Does it matter how accurately 2 radio dishes are pointed at a sky object when used for interferometry, as long as time signal is perfect for both?

Yes. Pointing accuracy still matters in interferometry, even if the timing between the two receivers is perfect.

The important distinction is:

TIMING

Determines whether the signals from the two dishes can be combined coherently.

POINTING

Determines how strongly each dish receives the astronomical source.

Ideally:

                     SKY SOURCE
                         *
                        / \
                       /   \
                      /     \
                     /       \
                    /         \
               DISH A         DISH B
                  \             /
                   \           /
                    \         /
                     RECEIVERS
                         |
                     CORRELATOR
                         SKY SOURCE
                             *
                            / \
                           /   \
                          /     \
                         /       \
                        /         \
                   DISH A         DISH B
                      \             /
                       \           /
                        \         /
                         RECEIVERS
                             |
                         CORRELATOR

Both dishes should have the source reasonably close to the centre of their beams:

       DISH A                         DISH B

          *                              *
        / | \                          / | \
      /   |   \                      /   |   \
    /     |     \                  /     |     \
          |                              |
          V                              V
        DISH A                         DISH B

If one dish is mispointed:

       DISH A                         DISH B

          *                       *
        / | \                       \
      /   |   \                      \
    /     |     \                     \
          |                             \ beam
          V                              V
        DISH A                         DISH B

Dish B still receives the source, but at lower gain.

The correlated interferometer signal is approximately:

Signal proportional to:

          __________________
         /
        / G1 x G2
       V

where G1 and G2 are the gains of the two dishes in the direction of the source.

Therefore:

Perfect timing
     |
     +---- does NOT compensate for poor pointing.

However, there is an important bit of good news.

The dishes do NOT have to be pointed as accurately as the angular resolution or fringe spacing of the interferometer.

There are two different angular scales:

INDIVIDUAL DISH

        <------ broad beam ------>

               \       /
                \     /
                 \   /
                  \ /
                   *
                   |
                 DISH


INTERFEROMETER

        /\/\/\/\/\/\/\/\/\/\/\/\
          narrow fringe pattern

The individual dish diameter determines the broad primary beam.

The separation between the dishes determines the much narrower interferometer fringe pattern.

For example, at the hydrogen line:

Frequency = 1420 MHz
Wavelength = approximately 0.211 m

For a 1.5 m dish:

Beamwidth approximately:

        1.2 x wavelength
        ----------------
          dish diameter


        1.2 x 0.211
      = -----------
             1.5

      = 0.169 radians

      = approximately 9.7 degrees

So a 1.5 m dish at 1420 MHz has a surprisingly broad beam of roughly:

             about 10 degrees

          <---------------->
                 \      /
                  \    /
                   \  /
                    \/
                    *
                    |
                   DISH

Consequently, if your two dishes differ in pointing by only:

0.1 degree    Excellent
0.5 degree    Very good
1 degree      Probably little problem
2 degrees     Still likely quite usable
several deg   Increasing loss of correlated signal

Now compare this with the interferometer baseline.

Suppose:

Dish separation = 10 metres
Wavelength       = 0.211 metres

Then the approximate interferometric angular scale is:

wavelength
----------
 baseline

  0.211
= -----
   10

= 0.0211 radians

= approximately 1.2 degrees

So you could have:

Individual dish beam:

|<----------- about 10 degrees ----------->|


Interferometer fringes:

| /\  /\  /\  /\  /\  /\  /\  /\ |
|/  \/  \/  \/  \/  \/  \/  \/  \|

       about 1.2 degrees/fringe

This is the crucial point:

        DISH POINTING ACCURACY

                  is NOT

     INTERFEROMETER ANGULAR RESOLUTION

The dishes simply need sufficient overlap of their primary beams:

Dish A beam
        \             /
         \           /
          \         /
           \       /
            \     /
             \   /
              \ /
               X   <-- useful common sky area
              / \
             /   \
            /     \
           /       \
          /         \
         /           \
        /             \
Dish B beam

For your 1420 MHz interferometer, I would therefore aim to get the dishes pointing in the same direction to within roughly 1 degree or better. There is no need to achieve arcminute pointing accuracy with dishes of this size.

And perfect clocks solve a different problem:

GOOD POINTING + BAD TIMING
          |
          V
Strong signals but poor correlation


BAD POINTING + PERFECT TIMING
          |
          V
Perfectly synchronised weak signals


GOOD POINTING + GOOD TIMING
          |
          V
       BEST RESULT

So for your ezCon interferometer, getting both dishes reasonably well aligned is important, but you don’t need extraordinarily precise mechanical pointing.

By Admin

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