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
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3. Geometrical Optics
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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
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Image Formation by Reflection
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Application of Double Reflection-Periscope
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DIY Periscope
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DIY Periscope (Cont’)
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Law of reflection (Snell’s law)
2211 sinsin nn
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Types of Lenses
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Ray Tracing through Thin Lenses
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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
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ABCD Matrix
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ABCD Matrix (Cont’)
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ABCD Matrix (Cont’)
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ABCD Matrix (Cont’)
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ABCD Matrix (Cont’)
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ABCD Matrix (Cont’)
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ABCD Matrix (Cont’)
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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
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General Method of Reducing Aberration
in Optical Systems-Multiple Lenses
United States Patent 6844972
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General Method of Reducing Aberration in Optical Systems-Multiple Lenses
(Cont’)
United States Patent 6995908
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Chromatic Aberration
The focal lengths of lights with distinct wavelengths are different.
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Solution of Chromatic Aberration-Using Doublet, Triplet, or Diffractive Lens
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Spherical Aberration (SA)
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Spherical Aberration for Different Lenses
(a) Simple biconvex lens(b) “Best-form” lens(c) Two lenses(d) Aspheric, almost plano-convex lens
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Solutions of Spherical Aberration-Using Aspherical Lens or Stop
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Coma
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Coma (Cont’)
(a) Negative coma (b) Postive coma
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Astigmatism
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Astigmatism (Cont’)
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Solutions of Astigmatism-Using Multiple Lenses
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Curvature of field
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Solutions of Curvature of field-Using Multiple Lenses
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Distortion
Picture taken by a wide-angle camera in front of graph paper with square grids
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Solution of Distortion-Using Multiple Lenses
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Nearsightedness (Myopia) and Farsightedness (Hyperopia)
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Image Formation Camera
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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
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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
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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.
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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,
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Telescope
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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
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Galileo Telescope
0'
e
o
f
fM
General Galileo telescope: d=fo-fe
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Terrestrial TelescopeAll images are erecting
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Optical Microscope
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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
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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
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Simple Projection System
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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