2 What is light?• Light is a form of electromagnetic energy – detected through itseffects, e.g. heating of illuminated objects, conversion of light tocurrent, mechanical pressure (“Maxwell force”) etc.• Light energy is conveyed through particles: “photons”– ballistic behavior, e.g. shadows• Light energy is conveyed through waves– wave behavior, e.g. interference, diffraction• Quantum mechanics reconciles the two points of view, through the“wave/particle duality” assertion
3 Particle properties of light Photon=elementary light particleMass=0Speed c=3⊥108m/secAccording to According to Special Relativity, a mass-less particle travellingat light speed can still carry momentum!Energy E=hνrelates the dual particle & wavenature of light;h=Planck’s constant=6.6262⊥10-34 J secν is the temporal oscillationfrequency of the light waves
5 Wave/particle duality for light Photon=elementary light particleMass=0Speed c=3⊥108 m/secEnergy E=hνh=Planck’s constant=6.6262⊥10-34 J secν=frequency (sec-1)λ=wavelength (m)“Dispersion relation”(holds in vacuum only)
6 Light in matter Speed c/n Speed c=3×108 m/sec n : refractive index light in vacuumlight in matterSpeed c/nn : refractive index(or index of refraction)Absorption coefficient αenergy decay coefficient,after distance L : e–2αLSpeed c=3×108 m/secAbsorption coefficient 0E.g. vacuum n=1, air n ≈ 1;glass n≈1.5; glass fiber has α ≈0.25dB/km=0.0288/km
7 Materials classification • Dielectrics– typically electrical isolators (e.g. glass, plastics)– low absorption coefficient– arbitrary refractive index• Metals– conductivity large absorption coefficient• Lots of exceptions and special cases (e.g. “artificial dielectrics”)• Absorption and refractive index are related through the Kramers–Kronig relationship (imposed by causality)absorptionrefractive index
8 Overview of light sources non-LaserThermal: polychromatic,spatially incoherent(e.g. light bulb)Gas discharge: monochromatic,(e.g. Na lamp)Light emitting diodes (LEDs):monochromatic, spatiallyincoherentLaserContinuous wave (or cw):strictly monochromatic,spatially coherent(e.g. HeNe, Ar+, laser diodes)Pulsed: quasi-monochromatic,(e.g. Q-switched, mode-locked)~nsec~psec to few fsecpulse durationmono/poly-chromatic = single/multi color
9 Monochromatic, spatially coherent light• nice, regular sinusoid• λ, ν well defined• stabilized HeNe lasergood approximation• most other cw lasersrough approximation• pulsed lasers & nonlasersources needmore complicateddescriptionIncoherent: random, irregular waveform
10 The concept of a monochromatic “ray”t=0(frozen)direction ofenergy propagation:light raywavefrontsIn homogeneous media,light propagates in rectilinear paths
11 The concept of a monochromatic “ray”t=Δt(advanced)direction ofenergy propagation:light raywavefrontsIn homogeneous media,light propagates in rectilinear paths
12 light propagates in rectilinear paths The concept of a polychromatic “ray”t=0(frozen)energy frompretty muchall wavelengthspropagates alongthe raywavefrontsIn homogeneous media,light propagates in rectilinear paths
13 Fermat principle Γ is chosen to minimize this “path” integral, compared toalternative paths(aka minimum path principle)Consequences: law of reflection, law of refraction
14 The law of reflection a) Consider virtual source P” instead of P b) Alternative path P”O”P’ islonger than P”OP’c) Therefore, light follows thesymmetric path POP’.mirror
15 The law of refraction reflected reflected incident Snell’s Law of Refraction
16 Total Internal Reflection (TIR) becomes imaginary whenrefracted beam disappears, all energy is reflected
18 Dispersion Refractive index n is function of the wavelength white light(all visiblewavelengths)redairglassgreenblueNewton’s prism
19 Frustrated Total Internal Reflection (FTIR)otherglassmaterialReflected rays are missingwhere index-matched surfacestouch shadow is formedAngle of incidenceexceeds critical angleair gap
20 Fingerprint sensor finger air glass | air glass | finger TIR occurs TIR does not occurs(FTIR)
21 Optical waveguide • Planar version: integrated optics • Cylindrically symmetric version: fiber optics• Permit the creation of “light chips” and “light cables,” respectively, wherelight is guided around with few restrictions• Materials research has yielded glasses with very low losses (<0.25dB/km)• Basis for optical telecommunications and some imaging (e.g. endoscopes)and sensing (e.g. pressure) systems
23 Imaging a point sourcepointsourcepointsourceLens
24 plane wave (or parallel ray bundle); Model for a thin lenspoint objectat 1st FP1st FPfocal length fplane wave (or parallel ray bundle);image at infinity
25 plane wave (or parallel ray bundle); Model for a thin lenspoint imageat 2nd FPfocal length fplane wave (or parallel ray bundle);object at infinity
26 Types of lenses positive (f > 0) negative (f < 0) BICONVEXBICONCAVEPLANO CONVEXPLANO CONCAVEfrom Modern OpticalEngineeringby W. SmithPOSITIVE MENISCUSNEGATIVE MENISCUSFigure The location of the focal points and principal points for several shapes of converging and diverging elements.
27 Huygens principle Each point on the wavefront acts as a secondary light sourceemitting a spherical waveThe wavefront after a shortpropagation distance is theresult of superimposing allthese spherical waveletsopticalwavefronts
28 Why imaging systems are needed • Each point in an object scatters the incident illumination into a spherical wave,according to the Huygens principle.• A few microns away from the object surface, the rays emanating from allobject points become entangled, delocalizing object details.• To relocalize object details, a method must be found to reassign (“focus”) allthe rays that emanated from a single point object into another point in space(the “image.”)• The latter function is the topic of the discipline of Optical Imaging.
29 Imaging condition: ray-tracing thin lens (+)image(real)2nd FP1nd FPobject• Image point is located at the common intersection of all rays whichemanate from the corresponding object point• The two rays passing through the two focal points and the chief raycan be ray-traced directly• The real image is inverted and can be magnified or demagnified
31 Imaging condition: ray-tracing thin lens (+)Image(virtual)2nd FP1st FPobject• The ray bundle emanating from the system is divergent; the virtualimage is located at the intersection of the backwards-extended rays• The virtual image is erect and is magnified• When using a negative lens, the image is always virtual, erect, anddemagnified
32 the Scheimpflug condition Tilted object:the Scheimpflug conditionLENS PLANEOBJECT LANEIMAGEPLANEOPTICALAXISThe object plane and the image planeintersect at the plane of the thin lens.
33 Lens-based imaging • Human eye • Photographic camera • Magnifier • Microscope• Telescope
34 The human eye Anatomy Remote object (unaccommodated eye) CORNEAAQUEOUSIRISLENSLIGAMENTSMUSCLESCLERARemote object (unaccommodated eye)RETINABLINDSPOTMACULA-FOVEAOPTIC NERVENear point (comfortable viewing)~25cm from the corneaNear object (accommodated eye)
35 Eye defects and their correction Hypermetropia, farsightedMyopia, nearsightedfrom Fundamentalsof Opticsby F. Jenkins & H.WhiteFIGURE 10KTypical eye defects, largely present in the adult population.Farighted eye correctedNearsighted eye correctedFIGURE 10LTypical eye defects can be corrected by spectacle lenses.
36 The photographic camera BellowsFocalplaneAxisObjectStopmeniscuslensor (nowadays)zoom lensFilmor“digital imaging” detector array (CCD or CMOS)
38 The compound microscope from Opticsby M. Klein &T. FurtakL: distance to near point (10in=254mm)Objective magnificationEyepiece magnificationCombined magnification
39 The telescope (afocal instrument – angular magnifier) from Optics Flg Astronomical telescope.from Opticsby M. Klein &T. FurtakFlg Galilean telescope (fashioned after the first telescope).
40 The pinhole camera image object opaquescreenimagepin-holeobject• The pinhole camera blocks all but one ray per object point from reaching theimage space an image is formed (i.e., each point in image space corresponds toa single point from the object space).• Unfortunately, most of the light is wasted in this instrument.• Besides, light diffracts if it has to go through small pinholes as we will see later;diffraction introduces undesirable artifacts in the image.
41 Field of View (FoV)FoV=angle that the chief ray from an object can subtendtowards the imaging system
42 Numerical Aperture Numerical Aperture (NA) = n sinθ medium ofrefr. index nNumerical Aperture(NA) = n sinθSpeed (f/#)=1/2(NA)pronounced f-number, e.g.f/8 means (f/#)=8.θ: half-angle subtended bythe imaging system froman axial object
43 Resolution How far can two distinct point objects be before their images cease to be distinguishable?
44 Factors limiting resolution in an imaging system • Diffraction• Aberrations• NoiseIntricately related; assessment of imagequality depends on the degree that the “inverseproblem” is solvable (i.e. its condition)2.717 sp02 for details– electronic noise (thermal, Poisson) in cameras– multiplicative noise in photographic film– stray light– speckle noise (coherent imaging systems only)• Sampling at the image plane– camera pixel size– photographic film grain size
45 Point-Spread Function Light distributionnear the Gaussian(geometric) focus(rotationallysymmetricwrt optical axis)Point source(ideal)The finite extent of the PSF causes blur in the image
48 Diffraction grating incident plane Grating spatial frequency: 1/Λ wave Angular separation between diffracted orders: Δθ ≈1/Λ“straight-through” order or DC termCondition for constructive interference:( m integer)diffraction order
51 Fresnel diffraction as a linear, shift-invariant system Thin transparencyimpulse responseconvolutiontransfer functionmultiplicationFouriertransform(≡plane wavespectrum)g(x, y)t(x, y)
52 The 4F systemobject planeFourier planeImage plane
53 The 4F systemobject planeFourier planeImage plane
54 The 4F system with FP aperture object planeFourier plane: aperture-limitedImage plane: blurred(i.e. low-pass filtered)
55 The 4F system with FP aperture Transfer function:circular apertureImpulse response:Airy function
56 Coherent vs incoherent imaging field inintensity infield outintensity outCoherentopticalsystemIncoherent
57 Coherent vs incoherent imaging Coherent impulse response(field in ⇒field out)Coherent transfer function(FT of field in ⇒ FT of field out)Incoherent impulse response(intensity in ⇒intensity out)Incoherent transfer function(FT of intensity in ⇒ FT of intensity out)| (u,v)|: Modulation Transfer Function (MTF)(u, v): Optical Transfer Function (OTF)
58 Coherent vs incoherent imaging Coherent illuminationIncoherent illumination
59 Aberrations: geometrical Paraxial(Gaussian)image pointNon-paraxial rays“overfocus”Spherical aberration• Origin of aberrations: nonlinearity of Snell’s law (n sinθ=const., whereas linearrelationship would have been nθ=const.)• Aberrations cause practical systems to perform worse than diffraction-limited• Aberrations are best dealt with using optical design software (Code V, Oslo,Zemax); optimized systems usually resolve ~3-5λ (~ μm in the visible)
60 Aberrations: wave Aberration-free impulse response Aberrations introduce additional phase delay to the impulse responseEffect of aberrationson the MTFunaberrated(diffractionlimited)aberrated
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