mit 2.71/2.710 review lecture p- 1 optics overview
TRANSCRIPT
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1MIT 2.71/2.710Review Lecture p-
Optics Overview
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2MIT 2.71/2.710Review Lecture p-
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
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Particle properties of light
Photon=elementary light particle
Mass=0Speed c=3 10⊥ 8m/sec
According to According to Special Relativity, a mass-less particle travellingat light speed can still carry momentum!
Energy E=hν relates the dual particle & wavenature of light;
h=Planck’s constant=6.6262 10⊥ -34 J sec
ν is the temporal oscillationfrequency of the light waves
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4MIT 2.71/2.710Review Lecture p-
Wave properties of lightλ: wavelength
(spatial period)
k=2π/λwavenumber
ν: temporalfrequency
ω=2πνangular frequency
E: electricfield
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5MIT 2.71/2.710Review Lecture p-
Wave/particle duality for light
Photon=elementary light particle
Mass=0Speed c=3⊥108 m/sec
Energy E=hν
h=Planck’s constant=6.6262⊥10-34 J sec
ν=frequency (sec-
1)λ=wavelength (m)
“Dispersion relation”(holds in vacuum
only)
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6MIT 2.71/2.710Review Lecture p-
Light in matter
light in vacuum
Speed c=3108 m/sec
Absorption coefficient 0
Speed c/nn : refractive index(or index of refraction)
Absorption coefficient αenergy decay coefficient,after distance L : e–2αL
light in matter
E.g. vacuum n=1, air n ≈ 1;
glass n≈1.5; glass fiber has α ≈0.25dB/km=0.0288/km
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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
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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, spatiallyincoherent
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
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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
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The concept of a monochromatic
“ray”t=0(frozen)
direction ofenergy
propagation:light ray
wavefronts
In homogeneous media,light propagates in rectilinear paths
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The concept of a monochromatic
“ray”t=Δt(advanced)
direction ofenergy
propagation:light ray
wavefronts
In homogeneous media,light propagates in rectilinear paths
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The concept of a polychromatic “ray”
t=0(frozen)
wavefronts
energy frompretty much
all wavelengthspropagates along
the ray
In homogeneous media,light propagates in rectilinear paths
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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
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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
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The law of refractionreflected
incident
reflected
Snell’s Law of Refraction
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Total Internal Reflection (TIR)
becomes imaginary when
refracted beam disappears, all energy is reflected
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Prisms
air air
air air
air air
glass
glass
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DispersionRefractive index n is function of the wavelength
white light(all visiblewavelengt
hs)
Newton’s prism
air glass
red
green
blue
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Frustrated Total Internal Reflection
(FTIR)Reflected rays are missingwhere index-matched surfacestouch shadow is formed
Angle of incidenceexceeds critical angle
glass other
material
air gap
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Fingerprint sensor
airfinger
glass | air glass | finger
TIR occurs TIR does not occurs (FTIR)
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21MIT 2.71/2.710Review Lecture p-
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
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Refraction at a spherical surface
pointsource
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Imaging a point source
pointsource
pointsource
Lens
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Model for a thin lens
point object at 1st FP
1st FP
focal length fplane wave (or parallel ray bundle);
image at infinity
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Model for a thin lens
point image at 2nd FP
focal length fplane wave (or parallel ray bundle);
object at infinity
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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 OpticalEngineeringby W. Smith
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27MIT 2.71/2.710Review Lecture p-
Huygens principleEach point on the wavefrontacts as a secondary light sourceemitting a spherical wave
The wavefront after a shortpropagation distance is theresult of superimposing allthese spherical wavelets
opticalwavefronts
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Why imaging systems are needed• Each point in an object scatters the incident illumination into a sp
herical 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.
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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 (+)
2nd FP
1nd FP
image(real)
object
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Imaging condition: ray-tracing
thin lens (+)
2nd FP
1nd FP
image
object
Lens Law Lateral Angular Energy magnification magnification conservation
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Imaging condition: ray-tracingthin lens (+)
Image(virtu
al) 2nd FP
1st 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
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Tilted object:the Scheimpflug condition
LENS PLANE
IMAGE PLANE
OBJECT LANE
OPTICAL
AXIS
The object plane and the image planeintersect at the plane of the thin lens.
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Lens-based imaging
• Human eye
• Photographic camera
• Magnifier
• Microscope
• Telescope
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The human eyeAnatomy
AQUEOUSCORNEA
IRIS
LENS LIGAMENTS
MUSCLE
SCLERA
RETINA
MACULA-FOVEA
OPTIC NERVE
BLINDSPOT
Remote object (unaccommodated eye)
Near object (accommodated eye)Near point (comfortable viewing)
~25cm from the cornea
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Eye defects and their correction
from Fundamentalsof Opticsby F. Jenkins & H.White
Hypermetropia, farsighted Myopia, nearsighted
Farighted eye corrected Nearsighted eye corrected
FIGURE 10KTypical eye defects, largely present in the adult population.
FIGURE 10LTypical eye defects can be corrected by spectacle lenses.
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The photographic camera
meniscuslensor
(nowadays)zoom lens Film
or
Object
Axis
Stop
Bellows
Focalplane
“digital imaging” detector array (CCD or CMOS)
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The magnifier
FIGURE 10IThe 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 Opticsby M. Klein &T. Furtak
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The compound microscope
from Opticsby M. Klein &T. Furtak
L: distance to near point (10in=254mm)
Objective magnification
Eyepiece magnificationCombined magnification
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The telescope(afocal instrument – angular magnifier)
Flg. 3.40 Astronomical telescope.
Flg. 3.41 Galilean telescope (fashioned after the first telescope).
from Opticsby M. Klein &T. Furtak
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The pinhole camera
• 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.
opaquescreen image
object
pin-hole
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Field of View (FoV)
FoV=angle that the chief ray from an object can subtendtowards the imaging system
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Numerical Aperture
medium ofrefr. index n
θ: half-angle subtended bythe imaging system froman axial object
Numerical Aperture(NA) = n sinθ
Speed (f/#)=1/2(NA)pronounced f-number, e.g.f/8 means (f/#)=8.
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Resolution
How far can two distinct point objects bebefore their images cease to be distinguishable?
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Factors limiting resolution in an
imaging system• Diffraction• Aberrations• Noise
Intricately related; assessment of imagequality depends on the degree that the “inverse
problem” 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
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Point-Spread Function
Point source(ideal)
Light distribution
near the Gaussian
(geometric) focus
(rotationallysymmetric
wrt optical axis)
The finite extent of the PSF causes blur in the image
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46MIT 2.71/2.710Review Lecture p-
Diffraction limited resolution
light
inte
nsi
ty (
arb
itra
ry
un
its)
lateral coordinate at image plane (arbitrary units)
object
spacingδx
Point objects “justresolvable” when
Rayleigh resolutioncriterion
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Wave nature of light
• Polarization: polaroids, dichroics, liquid crystals, ...
• Diffraction
broadening ofpoint images
• Inteference
Michelson interferometer
Fabry-Perot interferometer Interference filter(or dielectric mirror)
diffraction grating
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Diffraction gratingincidentplanewave
Grating spatial frequency: 1/ΛAngular separation between diffracted orders: Δθ ≈1/Λ
“straight-through” order or DC term
Condition for constructive interference:
( m integer)
diffraction order
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polychromatic
(white)light
Anomalous(or negative)
dispersion
Glass prism:normal dispersion
Grating dispersion
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Fresnel diffraction formulae
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Fresnel diffractionas a linear, shift-invariant syst
emThin transparency
impulse responseconvoluti
on
transfer function
multiplication
Fouriertransfor
m
Fouriertransfor
m
(≡plane wave
spectrum)
gx, y
t(x, y)
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The 4F system
object planeFourier plane Image plane
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53MIT 2.71/2.710Review Lecture p-
The 4F system
object planeFourier plane Image plane
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The 4F system with FP aperture
object plane Fourier plane: aperture-limited
Image plane: blurred
(i.e. low-pass filtered)
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The 4F system with FP aperture
Transfer function:circular aperture
Impulse response:Airy function
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Coherent vs incoherent imaging
field in
intensity in
field out
intensity out
Coherent
opticalsystem
Incoherentopticalsystem
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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)
H~
H~
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58MIT 2.71/2.710Review Lecture p-
Coherent vs incoherent imaging
Coherent illumination Incoherent illumination
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Aberrations: geometrical
Paraxial(Gaussian)image point
Non-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 (~1.5-2.5μm in the visible)
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60MIT 2.71/2.710Review Lecture p-
Aberrations: waveAberration-free impulse response
Aberrations introduce additional phase delay to the impulse response
Effect of aberrationson the MTF
unaberrated(diffraction
limited)
aberrated