Optics Optics
www.optics.rochester.edu/classes/opt100/opt100page.html
Light is a Ray (Geometrical Optics) 1. Nature of light
2. Production and measurement of light 3. Geometrical optics
4. Matrix methods in paraxial optics 5. Aberration theory
6. Optical instrumentation
27. optical properties of materials
Light is a Wave (Physical Optics) 8. Wave equations
9. Superposition of waves 10. Interference of light 11. Optical interferometry 12. Coherence
13. Holography
14. Matrix treatment of polarization 15. Production of polarized light
Course outline Course outline
Light is a Wave (Physical Optics) 25. Fourier optics
16. Fraunhofer diffraction 17. The diffraction grating 18. Fresnel diffraction
19. Theory of multilayer films 20. Fresnel equations
* Evanescent waves 26. Nonlinear optics
Light is a Photon (Quantum Optics) 21. Laser basics
22. Characteristics of laser beams 23. Laser applications
24. Fiber optics
Radiometric and Photometric Definitions and Units
Radiometric and Photometric Radiometric and Photometric
Definitions and Units Definitions and Units
radiometry photometry
watt (W) W/m
2W/sr W/(sr
.m
2)
lumen (lm) lux (lx)
candela (cd) Cd/m
2Radiant flux : Irradiance : Radiant intensity : Radiance :
: Luminous flux : illuminance
: luminous intensity
: luminance
Photometric Units Photometric Units Photometric Units
555 nm Radiant flux
of 1 Watt at 555 nm the luminous flux is of 685 lm (lumen)
Radiant flux of 1 Watt at 610 nm
the luminous flux is of 342.5 lm (lumen)
Photometric unit
685 x V(λ) x radiometric unit =
610 nm
Luminous efficiency V(λ)
Plane of incidence Plane of incidence
i r
θ θ = : Law of reflection
i i t t
n θ = n θ : Law of refraction
in paraxial approx.
Image Formation Summary Table
Image Formation Summary Table
Matrix Method Matrix Method
⎟⎟ ⎠
⎜⎜ ⎞
⎝
⎟⎟ ⎛
⎠
⎜⎜ ⎞
⎝
= ⎛
⎟⎟ ⎠
⎜⎜ ⎞
⎝
⎛
1 1 2
2
α α
y D
C
B A
y
1 1
2
1 1
2
θ α
θ D Cy
B Ay
y
+
=
+
=
D=0 A=0
B=0 C=0
Aberrations Aberrations
Chromatic
Chromatic Monochromatic Monochromatic
Unclear Unclear
image image
Deformation Deformation of image
of image
Spherical Spherical Coma Coma
astigmatism astigmatism
Distortion Distortion Curvature Curvature
n ( n ( λ λ ) )
Third-order (Seidel) aberrations Third-order (Seidel) aberrations
Æ Paraxial approximation
Third-Order Aberration Theory Third-Order Aberration Theory
After some very complicated analysis the third-order aberration equation is obtained:
( )
0 40 43 1 31
2 2 2
2 22
2 2 2 20
3 3 11
cos cos
cos a Q C r
C h r C h r C h r C h r
θ θ
θ
= + ′ + ′ + ′ + ′
Spherical Aberration
Coma
Astigmatism
Curvature of Field
Distortion Q
O B
ρ ’ r
θ
Stops, pupils and windows in an optical system
Stops, pupils and windows in an optical system
AS AS FS FS E E x x P P E E x x W W E E n n W W
E E n n P P
α α ’ ’
α α
Camera: Brightness and f-number Camera: Brightness and f-number
Brightness of image is determined by the amount of light falling
Brightness of image is determined by the amount of light falling on the film. on the film.
Each point on the film subtends a solid angle Each point on the film subtends a solid angle
2 2 2
2
2
4 ' 4 f
D s
D r
d Ω = dA = π = π
D D ’ ’
s s ’ ’ ≈ ≈ f f D D
Irradiance at any point on Irradiance at any point on film is proportional to (D/f) film is proportional to (D/f)
22D A = f
Define f
Define f- -number, number,
2
1 I p A
This is a measure of the
This is a measure of the speed of the lens speed of the lens Small f# (big aperture)
Small f# (big aperture) I I large , t large , t short short Large f# (small aperture)
Large f# (small aperture) I I small, t small, t long long
Numerical Aperture Numerical Aperture
Measure of light gathering power Measure of light gathering power
Cover Glass Cover Glass
α α
ggα α
aaAir Air
Oil Oil
α α
gg’ ’ α α
oon n
ggN. A. = n sin N. A. = n sin α α
Lens Lens
O O
Microscopes Microscopes
In most microscopes, L = 16
In most microscopes, L = 16 - - 17 cm 17 cm
Telescopes Telescopes
Astronomical telescope
Appendix : From Maxwell Equations to Wave Equations Appendix : From Maxwell Equations to Wave Equations
Professor Vladimir M. Shalaev, Univ of Purdue
Dispersion
One-dimensional Wave Equation
v = 1 m/s, -z
v = 2 m/s, +x
Poynting vector Poynting vector
1
o
S E H Poynting Vector
S E B
μ
= × ≡
= × r r r r r r
For an isotropic media energy flows in the direction of propagat
For an isotropic media energy flows in the direction of propagation, so ion, so both the magnitude and direction of this flow is given by,
both the magnitude and direction of this flow is given by,
( ) t S E H
I
I r r
×
=
=
=
The corresponding intensity or irradiance is then,
The corresponding intensity or irradiance is then,
Phase velocity and Group velocity Phase velocity and Group velocity
phase velocity :
1 21 2
p p
p
v k k k k
ω ω ω + ω
= = ≈
+
1 2
1 2
g g
g
v d
k k k dk
ω ω ω − ω
= = ≈
group velocity : −
( )
( )
2 1
1 2 /
g
p
p p
p p p
p
v d
dk d dv
kv v k
dk dk
d c c dn k dn
v k v k v
dk n n dk n dk
v dn k
n d
ω
λ π λ
λ
=
⎛ ⎞
= = + ⎜ ⎟
⎝ ⎠
− ⎡ ⎤
⎛ ⎞ ⎛ ⎞⎛ ⎞ ⎛ ⎞
= + ⎜ ⎟⎝ ⎠= + ⎜⎝ ⎟⎜⎠⎝ ⎟⎠ = ⎢⎣ + ⎜⎝ ⎟⎠⎥⎦
⎡ ⎛ ⎞⎤
= ⎢⎣ + ⎜⎝ ⎟⎠⎥⎦ ← =
Two-Beam Interference Two-Beam Interference
The total irradiance is given by
There is a maximum in the interference pattern when
This is referred to as constructive interference.
There is a minimum in the interference pattern when
This is referred to as destructive interference
When
Visibility Visibility
Visibility = fringe contrast
{ 0 1 }
min max
min
max
≤ ≤
+
≡ − V
I I
I V I
When
Therefore, V = 1
Reflection and Interference in Thin Films Reflection and Interference in Thin Films
• 180 º Phase change of the reflected light by a media
with a larger n
• No Phase change of the reflected light by a media
with a smaller n
Interference
Young’s Double-Slit Experiment
The Michelson Interferometer The Michelson Interferometer
Beam splitter Light source
Bright fringe :
Dark fringe :
Laser
CCD mirror
PZT mirror Spatial filtering
& collimation
Beam splitter
2f 2f
Imaging lens
monitor
Test sample
