![Page 1: Lens Design Lecture #1 - University of Arizona...11 1 1 00 0 0 Y a X bY cZ d aX bY cZ d ' 22 2 2 00 0 0 Z a X bY cZ d aX bY cZ d ' 33 3 3 00 0 0 Collinear transformation Maxwell’s](https://reader035.vdocuments.us/reader035/viewer/2022081402/5f1252578a2c7b204e2441ca/html5/thumbnails/1.jpg)
Prof. Jose Sasian
Lens DesignLecture #1
College of Optical SciencesUniversity of Arizona
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Prof. Jose Sasian
What is imaging?Photo credit:Gary Mackender
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Prof. Jose Sasian
Imaging with rays: theories
X a X b Y c Z da X b Y c Z d
'
1 1 1 1
0 0 0 0
Y a X b Y c Z da X b Y c Z d
'
2 2 2 2
0 0 0 0
Z a X b Y c Z da X b Y c Z d
'
3 3 3 3
0 0 0 0
Collinear transformation
Maxwell’s Ideal:
1) Each point is imaged stigmatically2) The images of all points in an object plane lie on an image plane3) The ratio of image to heights to object heights is the same for all points.
![Page 4: Lens Design Lecture #1 - University of Arizona...11 1 1 00 0 0 Y a X bY cZ d aX bY cZ d ' 22 2 2 00 0 0 Z a X bY cZ d aX bY cZ d ' 33 3 3 00 0 0 Collinear transformation Maxwell’s](https://reader035.vdocuments.us/reader035/viewer/2022081402/5f1252578a2c7b204e2441ca/html5/thumbnails/4.jpg)
Prof. Jose Sasian
Central Projection 1D
X’
OBJECT LINE
IMAGE LINE
PROJECTION POINT
OBJECTPOINT
IMAGEPOINT
X
X a Xa X b
'
1
0 0
![Page 5: Lens Design Lecture #1 - University of Arizona...11 1 1 00 0 0 Y a X bY cZ d aX bY cZ d ' 22 2 2 00 0 0 Z a X bY cZ d aX bY cZ d ' 33 3 3 00 0 0 Collinear transformation Maxwell’s](https://reader035.vdocuments.us/reader035/viewer/2022081402/5f1252578a2c7b204e2441ca/html5/thumbnails/5.jpg)
Prof. Jose Sasian
Central Projection 2D
X X’
Y Y’OBJECT
LINEIMAGELINE
OBJECTPLANE
IMAGEPLANE
PROJECTIONPOINT
X a Xa X b Y c
'
1
0 0 0
Y a Ya X b Y c
'
2
0 0 0
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Prof. Jose Sasian
Central Projection 3D
X a X b Y c Z da X b Y c Z d
'
1 1 1 1
0 0 0 0
Y a X b Y c Z da X b Y c Z d
'
2 2 2 2
0 0 0 0
Z a X b Y c Z da X b Y c Z d
'
3 3 3 3
0 0 0 0
Point into points, lines into lines, and planes into planes.
![Page 7: Lens Design Lecture #1 - University of Arizona...11 1 1 00 0 0 Y a X bY cZ d aX bY cZ d ' 22 2 2 00 0 0 Z a X bY cZ d aX bY cZ d ' 33 3 3 00 0 0 Collinear transformation Maxwell’s](https://reader035.vdocuments.us/reader035/viewer/2022081402/5f1252578a2c7b204e2441ca/html5/thumbnails/7.jpg)
Prof. Jose Sasian
X a Xc Z d
'
1
0 0
Y a Yc Z d
'
1
0 0
Z c Z dc Z d
'
3 3
0 0
.
22 yx
Axial symmetry I22 ''' yx
‘ and Z’ must be only a function of and Z, leads to:
•Origins transform into the origins: d3=0•Origins located at the planes of unit magnification implies: a1 equal to d0
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Prof. Jose Sasian
Axial Symmetry II
X Xc Z
' 0 1
Y Yc Z
' 0 1
Z c Zc Z
'
3
0 1
mc Z
110
Z f cc
' ' 3
0
Z fc
1
0
![Page 9: Lens Design Lecture #1 - University of Arizona...11 1 1 00 0 0 Y a X bY cZ d aX bY cZ d ' 22 2 2 00 0 0 Z a X bY cZ d aX bY cZ d ' 33 3 3 00 0 0 Collinear transformation Maxwell’s](https://reader035.vdocuments.us/reader035/viewer/2022081402/5f1252578a2c7b204e2441ca/html5/thumbnails/9.jpg)
Prof. Jose Sasian
Gaussian equations
mZ f
11 \
Zf m 1 1
Zf
m'' 1 m Z
f 1 '
'
fZ
fZ
'' 1
.
![Page 10: Lens Design Lecture #1 - University of Arizona...11 1 1 00 0 0 Y a X bY cZ d aX bY cZ d ' 22 2 2 00 0 0 Z a X bY cZ d aX bY cZ d ' 33 3 3 00 0 0 Collinear transformation Maxwell’s](https://reader035.vdocuments.us/reader035/viewer/2022081402/5f1252578a2c7b204e2441ca/html5/thumbnails/10.jpg)
Prof. Jose Sasian
Newtonian Equations
Zf
= - 1m
Zf''
= - m
ZZ ff' '
![Page 11: Lens Design Lecture #1 - University of Arizona...11 1 1 00 0 0 Y a X bY cZ d aX bY cZ d ' 22 2 2 00 0 0 Z a X bY cZ d aX bY cZ d ' 33 3 3 00 0 0 Collinear transformation Maxwell’s](https://reader035.vdocuments.us/reader035/viewer/2022081402/5f1252578a2c7b204e2441ca/html5/thumbnails/11.jpg)
Prof. Jose Sasian
Scheimpflug condition(Plane symmetry)
P P’
theta
theta’
objectplane
imageplane
Scheimpflug construction
tan(’) – (Z’\Z) tan() = 0
X m XKY
' 1
Y m YKY
' 1
tan( ) tan( ')=
'K m
f f
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Prof. Jose Sasian
Civil War 1859
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Prof. Jose Sasian
And much more…•Gaussian equations•Newtonian equations•Anamorphic systems•Focal and afocal systems•Scheimpflug condition•Cardinal points•Keystone distortion•…and much more!
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Prof. Jose Sasian
Collinear transformation, camera obscura and lenses
Camera Obscura, Athanasius Kircher, 1646
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Prof. Jose Sasian
The secret in Vermeer’s paintings
Johannes Vermeer, XVII century
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Prof. Jose Sasian
Perspective of the painting
45tantan ffD
cmf 68
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Prof. Jose Sasian
However…
• Image parity issues• Needed a flat mirror or• To copy again the image
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Prof. Jose Sasian
Central projection
By Don Cowen
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Prof. Jose Sasian
Other “perspectives”
A plurality of new and excitingnew concepts in imaging
Classical Impressionism Cubism
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Prof. Jose Sasian
Imaging on the sphere
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Prof. Jose Sasian
IPADImaging
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Prof. Jose Sasian
Class summary
• Syllabus• Imaging• Collinear transformation• Art application
• Codev, OSLO, Zemax• Review of first-order optics