1. Image Error Analysis Fourier-domain analysis of errors.
2-D Fourier transform concepts
Examples of errors in UV-plane and image plane.
Some common ATCA image errors.
Practical talk: How to identify errors in images, and common types of errors.
Talk is aimed at basic imaging, not polarimetry or spectroscopy.
Should use both visibilities and images to identify errors.
What sort of errors you typically get in ATCA observations: some things I found out without being told.

2. Fourier–domain Analysis
Errors occur in the visibility (uv) domain.
These errors are Fourier transformed into the image.
Circular
Broad
Narrow
Crap
Crap
Errors occur in visibility domain – what you measure is in error.
Errors are Fourier transformed, so you need to put your 2-D Fourier hat on.
Features broad in one dimension trasnform to features which are narrow in that dimension
Delta function FTs to a what??
Circular features transform to circular features
Gaussian FTs to a ??
Linear features transform to rectangular features
Random noise will not FT to look like source structure.

3. Bad Scan - Visibilities:
Unflagged:
Flagged:
Only two scans on 1/15 baselines affected.

4. Bad Scan - Images: Unflagged: Flagged: What is going on?
The bad visibility is a sharp feature ~delta function in UV
So it transfoms to a broad feature in the image – the effect is spread out over many pixels,
And you cant notice it.

5. Bad Gain - Visibilities:
2.5% Gain error:
Properly Calibrated:
Certainly wouldn’t notice the offset if you were flagging.
Gain error affects all visibilities on 5/15 baselines

6. Bad Gain - Visibilities:
2.5% Gain error:
Properly Calibrated:
Many small visibility errors contain much more flux than a few bad scans.

7. Does this make sense!? Broad component,
High spatial frequency structure,
Circular form.
Does this make sense?
- Errors have both a broad component.
- Has some very high spatial frequency strucure – the negative rings.
- Also, note that errors have circular form.
WHY??

8. UV Distribution of Errors
Baselines to antenna 5
in red.
Baselines to antenn 5 in red.
Baseline 45 is very short, causing the broad error feature.
Other baselines intermediate, causing sharper error features.
Reason for circular error form is that errors only occur at points on uv-plane where visibilities are measured.
For ATCA, visibilities trace elliptical paths in uv-plane (see next overhead),
So any long-duration error will tend to have a circular form in the image domain.

9. Effect of missing short baselines
No short baselines
“Classic” effect is that structures are surrounded by negative emission.
(and, of course, the extended structure is missing)

10. Inadequate UV Coverage:
ATCA:
No gain/phase errors.
8 hours
Declination –15°
Often make images from a single observation:
Spacing between baselines
Observations shorter than 12 hours
No zero (or short) spacings

11. Inadequate UV coverage:
CLEAN
3 clean boxes
1000 iterations
MAXEN
3 boxes
30 iterations
Because ATCA uvcoverage is often missing “wedges” of baselines, the negative artifacts are more complex.
- crap on large angular scales.
- negative regions on opposite sides of stucture
(note that this is simulation data – there are no gain errors! All the noise in the image is due to missing short spacings!)

12. Recognizing Poor UV Coverage:
Fourier Transform the Source Model and Beam!
Use different array configuration.
Different frequency, if possible.
North-spur, when available.

13. CLEAN Errors in the Image:

14. CLEAN errors in UV-plane:

15. Non-closing Errors in UV:
Peak variations about 2%

16. Non-closing Errors in the Image:
Peak variations about 0.1%

17. Other things to consider:
Check your calibrators!!
Resolved
Intra-day variability!
Elevation dependent gains
Esp. atmospheric opacity at high frequencies.
Primary beam
Images attenuated away from image centre.
Antenna gain very sensitive near half-power.

18. Example of a Resolved Calibrator

19. Gain errors at beam half-power:

20. Summary Errors occur in the UV-domain. Be awake, be skeptical.
An error which looks bad in the visibilities might not give a bad image error.
An error which is invisible in the visibilities might have a dramatic effect on the image.
Be awake, be skeptical.
Have fun!