GEOMETRICAL OPTICS

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GEOMETRICAL OPTICS
Lectures 1/8 1/10 Engineering Optics for
Medical Applications Albert Cerussi acerussi_at_uci.e
du 824-8838 Beckman Laser Institute
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Some Course Notes

• Lecture Notes will be provided on the web
• Office Hours will be
• Email for appointment acerussi_at_uci.edu

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Module Goal
Learn enough basic optics to communicate how
to couple light from point A to point B
?
optical fiber
couple laser into a fiber
laser
?
picture a fluorescing cell
camera
?
collect light from a tissue
PMT
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Items You Will Learn
(1) Lens basics conventions types of
lenses use of lens equations (2) Fiber
Optics working principles types of
fibers limitations (3) Key coupling
concepts f-number (f/) numerical aperture
(NA) aperture stops
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Book Notes
This may be the most boring part of the course,
but hang in there!

• In Hecht Read Chapter 5, especially sections
• 5.1, 5.2 (refraction at a surface,
  lenses) 5.3 (stops) 5.6 (fibers) 5.71-5.76
  (optical systems)
• other sections are important (such as 5.4 5.5)
  but we will not have time to discuss in class
• Skim through Chapter 6, but look at 6.3 and 6.4
• Review concepts from 4.1-4.7 you dont remember,
  particularly 4.3, 4.4.1, 4.7 Fresnel Equations

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Outline for Lenses
Snells Law and refraction Thin Lenses Lens
Conventions A True Optics Problem Collection
Efficiency (f/ and NA) Example leading to the
Aperture Stop Focusing Concerns
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Preliminary Refraction The Thin Lens
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A Simple Example
How can I couple light from a 1 mm filament
lamp into a 0.1 mm diameter optical fiber?
of course, we may use a lens but how do we
calculate?
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The Fundamental Law
Snells Law(pg 101)
?1

• ? taken wrt normal
• for n2 gt n1 ray bends towards normal

?2
n1
n2
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The Power of Snells Law
note these rays are NOT paraxial
h 0.7 mm
h 1 mm

• Snells Law can calculate the focal spot of the
  glass sphere.
• Glass spheres are used to couple light into and
  from optical fibers. Use Snells law and that
  is all!

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Paraxial Rays
We want to simplify the end results of light ray
physics We assume in the following equations that
light rays make small angles with the optic axis
15deg sin(.262 rad) ? 0259
10 deg sin(.175 rad) ? 0.174
5 deg sin(.873 rad) ? 0.872
1 deg sin(30.5 mrad) ? 30.5 E-3
optic axis
30 deg sin(.524 rad) ? .5
45 deg sin(.785 rad) ? .707
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Refraction at a Surface
?
for paraxial rays (i.e. small angle, lt 15 deg)
pg 154
R
n1
n2
so
si
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Thin Lenses
paraxial rays, in air
Thin Lens Equation(pg 159)
if the lens is thin, then
Gaussian Lens Formula(pg 159)
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Conventions Light Incident on Left
Before we can calculate the good stuff, we will
need to adopt some conventions concerning our new
found friends.
Conventions needed for (1) object distance
(so) (2) image distance (si) (3) radius
of curvature (R) (4) focal point ( f )
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Conventions
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(1) Object Conventions
principal rays
object is REAL when rays diverge from object so
gt 0
so
object is VIRTUAL when rays converge to
object so lt 0
usually only with lens combinations
so
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(2) Image Conventions
image is REAL when rays converge si gt 0
si
rays focus on the image
image is VIRTUAL when rays diverge si lt 0
si
rays project back to the image
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(3) R Conventions
R1
R1 gt 0 R2 lt 0
R2
R gt 0 when line lands on right R lt 0 when line
lands on left
R1
R1 lt 0 R2 gt 0
R2
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(4) f Conventions
?
lens is CONVERGING when rays converge f gt 0
f
f
lens is DIVERGING when rays diverge f lt 0
check rays from ?
f
f
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Common Lens Types
planar convex
bi-convex

• symmetric lenses cancel some aberrations

• focus or magnify light
• produce real or virtual images

f gt 0
f gt 0
bi-concave
planar concave

• increase f of systems
• symmetric lenses cancel some aberrations

• light expanders
• produce real or virtual images

f lt 0
f lt 0
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Lenses Mommy Never Mentioned
meniscus
cylindrical

• used when magnification needed in only one
  dimension (slits, etc)

• used to change f or light collection in system
• aplanatic wont introduce spherical abbs

f gt 0 or f lt 0
f gt 0 or f lt 0
graded index (GRIN)
ball

• collimate high-angle outputs (diode lasers,
  fibers)
• easy alignment, high coupling efficiencies

• easy to correct aberrations
• used in laser diode coupling

f gt 0
f gt 0
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Coupling Lamp to Fiber
?
Goal couple as much light as possible from this
lamp into the fiber
Solution f 10 mm, D 5 mm planar convex lens
(cheap)
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Collection Efficiency
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We Forgot Collection Efficiency
So, now we couple this system, and find out that
we havetoo little light striking the tissue
what went wrong?
D/2
?
so
power is gt 1/360 !
? 1o
notice that a collimated beam (I.e. laser) would
couple nicely
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The Numerical Aperture (NA)
CASE 1
CASE 2
CASE 3
2?
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Numerical Aperture
?

• describes light gathering capability for
• lenses
• microscope objectives (where n may not be 1)
• optical fibers

? NA ? ? photons gathered
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Collection Efficiency Revisited
Which lens collects more light?
D 5 mm
f 10 mm
D 10 mm
f 10 mm
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The F/
?
f/(pg 176)

• referred to as the f-number or speed
• measure of the collection efficiency of a system
• smaller f/ implies higher collected flux
• ? f or ?D decreases the flux area
• ? f or ? D increases the flux area

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