  We propose a generalized spiral transformation scheme that is versatile to
incorporate various types of spirals such as the Archimedean spiral and the
Fermat spiral. Taking advantage of the equidistant feature, we choose the
Archimedean spiral mapping and demonstrate its application in high-resolution
orbital angular momentum mode sorting. Given a fixed minimum spiral width, the
Archimedean spiral mapping shows superior performance over the logarithmic
spiral mapping. This generalized transformation scheme may also find various
applications in optical transformation and can be easily extended to other
fields related to conformal mapping.
