image formation iii chapter 1 (forsythponce) cameras lenses guido gerig cs-gy 6643, spring 2016...
DESCRIPTION
Pinhole vs. lens K. GraumanTRANSCRIPT
![Page 1: Image Formation III Chapter 1 (ForsythPonce) Cameras Lenses Guido Gerig CS-GY 6643, Spring 2016 (slides modified from Marc Pollefeys, UNC Chapel Hill](https://reader031.vdocuments.net/reader031/viewer/2022012919/5a4d1b797f8b9ab0599b8876/html5/thumbnails/1.jpg)
Image Formation IIIChapter 1 (Forsyth&Ponce)
Cameras “Lenses”Guido Gerig
CS-GY 6643, Spring 2016
(slides modified from Marc Pollefeys, UNC Chapel Hill/ ETH Zurich)
![Page 2: Image Formation III Chapter 1 (ForsythPonce) Cameras Lenses Guido Gerig CS-GY 6643, Spring 2016 (slides modified from Marc Pollefeys, UNC Chapel Hill](https://reader031.vdocuments.net/reader031/viewer/2022012919/5a4d1b797f8b9ab0599b8876/html5/thumbnails/2.jpg)
Pinhole size / aperture
Smaller
Larger
How does the size of the aperture affect the image we’d get?
K. Grauman
![Page 3: Image Formation III Chapter 1 (ForsythPonce) Cameras Lenses Guido Gerig CS-GY 6643, Spring 2016 (slides modified from Marc Pollefeys, UNC Chapel Hill](https://reader031.vdocuments.net/reader031/viewer/2022012919/5a4d1b797f8b9ab0599b8876/html5/thumbnails/3.jpg)
Pinhole vs. lens
K. Grauman
![Page 4: Image Formation III Chapter 1 (ForsythPonce) Cameras Lenses Guido Gerig CS-GY 6643, Spring 2016 (slides modified from Marc Pollefeys, UNC Chapel Hill](https://reader031.vdocuments.net/reader031/viewer/2022012919/5a4d1b797f8b9ab0599b8876/html5/thumbnails/4.jpg)
Adding a lens
A lens focuses light onto the film– Rays passing through the center are not
deviated– All parallel rays converge to one point on
a plane located at the focal length fSlide by Steve Seitz
focal point
f
![Page 5: Image Formation III Chapter 1 (ForsythPonce) Cameras Lenses Guido Gerig CS-GY 6643, Spring 2016 (slides modified from Marc Pollefeys, UNC Chapel Hill](https://reader031.vdocuments.net/reader031/viewer/2022012919/5a4d1b797f8b9ab0599b8876/html5/thumbnails/5.jpg)
Cameras with lenses
focal point
F
optical center(Center Of Projection)
• A lens focuses parallel rays onto a single focal point• Gather more light, while keeping focus; make
pinhole perspective projection practical
K. Grauman
![Page 6: Image Formation III Chapter 1 (ForsythPonce) Cameras Lenses Guido Gerig CS-GY 6643, Spring 2016 (slides modified from Marc Pollefeys, UNC Chapel Hill](https://reader031.vdocuments.net/reader031/viewer/2022012919/5a4d1b797f8b9ab0599b8876/html5/thumbnails/6.jpg)
Lenses
Snell’s law
n1 sin a1 = n2 sin a2
Descartes’ law
![Page 7: Image Formation III Chapter 1 (ForsythPonce) Cameras Lenses Guido Gerig CS-GY 6643, Spring 2016 (slides modified from Marc Pollefeys, UNC Chapel Hill](https://reader031.vdocuments.net/reader031/viewer/2022012919/5a4d1b797f8b9ab0599b8876/html5/thumbnails/7.jpg)
Paraxial (or first-order) optics
Snell’s law:
n1 sin a1 = n2 sin a2
Small angles:
n1 a1 n2a2Rnn
dn
dn 12
2
2
1
1
R γβα
111
hdh
222 R
βγαdhh
22
11 RR d
hhnhdhn
![Page 8: Image Formation III Chapter 1 (ForsythPonce) Cameras Lenses Guido Gerig CS-GY 6643, Spring 2016 (slides modified from Marc Pollefeys, UNC Chapel Hill](https://reader031.vdocuments.net/reader031/viewer/2022012919/5a4d1b797f8b9ab0599b8876/html5/thumbnails/8.jpg)
Thin Lenses
)1(2 and11
'1 e wher
''
''
nRf
fzzzyzy
zxzx
http://www.phy.ntnu.edu.tw/java/Lens/lens_e.html
spherical lens surfaces; thickness << radii; same refractive index on both sides; all rays emerging from P and passing through the lens are focused at P’. Let n1=1 (vacuum) and n2=n.
![Page 9: Image Formation III Chapter 1 (ForsythPonce) Cameras Lenses Guido Gerig CS-GY 6643, Spring 2016 (slides modified from Marc Pollefeys, UNC Chapel Hill](https://reader031.vdocuments.net/reader031/viewer/2022012919/5a4d1b797f8b9ab0599b8876/html5/thumbnails/9.jpg)
Thick Lens
![Page 10: Image Formation III Chapter 1 (ForsythPonce) Cameras Lenses Guido Gerig CS-GY 6643, Spring 2016 (slides modified from Marc Pollefeys, UNC Chapel Hill](https://reader031.vdocuments.net/reader031/viewer/2022012919/5a4d1b797f8b9ab0599b8876/html5/thumbnails/10.jpg)
Focus and depth of field
Image credit: cambridgeincolour.com
![Page 11: Image Formation III Chapter 1 (ForsythPonce) Cameras Lenses Guido Gerig CS-GY 6643, Spring 2016 (slides modified from Marc Pollefeys, UNC Chapel Hill](https://reader031.vdocuments.net/reader031/viewer/2022012919/5a4d1b797f8b9ab0599b8876/html5/thumbnails/11.jpg)
The depth-of-field
![Page 12: Image Formation III Chapter 1 (ForsythPonce) Cameras Lenses Guido Gerig CS-GY 6643, Spring 2016 (slides modified from Marc Pollefeys, UNC Chapel Hill](https://reader031.vdocuments.net/reader031/viewer/2022012919/5a4d1b797f8b9ab0599b8876/html5/thumbnails/12.jpg)
Focus and depth of field• Depth of field: distance between image
planes where blur is tolerable
Thin lens: scene points at distinct depths come in focus at different image planes.
(Real camera lens systems have greater depth of field.)
Shapiro and Stockman
“circles of confusion”
![Page 13: Image Formation III Chapter 1 (ForsythPonce) Cameras Lenses Guido Gerig CS-GY 6643, Spring 2016 (slides modified from Marc Pollefeys, UNC Chapel Hill](https://reader031.vdocuments.net/reader031/viewer/2022012919/5a4d1b797f8b9ab0599b8876/html5/thumbnails/13.jpg)
Focus and depth of field• How does the aperture affect the depth of field?
• A smaller aperture increases the range in which the object is approximately in focus
Flower images from Wikipedia http://en.wikipedia.org/wiki/Depth_of_field Slide from S. Seitz
![Page 14: Image Formation III Chapter 1 (ForsythPonce) Cameras Lenses Guido Gerig CS-GY 6643, Spring 2016 (slides modified from Marc Pollefeys, UNC Chapel Hill](https://reader031.vdocuments.net/reader031/viewer/2022012919/5a4d1b797f8b9ab0599b8876/html5/thumbnails/14.jpg)
The depth-of-field
![Page 15: Image Formation III Chapter 1 (ForsythPonce) Cameras Lenses Guido Gerig CS-GY 6643, Spring 2016 (slides modified from Marc Pollefeys, UNC Chapel Hill](https://reader031.vdocuments.net/reader031/viewer/2022012919/5a4d1b797f8b9ab0599b8876/html5/thumbnails/15.jpg)
The depth-of-field
fZo
1 Z1 1
i
iii ZZZ
fZ
Zf
i
i
Zo
yields
dZZ
bZ iii
ii Z
bdbZ
fbdfZfZZ oo
o / ) ( Z Z Z
0oo
Similar formula for Z Z Z oo o
)( / Z bddZ ii
fZZfZ
o
oi
)( Z
0o bdfZb
Zdf o
![Page 16: Image Formation III Chapter 1 (ForsythPonce) Cameras Lenses Guido Gerig CS-GY 6643, Spring 2016 (slides modified from Marc Pollefeys, UNC Chapel Hill](https://reader031.vdocuments.net/reader031/viewer/2022012919/5a4d1b797f8b9ab0599b8876/html5/thumbnails/16.jpg)
The depth-of-field
fbdfZfZZZZZ
/ )(
0
00000
decreases with d+, increases with Z0+
strike a balance between incoming light and sharp depth range
![Page 17: Image Formation III Chapter 1 (ForsythPonce) Cameras Lenses Guido Gerig CS-GY 6643, Spring 2016 (slides modified from Marc Pollefeys, UNC Chapel Hill](https://reader031.vdocuments.net/reader031/viewer/2022012919/5a4d1b797f8b9ab0599b8876/html5/thumbnails/17.jpg)
Deviations from the lens model
3 assumptions :
1. all rays from a point are focused onto 1 image point
2. all image points in a single plane
3. magnification is constant
deviations from this ideal are aberrations
![Page 18: Image Formation III Chapter 1 (ForsythPonce) Cameras Lenses Guido Gerig CS-GY 6643, Spring 2016 (slides modified from Marc Pollefeys, UNC Chapel Hill](https://reader031.vdocuments.net/reader031/viewer/2022012919/5a4d1b797f8b9ab0599b8876/html5/thumbnails/18.jpg)
Aberrations
chromatic : refractive index function of wavelength
2 types :
1. geometrical
2. chromatic
geometrical : small for paraxial rays
study through 3rd order optics
![Page 19: Image Formation III Chapter 1 (ForsythPonce) Cameras Lenses Guido Gerig CS-GY 6643, Spring 2016 (slides modified from Marc Pollefeys, UNC Chapel Hill](https://reader031.vdocuments.net/reader031/viewer/2022012919/5a4d1b797f8b9ab0599b8876/html5/thumbnails/19.jpg)
Geometrical aberrations
spherical aberration
astigmatism
distortion
coma
aberrations are reduced by combining lenses
![Page 20: Image Formation III Chapter 1 (ForsythPonce) Cameras Lenses Guido Gerig CS-GY 6643, Spring 2016 (slides modified from Marc Pollefeys, UNC Chapel Hill](https://reader031.vdocuments.net/reader031/viewer/2022012919/5a4d1b797f8b9ab0599b8876/html5/thumbnails/20.jpg)
Spherical aberration
rays parallel to the axis do not converge
outer portions of the lens yield smaller focal lenghts
![Page 21: Image Formation III Chapter 1 (ForsythPonce) Cameras Lenses Guido Gerig CS-GY 6643, Spring 2016 (slides modified from Marc Pollefeys, UNC Chapel Hill](https://reader031.vdocuments.net/reader031/viewer/2022012919/5a4d1b797f8b9ab0599b8876/html5/thumbnails/21.jpg)
AstigmatismDifferent focal length for inclined rays
![Page 22: Image Formation III Chapter 1 (ForsythPonce) Cameras Lenses Guido Gerig CS-GY 6643, Spring 2016 (slides modified from Marc Pollefeys, UNC Chapel Hill](https://reader031.vdocuments.net/reader031/viewer/2022012919/5a4d1b797f8b9ab0599b8876/html5/thumbnails/22.jpg)
Distortionmagnification/focal length different for different angles of inclination
Can be corrected! (if parameters are know)
pincushion(tele-photo)
barrel(wide-angle)
![Page 23: Image Formation III Chapter 1 (ForsythPonce) Cameras Lenses Guido Gerig CS-GY 6643, Spring 2016 (slides modified from Marc Pollefeys, UNC Chapel Hill](https://reader031.vdocuments.net/reader031/viewer/2022012919/5a4d1b797f8b9ab0599b8876/html5/thumbnails/23.jpg)
Comapoint off the axis depicted as comet shaped blob
![Page 24: Image Formation III Chapter 1 (ForsythPonce) Cameras Lenses Guido Gerig CS-GY 6643, Spring 2016 (slides modified from Marc Pollefeys, UNC Chapel Hill](https://reader031.vdocuments.net/reader031/viewer/2022012919/5a4d1b797f8b9ab0599b8876/html5/thumbnails/24.jpg)
Chromatic aberration
rays of different wavelengths focused in different planes
cannot be removed completely
sometimes achromatization is achieved formore than 2 wavelengths
![Page 25: Image Formation III Chapter 1 (ForsythPonce) Cameras Lenses Guido Gerig CS-GY 6643, Spring 2016 (slides modified from Marc Pollefeys, UNC Chapel Hill](https://reader031.vdocuments.net/reader031/viewer/2022012919/5a4d1b797f8b9ab0599b8876/html5/thumbnails/25.jpg)
Vignetting