HeterodyningPrinciple of heterodyne interferometerDifference frequency generationPrinciple of heterodyne interferometerSplitting the two frequenciesMapping position and velocityPrinciple of heterodyne interferometerPosition measurement principleHeterodyningfrequency f1MIT 2.71703/28/05 – wk8-a-1+=(not to scale)inphaseslightlyout ofphasefrequency f2moreout ofphaseenvelope (beat)difference-frequencyoscillation ~1MHzdetectable byelectronicssum-frequencyoscillation ~1015Hztoo fast for detectorPrinciple of heterodyne interferometerreference retro-reflector (fixed)f2MIT 2.71703/28/05 – wk8-a-2f1& f2movable retro-reflectorf1f1& f2polarizerdetectorphasecomparatorrelativeposition & velocityinformationoutputDifference frequency generationf1f2MIT 2.71703/28/05 – wk8-a-3polarizerdetector,can followbeat frequencyonlyorthogonallypolarizedpolarizerdirectionpolarizationof field @ f1polarizationof field @ f2@ 45° wrtboth f1& f2f1& f2, both parallel-polarized at 45°f1− f2Principle of heterodyne interferometerreference retro-reflector (fixed)f2MIT 2.71703/28/05 – wk8-a-4f1& f2movable retro-reflectorf1f1& f2polarizerdetectorphasecomparatorrelativeposition & velocityinformationf1− f2outputSplitting the two frequenciesreference retro-reflector (fixed)f2f1polarizing beam-splitter(reflects polarization;transmits polarization)f2 polarizedf1 polarizedmovable retro-reflectorMIT 2.71703/28/05 – wk8-a-5Mapping position and velocityreference retro-reflector (fixed)f2f2movable retro-reflectorMIT 2.71703/28/05 – wk8-a-6f1polarizing beam-splitter(reflects polarization;transmits polarization)f1±∆f1f1±∆f1f2field is Doppler-shiftedand phase-delayedPrinciple of heterodyne interferometerreference retro-reflector (fixed)f2MIT 2.71703/28/05 – wk8-a-7f1& f2movable retro-reflectorf1f1±∆f1f2f1±∆f1f1& f2polarizerdetectorphasecomparatorrelativeposition & velocityinformationf1±∆f1− f2f1− f2outputMIT 2.71703/28/05 – wk8-a-8Position measurement principlebeat frequency = f1− f2beat phase ∝