The　radial　vibration　signals　of　the　rotor　can　provide　abundant　information　about　the　health　condition　of　the　machine.　In　this　paper,　a　simple　vision-based　measurement　system　is　proposed　to　simultaneously　measure　two-dimensional　displacements　in　radial　directions　for　the　rotating　shaft,　where　the　system　consists　of　a　constant　density　fringe　pattern　(CDFP),　a　line　scan　camera　(LSC),　and　a　lens.　The　CDFP　should　be　installed　around　the　surface　of　the　rotating　shaft　to　make　the　density　of　the　fringe　constant　along　the　shaft　axis,　while　the　shaft　axis　is　vertical　to　the　optical　axis　of　the　LSC　but　not　parallel　to　the　line-array　sensor　of　the　LSC.　Therefore,　the　density　of　the　fringe　imaged　on　the　LSC　is　not　constant　because　of　the　modulation　of　the　circular　surface　of　the　shaft,　and　the　distribution　of　the　fringe　density　on　the　LSC　is　a　U-shaped　curve.　Thus,　the　shaft　centreline　orbit　can　be　tracked　by　the　lowest　point　of　the　density　distribution　curve　(DDC)　of　the　fringe.　Then,　an　efficient　and　accurate　parameterized　instantaneous　frequency　estimation　method　is　employed　to　estimate　the　DDC　of　the　fringe,　because　the　variable　density　fringe　can　be　regarded　as　an　amplitude-modulated　and　frequency-modulated　nonstationary　signal　whose　instantaneous　frequency　function　is　equivalent　to　the　DDC.　Experimental　results　verify　the　feasibility　and　effectiveness　of　the　proposed　method　by　comparing　it　to　the　eddy　current　sensors.　©　2024　IOP　Publishing　Ltd.