1. Introduction
Textbooks and References
• K. K. Sharma, “Optics: Principles and Applications,”
Academic Press.
• E. Hecht: “Optics,” Addison Wesley.
• L. Setian, “Applications in Electro-Optics,” Prentice
Hall.
• R. G. Hunsperger, “ Integrated Optics: Theory and
Technology,” Springer.
• F. T. S. Yu and X. Yang, “Introduction to Optical
Engineering,” Cambridge Univ. Press.
• E. Uiga, “Optoelectronics, “Prentice Hall.
• F. G. Smith and T. A. King, “Optics and Photonics: An
Introduction,” Prentice Hall.
• Wikipedia
Propagation of Light
Velocity of light
v
Reflection and refraction
1
c

 n
: permeability of medium
: permittivity of medium
c: velocity of light in a vacuum
n: refractive index of medium
Law of reflection: 1 = 
Law of refraction: n1sin 1 = n2sin 2
(Snell’s law)
Fermat’s Principle: the path taken
between two points by a ray of light is
the path that can be traversed in the
least time.
Snell’s Law proved by Fermat’s Principle
Mathematical Expression of Fermat’s Principle
Proof of the Reflection Law
Image Formation by Reflection
3D Imaging in Human Brain
3D Imaging by Parallax Barrier
Refraction
Refractive Index
• Velocity of light in medium with refractive index n:
v=c/n=fλ
where f, λ, and c are the frequency, the wavelength,
the vacuum velocity of light, respectively.
• Refractive index is not a constant. It depends on the
frequency (wavelength), the polarization of light
(direction of E-field), etc.
• Some materials are birefringence crystals (two
refractive indices, ne and no, for two orthogonal
polarizations).
Example of Birefringence Crystal-Calcite
Another Proof of Snell’s Law
Total Reflection
Left: top view of LED with no
water
Right: top view of LED under
water
Opaque and Transparent Materials
• Opaque nonmetal : Nonmetal objects that do not
allow any light to pass through.
• Opaque metal : Metals that do not allow any light
to pass through – Aluminum pan, chrome
faucet, …
• Transparent material : Objects allow much of the
light from light source to pass through – A glass
window, water, …
• Translucent material : Objects that allow some
light to pass through – A single sheet of paper,
orange juice, …
Bouguer-Lamber’s Law
• Bouguer-Lamber’s law :
T=I/I0=exp(-αl), where
T is the transmittance, I0
is the incident radiance,
I is the transmitted
radiance, α is the
absorption coefficient of
the material, and l is the
thickness (path length).
Colorimetry
• Colorimetry is the science and technology used to quantify
and describe physically the human color perception.
• Colorimetric equipment:
1. A tristimulus colorimeter measures the tristimulus values of a
color.
2. A spectroradiometer measures the absolute spectral radiance
(intensity) or irradiance of a light source.
3. A spectrophotometer measures the spectral reflectance,
transmittance, or relative irradiance of a color sample.
4. A spectrocolorimeter is a spectrophotometer that can calculate
tristimulus values.
5. A densitometer measures the degree of light passing through
or reflected by a subject.
6. A color temperature meter measures the color temperature of
an incident illuminant.
RGB Color Model and Color Addition
R-red G-green B-blue C-cyan
M-magenta Y-yellow W-white
• Red (R), green (G),
and blue (B) are
primary colors of light.
• The RGB color model
is an additive color
model.
• A computer monitor
mixes composition of
RGB to create color
pictures.
Inks/Paints/Pigments and
Complementary Colors
•
Pure inks/paints/pigments absorb
a single frequency or color of light.
The color of light absorbed by a
pigment is merely the
complementary color of that
pigment.
Two spectral reflectance curves. The objects reflect lights
with shorter wavelengths while absorbing those in others,
lending them blue appearances.
• Magenta ink/paints/pigments
absorb green light and green
paints/pigments absorb
magenta light (Green and
magenta are the
complementary colors to each
other).
• Cyan ink/paints/pigments
absorb red light and red
paints/pigments absorb cyan
light (Red and cyan are the
complementary colors to each
other).
• Yellow ink/paints/pigments
absorb blue light and blue
paints/pigments absorb yellow
light (Blue and yellow are the
complementary colors to each
other).
CMY/CMYK Color Model and
Color Subtraction
• Cyan (C), magenta (M),
yellow (Y), and key (K,
black) are used in mixing
paints or color printing.
• The CMY/CMYK color
model is a subtractive
color model.
• Eg1. C+M=(W-R)+(WG)=W-R-G=(R+G+B)-RG=B
• Eg2. Y+C=(W-B)+(WR)=W-B-R=(R+G+B)-BR=G
Are they color addition or
subtraction?
Questions about Color Addition/Subtraction
•
•
•
•
•
•
•
•
•
White paper does not absorb any colors.
R+G+B-nothing=R+G+B=white, so the
paper appears white.
White paper does not absorb any colors.
R+G-nothing = R+G = Y, so the paper
appears yellow.
White paper does not absorb any colors.
G+B-nothing=G+B=C, so the paper appears
cyan.
Red paper absorbs cyan light; R+G+B–
(G+B) =R, so the paper appears red.
Red paper absorbs cyan light; G is absorbed
(B would be absorbed if it were present).
R+G-G =R, so the paper appears red.
Red paper absorbs cyan light. B+G–(B+G)=
nothing, so the paper appears black.
Yellow paper absorbs blue; R+G+B-B=R+G
= Y., so the paper appears yellow.
Yellow paper absorbs blue light, but there is
no B in the incident light. Thus nothing gets
absorbed. R+G-nothing=R+G=Y, so the
paper appears yellow.
Yellow paper absorbs blue. G+B-B=G, so
the paper appears green.
3D Imaging by Colors
Brightness and Lightness
Decreasing brightness with depth (underwater photo as example
• Brightness:
Perceptional
luminance of a visual
target.
• Lightness:
The Munsell color model of lightness: a color with a low value is nearly black.
Colorfulness, Chroma, and Saturation
• Colorfulness: The degree of
difference between a color and
gray.
• Chroma:
• Saturation:
Contrast
• The contrast is the ratio
of white brightness and
black brightness. If we
make the white parts
become brighter and the
black parts become
darker, the image looks
sharper. A good LCD TV
requires 800:1 at least.
Metamerism (異譜同色)
• Two light sources made up of different mixtures
of various wavelengths but appear to be the
same color; this effect is called metamerism.
• The concept of color can be divided into two
parts: brightness and chromaticity. For example,
white is a bright color but grey is considered to
be a less bright version of that same white. In
other words, the chromaticity of white and grey
are the same while their brightness differs.
Hue(色相) Encodings of RGB
• A visual sensation
similar to one of the
primary colors, or a
combination of two of
them.
• In painting color
theory, a hue refers to
a pure color—one
without tint or shade
(added white or black
pigment, respectively).
HSL/HSV Color Spaces
Image with Hues Cyclically Shifted
in HSL Space
Human Vision
Color sensitivity
C.I.E. Standard observer
Human eye
Human Eye-Similar to a Camera
Cornea and lens: the two lens system.
Iris: like diaphragms (快門,光圈) or stop in a camera.
Pupil: camera aperture.
Retina: at the back of eyeball, like the film
Sensitivity of Human Eye to Distinct Wavelength
S, M, and L Cells in Human Eye
•
Rod cells are sensitive to
brightness/luminance,
saturated at daytime, for
peripheral and night vision
(scotopic vision), combined
maximum sensitivity peak 550 nm.
– Mostly distributed away from fovea.
• Cone cells have 3 types :
– S (short wavelength): blue sensitive
(peak at 445 nm)
– M (medium wavelength): yellow or
green sensitive (peak at 535nm)
– L (long wavelength): red sensitive
(peak at 575nm)
– Mostly distributed at the fovea.
• S: M: L cell count ratio = 1: 20: 40
⇒ human’s eyes are much more
sensitive to red than blue.
Spectral Responsibilities of the L,
M, S Cones and Rods
Color Stimulus
Spectral Power Distribution of
Human Color Vision
RGB Tristimulus Values
Given these scaled color
matching functions, the RGB
tristimulus values for a color
with a spectral power
distribution would then be
given by
CIE 1931 Chromaticity Diagram
• The CIE 1931 xy chromaticity
space, which shows the
chromaticities of black-body
light sources of various
temperatures, and lines of
constant correlated color
temperature
• X is roughly red, which is a
linear combination of cone
response curves chosen to be
nonnegative.
• Y means luminance.
• Z is quasi-equal to blue
stimulation (or the S cone
response).
CIE (Commission Internationale de
l'Eclairage) — the International Commission
on Illumination
Color Temperature
• The color temperature of
a light source is the
temperature of an ideal
black body radiator that
radiates light of
comparable hue to that of
the light source.
• Higher color
temperatures over 5000
K are called cool colors
(blueish white), but the
lower color temperatures
(2,700–3,000 K) are
called warm colors
(yellowish white through
red).
CIE Standard Illuminants
• A: A tungsten light source with correlated color
temperature of about 2,856 K producing a yellowish-red
light.
• C: A tungsten light source coupled with a liquid filter to
simulate indirect sunlight with a correlated color
temperature of 6,774 K. (Obsolete)
• D (Daylight illuminants): Standard illuminant D65 is
nearly identical to standard illuminant C except that it is a
better simulation of indirect sunlight as it includes an
ultraviolet component for better evaluation of fluorescent
colors. D50 and D75 correspond to color temperatures of
5,000 K and 7,500 K, respectively.
CIE Standard Illuminants (Cont’)
• B: An illuminant having relative spectral power
distribution near to that of a direct sunlight with a
correlated color temperature of 4874 K.
(Obsolete)
• E: The equal-energy illuminant is of
mathematical utility. It is defined with a relative
spectral power of 100.0 at all wavelengths.
• F: Various types of fluorescent lamps including
cool-white fluorescent F2 (CCT of 4,230 K,
Obsolete), daylight fluorescent F7 (CCT of 6,500
K → D65), F8 (CCT of 5,000 K→ D50), and
triband fluorescent F11 (CCT of 4,000 K).
Dispersion by Prism
The refractive index n is the function of wavelength (frequency);
therefore, the light rays with distinct wavelengths have different
refractive angles and velocities.
Dispersion
Rainbow
The primary rainbow is easy to observe. It results from a single internal reflection and two refraction of the
light ray in water drops. The index of refraction of water depends on the wavelength. Under good conditions,
a secondary rainbow can also be observed. In this case, two internal reflections of light within the water
drops occur. The intensity of the secondary rainbow is much lower than for the primary or main rainbow.
Diffractions by Apertures/Sharp Edges
Diffraction — light path deviates from an initial propagation
Diffraction (Cont’)
Diffractions by Gratings
Grating: Periodical structure in optical component/device/equipment/system
Diffractions by Gratings (Cont’)
Reflection/Scattering by Grating
•
•
•
•
Consider a light ray traveling to the
right in the corrugated waveguide
(grating). The period of the grating
structure is Λ. The ray scattered by
the teeth fulfill sinθ=(mλ/Λng)-1,
where m is an integer.
Special case 1: Ray scattered in the
forward direction if m=0
Special case 2: Ray scattered in the
direction normal to the surface if m=1
and Λ=λ/ng
Special case 3: Ray scattered in the
backward direction if m=2 and
Λ=λ/ng. It is an optical reflection by
the grating.
3D Imaging by Lenticular Lens (Grating)
Scattering by Multiple Particles/Rough Surfaces
Light incident on rough surface