Transcript What is light?

Optics Overview
MIT 2.71/2.710
Review Lecture p- 1
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=0
Speed c=3⊥108m/sec
According to According to Special Relativity, a mass-less particle travelling
at light speed can still carry momentum!
Energy E=hν
h=Planck’s constant
=6.6262⊥10-34 J sec
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relates the dual particle & wave
nature of light;
ν is the temporal oscillation
frequency of the light waves
Wave properties of
light
λ: wavelength
(spatial period)
k=2π/λ
wavenumber
ν: temporal
frequency
ω=2πν
angular
frequency
E: electric
field
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Wave/particle duality for light
Photon=elementary light particle
Mass=0
Speed 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)
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“Dispersion relation”
(holds in vacuum only)
Light in matter
light in vacuum
light in matter
Speed c=3×108 m/sec
Speed c/n
n : refractive index
(or index of refraction)
Absorption coefficient
0
Absorption coefficient α
energy decay coefficient,
after distance L : e–2αL
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, 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, modelocked)
~nsec
pulse duration
mono/poly-chromatic = single/multi color
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Review Lecture p- 8
~psec to few fsec
Monochromatic, spatially
coherent
• nice, regular sinusoid
light
• 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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Review Lecture p- 9
The concept of a
monochromatic
t=0
“ray”
(frozen)
direction of
energy
propagation:
light ray
wavefronts
In homogeneous media,
light propagates in rectilinear paths
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The concept of a
monochromatic
t=Δt
“ray”
(advance
d)
direction of
energy
propagation:
light ray
wavefronts
In homogeneous media,
light propagates in rectilinear paths
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Review Lecture p-11
The concept of a polychromatic
“ray”
t=0
(frozen)
energy from
pretty much
all wavelengths
propagates along
the ray
wavefronts
In homogeneous media,
light propagates in rectilinear paths
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Review Lecture p-12
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’ is
longer than P”OP’
c) Therefore, light follows
the
symmetric path POP’.
mirror
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Review Lecture p-14
The law of refraction
reflected
reflected
incident
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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Review Lecture p-16
Prisms
air
glass
air
air
air
glass
air
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air
Dispersion
Refractive index n is function of the wavelength
white light
(all visible
wavelengths)
red
air
glass
green
blue
Newton’s prism
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Frustrated Total Internal
Reflection
(FTIR) glass other
Reflected rays are missing
where index-matched
surfaces
touch
shadow is
formed
Angle of incidence
exceeds critical
angle
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Review Lecture p-19
material
air gap
Fingerprint sensor
finger
air
glass | air
TIR occurs
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Review Lecture p-20
glass | finger
TIR does not occurs
(FTIR)
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)
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and
Review Lecture
p-21sensing (e.g. pressure) systems
Refraction at a spherical surface
point
source
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Imaging a point source
point
source
point
source
Lens
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Review Lecture p-23
Model for a thin lens
point object
at 1st FP
1st FP
focal length f
plane wave (or parallel ray bundle);
image at infinity
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Model for a thin lens
point image
at 2nd FP
focal length f
plane wave (or parallel ray bundle);
object at infinity
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Types of lenses
positive
(f > 0)
BICONVEX
PLANO CONVEX
POSITIVE MENISCUS
BICONCAVE
PLANO CONCAVE
NEGATIVE MENISCUS
Figure 2.12 The location of the focal points and principal
points for several shapes of converging and diverging
elements.
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Review Lecture p-26
negative
(f < 0)
from Modern
Optical
Engineering
by W. Smith
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
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Review Lecture p-27
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.
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Imaging condition: ray-tracing
thin lens (+)
2nd FP
image
(real)
1nd FP
object
• 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
MIT 2.71/2.710 • The
Review Lecture p-29
real image is inverted and can be magnified or
demagnified
Imaging condition: ray-tracing
thin lens (+)
image
2nd FP
1nd FP
object
Lens Law
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Review Lecture p-30
Lateral
magnification
Angular
magnification
Energy
conservation
Imaging condition: ray-tracing
thin lens (+)
Image
(virtual)
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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Review Lecture p-31
Tilted object:
the Scheimpflug condition
OBJECT LANE
LENS PLANE
IMAGE
PLANE
OPTICAL
AXIS
The object plane and the image plane
intersect at the plane of the thin lens.
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Review Lecture p-32
Lens-based imaging
• Human eye
• Photographic camera
• Magnifier
• Microscope
• Telescope
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The human eye
Anatomy
CORNEA
AQUEOUS
LENS
IRIS
LIGAMENTS
MUSCLE
SCLERA
Remote object (unaccommodated eye)
RETINA
BLIND
SPOT
MACULA-FOVEA
OPTIC NERVE
Near point (comfortable
viewing)
~25cm from the cornea
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Review Lecture p-34
Near object (accommodated eye)
Eye defects and their correction
Hypermetropia, farsighted
Myopia, nearsighted
FIGURE 10K
Typical eye defects, largely present in the adult population.
Farighted eye corrected
Nearsighted eye corrected
FIGURE 10L
Typical eye defects can be corrected by spectacle lenses.
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Review Lecture p-35
from Fundamentals
of Optics
by F. Jenkins & H.
White
The photographic camera
Bellows
Focal
plane
Axis
Object
Stop
meniscus
lens
or
(nowadays)
zoom lens
“digital imaging”
CMOS)
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Review Lecture p-36
Film
or
detector array (CCD or
The magnifier
from Optics
by M. Klein &
T. Furtak
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.
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Review Lecture p-37
The compound microscope
from Optics
by M. Klein &
T. Furtak
L: distance to near point (10in=254mm)
Objective magnification
Combined magnification
Eyepiece magnification
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Review Lecture p-38
The telescope
(afocal instrument – angular magnifier)
Flg. 3.40 Astronomical telescope.
from Optics
by M. Klein &
T. Furtak
Flg. 3.41 Galilean telescope (fashioned after the first telescope).
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Review Lecture p-39
The pinhole camera
opaque
screen
image
pinhole
object
• 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;
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diffraction
Review
Lecture p-40 introduces undesirable artifacts in the image.
Field of View (FoV)
FoV=angle that the chief ray from an object can subtend
towards the imaging system
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Review Lecture p-41
Numerical Aperture
medium of
refr. index n
θ: half-angle subtended by
the imaging system from
an axial object
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Review Lecture p-42
Numerical Aperture
(NA) = n sinθ
Speed (f/#)=1/2(NA)
pronounced f-number, e.g.
f/8 means (f/#)=8.
Resolution
How far can two distinct point objects be
before their images cease to be distinguishable?
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Review Lecture p-43
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)
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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Review Lecture p-44
Point-Spread Function
Light distribution
near the Gaussian
(geometric) focus
(rotationally
symmetric
wrt optical axis)
Point source
(ideal)
The finite extent of the PSF causes blur in the image
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light intensity (arbitrary units)
Diffraction limited resolution
object
spacin
g
δx
lateral coordinate at image plane (arbitrary units)
Point objects “just
resolvable” when
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Review Lecture p-46
Rayleigh resolution
criterion
Wave nature of light
• Diffraction
broadening of
point images
•
Inteference
diffraction grating
Fabry-Perot interferometer
Michelson interferometer
Interference filter
(or dielectric mirror)
• Polarization: polaroids, dichroics, liquid
crystals, ...
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Review Lecture p-47
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)
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Review Lecture p-48
diffraction order
Grating dispersion
Anomalous
(or negative)
dispersion
polychromati
c
(white)
light
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Review Lecture p-49
Glass prism:
normal
dispersion
Fresnel diffraction formulae
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Review Lecture p-50
Fresnel diffraction
as a linear, shift-invariant
system
Thin transparency
t(x, y)
g(x, y)
impulse
response
convolutio
n
Fourier
transform
(≡plane
wave
spectrum)
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Review Lecture p-51
transfer function
multiplication
Fourier
transform
The 4F system
object plane
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Review Lecture p-52
Fourier plane
Image plane
The 4F system
object plane
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Review Lecture p-53
Fourier plane
Image plane
The 4F system with FP
aperture
object plane
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Review Lecture p-54
Fourier plane: aperture-limited
Image plane: blurred
(i.e. low-pass filtered)
The 4F system with FP
aperture
Transfer function:
circular aperture
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Review Lecture p-55
Impulse response:
Airy function
Coherent vs incoherent
imaging
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Review Lecture p-56
field in
Coheren
t
optical
system
field out
intensity in
Incoherent
optical
system
intensity out
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)
~
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Review Lecture p-57
| H (u,v)|: Modulation Transfer Function (MTF)
~
H (u, v): Optical Transfer Function (OTF)
Coherent vs incoherent
imaging
Coherent illumination
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Review Lecture p-58
Incoherent illumination
Aberrations: geometrical
Paraxial
(Gaussian)
image point
Non-paraxial rays
“overfocus”
Spherical aberration
• Origin of aberrations: nonlinearity of Snell’s 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 (~1.5-2.5μm in the visible)
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Review Lecture p-59
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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Review Lecture p-60