  We report the first results of a systematic investigation to characterize
blazar variability power spectral densities (PSDs) at optical frequencies using
densely sampled (5--15 minutes integration time), high photometric accuracy
($\lesssim$0.2--0.5\%) R-band intranight light curves, covering timescales
ranging from several hours to $\sim$15\,minutes. Our sample consists of 14
optically bright blazars, including nine BL Lacertae objects (BL Lacs) and five
flat-spectrum radio quasars (FSRQs) which have shown statistically significant
variability during 29 monitoring sessions. We model the intranight PSDs as
simple power--laws and derive the best-fit slope along with uncertainty using
the `power spectral response' method. Our main results are the following: (1)
on 19 out of 29 monitoring sessions, the intranight PSDs show an acceptable fit
to simple power-laws at the rejection confidence $\leq$ 90\%; (2) for these 19
instances, the PSD slopes show a large range from 1.4 to 4.0, consistent with
statistical characters of red (slope$\sim$2) and black (slope$\geq$3) noise
stochastic processes; (3) the average PSD slopes for the BL Lacs and FSRQs are
indistinguishable from one another; (4) the normalization of intranight PSDs
for individual blazar sources which were monitored on more than one occasion
turns out to be consistent with one another with a few exceptions. The average
PSD slope, 2.9$\pm$0.3 (1$\sigma$ uncertainty) is steeper than the red-noise
type character of variability found on longer timescales (many decades to
days), indicative of a cutoff in the variability spectrum on timescales around
a few days at the synchrotron frequencies of the emission spectrum.
