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We present a study of 581 Hz oscillations observed during a thermonuclearX-ray burst from the low mass X-ray binary (LMXB) 4U 1636-54 with the RossiX-ray Timing Explorer (RXTE). We argue that the combination of large pulsedamplitudes near burst onset and the spectral evidence for localized emissionduring the rise strongly supports rotational modulation as the mechanism forthe oscillations. We discuss how theoretical interpretation of spin modulationamplitudes, pulse profiles and pulse phase spectroscopy can provide constraintson the masses and radii of neutron stars. We also discuss the implication ofthese findings for the beat frequency models of kHz X-ray variability in LMXB.Comment: AASTEX Latex, 13 pages including 5 figures. Accepted for publication  in the Astrophysical Journal Letter

On the Amplitude of Burst Oscillations in 4U 1636−54: Evidence for Nuclear-powered Pulsars