Cleaning opticsCleaning opticsGeometric opticsMagnificationParaxial approximationThin lens equationGeometric opticsHigher approximation (primary abberrations)AberrationsAberrationsAberrationsFourier OpticsFourier OpticsFourier OpticsFourier OpticsConsequences (E. Abbe)Microscopy (this lab)Brightfield light pathDarkfieldPhase contrastTIRFOptical tweezersFluorescenceFluorescenceCleaning opticsGeometric opticsAberrationsFourier opticsModern microscopy in Aph162 labOptics primerCleaning optics• Don’t clean optics… but if its dirtyBare optics:1)Blow off dust (not with organics)2)Drag and drop* Make sure solventis good for coatings* don’t clean bare metalsurfaces with tissues* Don’t contaminate lens tissueCleaning optics• Objectives– 1) roll up lens tissue– 2) blot off excess oil– 3) roll up lens tissue and apply solvent; shake off excess– 4) wipe center outward and discard.Geometric opticsfffImage is real Image is virtualMagnificationf2f1M = f1/f2f2f1M = f1/f2Paraxial approximationThin lens equationNow, let nm~1, dÆ 0()⎟⎟⎠⎞⎜⎜⎝⎛−−=+2111111RRnsslioIf soÆinf, siÆ fi(and vice versa)Gaussian lens formulamGeometric opticsfffImage is real Image is virtualHigher approximation (primary abberrations)Fixes:>Apertures>1 surface (PCXÆBCX)>aspherics>doubletsActually, this lensis backwards…Aberrations•Coma• astigmatismAberrations• Field curvature• DistortionsAberrations• Chromatic aberrationFourier Optics))](2exp()(Re[),( rivtirAtruφπ+−=022222=∂∂−∇tucnu0))(exp()()(22=+∇ rirAkφsatisfiesU(r)cnvkπλπ22==Fourier Optics1) Outgoing waves only (Sommerfeld radiation condition)2) Field through opening not influenced by aperture3) Over opaque screen, field is zero4) ÆAperture dimensions >> λ (neglect fringing)5) Aperture to observation is far compared to wavelength01∫∫Σ∝ dsreUUikrθcos)1()0(0101(Huygens-Fresnel principle)(Fresnel Approximation)Good to distances very close to apertureηξηξηξλπηξ∫∫+−+∝ ddeeUyxUyxzizik)(2)(222),(),(θ is angle between observation and normal to apertureΣFourier OpticsFraunhofer Approximationηξηξηξλπ∫∫+−∝ ddeUyxUyxzi)(2),(),(()222ηξ+>>kzFor visible light, and 1 inch aperture, z is 1600 meters!Note: spherical waves passing through an aperture is diffraction. FT of a circular aperture is an Airy pattern – how we define optical resolution – width of central lobe NAwzd222.1λλ⎯→⎯=Rayleigh criterionFourier OpticsSo, light diffracts off an object – and we collect it with a lens.What’s going on? – The lens moves the far-field diffraction pattern closer.Amplitude function behind a lens is:Thus, a lens computes the Fraunhofer diffraction pattern.ηξηξηξλπ∫∫+−= ddeTyxUyxfi)(2),(),(Consequences (E. Abbe)An image is always imperfect since a lens with a finite diameter captures limited frequency informationPSF is the Green’s function for an optical system.OTF is its Fourier Transform, characterizes a systems frequency response.Microscopy (this lab)• Brightfield• Darkfield• Phase contrast•TIRF• Optical tweezers• Fluorescence (epi-illumination)Brightfield light pathWe can understand from this how to align the only movable element, the condenser for Kohler illumination.conobjNANAR+=λ22.1DarkfieldThe condenser blocks out the 0thorder light, only allowing higher orders to pass, enhancing contrast.Phase contrastBy “speeding up” the 0thorder light by ¼ wave, it destructively interferes with the diffracted light (green).This is an instance of Fourier plane filtering.TIRFSnell’s lawOptical tweezers2EnFoε∝Need high NA to achieve high enough intensity to trap stuffFluorescenceFluorescence is an electronic state relaxation phenomenom-Photobleaching-FRAP-FRET-High resolution localizationFluorescenceSo… how do we align the arc lamp of a fluorescence
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