An accelerometer instrument is provided for measuring acceleration. The instrument includes a laser, a Mach-Zender interferometer (MZI), a mechanical spring, a detector, a camera, and an analyzer. The laser emits a coherent light beam of photons. The MZI includes first and second beam-splitters along with first and second mirrors. The first mirror has an established mass m and connects to the spring for vibrating substantially perpendicular to its reflection plane. The mechanical spring has an established spring constant k. The MZI has an established weak measurement Nw based on a known offset ε for the beam-splitters. The detector detects the beam beyond the second beam-splitter. The camera provides a pointer measurement shift δq of the photons. The camera is disposed after the detector. The analyzer determines the acceleration α based on a = ( k mN w ) ⁢ δ ⁢ ⁢ q .