Single-shot diffraction-limited imaging through scattering layers via bispectrum analysis

Abstract

Recently introduced speckle‐correlations based techniques behind . In object light autocorrelation , and the lost Fourier phase is recovered , which suffer and . Here, inspired by notions used in astronomy , we experimentally demonstrate that in addition to Fourier amplitude , the inherently encoded in scattered light bispectrum(the Fourier of) ,andalsobeextractedfromasinglehigh‐resolutionspecklepattern,basedtodeterministicallyandunambiguouslyretrievediffraction‐limitedimagesofobjectshiddenbehindscattering.Themanyimagingscenariosinduceslightscattering,whichdiffusesthelightfromanyobjectburiedinsideorhiddenbehindsuchsamplesintoacomplexspecklepattern[1],andmakesdirectimagingofsuchobjectsimpossible.Inrecentyears,severalapproacheshavebeenputforwardtoovercomethisseeminglyintractable.Wavefrontamedia[2‐11].However,thesemethodsrequireadetectororanoptical/acoustical.Thesearetime‐consumingduetotherequiredlongsequenceofmeasurementssteps,oneforeachimagingpixel,andarethusdifficulttousewithdynamicsamples.Arecentbreakthroughapproachbyet.,whichcorrelationsofscatteredlightspecklepatterns,knownasthe'memory'[12,13]hasrealizedimagingthroughscatteringlayerswithoutanyguidestarorcomplexwavefrontshapingprocess[14].However,thistechniquerequiresalongangular‐scanningacquisitionsequence,whichlimitsitsusetorelativelystaticsamples.Basedonthesamespeckle‐correlationsandinspiredbytheastronomicaltechniqueofstellarspeckleinterferometry,Katzetal.[15]havedemonstratedthatobjectshiddenbehindscatteringlayerscanberetrievedfromtheautocorrelationofasinglehigh‐resolutionscatteredlightimage,capturedbyastandardcamera,viaiterativephase‐retrievalalgorithms[16,17].Thesingle‐shottechniquebenefitsfromashort,whichimaging.However,thisof:i).itofiterationsandindependentrunswithdifferentrandominitialguessestoavoidstagnatingatlocaloptimalsolution;ii).Theconvergenceofphase‐retrievalalgorithmdependsonthepriorinformation(e.g.theof)or(e.g.the[16]).InthisLetterweexperimentallydemonstrateasingle‐shotnoninvasiveimagingschemeforrealizingdiffraction‐limitedobservation,withoutuse.Inspiredusedinastronomyandbasedonthenotionofclosure‐phasepioneeredinradio‐astronomy,weextracttheobject'sFourierphase(triple‐correlation)analysisasinglescatteredlightpattern.JustKatz's.work[15]only.Inaddition,thetoadditiveGaussiannoise[18],whichisanimportantpracticaladvantage.TheschematicoftheexperimentalsetupandanumericalsimulationofourimagingschemearepresentedinFig.1.InFig.1(a),anobjectthatisplacedatadistanceubehindahighlyscattering,is.Ahigh‐resolutionof.Ifobjectlieswithintherangedeterminedbytheopticalmemoryeffect,points,butrandom.For,thecamerapatterns,which.1(a)to