GEOMETRICAL OPTICS

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GEOMETRICAL OPTICS
Lectures 4/6 Engineering Optics for Medical
Applications Albert Cerussi acerussi_at_uci.edu 824-8
838 Beckman Laser Institute
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Review
Basic refraction Snells Law Thin lens
equation optics conventions different types of
lenses multiple lens problems Collection
efficiency NA light collection
capacity F-number
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Aperture Stops and Focusing
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Example of Aperture Stop
?
evil stray ray (prolongs graduation)
aperture stop (pinhole)
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Aperture Stops

• The aperture stop (AS) determines the amount of
  light reaching the image
• Note the AS increases the f/
• AS needed to clean up optical signals such as
• in front of a detector, such as in confocal
  microscopy
• in front of an objective to reduce stray light

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Example Beam Expander
b
a
f1
f2

• example of usage He Ne laser beam diameter 1
  mm microscope objective few mm
• note that low divergence of laser means high
  coupling! (there are other considerations
  Gaussian Beam Optics, which is not covered
  here)

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Focusing Light in the Real World (1)
Things to consider when focusing 1
Light can not be focused through an aperture
smaller than a diffraction-limited spot
diffraction thru circular aperture (pg 461)
for a standard lens _at_ 630 nm, this is 3 ?m
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Focusing Light in the Real World (2)
?min
f

• In case we want to collimate
• limitation will always be at least ?min
• increasing f may be required to reduce spot
  size at the expense of loosing light

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Focusing Light in the Real World (3)
Things to consider when focusing 3

• Lens imperfections will only increase the spot
  size
• These imperfections are known as aberrations
• Nowadays, computers generate lens combinations
  and surfaces to minimize these defects.

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Aberrations
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Spherical Aberration
spot size due to spherical aberration
in our lamp to fiber examplespot 84 ?m
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Chromatic Aberration

• n varies with wavelength, causing color-sensitive
  image changes
• may be corrected using achromatic doublets
  (cancels abbs)

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Astigmatism

• image distortion due to lens asymmetry
• very common eye defect (see eye test on pg 211)

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FIBER OPTICS
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Outline
Types of optical fibers modes step index versus
GRIN How fibers work Fiber NA Dispersion in
fibers Picking that fiber
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An example
I need a fiber that will conduct NIR light. I
have to keep a tight pulse pattern. It must
couple into an LED. What do I do?
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What is an Optical Fiber?
An optical fiber is a waveguide for light
consists of core inner part where wave
propagates cladding outer part used to keep
wave in core buffer protective
coating jacket outer protective shield
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Types of fibers
nc
step-indexmultimode
nf
nc
nc
step-indexsinglemode
nf
nc
nc
GRIN
nf
nc
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Fibers carry modes of light

• a mode is
• a solution to the wave equation
• a given path/distribution of light (pg 196)

higher modes gives more light, which is not
always desirable
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Example of of Modes _at_ 850nm
Silica step-index fiber has nf 1.452, nc
1.442 (NA 0.205)
SELFOC graded index fiber with same NA
high modes implies classical optics
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How Fibers Work
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Step Index Fiber TIR
?
escapes core (freedom!)
escapes core (freedom!)
nt
cladding
ni
stuck in core(did not graduate)
core
?i
?i
?i
ciritcal angle(pg 121)
?i ? ?c for TIR
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Graded Index Fiber
nc
n varies quadratically
nf
nc
like a restoring force !
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Fiber Numerical Aperture
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NA of a Step Index Fiber
?
nc
nf
ni
90-?t
?t
?max
NA in air(pg 197)
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NA of a GRIN Fiber
Condition below assures a ray will have enough
fiber to bend back towards the center axis
NA in air
? is a parameter describing how n changes in the
GRIN fiber
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NA and of Modes
killed ray
propagated ray
largeNA
smallNA
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Exit ports for fibers
beam patterns can be spherical cylindrical
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Tissue Optical Properties
F. P. Bolin, L. E. Preuss, R. C. Taylor, and R.
J. Ference, "Refractive index of some mammalian
tissues using a fiber optic cladding method,"
Appl. Opt. 28, 2297-2303 (1989).
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• Effects of beveling
• right angle exit
• change illumination area

U. Utzinger, and R. R. Richards-Kortum, "Fiber
optic probes for biomedical optical
spectroscopy," J Biomed Opt 8, 121-147 (2003)
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Some Fiber Geometries
U. Utzinger, and R. R. Richards-Kortum, "Fiber
optic probes for biomedical optical
spectroscopy," J Biomed Opt 8, 121-147 (2003)
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Critical Bend radius
?
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Dispersion
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Dispersion The Basics
Light propagates at a finite speed
fastest ray
slowest ray
fastest ray one traveling down middle (axial
mode)
slowest ray one entering at highest angle (high
order mode)
will be a difference in time for these two rays
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Mode Dispersion
(pg 201)
modal dispersion increases with L NA2
usually the biggest dispersion problem in step
index multi-mode fibers
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Attenuation
page 297
IR absorption
Rayleigh Scattering
absorption and scattering in fiber in the IR
low-OH versus high-OH
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Types of Dispersion in Fibers
modal time delay from path length
differences usually the biggest culprit in
step-index material n(?) different times to
cross fiber (note smallest effect 1.3
?m) waveguide changes in field distribution
(important for SM) non-linear n can become
intensity-dependent
NOTE GRIN fibers tend to have less modal
dispersion because the ray paths are shorter
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Effect of Dispersion
initial pulse
farther down
farther still
time
time
time
modal example step index 24 ns km -1
GRIN 122 ps km-1
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Putting It All together
get a low OH fiber
(a) I needed a fiber that will conduct NIR
light. (b) I had to keep a tight pulse
pattern. (c) It must couple into an LED.
you want low dispersion SM or a GRIN fiber, low
diameter, low NA
The LED has a high divergence angle better get a
bright one. A laser might be better, and use a
GRIN lens to couple. These are design
considerations, as well as cost!
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Other Resources
Believe it or not, the best books are often
commercial catalogs Oriel (www.oriel.com) Mell
es Griot (www.mellesgriot.com) Ploymicro
Technologies Nanoptics, Inc (www.nanoptics.com)
www.fotec.com/fiberu-online/fuonline.htm Useful
Textbooks Optics, by Hecht Fundamentals of
Photonics, by Saleh Teich