Lissajous Scan

For mapping areas of size on order the SHARC-II array field of view (2'x1'), or for observing point sources, we use a lissajous pattern. Starting from the center of the map, the telescope modulates it's X and Y position with a different sine wave for each. X and Y are either azimuthal, equatorial, or galactic coordinates, and the user is also free to choose the amplitudes and periods of the sine waves in each direction. The offsets, dx, and dy are given by: 

dx(t) = AX cos(2*pi*t/TX)
 
dy(t) = AY sin(2*pi*t/TY)

where:
AX,AY = amplitude in arcseconds
TX,TY = period in seconds

As it turns out, if the ratio of the periods can be expressed as a rational number, then the scan will be cyclical and repeatable. Because we would like to prevent any periodic motion (we become unable to separate sky noise at those frequencies with true astronomical signal), we use ratios that are irrational.

scan patterns
Here we show the progress of the scan at 3 different times.  

Sample Lissajous commands

We tend to always use 10 minute integration times for lissajous scans. The UIP command and format is:

SWEEP AX TX /Y AY TY [/alt,/equ]
Size of uniform coverage
(arcseconds)
Size of uniform area in units of # of 9" beams
UIP Command
 Comment
115x38
13x4
 SWEEP 20 20 /Y 10 14.142 Our standard scan
77x29
8x3
 SWEEP 38.8 20 /Y 14.6 14.142 Sweeps over 1/2 of the array
38x14
4x2
 SWEEP 58.2 20 /Y 21.8 14.142 Sweeps over 2/3 of the array
** Sensitivity for the uniform coverage area is around 1Jy/sqrt(s) per beam

The scan can be done in the alt-az or ra-dec coordinate frames (/altaz or /equ in UIP).

Designing your own scan

We strongly recommend that you use one of the above example scans. However, Lissajous scans are much easier to design than box-scans, provided one follows these simple guidelines:
  1. You should use a ratio of periods that is an irrational number. We typically use sqrt(2)=1.414.
  2. The area of uniform coverage decreases as the scan amplitude increases.
    For example, assume you are doing an azimuthal scan. The SHARC-II long axis is 2', and aligned with azimuth. If
    the AX amplitude is 20", then the width of uniform coverage is 2' - 2*20" = 1.3'
  3. When setting the amplitudes, keep in mind that the array is a rectangle, and roughly twice as wide as it is high.
    It is also worth thinking of the amplitude in units of pizel size (4.9").
  4. The amplitude and period for a given direction should be such that you don't scan too fast and smear the beam.
  5. Unless you use VERY long periods, the integration time should be 10 minutes per scan.   Consult us if you want to
    a scan that is much different from any of the example ones listed in the table above.

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