1. Optics Overview

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. 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
relates the dual particle & wave
nature of light;
h=Planck’s constant
=6.6262⊥10-34 J sec
ν is the temporal oscillation
frequency of the light waves

4. Wave properties of light
λ: wavelength
(spatial period)
k=2π/λ
wavenumber
ν: temporal
frequency
ω=2πν
angular frequency
E: electric
field

5. 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)
“Dispersion relation”
(holds in vacuum only)

6. Light in matter Speed c/n Speed c=3×108 m/sec n : refractive index
light in vacuum
light in matter
Speed c/n
n : refractive index
(or index of refraction)
Absorption coefficient α
energy decay coefficient,
after distance L : e–2αL
Speed c=3×108 m/sec
Absorption coefficient 0
E.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)
absorption
refractive index

8. Overview of light sources
non-Laser
Thermal: polychromatic,
spatially incoherent
(e.g. light bulb)
Gas discharge: monochromatic,
(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,
(e.g. Q-switched, mode-locked)
~nsec
~psec to few fsec
pulse duration
mono/poly-chromatic = single/multi color

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. 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. The concept of a monochromatic
“ray”
t=Δt
(advanced)
direction of
energy propagation:
light ray
wavefronts
In homogeneous media,
light propagates in rectilinear paths

12. light propagates in rectilinear paths
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

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. 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

15. The law of refraction reflected reflected incident
Snell’s Law of Refraction

16. Total Internal Reflection (TIR)
becomes imaginary when
refracted beam disappears, all energy is reflected

17. Prisms
air
glass
air
air
air
glass
air
air

18. Dispersion Refractive index n is function of the wavelength
white light
(all visible
wavelengths)
red
air
glass
green
blue
Newton’s prism

19. Frustrated Total Internal Reflection
(FTIR)
other
glass
material
Reflected rays are missing
where index-matched surfaces
touch shadow is formed
Angle of incidence
exceeds critical angle
air 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, 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. Refraction at a spherical surface
point
source

23. Imaging a point source
point
source
point
source
Lens

24. plane wave (or parallel ray bundle);
Model for a thin lens
point object
at 1st FP
1st FP
focal length f
plane wave (or parallel ray bundle);
image at infinity

25. plane wave (or parallel ray bundle);
Model for a thin lens
point image
at 2nd FP
focal length f
plane wave (or parallel ray bundle);
object at infinity

26. Types of lenses positive (f > 0) negative (f < 0)
BICONVEX
BICONCAVE
PLANO CONVEX
PLANO CONCAVE
from Modern Optical
Engineering
by W. Smith
POSITIVE MENISCUS
NEGATIVE MENISCUS
Figure 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 source
emitting a spherical wave
The wavefront after a short
propagation distance is the
result of superimposing all
these spherical wavelets
optical
wavefronts

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. Imaging condition: ray-tracing
thin lens (+)
image
(real)
2nd FP
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
• The real image is inverted and can be magnified or demagnified

30. Imaging condition: ray-tracing
thin lens (+)
image
2nd FP
1nd FP
object
Lens Law Lateral Angular Energy
magnification magnification conservation

31. 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

32. the Scheimpflug condition
Tilted object:
the Scheimpflug condition
LENS PLANE
OBJECT LANE
IMAGE
PLANE
OPTICAL
AXIS
The object plane and the image plane
intersect 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)
CORNEA
AQUEOUS
IRIS
LENS
LIGAMENTS
MUSCLE
SCLERA
Remote object (unaccommodated eye)
RETINA
BLIND
SPOT
MACULA-FOVEA
OPTIC NERVE
Near point (comfortable viewing)
~25cm from the cornea
Near object (accommodated eye)

35. Eye defects and their correction
Hypermetropia, farsighted
Myopia, nearsighted
from Fundamentals
of Optics
by F. Jenkins & H.
White
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.

36. The photographic camera
Bellows
Focal
plane
Axis
Object
Stop
meniscus
lens
or (nowadays)
zoom lens
Film or
“digital imaging” detector array (CCD or CMOS)

37. 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.

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. The telescope (afocal instrument – angular magnifier) from Optics
Flg Astronomical telescope.
from Optics
by M. Klein &
T. Furtak
Flg Galilean telescope (fashioned after the first telescope).

40. The pinhole camera image object
opaque
screen
image
pin-
hole
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;
diffraction introduces undesirable artifacts in the image.

41. Field of View (FoV)
FoV=angle that the chief ray from an object can subtend
towards the imaging system

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

45. 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

46. Diffraction limited resolution
object
spacing δx
light intensity (arbitrary units)
lateral coordinate at image plane (arbitrary units)
Point objects “just
resolvable” when
Rayleigh resolution
criterion

47. Wave nature of light • Diffraction • Inteference
broadening of
point images
• Inteference
diffraction grating
Fabry-Perot interferometer
Interference filter
(or dielectric mirror)
Michelson interferometer
• Polarization: polaroids, dichroics, liquid crystals, ...

48. Diffraction grating incident plane Grating spatial frequency: 1/Λ wave
Angular separation between diffracted orders: Δθ ≈1/Λ
“straight-through” order or DC term
Condition for constructive interference:
( m integer)
diffraction order

49. Grating dispersion Anomalous (or negative) dispersion polychromatic
(white)
light
Glass prism:
normal dispersion

50. Fresnel diffraction formulae

51. Fresnel diffraction as a linear, shift-invariant system
Thin transparency
impulse response
convolution
transfer function
multiplication
Fourier
transform
(≡plane wave
spectrum)
g(x, y)
t(x, y)

52. The 4F system
object plane
Fourier plane
Image plane

53. The 4F system
object plane
Fourier plane
Image plane

54. The 4F system with FP aperture
object plane
Fourier plane: aperture-limited
Image plane: blurred
(i.e. low-pass filtered)

55. The 4F system with FP aperture
Transfer function:
circular aperture
Impulse response:
Airy function

56. Coherent vs incoherent imaging
field in
intensity in
field out
intensity out
Coherent
optical
system
Incoherent

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 illumination
Incoherent illumination

59. 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 (~ μm in the visible)

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