Cardinal planes and matrix methods

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Cardinal planes and matrix methods
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Matrices in paraxial Optics
Translation (in homogeneous medium)
?
?0
y
yo
L
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Matrix methods in paraxial optics
Refraction at a spherical interface
?
y
?
?
?
f
n
n
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Matrix methods in paraxial optics
Refraction at a spherical interface
?
y
?
?
?
f
n
n
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Matrix methods in paraxial optics
Lens matrix
n
nL
n
For the complete system
Note order matrices do not, in general, commute.
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Matrix methods in paraxial optics
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Matrix properties
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Matrices General Properties
For system in air, nn1
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System matrix
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System matrix Special Cases
(a) D 0 ? ?f Cyo (independent of ?o)
?f
yo
Input plane is the first focal plane
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System matrix Special Cases
(b) A 0 ? yf B?o (independent of yo)
Output plane is the second focal plane
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System matrix Special Cases
(c) B 0 ? yf Ayo
yo
Input and output plane are conjugate A
magnification
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System matrix Special Cases
(d) C 0 ? ?f D?o (independent of yo)
Telescopic system parallel rays in parallel
rays out
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Examples Thin lens
Recall that for a thick lens
For a thin lens, d0
?
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Examples Thin lens
Recall that for a thick lens
For a thin lens, d0
?
In air, nn1
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Imaging with thin lens in air
?
?o
yo
y
Input plane
Output plane
s
s
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Imaging with thin lens in air
For thin lens A1 B0 D1 C-1/f
y Ayo B?o
For imaging, y must be independent of ?o
? B 0
B As B Css Ds 0 s 0 (-1/f)ss
s 0
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Examples Thick Lens
H
?
yo
y
f
n
nf
n
x
h
h - ( f - x )
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Cardinal points of a thick lens
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Cardinal points of a thick lens
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Cardinal points of a thick lens
Recall that for a thick lens
As we have found before
h can be recovered in a similar manner, along
with other cardinal points