Complex　small　components　are　widely　used　in　intelligent　instruments.　The　stable　and　accurate　operation　of　intelligent　instruments　relies　on　high-precision　detection　of　complex　small　components.　Point　autofocus　microscopy　has　comprehensive　advantages　in　the　field　of　complex　small　components　inspection　due　to　its　small　measurement　spot　and　high　vertical　resolution.　However,　for　surfaces　with　locally　significant　tilts,　microscopic　measurement　instruments　may　encounter　challenges　in　precise　measurement　due　to　the　limitations　imposed　by　the　objective　numerical　aperture,　particularly　pronounced　when　the　tested　surface　is　smooth.　This　paper　starting　from　the　principle　of　point　autofocusing　bias　measurement,　builds　a　paraxial　ray　tracing　model　of　a　point　self-focusing　light　probe　microscope　and　establishes　a　quantitative　model　for　the　offset　of　beam　displacement　and　the　MATA　of　the　point　autofocus　microscopy.　In　order　to　verify　the　accuracy　of　the　model,　a　reference　sphere　with　a　surface　roughness　of　0.06　μm　is　used　to　simulate　the　smooth　measured　surface,　and　the　deflection　of　the　smooth　surface　is　simulated　by　accurately　moving　the　reference　sphere.　The　difference　between　the　final　experimental　measurement　results　and　the　maximum　acceptable　tilt　angles　calculated　by　the　quantitative　model　is　less　than　0.5°.　Research　findings　show　that　the　MATA　of　a　point　autofocus　microscope　varies　across　different　the　offset　of　beam　displacement,　and　there　exists　a　well-defined　quantitative　relationship　between　them.　©　2024