Are real(4) U,V,W coordinates sufficient?
Keywords: sic-gdfv2

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#### Are `real(4)` U,V,W coordinates sufficient?

A peculiar case could be the U,V,W coordinates. With very long baselines (20km with ALMA) and short wavelengths (0.3mm), one is tempted to say that U,V,W should be `real(8)`, as absolute baseline lengths are measured (and defined by the ultimate antenna stability) to a fraction of wavelength, say 40 m for example. 40m/20km equals which exceeds the precision of `real(4)` numbers by 2 digits. So in principle, `real(4)` are insufficient.

But this is only true if full astrometric calibration is required. GILDAS UV tables are intended for imaging purposes, including self-calibration. `real(4)` precision will only limit the field of view for a given angular resolution. The phase error due to a (relative) numerical precision is given by

| (4)

Hence, we must have

| (5)

to obtain for example a phase error lower than 0.1 radian or 6 degree. Plugging extreme numbers ( , km, mm), we obtain radian, or , which is quite a wide field of view.

In summary, the `real(4)` precision do not allow to perform normal calibration (phase calibrators being in general more than a (few) degree(s) away), but it is quite sufficient for even wide field imaging and self-calibration.

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