  When two bodies get into contact, only a small portion of the apparent area
is actually involved in producing contact and friction forces, because of the
surface roughnesses. It is therefore crucial to accurately describe the
morphology of rough surfaces for instance by extracting the fractal dimension
and the so-called Hurst exponent which is a typical signature of rough
surfaces. This can be done using harmonic decomposition, which is easy for
periodic and nominally flat surfaces since Fourier transforms allow fast and
reliable decomposition. Yet, it remains a challenging task in the general
curved and non-periodic cases, where more appropriate basis functions must be
used. In this work, disk harmonics based on Fourier-Bessel basis functions are
employed for decomposing open single-edge genus-0 surfaces (no holes) as a
practical and fast alternative to characterise self-affine rough surfaces with
the power Fourier-Bessel spectral density. An analytical relationship between
the power spectrum density decay and the Hurst exponent is derived through an
extension of the Wiener-Khinchin theorem, in the special case where surfaces
are assumed self-affine and isotropic. Finally, this approach is demonstrated
to successfully measure the fractal dimension, and the Hurst exponent, without
introducing typical biases coming from basis functions boundary conditions,
surface discretisation or curvature of the surface patches. This work opens the
path for contact mechanics studies based on the Fourier-Bessel spectral
representation of curved and rough surface morphologies. All implementation
details for this method are available under GNU LGPLv3 terms and conditions.
