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We demonstrate an efficient high-precision optical spectroscopy technique forsingle trapped ions with non-closed transitions. In a double-shelvingtechnique, the absorption of a single photon is first amplified to severalphonons of a normal motional mode shared with a co-trapped cooling ion of adifferent species, before being further amplified to thousands of fluorescencephotons emitted by the cooling ion using the standard electron shelvingtechnique. We employ this extension of the photon recoil spectroscopy techniqueto perform the first high precision absolute frequency measurement of the$^{2}$D$_{3/2}$ $\rightarrow$ $^{2}$P$_{1/2}$ transition in $^{40}$Ca$^{+}$,resulting in a transition frequency of $f=346\, 000\, 234\, 867(96)$ kHz.Furthermore, we determine the isotope shift of this transition and the$^{2}$S$_{1/2}$ $\rightarrow$ $^{2}$P$_{1/2}$ transition for $^{42}$Ca$^{+}$,$^{44}$Ca$^{+}$ and $^{48}$Ca$^{+}$ ions relative to $^{40}$Ca$^{+}$ with anaccuracy below 100 kHz. Improved field and mass shift constants of thesetransitions as well as changes in mean square nuclear charge radii areextracted from this high resolution data.

Precision isotope shift measurements in Ca$^+$ using highly sensitive detection schemes