In the point-source photometry mode the properly imaged field (i.e. with chopping and nodding) is rectangular : about 52 arcsec x 2.5 arcmin (see Figure 4.2). The user might therefore want to exclude some position angles of the chopping direction to avoid chopping into a bright close-by infrared source.

For this purpose an interval of chopper avoidance angles can be entered in HSpot. The chopper avoidance angle is counted positive east of north, i.e. counterclockwise in the sky, from the north to the direction of the object to avoid, i.e. the +Y spacecraft axis. As the chopper cannot rotate, this effectively defines an avoidance angle for the satellite orientation. Hence it is a scheduling constraint.

The range of position angles that will be available for a given target can be visualized with the AOR footprint overlay functionality for different observing dates in the visibility windows. The exact angle values can be determined with the 'Herschel Focal Plane' overlay functionality.

	Note
	The position angle returned by HSpot in the AOR overlays is the angle from the north to the spacecraft +Z axis counterclockwise, perpendicular to the chopping direction. Therefore the chopper avoidance angle can be derived from the position angle by adding 90 degrees (modulo 180 degrees).

Warning

For pointings close to the ecliptic plane, the position angle is constrained to a very narrow range of values : the inclination of the ecliptic plane, and the chopping direction is perpendicular to the ecliptic plane. For such targets, the chopping avoidance angle is at best unnecessary, and at worse renders the observation impossible. For observations at higher ecliptic latitudes, the user shall check that the range of chopping avoidance angles is compatible with the position angles in the visibility windows.

	Warning
	When a chopping avoidance angle is set, the constraint is not yet fed back in HSpot to the visibility calculation, so that the Herschel visibility windows are not affected by that constraint. The user is thus invited to assess himself the impact on the visibility of that constraint.

As the the area covered in the small-source photometry mode is rectangular : 3.2'x1.5', (see Figure 4.4), the user might want to exclude some position angles of the chopping direction to avoid chopping into a bright close-by infrared source.

For this purpose an interval of chopper avoidance angles can be entered in HSpot. The chopper avoidance angle is counted positive east of north, i.e. counterclockwise in the sky, from the north to the direction of the object to avoid, i.e. the +Y spacecraft axis. As the chopper cannot rotate, this effectively defines an avoidance angle for the satellite orientation. Hence it is a scheduling constraint.

The range of position angles that will be available for a given target can be visualized with the AOR footprint overlay functionality for different observing dates in the visibility windows. The exact angle values can be determined with the 'Herschel Focal Plane' overlay functionality.

	Note
	The position angle returned by HSpot in the AOR overlays is the angle from the north to the spacecraft +Z axis counterclockwise, perpendicular to the chopping direction. Therefore the chopper avoidance angle can be derived from the position angle by adding 90 degrees (modulo 180 degrees).

Warning

For pointings close to the ecliptic plane, the position angle is constrained to a very narrow range of values : the inclination of the ecliptic plane, and the chopping direction is perpendicular to the ecliptic plane. For such targets, the chopping avoidance angle is at best unnecessary, and at worse renders the observation impossible. For observations at higher ecliptic latitudes, the user shall check that the range of chopping avoidance angles is compatible with the position angles in the visibility windows.

	Warning
	When a chopping avoidance angle is set, the constraint is not yet fed back in HSpot to the visibility calculation, so that the Herschel visibility windows are not affected by that constraint. The user is thus invited to assess himself the impact on the visibility of that constraint.

If a bright source is to be avoided on the chopped position or on the nodded position a range of chopper avoidance angles - and only one - can be introduced as illustrated in Figure 4.4. The functionality 'overlays' --> 'Herschel Focal Plane' can be used for this purpose in HSpot, (selecting the right aperture in 'configure focal plane')

Figure 4.4.  Chopper avoidance angle in small-source photometry. Illustration of the chopper avoidance angle. In this particular case in order to avoid the bright source shown to enter the field-of-view of the Nod 1 / Chop B position, observations at position angle around 90 degrees shall be avoided, for instance with a chopper angle avoidance interval of [70-110] degrees.

Rastering is intended to cover larger area than the PACS FOV, yet not too large either. A reasonable maximum size is probably of the order of 15'x15', as above a certain size the raster becomes difficult to handle and moreover it becomes very inefficient due to the large slewing overheads (about 30 seconds between raster positions, depending on the raster step size) with respect to line scan mapping mode.

Rasters are only allowed in the instrument reference frame, with the raster X-axis along the spacecraft Y-axis (long edge of the detectors) and the raster Y-axis along the spacecraft Z-axis (small edge of the detector). Chopping by one full FOV is performed on each raster position (3.5 arcmin along the raster X-axis). Therefore for large rasters chopping is done inside the raster map, which might complicate the data processing.

The target position entered in HSpot is the centre of the rectangular rastered area. The dwell time per raster position is fixed to 64 seconds, chopping every 4 seconds hence 8 chopper cycles on each raster position. Then the spacecraft moves to the next raster position on the line (raster X-axis) and so on for the number of steps (m = number of raster points) entered in HSpot. It turns then left to continue with the next raster line in the reverse direction and so on for number of raster lines entered in HSpot ('n').

An example of a PACS photometer raster map is shown in Figure 4.5.

Figure 4.5.  Example of a photometer raster map with m=4 and n=6 and raster step sizes of 100 arcsec in both directions, giving a redundancy factor of 2 in the raster X axis direction. The area covered by the raster chop-on positions is shown with the blue rectangle (about 8x10 arcmin). But for symmetrical reasons the nod-off position is imaged in the fashion as the chop-on position so the actual raster map area covered is the dashed blue rectangle about 11.5x10 arcmin.

The number of steps on the X and Y raster axis, as well as the raster step sizes are left open to the user. The observer can therefore choose the redundancy factor, i.e. the number of raster positions that observe a given sky position, a key factor for the detection of faint sources with previous IR missions. It is advised to visualize the raster footprint on the sky with the 'Overlays' menu in HSpot.

Small areas of the order of 3x3 arcmin can be covered with raster maps with very small step sizes (a few arcseconds), allowing to chop mostly out of the map.

Sparse sample maps are not allowed, therefore the maximum step size in the raster X direction is 210 arcsec and in the raster Y direction 105 seconds to allow contiguous area mapping in all cases.

Nodding is currently not implemented in this mode, the observer can build a nodding-like raster by choosing a raster step size along the raster X-axis which is an integer divider of the chopper throw (3.5 arcmin).

The achieved sensitivity of the map depends on the number of times a sky pixel is seen by different raster positions. Depending on the raster step sizes the sensitivity may not be homogeneous and will vary across the rastered area, the sensitivity usually getting higher towards the centre of the map.

	Note
	HSpot returns the mean sensitivity in the mapped area including the edge effects. The sensitivity will be higher in the central area with higher spatial redundancy. For rasters with very small step sizes this effect might be significant, as the exposure map will have a small flat part in the centre.

4.1.3.1.1. Raster map orientation constraint

In order to be immune against field rotation due the changes of position angle with time, the user should cover square areas as far as possible. For this purpose the number of steps and step size on both axis shall be computed, depending on the step sizes on both axis. The result can be visualized with the "Overlay AOR" functionality. However if rectangular area in the sky is to be covered and/or a bright object is to be avoided, a constraint on the orientation of the raster in the sky can be imposed. This is achieved by selecting a range of map orientation angle in HSpot. But this means a constraint in the scheduling, as this limits the time window to carry out the observation.

Warning

Depending on the target coordinates, some ranges in position angles are not possible, this should be checked with the 'Overlay AOR' functionality in HSpot. For instance for targets close to the ecliptic plane, the raster Y axis ( = Z spacecraft axis) will be closely aligned with the ecliptic plane. Hence a very narrow range of map orientation angle is physically possible. For targets at higher ecliptic latitudes, if the map orientation angle constraint is not compatible with possible ranges of position angles, the observation cannot be scheduled.

	Warning
	When a map orientation angle is set, the constraint is not yet fed back in HSpot to the visibility calculation, so that the Herschel visibility windows are not affected by that constraint. The user is thus invited to assess himself the impact on the visibility of the constraint.

Table 4.3 lists the user inputs required in HSpot.

Scan maps will be the default to map large areas of the sky, for galactic as well as extragalactic surveys. Scan maps are performed by slewing the spacecraft at a constant speed along parallel lines to cover a large area, as illustrated in Figure 4.6. The lines are actually great circles which approximates parallel lines over short distances. Scans mapping does not make use of chopping, the signal modulation being provided by the spacecraft motion.

Figure 4.6. Example of PACS photometer scan map. Schematic of a scan map with 6 scan line legs. After the first line, the satellite turns left and continue with the next scan line in the opposite direction, just like in the raster map case. The reference scan direction is the direction of the first leg. Note that the turn around between line does take place as simplistically drawn in the figure.

Three scan speeds are offered: a low speed: 10 arcsec per second, a medium speed: 20 arcsec/s, and a high speed: 60 arcsec/s.

The highest speed (default value) is envisaged for galactic surveys, with a serious degradation of the PSF due to the on-board averaging of 4 frames (final 10 Hz sampling).

The slow scan speed shall be used for extragalactic surveys, it allows to cover 1 square degree area in about three hours. The PSF degradation and smearing due to the scanning should be almost negligible with the two lowest scan speeds, according to simulations.

As the duration time for turnover manoeuvre between scan legs is constant (for a given slew speed), the mapping efficiency increases for longer slew legs and for a given scan leg length decreases for higher slew speeds. This effect can be appreciated in Figure 4.7. As a consequence the slewing shall be adapted to the size of the area covered, with slow slew speed areas less than 30 arcmin in size and high slew speed only for scan legs longer than about 2 degrees.

Note

Small area scan maps carry an intrinsic high overhead fraction (up to 50%), due to the relatively high turnover time between legs. (for instance on Figure 4.11) But this time might not be completely lost for science, as the continuous 40Hz detector readout is not stopped during these intervals. But it is not clear at this stage what will be the attitude reconstruction accuracy for these data acquired at a non constant speed (acceleration and deceleration).

Figure 4.7. PACS photometer scan mapping efficiency

It is suggested to perform two scan maps of the same area with orthogonal coverage in order to remove more efficiently the stripping effects of the 1/f noise. For this purpose two AORs shall be concatenated in HSpot. In the second AOR the map orientation angle is then increased by 90 degrees to get an orthogonal coverage.

PACS scan maps can be performed either in the instrument reference frame or in sky coordinates.

4.1.3.2.1. Scan maps in instrument reference frame

When scan maps are performed in instrument reference frame, an 'array-to-map angle' is chosen observer, The array-to-map angle is the angle from the spacecraft +Z axis to the line scan direction in the first leg, counted positive counterclockwise in the sky. This configuration corresponds to 'reference frame' = 'array' in HSpot and is illustrated in Figure 4.8.

PACS does not have a fixed 'magic angle' like SPIRE, it it left as a free parameter to the user. It is however advised not to use 0 or 90 degrees as gaps between matrices would then stay in the final map, if a sky position is visited only by one scan line leg. An array-to-map angle of 45 degrees allows to get the same depth in two scan maps with orthogonal mapping directions.

Figure 4.8.  Scan maps in instrument reference frame. The array-to-map angle (α), is defined by the user. This effectively defines the map orientation angle in the sky (β), as the array position angle is not a free parameter, it is function of target coordinates and observation time. However a constraint on the map orientation angle can be put in HSpot.

In this configuration if the 'homogeneous coverage' parameter is selected, HSpot computes the appropriate distance between scan legs ('cross-scan step') to achieve an homogeneous coverage, which is a function of the array-to-map angle selected above.

	Note
	In the case of a square scan map in instrument reference frame, the orthogonal coverage to cover the same area is achieved by simply adding 90 degrees to the array-to-map angle and recomputing the cross-scan distance. If the array-to-map angle is 45 degrees, the cross-scan distance if even the same.

	Note
	A small array-to-map angle, for instance 10 degrees (modulo 90 degrees), allows to get rid of the effect of gaps between matrices, but also to get a homogeneous exposure map toward the edges for small scan maps, hence minimizing the the science time.

Scan map orientation

Scan maps defined in instrument reference frame should in principle be used to cover square areas, as the orientation of the scan map on the sky can not be known in advance, it depends on the array position angle, which itself depends on the exact observation day.

However in order to cover specific rectangular areas in the sky, a constraint on the orientation of the scan map in the sky can be introduced by selecting a range for the 'map position angle', i.e. the angle from the celestial equatorial north to the scan line direction, counted positively east of north. This corresponds to the option 'array with sky constraint' in HSpot, shown in Figure 4.8.

Warning

Introducing a sky constraint puts a constraint on the scheduling, and therefore shall be used only if necessary. Moreover certain combinations of array-to-map angle and ranges of map position angle might not be feasible. For instance for pointing close to the ecliptic plane, the array position angle gets constrained to a very narrow range of values (modulo 180 degrees), as the +Z axis is always pointing towards the sun (+/- 1 degree) in the ecliptic plane. Therefore the map orientation angle cannot be too different from the array-to-map angle + 90 degrees (modulo 180). This shall be checked with the overlay AOR facility in HSpot.

	Warning
	When a map orientation angle is set, the constraint is not yet fed back in HSpot to the visibility calculation, so that the Herschel visibility windows are not affected by that constraint. The user is thus invited to assess himself the impact on the visibility of the constraint.

4.1.3.2.2. Scan maps in sky coordinates

Figure 4.9.  Scan maps in sky coordinates. The map orientation angle in the sky β), is fixed by the observer, therefore there is no control on the array-to-map angle (α), which depends on the target coordinates and exact observation time. However a constraint on the array-to-map angle can be put in HSpot.

Another way to define rectangular areas in the sky with scan mapping is to select mapping in sky coordinates, with the option 'sky' in HSpot. In this configuration the map orientation angle is defined by the observer, i.e. the angle from the equatorial celestial north to the line scan direction in the first leg.

However, in this case, there is no direct control of the homogeneity of the map coverage, as the cross-scan distance to achieve this purpose depends on the array position angle, which itself depends on the exact observation day. The user shall be very careful in selecting a cross-scan distance when in sky coordinates. Values above 105 arcsec may lead to non overlapping legs depending on the array-to-map angle. In order to allow a minimum overlap between consecutive legs, the user is advised not to select a cross-scan distance above 105 arcsec, to be immune against all possible values of the array-to-map angle.

	Note
	A cross-scan distance of 51 arcsec (i.e the size of single blue array matrix) gives relatively flat exposure maps for scan map in sky coordinates, whatever the array-to-map orientation angle. In analogy to SPIRE terminology we call it the 'magic distance'.

Conversely the array-to-map angle of scan maps in sky coordinates can be constrained with the option 'sky with array constraint' in HSpot, as shown in Figure 4.9.

Again certain combinations of map orientation angle and constraints on array-to-map angle might be impossible, this shall be checked by the user with the overlay AOR functionality of HSpot.

Table 4.4 lists the user input parameters required in HSpot in scan map mode.

A decision tree to choose the most appropriate orientation reference frame a scan map is given in Figure 4.10.

Figure 4.10. Decision tree for scan maps orientation reference frame.

As for raster maps, the sensitivity returned by HSpot is the mean sensitivity across the scan map. Due to edge effects the sensitivity in the central part of the scan map where the exposure map is flat will be slightly higher. For scan maps with small cross-scan distances, the lower the number of scan legs the higher this effect as the exposure map becomes less homogeneous.

The homogeneity of the map can be assessed with the exposure map tool in HSpot v3.0 onwards (Overlays --> Show Depth of Coverage Maps on current image). The sky integration time in seconds can be deduced from DoC values, by dividing by 6,12 and 36 respectively for the 3 scan speeds 10, 20 and 60"/sec respectively. And then the sensitivity at any point can be derived by scaling the sensitivity numbers in Table 3.2 with the inverse of the square root of the integration time.

	Note
	The sensitivity computed by HSpot for scan maps simply scales with the square root of integration time on the sky. In high scan speed (60"/s) the sensitivity is probably overestimated, because of the PSF distorsion (elongation along the scan direction) and the bolometer cut-off frequency.

Figure 4.11.  Example of a depth of coverage map for a small scan map as given by HSpot together with AOR display overlaid.