Signal　processing　in　a　quadrant　photodiode　used　to　track　target　movement　velocity　and　reflect　target　displacement　must　provide　rapid　and　accurate　dynamic　response　for　a　laser　tracker.　According　to　the　operation　principle　of　a　quadrant　photodiode,　we　derived　the　relationship　between　the　output　signal　and　the　spot　offset　using　a　diagonal　algorithm　for　the　transcendental　function.　Considering　that　it　is　not　easy　to　solve　the　transcendental　function,　in　combination　with　the　laser　spot　characteristics,　a　Taylor　series　expansion　algorithm　was　adopted.　A　verification　experiment　for　the　spot　offset　measurement　system　was　performed　using　a　high-precision　rectangular　coordinate　measuring　machine.　The　results　show　that　the　system　possesses　a　fast　measurement　speed　and　high　measurement　accuracy.　The　measurement　can　reach　1050　times　per　second,　and　the　accuracy　is　6　μm　within　a　measurement　range　of　±400　μm.　The　system　can　be　widely　applied　in　related　fields　in　which　a　microdisplacement　measurement　is　necessary.　©　2017,　Editorial　Department　of　Journal　of　HEU.　All　right　reserved.