  This paper, the first of two, introduces an observational study of spiral
structure in galaxies chosen from the SINGS survey. Near infrared (NIR) and
optical data are used to produce mass surface density maps, and from these the
morphology of the disc is examined. The aim of this work is to characterise the
prevalence of spiral structure in this sample and, in the cases where a clear
spiral pattern is found, include the findings in a comparative study (reported
in paper II). A two-armed (`grand design') spiral pattern is found in
approximately half the galaxies studied, including all those that are
designated as grand design in the optical, but also including some, but not
all, optically flocculent galaxies. It is found that the level of
non-axisymmetric structure in the galaxies' mass distributions is only modestly
higher in those galaxies that are classified as `grand design' compared with
those that are not, implying that non-grand design galaxies possess significant
power in higher order modes. There is no evidence that bars preferentially
trigger the spirals, but they do appear to stir up non-axisymmetric structure
in the disc. In contrast, there is evidence that strong/close tidal
interactions with companion galaxies are associated with strong two-armed
spiral structure in the infrared, though there are a number of galaxies with
relatively weak infrared spiral structure that do not possess such companions.
