  We report a new 40 ppb measurement of the positronium
$\text{1}^\text{3}\text{S}_\text{1} \to \text{2}^\text{3}\text{S}_\text{1}$
interval using pulsed two-photon optical spectroscopy. The transition is
detected via field-ionization of atoms excited from the 2S to the 20P Rydberg
state. Precise Monte-Carlo line-shape simulations allow for the accounting of
effects such as Doppler and AC Stark shifts, while an optical heterodyne
measurement of the excitation laser pulse is used to correct for laser
frequency chirp. A value of $1\,233\,607\,210.5\pm 49.6\, \mathrm{MHz}$ was
obtained. This scheme allows for the measurement of the velocity distribution
of positronium atoms to correct for the second-order Doppler effect. This is
the major source of systematic uncertainty expected for future measurements of
this transition with a CW laser, thus, our technique paves the way toward a new
generation of a high precision determination of this interval in positronium.
