Human Eye • Human eye is a simple single lens system • Crystalline lens provide focus • Cornea: outer surface protection • Iris: control light • Retina: where image is focused • Note images are inverted

Human Eye Distance • Crystalline lens to retina distance 24.4 mm • Eye focuses object up to 25 cm from it • Called the near point or Dv = 25 cm • Eye muscles to change focal length of lens over 2.22<f<2.44 cm • Near sighted: retina to lens distance too long, focused in front • Infinity object focused in front of retina: out of focus at it • When bring objects closer focus moves to retina • Near sighted people can see objects with Dv < 25 cm • Far sighted: eye is too short, focuses behind retina, Dv > 25 cm

Magnification of Lens • Lateral change in distance equals change in image size • Measures change in apparent image size

ss

yyMm

′−=

′==

Magnification with Index Change • Many different ways of measuring magnification • With curved index of refraction surface measure apparent change in distance to image • Called Lateral Magnification

rsrsm

+−′

−=

• m is + if image virtual, - if real

Angular Magnification • For the eye look at angular magnification

θθ ′

== Mm

• Represents the change in apparent angular size

Simple Magnifying Glass • Human eye focuses near point or Dv = 25 cm • Magnification of object: ratio of angles at eye between unaided and lens • Angle of Object with lens

θθ ≈==25y

Dy)tan(

v

• For maximum magnification place object at lens f (in cm)

fy

=′θ

• Thus magnification is (where f in cm)

fm 25

=′

=θθ

• e.g. What is the magnification of a lens f = 1 inch = 2.5 cm

1052

2525===

′=

.fm

θθ

Power of a Lens or Surface • Power: measures the ability to create converging/diverging light by a lens • Measured in Diopters (D) or 1/m • For a simple curved surface

rnnP −′

=

• For a thin lens

fP 1=

• Converging lens have + D, diverging - D • eg f = 50 cm, D = +2 D f = -20 cm, D = -5 D • Recall that for multiple lens touching

L321

1111ffffe

++=

• Hence power in Diopters is additive

L21 DDD +=

Eyeglasses • Use Diopters in glasses • Farsighted, Hypermetopia: focus light behind retina Use convex lens, +D to correct • Nearsighted, Myopia: focus in front of retina use concave lens, -D to correct • Normal human eye power is ~58.6 D • Nearsighted glasses create a reverse Galilean telescope • Makes objects look smaller.

Classical Compound Microscope • Classical system has short fo objective lens object is near focal length when focused • Objective creates image at distance g from focal point • Objective working distance typically small (20-1 mm) • Eyepiece is simple magnifier of that image at g • Magnification of Objective

oo f

gm =

• where g = Optical tube length • Eyepiece magnification is

ee f

m 25=

• Net Microscope Magnification

eoeo ff

gmmM 25==

Classic Microscope • To change power change objective or eyepiece

Infinite Corrected Microscopes • Classical Compound Microscope has limited tube length • New microscope "Infinite Corrected" • Objective lens creates parallel image • Tube lens creates converging image • Magnification now not dependent on distance to tube lens: thus can make any distance • Good for putting optics in microscope • Laser beam focused at microscope focus

Telescope • Increases magnification by increasing angular size • Again eyepiece magnifies angle from objective lens • Simplest "Astronomical Telescope" or Kepler Telescope two convex lenses focused at the same point • Distance between lenses:

eo ffd +=

• Magnification is again

e

o

o

e

ffm ==

θθ

Different Types of Telescopes • Galilean: concave lens at focus of convex

eo ffd +=

• Eyepiece now negative fe • Most others mirror types

Telescopes as Beam Expanders • With lasers telescopes used as beam expanders qc� Parallel light in, parallel light out • Ratio of incoming beam width W1 to output beam W2

11

22 W

ffW =

Telescopes as Beam Expanders • Can be used either to expand or shrink beam • Kepler type focuses beam within telescope: • Advantages: can filter beam • Disadvantages: high power point in system • Galilean: no focus of beam in lens • Advantages: no high power focused beam more compact less corrections in lenses • Disadvantages: Diverging lens setup harder to arrange

Lens Aberrations: Spherical • Aberrations are failures to focus to a "point" • Some are failures of paraxial assumption

L!!

)sin(53

53 θθθθ +−=

• Formalism developed by Seidel • Light through edge of lens at different focus • Longitudinal Spherical Aberration along axis • Transverse Spherical Aberration across axis • Make Aspheric surfaces to compensate • Or can use combine two or more spherical surfaces

Astigmatism Aberration • Off axis rays are not focused at the same plane as the on axis rays • Called "skew rays" • Principal ray, from object through optical axis to focused object • Tangental rays (horizontal) focused closer • Sagittal rays (vertical) further away • Corrected using multiple surfaces

Coma Aberration • Comes from third order sin correction • Off axis distortion • Results in different magnifications at different points • Single point becomes a comet like flare • Coma increase with NA • Corrected with multiple surfaces

Field Curvature Aberration • All lenses focus better on curved surfaces • Called Field Curvature • positive lens, inward curves • negative lens, outward (convex) curves • Reduced by combining positive & neg lenses

Distortion Aberration • Distortion means image not at paraaxial points • Grid used as common means of projected image • Pincushion: pulled to corners • Barrel: Pulled to sides

Lens Shape • Coddingdon Shape Factor

12

12

rrrrq

−+

=

• Shows how aberrations change with shape

Index of Refraction & Wavelength: Chromatic Aberration • Different wavelengths have different index of refraction • Often list wavelength by spectral colour lines (letters) • Index change is what makes prism colour spread • Typical changes 1-2% over visible range • Generally higher index at shorter wavelengths

Chromatic Aberration • Chromatic Aberrations different wavelength focus to different points • Due to index of refraction change with wavelength • Hence focuses rays at different points • Generally blue closer (higher n) Red further away (lower index) • Important for multiline lasers • Achromatic lenses: combine different n materials whose index changes at different rates • Compensate each other

Lateral Colour Aberration • Blue rays refracted more typically than red • Blue image focused at different height than red image

Singlet vs Achromat Lens • Combining two lens significantly reduces distortion • Each lens has different glass index • positive crown glass • negative meniscus flint • Give chromatic correction as well

Combined lens: Unit Conjugation • Biconvex most distortion • Two planocovex significant improvement • Two Achromats, best

Materials for Lasers Lenses/Windows • Standard visible BK 7 • Boro Silicate glass, pyrex • For UV want quartz, Lithium Fluroide • For IR different Silicon, Germanium