  It is prohibitively expensive to deposit customized dielectric coatings on
individual optics. One solution is to batch-coat many optics with extra
dielectric layers, then remove layers from individual optics as needed. Here we
present a low-cost, single-step, monitored wet etch technique for reliably
removing (or partially removing) individual SiO$_2$ and Ta$_2$O$_5$ dielectric
layers, in this case from a high-reflectivity fiber mirror. By immersing in
acid and monitoring off-band reflected light, we show it is straightforward to
iteratively (or continuously) remove six bilayers. At each stage, we
characterize the coating performance with a Fabry-P\'{e}rot cavity, observing
the expected stepwise decrease in finesse from 92,000$\pm$3,000 to
3,950$\pm$50, finding no evidence of added optical losses. The etch also
removes the fiber's sidewall coating after a single bilayer, and, after six
bilayers, confines the remaining coating to a $\sim$50-$\mu$m-diameter pedestal
at the center of the fiber tip. Vapor etching above the solution produces a
tapered "pool cue" cladding profile, reducing the fiber diameter (nominally 125
$\mu$m) to $\sim$100 $\mu$m at an angle of $\sim$0.3$^\circ$ near the tip.
Finally, we note that the data generated by this technique provides a sensitive
estimate of the layers' optical depths. This technique could be readily adapted
to free-space optics and other coatings.
