  We present a study of 581 Hz oscillations observed during a thermonuclear
X-ray burst from the low mass X-ray binary (LMXB) 4U 1636-54 with the Rossi
X-ray Timing Explorer (RXTE). We argue that the combination of large pulsed
amplitudes near burst onset and the spectral evidence for localized emission
during the rise strongly supports rotational modulation as the mechanism for
the oscillations. We discuss how theoretical interpretation of spin modulation
amplitudes, pulse profiles and pulse phase spectroscopy can provide constraints
on the masses and radii of neutron stars. We also discuss the implication of
these findings for the beat frequency models of kHz X-ray variability in LMXB.
