... 27¹

Non-linear Coordinate Systems in AIPS by Eric W. Greisen, May 20th, 1983, revised on January 16th, 1993; link http://www.aips.nrao.edu/aipsmemo.html

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... 46²

Additional Non-linear Coordinates by Eric W. Greisen, May 20, 1986, revised on January 16, 1993

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... paper³

Representations of celestial coordinates in FITS, M. R. Calabretta and E. W. Greisen, A&A 395, 1077-1122 (2002)

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... Equator)⁴

Quoting CG02: A translation into the new formalism exists for non-zero CRVALi but only if CROTAi is zero. It consists of setting CRVALi to zero and adjusting CRPIXj and CDELTi accordingly in the AIPS header whereupon the above situation is obtained. The corrections to CRPIXj are obtained by computing the pixel coordinates of $(\alpha,\delta) = (0,0)$ within the AIPS convention. [...] Of the three projections only GLS is known to have been used with non-zero CRVALi. Consequently we have renamed it as SFL as a warning that translation is required. CG02 chose the name Sanson-Flamsteed (SFL) for the new formalism because GLS has been used with non-zero declination, and these cases have no general equivalent in the new formalism.

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... projection⁵

see CG02 section 6.1.2

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... identities⁶

$\tan x = \frac{\sin x}{\cos x} = \frac{2 \sin x \cos x}{2 \cos^2 x} = \frac{\sin 2x}{1 + \cos 2x}$

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... compatible⁷

The formulae have not been checked, but the maps compatibility with other software is confirmed.

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... one⁸

Since the GILDAS data format used to save any declination value while the projection was defined for $\delta _0 = 0$, we should then introduce a new internal projection code to distinguish with the backward compatible case where the reference declination is ignored.

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