  Optical nanofibers (ONF) of subwavelength dimensions confine light in modes
with a strong evanescent field that can trap, probe, and manipulate nearby
quantum systems. To measure the evanescent field and propagating modes, and to
optimize ONF performance, a surface probe is desirable during fabrication. We
demonstrate a nondestructive measurement of light propagation in ONFs by
sampling the local evanescent field with a microfiber. This approach reveals
the behavior of all propagating modes, and because the modal beat lengths in
cylindrical waveguides depend strongly on radius, simultaneously provides
exquisite sensitivity to the ONF radius. We show that our measured spatial
frequencies provide a map of the average ONF radius (over a 600 micrometer
window) along the 10 mm ONF waist with 40 picometer resolution and high
signal-to-noise ratio. The measurements agree with scanning electron microscopy
(SEM) to within SEM instrument resolution. This fast method is immune to
polarization, intrinsic birefringence, mechanical vibrations, scattered light,
and provides a set of constraints to protect from systematic errors in the
measurements
