Ultra-precision　grinding　is　crucial　for　manufacturing　high-end　optics　and　molds,　while　the　unbalanced　wheel　vibration　is　inevitable　and　becomes　even　more　critical　in　surface　generation,　which　resulted　in　undesired　waviness　and　micro-texture　on　the　ground　surface.　In　this　paper,　to　understand　and　control　the　micro-texture　generation,　a　theoretical　model　has　been　developed　to　predict　the　deterministic　surface　micro-texture　generation　resulted　from　unbalanced　tool　vibration　in　ultra-precision　grinding,　in　which　the　overlap　trajectories　of　grinding　wheel　with　an　arc　cutting　edge　were　analyzed　and　calculated.　The　simulation　work　was　performed　and　a　double　phase　mechanism　involved　in　deterministic　textural　pattern　and　structure　has　been　revealed.　Both　theoretical　and　experimental　results　proved　that　phase　shift　is　an　important　factor　to　determine　micro-texture　evolution　in　the　ultra-precision　grinding　process.　On　this　basis,　a　novel　tool　path　strategy　has　been　proposed　to　fabricate　deterministic　micro-structure　by　coordinating　oscillation　motion　of　the　grinding　wheel　and　phase　shift　control,　in　which　a　rhombus-shaped　micro-structure　array　can　be　generated.　A　small　adjustment　for　the　phase　shift　was　conducted　and　it　was　found　that　the　more　complex　micro-texture　with　different　textural　patterns　and　micro-structure　can　be　machined.　The　results　indicated　that　the　phase　control　for　the　tool　path　planning　is　an　effective　method　to　fabricate　flexible　and　tunable　micro-texture　surfaces　in　ultra-precision　grinding.　(C)　2022　Optica　Publishing　Group　under　the　terms　of　the　Optica　Open　Access　Publishing　Agreement