Foveated　imaging,　which　has　the　ability　to　provide　overall　situational　awareness　over　a　large　field　of　view　and　high-resolution　perception　of　local　details,　has　significant　advantages　in　many　specific　applications.　However,　existing　artificially　foveated　imaging　systems　are　complex,　bulky,　and　expensive,　and　the　flexibility　of　the　fovea　specifically　has　many　limitations.　To　overcome　these　deficiencies,　this　paper　proposes　a　method　for　foveated　imaging　by　collecting　multiple　partially　overlapping　sub-fields　of　view.　To　capture　the　above　special　sub-fields　of　view,　we　propose　a　high-efficiency　algorithm　based　on　the　characteristics　of　the　field　of　view　deflected　by　the　Risley-prism　and　aimed　at　solving　the　prism　rotation　angles.　In　addition,　we　prove　the　reliability　of　the　proposed　algorithm　by　cross-validation　with　the　particle　swarm　optimization　algorithm.　The　experimental　results　show　that　the　proposed　method　can　achieve　flexible　foveated　imaging　using　a　single　Risley-prism　imaging　system.　(C)　2021　Optical　Society　of　America　under　the　terms　of　the　OSA　Open　Access　Publishing　Agreement