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光學元件、光電儀器的特性與應用
研究員/教授 李超煌
中央研究院應用科學研究中心
國立陽明大學生醫光電研究所
Optical Elements
spherical lens
polarizer or nonplarizing beam splitter
window
mirror
cylindrical lens
objective
prism
filter
wave plate
Optical Spectrum
eV  1.24 104 1 /  (cm-1)
eV 
1240
 (nm)
UV Category
• Terrestrial Solar UV: 290 – 380 nm.
• UV-A: 320 – 380 nm. Ozone is transparent. Cellular
damage by photochemical reactions.
• UV-B: 290 – 320 nm. Ozone is absorptive. DNA absorbs
and induces many bioeffects.
• UV-C: 190 – 290 nm. Air is transparent but ozone
absorbs so heavily that we do not see this range at earth
surface.
• Vacuum UV: < 190 nm. Ionizing N2 and O2.
• Extreme UV: < 50 nm.
• Soft x-ray: < 30 nm.
• X-ray: < 1 nm.
Ref: Lasers in Medicine, edited by R. W. Waynant (CRC Press, London,
2002), Chap. 4.
Substrate Materials
Mirror
Pyrex: excellent mirror substrate; low coefficient of thermal expansion
Zerodur: “zero” thermal expansion
Lens or window
UV fused silica: excellent
transmissive properties from
IR to UV
Calcium Fluoride (CaF2):
wider transmission bands
than fused silica
Glasses: BK7, SF14, etc:
different transmission,
dispersion....
Dispersion
Dispersion: n is a function of .
Sellmeier equation:
In catalogs of optical materials, the coefficients a, b, c ...
can be found for various transparent materials.
Optical Surfaces
Surface flatness: How flat the surface is.
RMS amplitude of surface ripples
When preservation of wavefront is critical, a /10 to
/20 surface should be selected.
Surface quality: How much the surface scatters.
In the scratch-dig specification, the first number is the
width of the largest scratch (in 0.1 mm), and the second is
the diameter of the largest bubble or pit (in 10 mm).
For demanding laser systems 20-10 to 10-5 scratch-dig is
appropriate. If some scatter is tolerable, 40-20 can be
used.
Coating
Reflective coatings
Metallic: broadband, insensitive to wavelength, angle of incidence, and
polarization. But lower damage threshold.
Dielectric: reflectivity can be specified from low (10%) to near total reflection.
Available either broadband or narrowband. Best for 0-45° angle of incidence.
High energy: resist optical damage of high power CW lasers and high energy
pulsed lasers. Wavelength must be specified.
Ultrafast mirror coating : to minimize dispersion effects on ultrashort laser
pulses.
Dichromatic coating: high transmission for wavelengths longer than a
specific value and high reflection for wavelengths shorter than that.
Coating
Anti-reflection coatings
V-coating
BBAR-coating
Damage Threshold
Fluence threshold: thermal effects. Energy fluence = pulse energy/beam area.
(Unit: J/cm2)
This is often noted on coatings for pulsed lasers. As a rule of thumb, the
fluence threshold increases as a function of the square root of the time
domain. For instance, if the damage threshold is 2 J/cm2 for 10 ns
pulses, at the 1 ms time domain the coating can withstand 20 J/cm2.
Intensity threshold: electric field breakdown. Intensity = (peak) power/beam area.
(Unit: MW/cm2)
This is important for both cw and pulsed lasers. The intensity threshold
scales with wavelength, so the intensity threshold at 532 nm will be half of
that at 1064 nm.
Beyond either threshold, laser light can damage the optics.
Unit of Light Intensity
1
n
2
I  E0 H 0 
E0
2
2Z 0
Z 0  m 0  0  377 
vacuum impedance
For E0 in V/m, the unit of intensity is then W/m2.
In optics, however, W/cm2 is used frequently.
Light intensity can also be used to calculate the photon
density r (m-3): I = chnr
c: speed of light (m/s)
hn: photon energy (J)
Cleaning of Optics
Drop and Drag
Brush
hemostats
methanol
or
acetone
lens tissue
Before first-time use or storage.
For installed optics.
Ref: Newport Resource 2006/2007, p. 688.
Selecting the Right Lens
f/# = focal length/beam diameter
On a lens, it means the lowest f/# this lens can achieve.
spherical aberration
chromatic aberration
focal spot diameter
d
4

 f /#
Selecting the Right Lens
Plano-convex lenses: Focusing parallel rays
of light to a point. Minimize spherical
aberration in situations where the object and
image are at unequal distances from the lens.
For optimum performance, the curved
surface should face the infinite conjugate.
Bi-convex lenses: Minimize spherical
aberration in situations where the object and
image are at equal or near equal distances
from the lens.
Aberrations
Images are from http://micro.magnet.fsu.edu/
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Astigma
Images are from http://micro.magnet.fsu.edu/
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Beam Collimation and Expansion
f1
f
d2
d1
q2/2
q1
f2
d2
d2/d1= f2/f1
d1
-f1
d1q1 = d2q2
d2 = q1f
When used with high pulse energy
lasers, use this configuration to
avoid the unnecessary focus.
f2
d1
d2
d2/d1= f2/-f1
Note: For minimum spherical aberration, the
curved surfaces should face the parallel rays.
Beam Shaping with Cylindrical Lenses
shorter focal length for wider
divergence angle
laser diode
To shape an elliptic beam into a circular beam or vice versa.
Birefringent Effect
O-wave
polarization
E-wave
polarization
(a) When the optical axis is unparallel to the crystal surface, the
incident extraordinary wave does not obey Snell’s law.
(b) In this condition, birefringence results in a double image. The
polarization of the two images are orthogonal.
Ref: R. Guenther, Modern Optics (John Wiley & Sons, New York, 1990), Chap. 13.
Polarization Optics: Waveplate
Waveplates are birefringent crystals, which have different refractive
indices for different polarizations.

0

nfast
Retardation

2π
0
0
nslow
 nslow  nfast  L
Polarization Optics: Waveplate
 = (2m+1): m-order half wave plate
The half-waveplate can be used to
rotate the polarization of linearly
polarized light.
Rotate the half-waveplate exactly q
around the beam axis (in either
direction) and we will have rotated
the polarization of the beam by 2q.
 = (2m+1/2): m-order quarter wave plate
Quarter-waveplates are used to turn
linearly-polarized light into circularlypolarized light, and vice versa. To do
this, we must orient the waveplate so
that equal amounts of fast and slow
waves are excited.
Polarization Optics: Polarizer
Broadband polarizer
At this port, Tp/Ts = 100 - 1000
Glan-laser polarizer
At this port, Tp/Ts > 105
multilayer
dielectric
coating
air gap
Tp/Ts is the extinction ratio, which is the most important specification
of a polarizer.
Spectral Filters
long wavelength pass filter
Color-glass (long pass) filters
band pass filter
interference filter
Attenuation (Neutral Density) Filters
Iin
Iin
Iout
Iout = Iin x 10-O.D.
Iout
Iout = Iin x 10-S(O.D.)
O.D.is optical density.
Grating
sin q '( n )  sin q 
angular dispersion
n
d
q 
n

 d  cosq 
Do not touch the face of gratings! Even lens-tissue is prohibited!
Acousto-optic (AO) Modulator
from Wikipedia
Acousto-optic (AO) Deflector
qd
The acousto-optic deflector makes use of the
acoustic frequency dependent diffraction angle,
where a change in the angle Dqd as a function of
the change in acoustic frequency Df given as
Dq d 

va
Df
: optical wavelength
va: velocity of acoustic wave
from Wikipedia
In addition, because sin q d 
m
d
, at a given qd one can tune the modulation
period d to obtain different . In this mode the device is an AO filter.
Electro-optic (EO) Modulator
An electro-optic modulator (EOM) is a device used for
controlling the power, phase or polarization of a laser beam
with an electrical control signal. The most common devices are
Pockels Cells.
longitudinal mode
transverse mode
Types of EO Modulation
Phase Modulators
The simplest type of electro-optic modulator is a phase modulator containing only a Pockels cell,
where an electric field (applied to the crystal via electrodes) changes the phase delay of a laser
beam sent through the crystal. The polarization of the input beam often has to be aligned with one
of the optical axes of the crystal, so that the polarization state is not changed.
Polarization Modulators
Depending on the type and orientation of the nonlinear crystal, and on the direction of the applied
electric field, the phase delay can depend on the polarization direction. A Pockels cell can thus be
seen as a voltage-controlled wave plate, and it can be used for modulating the polarization state.
Amplitude Modulators
Combined with polarizers, Pockels cells can be used for amplitude modulation. The following figure
is based on a Pockels cell for modifying the polarization state and a polarizer for subsequently
converting this into a change of transmitted optical amplitude and power.
Objective Lens
numerical aperture (NA)
tube length
magnification (M)
thickness of
cover glass
M = b/a
achromatic, planar focal plane
Objective Lens: Resolution and Focusing
Rayleigh criterion:
resolution ~ 0.61/NA
NA ~ 1/(2f/#)
clearly resolved
resolution limit
To focus a laser beam, the smallest spot radius ~ 0.82/NA.
A better estimation is
w0 
f
w
effective focal length
Light Source: Mercury-Arc Lamp
i-line (365 nm) g-line (436 nm)
Light Source: Lasers
Diode-Pumped Solid-State (DPSS) Lasers
Excimer Lasers
 XeCl: 308 nm
 KrF: 248 nm
 ArF: 193 nm
Typical Output:
• Pulse duration: 10 – 50 nsec
• Pulse energy: 0.2 – 1.0 J/pulse
• Repetition rate: several hundred Hz
Excimer Laser and Photolithography
Light Source: Light-Emitting Diode (LED)
LED chip
Epoxy dome lens
reflector cup
anode
cathode
Wavelengths of LEDs
Detection of Light
Semiconductor detectors: photodiode
Usually the photodiode is reversely biased.
Detection of Light
Photo-emission detectors: photocathode
Detection of Light
Photomultiplier Tube (PMT):
Detection of Light
CCD camera
Specifications of CCD or CMOS cameras
 Pixel size (8 mm; 23 mm)
 Pixel resolution (640 x 480; 1024 x 1024)
 Spectral response (300 nm to 1000 nm)
 Well depth (> 300,000 e-)
 Dark current (20 e-/pixel/s @ 20 oC)
 Dynamic range (> 85 dB)
 Digital or analog
 Bit depth or A/D levels (10 bit; 12 bit; 14 bit...)
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Bandwidth of Digital Data Interfaces
Interface
Bandwidth (Mbit/s)
IEEE-1394a
400
IEEE-1394b
786.4
USB 2.0
480
USB 3.0
4800
Camera Link
2380
GigE
1000
PCI Bus
1056
PCI-Express 2.0 16x
64000
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CCD vs. CMOS
CCD: larger dynamic range,
smaller dark current.
CMOS: higher response speed,
lower power consumption,
compactness.
Ref: D. Litwiller, “CCD vs. CMOS: Facts and Fiction,” Photonics Spectra, Jan. 2001.
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Noise in Optical Detection
Receiver
Noise
Also called
Physical source
Equation
Solid state
Johnson
Nyquist,
white,
thermal
Thermal motion of
charges in circuit
components
Vnoise = (4kTRB)1/2
k: Boltzmann’s constant
T: absolute temperature
R: resistance
B: bandwidth in Hz
4k = 5.53*10-23 V2/Hz/K-
Solid state
Shot
Dark current,
leakage current
Statistical fluctuation
in carriers at p-n
junction
Inoise = (2qIB)1/2
q: electron charge
I: average dc current
B: bandwidth in Hz
Photoemissive
Quantum
Photon
Statistical fluctuation
in arrival of signal
photons
Linear
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Interference
Linear superposition of two fields
E1  E01 exp ik1  r  t  1 
E2  E02 exp ik 2  r  t  2 
or
I  I1  I 2  2 I1I 2 cos D
where D  k1  r  k 2  r   1  2 
This term is optical path difference (OPD).
If light is from
the same source,
this term is zero.
Interference Fringe
(2m + 1)
Young’s Interferometer
, m = 0, 1, 2, 3.... for bright fringe
Michelson Interferometer
This interferometer is
widely used for
precision length
measurement.
I = I0[1+cos(4DL/)]
arm difference
OPD of /100 is easy
to determine.
Mach-Zehnder Interferometer
Mutual Coherence Function
Mutual coherence function:
where <•> denotes time average:
and t = OPD/c
1 T
f  lim  f t dt
0
T  T
Degree of Coherence
Complex degree of coherence:
g12(t) is a complex periodic function of t.
|g12(t)| = 1: complete coherence
|g12(t)| < 1: partial coherence
|g12(t)| = 0: complete incoherence
Coherence and Fringes
I  I1  I 2  2 I1I 2 cos D
can also be written as
I  I1  I 2  2 I1I 2 Reg 12 t 
When |g12(t)| = 0, there is no interference fringes at all.
Therefore we can use an interferometer to measure the
degree of coherence.
Coherence Time and Length
For a single light source, we
define coherence time t0:
g t   1  t t 0 for τ  τ 0
 0 for t  t 0
With a Michelson interferometer,
I  I 0 1  cos2πd  
If d > ct0, we see no fringes.
Coherence length: lc = ct0
Coherence Time and Spectral Width
D
A Michelson interferometer can
be used to determine the spectral
width:
c
1
lc  ct 0 
Dn 
Dn
t0
Since
Almost every light
source is band-limited.
So there is a spectral
width D.
Dn
n

D

2
lc 
D
Useful references:
1.
Technical Reference and Fundamental Applications of the
Optics Section of the Newport Resource.
2.
R. Guenther, Modern Optics (John Wiley & Sons, 1990).
3.
Dieter Meschede, Optics, Light and Lasers: The Practical
Approach to Modern Aspects of Photonics and Laser
Physics (Wiley-VCH, 2004).