Interferenceless　coded　aperture　correlation　holography　(I-COACH)　is　a　rapidly　developing　indirect　three-dimensional　(3D)　imaging　technique.　However　the　ideal　point　spread　function　of　imaging　system　is　not　obtained　in　most　cases,　the　object　hologram　is　usually　correlated　with　the　system　response　of　a　limited-size　pinhole　during　the　reconstruction　process.　As　a　result,　the　quality　of　reconstructed　images　is　contaminated　by　noise.　In　this　paper,　the　system　response　of　a　limited-size　pinhole　is　regarded　as　the　convolution　of　the　pinhole　(as　an　object)　intensity　and　the　ideal　point　spread　function　of　I-COACH,　a　mathematical　analysis　of　the　background　noise　is　conducted　and　a　general　high-quality　reconstruction　mathematic　model　of　I-COACH　system　is　derived　when　a　limited-size　pinhole　is　used　to　record　point　spread　hologram,　in　which　the　reconstructions　and　noise　is　separated.　Then　a　non-iterative　cross-correlation　reconstruction　algorithm　has　been　developed　here　to　achieve　high-quality　3D　reconstruction.　The　proposed　method　has　been　implemented　on　a　regular　I-COACH　system　in　both　transmission　as　well　as　reflection　illumination　modes　to　demonstrate　the　imaging　ability　of　our　method.　The　experimental　results　show　that　high　quality　reconstructions　can　be　achieved　by　our　proposal　with　a　single-exposure　object　hologram.　©　2023