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MIT 2.71/2.710 Review Lecture p- 1 Optics Overview.

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Presentation on theme: "MIT 2.71/2.710 Review Lecture p- 1 Optics Overview."— Presentation transcript:

1 MIT 2.71/2.710 Review Lecture p- 1 Optics Overview

2 MIT 2.71/2.710 Review Lecture p- 2 What is light? Light is a form of electromagnetic energy – detected through its effects, e.g. heating of illuminated objects, conversion of light to current, 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 MIT 2.71/2.710 Review Lecture p- 3 Particle properties of light Photon=elementary light particle Mass=0 Speed c= m/sec According to According to Special Relativity, a mass-less particle travelling at light speed can still carry momentum! Energy E=hν relates the dual particle & wave nature of light; h=Plancks constant = J sec ν is the temporal oscillation frequency of the light waves

4 MIT 2.71/2.710 Review Lecture p- 4 Wave properties of light λ: wavelength (spatial period) k=2π/λ wavenumber ν: temporal frequency ω=2πν angular frequency E: electric field

5 MIT 2.71/2.710 Review Lecture p- 5 Wave/particle duality for light Photon=elementary light particle Mass=0 Speed c= m/sec Energy E=hν h=Plancks constant = J sec ν=frequency (sec -1 ) λ=wavelength (m) Dispersion relation (holds in vacuum only)

6 MIT 2.71/2.710 Review Lecture p- 6 Light in matter light in vacuum Speed c= m/sec Absorption coefficient 0 Speed c/n n : refractive index (or index of refraction) Absorption coefficient α energy decay coefficient, after distance L : e –2αL light in matter E.g. vacuum n=1, air n 1; glass n1.5; glass fiber has α 0.25dB/km=0.0288/km

7 MIT 2.71/2.710 Review Lecture p- 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) absorption refractive index

8 MIT 2.71/2.710 Review Lecture p- 8 Overview of light sources non-Laser Thermal: polychromatic, spatially incoherent (e.g. light bulb) Gas discharge: monochromatic, spatially incoherent (e.g. Na lamp) Light emitting diodes (LEDs): monochromatic, spatially incoherent Laser Continuous wave (or cw): strictly monochromatic, spatially coherent (e.g. HeNe, Ar+, laser diodes) Pulsed: quasi-monochromatic, spatially coherent (e.g. Q-switched, mode- locked) ~nsec~psec to few fsec pulse duration mono/poly-chromatic = single/multi color

9 MIT 2.71/2.710 Review Lecture p- 9 Monochromatic, spatially coherent light nice, regular sinusoid λ, ν well defined stabilized HeNe laser good approximation most other cw lasers rough approximation pulsed lasers & nonlaser sources need more complicated description Incoherent: random, irregular waveform

10 MIT 2.71/2.710 Review Lecture p- 10 The concept of a monochromatic ray t=0 (frozen) direction of energy propagation: light ray wavefronts In homogeneous media, light propagates in rectilinear paths

11 MIT 2.71/2.710 Review Lecture p- 11 The concept of a monochromatic ray t=Δt (advance d) direction of energy propagation: light ray wavefronts In homogeneous media, light propagates in rectilinear paths

12 MIT 2.71/2.710 Review Lecture p- 12 The concept of a polychromatic ray t=0 (frozen) wavefronts energy from pretty much all wavelengths propagates along the ray In homogeneous media, light propagates in rectilinear paths

13 MIT 2.71/2.710 Review Lecture p- 13 Fermat principle Γ is chosen to minimize this path integral, compared to alternative paths (aka minimum path principle) Consequences: law of reflection, law of refraction

14 MIT 2.71/2.710 Review Lecture p- 14 The law of reflection a) Consider virtual source P instead of P b) Alternative path POP is longer than POP c) Therefore, light follows the symmetric path POP. mirror

15 MIT 2.71/2.710 Review Lecture p- 15 The law of refraction reflected incident reflected Snells Law of Refraction

16 MIT 2.71/2.710 Review Lecture p- 16 Total Internal Reflection (TIR) becomes imaginary when refracted beam disappears, all energy is reflected

17 MIT 2.71/2.710 Review Lecture p- 17 Prisms air glass

18 MIT 2.71/2.710 Review Lecture p- 18 Dispersion Refractive index n is function of the wavelength white light (all visible wavelengths) Newtons prism airglass red green blue

19 MIT 2.71/2.710 Review Lecture p- 19 Frustrated Total Internal Reflection (FTIR) Reflected rays are missing where index-matched surfaces touch shadow is formed Angle of incidence exceeds critical angle glass other material air gap

20 MIT 2.71/2.710 Review Lecture p- 20 Fingerprint sensor air finger glass | air glass | finger TIR occurs TIR does not occurs (FTIR)

21 MIT 2.71/2.710 Review Lecture p- 21 Optical waveguide Planar version: integrated optics Cylindrically symmetric version: fiber optics Permit the creation of light chips and light cables, respectively, where light 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

22 MIT 2.71/2.710 Review Lecture p- 22 Refraction at a spherical surface point source

23 MIT 2.71/2.710 Review Lecture p- 23 Imaging a point source point source point source Lens

24 MIT 2.71/2.710 Review Lecture p- 24 Model for a thin lens point object at 1 st FP 1 st FP focal length f plane wave (or parallel ray bundle); image at infinity

25 MIT 2.71/2.710 Review Lecture p- 25 Model for a thin lens point image at 2 nd FP focal length f plane wave (or parallel ray bundle); object at infinity

26 MIT 2.71/2.710 Review Lecture p- 26 Types of lenses Figure 2.12 The location of the focal points and principal points for several shapes of converging and diverging elements. BICONVEX BICONCAVE PLANO CONVEX PLANO CONCAVE POSITIVE MENISCUS NEGATIVE MENISCUS positive (f > 0) negative (f < 0) from Modern Optical Engineering by W. Smith

27 MIT 2.71/2.710 Review Lecture p- 27 Huygens principle Each point on the wavefront acts as a secondary light source emitting a spherical wave The wavefront after a short propagation distance is the result of superimposing all these spherical wavelets optical wavefront s

28 MIT 2.71/2.710 Review Lecture p- 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 all object points become entangled, delocalizing object details. To relocalize object details, a method must be found to reassign (focus) all the 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 MIT 2.71/2.710 Review Lecture p- 29 Imaging condition: ray-tracing Image point is located at the common intersection of all rays which emanate from the corresponding object point The two rays passing through the two focal points and the chief ray can be ray-traced directly The real image is inverted and can be magnified or demagnified thin lens (+) 2 nd FP 1 nd FP image (real) object

30 MIT 2.71/2.710 Review Lecture p- 30 Imaging condition: ray-tracing thin lens (+) 2 nd FP 1 nd FP image object Lens Law Lateral Angular Energy magnification magnification conservation

31 MIT 2.71/2.710 Review Lecture p- 31 Imaging condition: ray-tracing thin lens (+) Image (virtual) 2 nd FP 1 st FP object The ray bundle emanating from the system is divergent; the virtual image 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, and demagnified

32 MIT 2.71/2.710 Review Lecture p- 32 Tilted object: the Scheimpflug condition LENS PLANE IMAGE PLANE OBJECT LANE OPTICAL AXIS The object plane and the image plane intersect at the plane of the thin lens.

33 MIT 2.71/2.710 Review Lecture p- 33 Lens-based imaging Human eye Photographic camera Magnifier Microscope Telescope

34 MIT 2.71/2.710 Review Lecture p- 34 The human eye Anatomy AQUEOUS CORNEA IRIS LENS LIGAMENTS MUSCLE SCLERA RETINA MACULA-FOVEA OPTIC NERVE BLIND SPOT Remote object (unaccommodated eye) Near object (accommodated eye)Near point (comfortable viewing) ~25cm from the cornea

35 MIT 2.71/2.710 Review Lecture p- 35 Eye defects and their correction from Fundamentals of Optics by F. Jenkins & H. White Hypermetropia, farsighted Myopia, nearsighted Farighted eye correctedNearsighted eye corrected FIGURE 10K Typical eye defects, largely present in the adult population. FIGURE 10L Typical eye defects can be corrected by spectacle lenses.

36 MIT 2.71/2.710 Review Lecture p- 36 The photographic camera meniscus lens or (nowadays) zoom lens Film or Object Axis Stop Bellows Focal plane digital imaging detector array (CCD or CMOS)

37 MIT 2.71/2.710 Review Lecture p- 37 The magnifier FIGURE 10I The angle subtended by (a) an object at the near point to the naked eye, (b) the virtual image of an object inside the focal point, © the virtual image of an object at the focal point. from Optics by M. Klein & T. Furtak

38 MIT 2.71/2.710 Review Lecture p- 38 The compound microscope from Optics by M. Klein & T. Furtak L: distance to near point (10in=254mm) Objective magnification Eyepiece magnification Combined magnification

39 MIT 2.71/2.710 Review Lecture p- 39 The telescope (afocal instrument – angular magnifier) Flg Astronomical telescope. Flg Galilean telescope (fashioned after the first telescope). from Optics by M. Klein & T. Furtak

40 MIT 2.71/2.710 Review Lecture p- 40 The pinhole camera The pinhole camera blocks all but one ray per object point from reaching the image space an image is formed (i.e., each point in image space corresponds to a 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. opaque screen image object pin- hole

41 MIT 2.71/2.710 Review Lecture p- 41 Field of View (FoV) FoV=angle that the chief ray from an object can subtend towards the imaging system

42 MIT 2.71/2.710 Review Lecture p- 42 Numerical Aperture medium of refr. index n θ: half-angle subtended by the imaging system from an axial object Numerical Aperture (NA) = n sinθ Speed (f/#)=1/2(NA) pronounced f-number, e.g. f/8 means (f/#)=8.

43 MIT 2.71/2.710 Review Lecture p- 43 Resolution How far can two distinct point objects be before their images cease to be distinguishable?

44 MIT 2.71/2.710 Review Lecture p- 44 Factors limiting resolution in an imaging system Diffraction Aberrations Noise Intricately related; assessment of image quality depends on the degree that the inverse problem is solvable (i.e. its condition) 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 MIT 2.71/2.710 Review Lecture p- 45 Point-Spread Function Point source (ideal) Light distribution near the Gaussian (geometric) focus (rotationally symmetric wrt optical axis) The finite extent of the PSF causes blur in the image

46 MIT 2.71/2.710 Review Lecture p- 46 Diffraction limited resolution light intensity (arbitrary units) lateral coordinate at image plane (arbitrary units) object spacin g δx Point objects just resolvable when Rayleigh resolution criterion

47 MIT 2.71/2.710 Review Lecture p- 47 Wave nature of light Polarization: polaroids, dichroics, liquid crystals,... Diffraction broadening of point images Inteference Michelson interferometer Fabry-Perot interferometerInterference filter (or dielectric mirror) diffraction grating

48 MIT 2.71/2.710 Review Lecture p- 48 Diffraction grating incident plane wave Grating spatial frequency: 1/Λ Angular separation between diffracted orders: Δθ 1/Λ straight-through order or DC term Condition for constructive interference: ( m integer) diffraction order

49 MIT 2.71/2.710 Review Lecture p- 49 polychromati c (white) light Anomalous (or negative) dispersion Glass prism: normal dispersion Grating dispersion

50 MIT 2.71/2.710 Review Lecture p- 50 Fresnel diffraction formulae

51 MIT 2.71/2.710 Review Lecture p- 51 Fresnel diffraction as a linear, shift-invariant system Thin transparency impulse response convolutio n transfer function multiplication Fourier transform Fourier transform (plane wave spectrum) g x, y t(x, y)

52 MIT 2.71/2.710 Review Lecture p- 52 The 4F system object plane Fourier plane Image plane

53 MIT 2.71/2.710 Review Lecture p- 53 The 4F system object plane Fourier plane Image plane

54 MIT 2.71/2.710 Review Lecture p- 54 The 4F system with FP aperture object plane Fourier plane: aperture-limited Image plane: blurred (i.e. low-pass filtered)

55 MIT 2.71/2.710 Review Lecture p- 55 The 4F system with FP aperture Transfer function: circular aperture Impulse response: Airy function

56 MIT 2.71/2.710 Review Lecture p- 56 Coherent vs incoherent imaging field in intensity in field out intensity out Coheren t optical system Incoherent optical system

57 MIT 2.71/2.710 Review Lecture p- 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 MIT 2.71/2.710 Review Lecture p- 58 Coherent vs incoherent imaging Coherent illumination Incoherent illumination

59 MIT 2.71/2.710 Review Lecture p- 59 Aberrations: geometrical Paraxial (Gaussian) image point Non-paraxial rays overfocus Spherical aberration Origin of aberrations: nonlinearity of Snells law (n sinθ=const., whereas linear relationship 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 MIT 2.71/2.710 Review Lecture p- 60 Aberrations: wave Aberration-free impulse response Aberrations introduce additional phase delay to the impulse response Effect of aberrations on the MTF unaberrated (diffraction limited) aberrated


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