To　evaluate　the　intermediate-frequency　error　of　a　precision　optical　surface,　a　method　for　more　accurate　separation　and　identification　of　the　intermediate-frequency　error　is　proposed.　This　method　is　based　on　the　Hilbert　spectrum　and　the　instantaneous　frequency　separation　method.　Experimental　results　show　that　the　intermediate-frequency　error　spectrum　can　be　obtained　using　the　method　of　instantaneous　frequency　separation　based　on　the　Hilbert　spectrum.　This　method　separates　only　the　intermediate-frequency　error　component　(0.03　mm(-1)　＜=　f　＜=　8.33　mm(-1)).　Also,　the　method　accurately　identifies　the　non-qualified　component　distribution　(at　sampling　points　200,　840,　and　1000).　Therefore,　this　algorithm　is　a　useful　guide　for　deterministic　processing　of　optical　components.　(C)　2018　Society　of　Photo-Optical　Instrumentation　Engineers　(SPIE)