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 fibers 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.
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