This dissertation details the developments of a calcium thermal beam atom interferometer designed to act as an ultra-stable frequency reference over a broad range of timescales. The obtained fractional frequency instabilities of the final apparatus reached ≤ 10⁻¹⁶ after 10's of seconds of averaging without the aid of vibration isolation or significant apparatus temperature stabilization. The vastly superior stability performance of this calcium system compared to other thermal atomic references was facilitated by the enormous atom numbers from the thermal beam, which can be efficiently addressed with Bord\'e-Ramsey spectroscopy on the well-studied (4s²)¹S₀-(4s4p)³P₁ (m=0) clock transition in neutral ⁴⁰Ca. This method yields interrogation laser frequency dependent interference fringes with a linewidth of 1.6 kHz. This measurement is further enhanced with an electron-shelving detection scheme used for state detection after the interferometry process, causing each excited state atom to emit many hundreds of photons in the detection region.

The exceptional instability results from this atom interferometer highlight an underutilized realm of precision measurement science based on relatively simple thermal ensembles. An intuitive understanding of the Bordé-Ramsey process is presented and relevant experimental techniques explained such that this dissertation should prove useful to a broad readership.