3. geometrical optics
DESCRIPTION
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. Image Formation by Reflection. Application of Double Reflection -Periscope. DIY Periscope. - PowerPoint PPT PresentationTRANSCRIPT
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