introduction to aberrations lecture #1...introduction to aberrations lecture #1 college of optical...
TRANSCRIPT
![Page 1: Introduction to aberrations Lecture #1...Introduction to aberrations Lecture #1 College of Optical Sciences University of Arizona. ... IPAD Imaging. Prof. Jose Sasian Class summary](https://reader033.vdocuments.net/reader033/viewer/2022042521/5f77651db846b70f976ac8df/html5/thumbnails/1.jpg)
Prof. Jose Sasian
Introduction to aberrationsLecture #1
College of Optical SciencesUniversity of Arizona
![Page 2: Introduction to aberrations Lecture #1...Introduction to aberrations Lecture #1 College of Optical Sciences University of Arizona. ... IPAD Imaging. Prof. Jose Sasian Class summary](https://reader033.vdocuments.net/reader033/viewer/2022042521/5f77651db846b70f976ac8df/html5/thumbnails/2.jpg)
Prof. Jose Sasian
What is imaging?Photo credit:Gary Mackender
![Page 3: Introduction to aberrations Lecture #1...Introduction to aberrations Lecture #1 College of Optical Sciences University of Arizona. ... IPAD Imaging. Prof. Jose Sasian Class summary](https://reader033.vdocuments.net/reader033/viewer/2022042521/5f77651db846b70f976ac8df/html5/thumbnails/3.jpg)
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: Introduction to aberrations Lecture #1...Introduction to aberrations Lecture #1 College of Optical Sciences University of Arizona. ... IPAD Imaging. Prof. Jose Sasian Class summary](https://reader033.vdocuments.net/reader033/viewer/2022042521/5f77651db846b70f976ac8df/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: Introduction to aberrations Lecture #1...Introduction to aberrations Lecture #1 College of Optical Sciences University of Arizona. ... IPAD Imaging. Prof. Jose Sasian Class summary](https://reader033.vdocuments.net/reader033/viewer/2022042521/5f77651db846b70f976ac8df/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
![Page 6: Introduction to aberrations Lecture #1...Introduction to aberrations Lecture #1 College of Optical Sciences University of Arizona. ... IPAD Imaging. Prof. Jose Sasian Class summary](https://reader033.vdocuments.net/reader033/viewer/2022042521/5f77651db846b70f976ac8df/html5/thumbnails/6.jpg)
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: Introduction to aberrations Lecture #1...Introduction to aberrations Lecture #1 College of Optical Sciences University of Arizona. ... IPAD Imaging. Prof. Jose Sasian Class summary](https://reader033.vdocuments.net/reader033/viewer/2022042521/5f77651db846b70f976ac8df/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
![Page 8: Introduction to aberrations Lecture #1...Introduction to aberrations Lecture #1 College of Optical Sciences University of Arizona. ... IPAD Imaging. Prof. Jose Sasian Class summary](https://reader033.vdocuments.net/reader033/viewer/2022042521/5f77651db846b70f976ac8df/html5/thumbnails/8.jpg)
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: Introduction to aberrations Lecture #1...Introduction to aberrations Lecture #1 College of Optical Sciences University of Arizona. ... IPAD Imaging. Prof. Jose Sasian Class summary](https://reader033.vdocuments.net/reader033/viewer/2022042521/5f77651db846b70f976ac8df/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: Introduction to aberrations Lecture #1...Introduction to aberrations Lecture #1 College of Optical Sciences University of Arizona. ... IPAD Imaging. Prof. Jose Sasian Class summary](https://reader033.vdocuments.net/reader033/viewer/2022042521/5f77651db846b70f976ac8df/html5/thumbnails/10.jpg)
Prof. Jose Sasian
Newtonian Equations
Zf
= - 1m
Zf''
= - m
ZZ ff' '
![Page 11: Introduction to aberrations Lecture #1...Introduction to aberrations Lecture #1 College of Optical Sciences University of Arizona. ... IPAD Imaging. Prof. Jose Sasian Class summary](https://reader033.vdocuments.net/reader033/viewer/2022042521/5f77651db846b70f976ac8df/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
![Page 12: Introduction to aberrations Lecture #1...Introduction to aberrations Lecture #1 College of Optical Sciences University of Arizona. ... IPAD Imaging. Prof. Jose Sasian Class summary](https://reader033.vdocuments.net/reader033/viewer/2022042521/5f77651db846b70f976ac8df/html5/thumbnails/12.jpg)
Prof. Jose Sasian
Civil War 1859
![Page 13: Introduction to aberrations Lecture #1...Introduction to aberrations Lecture #1 College of Optical Sciences University of Arizona. ... IPAD Imaging. Prof. Jose Sasian Class summary](https://reader033.vdocuments.net/reader033/viewer/2022042521/5f77651db846b70f976ac8df/html5/thumbnails/13.jpg)
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!
![Page 14: Introduction to aberrations Lecture #1...Introduction to aberrations Lecture #1 College of Optical Sciences University of Arizona. ... IPAD Imaging. Prof. Jose Sasian Class summary](https://reader033.vdocuments.net/reader033/viewer/2022042521/5f77651db846b70f976ac8df/html5/thumbnails/14.jpg)
Prof. Jose Sasian
Collinear transformation, camera obscura and lenses
Camera Obscura, Athanasius Kircher, 1646
![Page 15: Introduction to aberrations Lecture #1...Introduction to aberrations Lecture #1 College of Optical Sciences University of Arizona. ... IPAD Imaging. Prof. Jose Sasian Class summary](https://reader033.vdocuments.net/reader033/viewer/2022042521/5f77651db846b70f976ac8df/html5/thumbnails/15.jpg)
Prof. Jose Sasian
The secret in Vermeer’s paintings
Johannes Vermeer, XVII century
![Page 16: Introduction to aberrations Lecture #1...Introduction to aberrations Lecture #1 College of Optical Sciences University of Arizona. ... IPAD Imaging. Prof. Jose Sasian Class summary](https://reader033.vdocuments.net/reader033/viewer/2022042521/5f77651db846b70f976ac8df/html5/thumbnails/16.jpg)
Prof. Jose Sasian
Perspective of the painting
45tantan ffD
cmf 68
![Page 17: Introduction to aberrations Lecture #1...Introduction to aberrations Lecture #1 College of Optical Sciences University of Arizona. ... IPAD Imaging. Prof. Jose Sasian Class summary](https://reader033.vdocuments.net/reader033/viewer/2022042521/5f77651db846b70f976ac8df/html5/thumbnails/17.jpg)
Prof. Jose Sasian
However…
• Image parity issues• Needed a flat mirror or• To copy again the image
![Page 18: Introduction to aberrations Lecture #1...Introduction to aberrations Lecture #1 College of Optical Sciences University of Arizona. ... IPAD Imaging. Prof. Jose Sasian Class summary](https://reader033.vdocuments.net/reader033/viewer/2022042521/5f77651db846b70f976ac8df/html5/thumbnails/18.jpg)
Prof. Jose Sasian
Central projection
By Don Cowen
![Page 19: Introduction to aberrations Lecture #1...Introduction to aberrations Lecture #1 College of Optical Sciences University of Arizona. ... IPAD Imaging. Prof. Jose Sasian Class summary](https://reader033.vdocuments.net/reader033/viewer/2022042521/5f77651db846b70f976ac8df/html5/thumbnails/19.jpg)
Prof. Jose Sasian
Other “perspectives”
A plurality of new and excitingnew concepts in imaging
Classical Impressionism Cubist
![Page 20: Introduction to aberrations Lecture #1...Introduction to aberrations Lecture #1 College of Optical Sciences University of Arizona. ... IPAD Imaging. Prof. Jose Sasian Class summary](https://reader033.vdocuments.net/reader033/viewer/2022042521/5f77651db846b70f976ac8df/html5/thumbnails/20.jpg)
Prof. Jose Sasian
Imaging on the sphere
![Page 21: Introduction to aberrations Lecture #1...Introduction to aberrations Lecture #1 College of Optical Sciences University of Arizona. ... IPAD Imaging. Prof. Jose Sasian Class summary](https://reader033.vdocuments.net/reader033/viewer/2022042521/5f77651db846b70f976ac8df/html5/thumbnails/21.jpg)
Prof. Jose Sasian
IPADImaging
![Page 22: Introduction to aberrations Lecture #1...Introduction to aberrations Lecture #1 College of Optical Sciences University of Arizona. ... IPAD Imaging. Prof. Jose Sasian Class summary](https://reader033.vdocuments.net/reader033/viewer/2022042521/5f77651db846b70f976ac8df/html5/thumbnails/22.jpg)
Prof. Jose Sasian
Class summary
• Imaging with rays• Central projection and collinear
transformation• Art application• Homework on symmetry