  We prove a novel result wherein the density function of the
gradients---corresponding to density function of the derivatives in one
dimension---of a thrice differentiable function S (obtained via a random
variable transformation of a uniformly distributed random variable) defined on
a closed, bounded interval \Omega \subset R is accurately approximated by the
normalized power spectrum of \phi=exp(iS/\tau) as the free parameter \tau-->0.
The result is shown using the well known stationary phase approximation and
standard integration techniques and requires proper ordering of limits.
Experimental results provide anecdotal visual evidence corroborating the
result.
