle of the projection of the V3 axis on the sky, measured from North towards East with the aperture denoting the origin. This is almost identical to the telescope roll angle. (There is a small difference between roll angles measured at the V1 axis and those measured at the aperture. This can amount to several tenths of a degree depending on the target declination.) When the position angle is zero, V3 points North and V2 points East. In the V2V3 coordinate system, as shown in Figure 7.8, aperture orientations are defined by βx and βy, the angles their x and y axes make with the V3 axis, measured in an anti-clockwise direction. (The value of βx as illustrated in Figure 7.8, would be considered negative.) Hence, the angles these axes make with North are found by adding the axis angles to the position angle.
Figure 7.8: Aperture and image feature orientation.
The science image header supplies the value of ORIENTAT, the angle the detector y axis makes with North, which is equal to p + βy. Another angle keyword supplied is PA_APER which is the angle the aperture y axis makes with North. Both angles are defined at the aperture so using them does not involve the displacement difference. Normally the aperture and detector y axes are parallel, and so PA_APER = ORIENTAT. Several STIS slit apertures were not aligned parallel to the detector axes, so this distinction was meaningful, but ACS has no slit apertures so this difference will probably not arise. In any case, we recommend using PA_APER.
Beyond establishing the direction of the aperture axes, it will often be necessary to know the orientation of a feature, such as the plane of a galaxy, within an image. Conversely, we need to know what direction within an image corresponds to North. To this end we define a feature angle α within the aperture as measured on the science image, anti-clockwise from the y-axis so that it is in the same sense as the previously defined angles. For an orthogonal set of aperture axes the direction of this feature would be PA_APER + α and the image direction of North would be the value of α which makes this angle zero, namely PA_APER, still measured in an anti-clockwise direction from the y axis.
Figure 7.9: ACS apertures in the V2/V3 reference frame.
The readout amplifiers (A,B,C,D) are indicated on the figure. The WFC data products from the calibration pipeline will be oriented so that WFC1 (chip 1, which uses amplifiers A and B) is on top. The HRC data products will also be oriented such that amps A and B are on top, but they will be inverted from WFC images with respect to the sky
The x and y axes projected on the sky are not necessarily orthogonal. For all instruments prior to the ACS the departure from orthogonality has been negligible, but for the ACS the angle between the axes is about 85. Figure 7.9 realistically represents the alignment of the ACS apertures and shows that the apertures are not square. The x and y axes indicated are those that will be used for the science images. The V2,V3 coordinates can be calculated from the x, y coordinates according to
where sx and sy are scales in arcseconds per pixel along the image x and y axes. V20 and V30 are the coordinates of the aperture origin, but they do not enter into the angle calculations. Figure 7.9 shows that a rotation from x to y is in the opposite sense to a rotation from V2 to V3. This will be the arrangement for ACS apertures. This is significant in defining the sense of the rotation angles. For a direction specified by displacements Δx and Δy in the image, the angle α is arctan(−Δx/Δy).
Because of the oblique coordinates, the angle αs on the sky will not be equal to α. To calculate the sky angle, it is convenient to define another set of orthogonal axes xs, ys, similar to the V2V3 but rotated so that ys lies along y, and xs is approximately in the x direction. Let ω = βy  βx be the angle between the projected detector axes and for simplicity let their origins be coincident.Then the transformation is
By comparing differentials and defining αs as arctan(−Δxs/Δys) we find
The equation as written will place the angle in the proper quadrant if the ATAN2 Fortran function or the IDL ATAN function is used. To get the true angle East of North, for a feature seen at angle α in the image, calculate αs  and add to PA_APER.
The inverse relation is
To find the value of α corresponding to North we need the value of αs such that PA_APER αs = 0. So substitute PA_APER for αs in the equation to get the angle α in the image which corresponds to North. The values of the scales and axis angles for all instruments are maintained on an Observatory Science Group webpage.
For the ACS apertures, the values in Table 7.10 have been derived from results of operating the ACS in the Refractive Aberrated Simulator. These should not be considered as true calibrations but they indicate some aperture features, such as the non-orthogonality of the aperture axes, and the x and y scale differences for HRC and SBC.
Table 7.10: Plate scales and axis angles for the 3 ACS channels.
sx
sy
βy−βx
7.8.1 Determining Orientation for Phase II
A particular orientation is specified in an HST Phase II proposal using yet another coordinate system: U2,U3. These axes are opposite to V2 and V3, so, for example, U3 = V3. The angle ORIENT, used in a Phase II proposal to specify a particular spacecraft orientation, is the position angle of U3 measured from North towards East. The direction of the V3 axis with respect to North is PA_APER  βy and so
ORIENT = PA_APER  βy  180.
The IRAF task rotate in the package images.geom takes a drizzled image and rotates it counter-clockwise by a specified angle. To orient the image so that its y axis becomes North, the angle to specify is PA_APER. The x axis of the coordinate system will then point East. Orientations can be checked by using APT.

Advanced Camera for Surveys Instrument Handbook for Cycle 22 > Chapter 7: Observing Techniques > 7.8 Specifying Orientation on the Sky

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