3. Geometrical Optics

Geometric optics—process of light ray through lenses and mirrors to determine the location and size of the image from a given object .

Reflection and Mirror

angle reflection:

angleincident :

reflection of Law

r

i

ri

Image Formation by Reflection

Application of Double Reflection-Periscope

DIY Periscope

DIY Periscope (Cont’)

Law of reflection (Snell’s law)

2211 sinsin nn

Types of Lenses

Ray Tracing through Thin Lenses

Image Formation by thin Lenses

form) (Newtonian

form)(Gaussian 111

212

21

zzf

fdd

Lens equation:

1

2

1

2

d

d

h

hM

ionMagnificat

ABCD Matrix

ABCD Matrix (Cont’)

ABCD Matrix (Cont’)

ABCD Matrix (Cont’)

ABCD Matrix (Cont’)

ABCD Matrix (Cont’)

ABCD Matrix (Cont’)

Aberrations of Lenses• Primary Aberration image deviate from the original

picture/the first-order approximation

Monochromatic aberrations

Spherical Aberration

Coma

Astigmatism

Curvature of field

Distortion

Chromatic aberration

General Method of Reducing Aberration

in Optical Systems-Multiple Lenses

United States Patent 6844972

General Method of Reducing Aberration in Optical Systems-Multiple Lenses

(Cont’)

United States Patent 6995908

Chromatic Aberration

The focal lengths of lights with distinct wavelengths are different.

Solution of Chromatic Aberration-Using Doublet, Triplet, or Diffractive Lens

Spherical Aberration (SA)

Spherical Aberration for Different Lenses

(a)  Simple biconvex lens(b)  “Best-form” lens(c)  Two lenses(d)  Aspheric, almost plano-convex lens

Solutions of Spherical Aberration-Using Aspherical Lens or Stop

Coma

Coma (Cont’)

(a) Negative coma (b) Postive coma

Astigmatism

Astigmatism (Cont’)

Solutions of Astigmatism-Using Multiple Lenses

Curvature of field

Solutions of Curvature of field-Using Multiple Lenses

Distortion

Picture taken by a wide-angle camera in front of graph paper with square grids

Solution of Distortion-Using Multiple Lenses

Nearsightedness (Myopia) and Farsightedness (Hyperopia)

Image Formation Camera

Camera

aperture ofdiameter

length focalnumberF Eg. 50 mm camera lens, aperture stop 6.25mm:

F-number = 8 (f/8)

F-number

Exposure

2

2

2 f4

dB

f

BAE

E: energy collected by camera lens

B: brightness of objectA: area of aperture d: diameter of aperture stop

2number)-(F

1Eobject given any For

Camera Lenses

• Wide-angle Lenses-the Aviogon and the Zeiss Orthometer lenses

• Standard Lenses-the Tessar and the Biotar lenses

• Lens of reducing the 3rd-order aberration-the Cooke triplet lens

Depth of Field (DOF)• The distance between the nearest

and farthest objects in a scene that appear acceptably sharp in an image.

• In cinematography, a large DOF is called deep focus, and a small DOF is often called shallow focus.

• For a given F-number, increasing the magnification decreases the DOF; decreasing magnification increases DOF.

• For a given subject magnification, increasing the F-number increases the DOF; decreasing F-number decreases DOF.

Numerical Aperture (NA)

• The numerical aperture of an optical system is a dimensionless number that characterizes the range of angles over which the system can accept or emit light.

• Generally, • For a multi-mode optical

fiber,

Telescope

Astronomical (Keplerian) Telescope

Magnification (magnifying power):

'

M

: angle subtended at input end in front of objective’: angle subtended at output end behind eyepiece

(inverted image)

For small angle:

0'

e

o

f

fM

General Keplerian telescope: d=fo+fe

Galileo Telescope

0'

e

o

f

fM

General Galileo telescope: d=fo-fe

Terrestrial TelescopeAll images are erecting

Optical Microscope

Microscope Theory

Objective

eommM

Overall magnification:

mo: linear magnification of objectiveme: angular magnification of eyepiece

f

'x

y

'ymo Linear magnification:

Numerical aperture (NA)

objective)(for number-F

1

f

DNA

Microscope Theory (Cont’)

)cm25f (usually, f

251

f

25'me

Angular magnification:

(normal reading distance)

1) (if 25

ytan

1)' (if x

y

25

'y'tan'

eo

eo

f

25

f

'x

mmM

Overall magnification of microscope:

fo: focal length of objectivefe: focal length of eyepiece

Eyepiece

Simple Projection System

Fresnel Lens and Plates

focusing point (in phase)

• Radius of the concentric circular: rn = [(n)2+2fn] ½ , n=0, 1, 2,….

• Sapce between two adjacent circular

• zone: rn = rn+1rn