16421: Vision Sensors
Lecture 3: Optical Elements of Imaging
Instructor: S. Narasimhan
Wean 5310, T-R 1:30pm – 2:50pm
Lenses
Types of Lenses
[Wikipedia]
Bi-convex Lens
[Wikipedia]
Bi-concave Lens
[Wikipedia]
Lensmaker’s Equation
f is the focal length of the lens,
n is the refractive index of the lens material,
R1 is the radius of curvature of the lens surface closest to the light source,
R2 is the radius of curvature of the lens surface farthest from the light source,
d is the thickness of the lens (the distance along the lens axis between the two surface vertices).
Optics of a Two Lens System
d
object
final
image
f2
i2
o2
i1
f1
o1
image
plane
lens 2
intermediate
virtual image
lens 1
• Rule : Image formed by first lens is the object for the second lens.
• Main Rays : Ray passing through focus emerges parallel to optical axis.
Ray through optical center passes un-deviated.
• Magnification:
i2 i1
m
o2 o1
Exercises: What is the combined focal length of the system?
What is the combined focal length if d = 0?
Changing Diameter of Collimated Beam
Fanning a Laser beam to a sheet
Used in Range Scanners
Cylindrical Lenses
Telecentric Lenses
Object-side and Image-side telecentricity:
Aperture at the focal point
of both lens systems
• Sizes of object and image do not change as they are translated.
• However, focus does change as in any lens.
Eliminating Perspective Distortion
Regular Lens
Telecentric Lens
Illusions with Telecentric Lenses
Relay Lenses (1:1 imaging)
Wide angle Lenses
Circular Fisheye
Full Frame Rectangular Fisheye
Common lens related Issues
Vignetting
L3
L2
B
L1
A
More light passes through lens L3 for scene point A than scene point B
Results in spatially non-uniform brightness (in the periphery of the image)
Lens Vignetting
• Usually brighter at the center and darker at the periphery.
Reading: http://www.dpreview.com
Vignetting
photo by Robert Johnes
Chromatic Aberration
longitudinal chromatic aberration
(axial)
transverse chromatic aberration
(lateral)
Chromatic Aberrations
longitudinal chromatic aberration
(axial)
transverse chromatic aberration
(lateral)
Chromatic Abberations
Reading: http://www.dpreview.com
Lens Glare
• Stray interreflections of light within the optical lens system.
• Happens when very bright sources are present in the scene.
Reading: http://www.dpreview.com
Geometric Lens Distortions
Radial distortion
Tangential distortion
Photo by Helmut Dersch
Both due to lens imperfection
Rectify with geometric camera calibration
Radial Lens Distortions
No Distortion
Barrel Distortion
• Radial distance from Image Center:
ru = rd + k1 rd3
Pincushion Distortion
Correcting Radial Lens Distortions
Before
After
http://www.grasshopperonline.com/barrel_distortion_correction_software.html
Our Eyes
Iris
Pupil Sclera
Cornea
 Index of refraction: cornea 1.376, aqueous 1.336, lens 1.406-1.386
 Iris is the diaphragm that changes the aperture (pupil)
 Retina is the sensor where the fovea has the highest resolution
Accommodation
shorter focal length
Changes the focal length of the lens
Myopia and Hyperopia
(myopia)
Astigmatism
The cornea is distorted causing images to be un-focused on the retina.
Blind Spot in Eye
Close your right eye and look directly at the “+”
Eyes in Nature
Mosquito
http://ebiomedia.com/gall/eyes/octopus-insect.html
Mosquitos have microscopic vision, but to focus at large distances the eye would need to be 1 m!
Curved Mirrors in Scallop Eyes
Telescopic Eye
(by Mike Land, Sussex)
… More in the second part of the course
Filters
Neutral Density Filters
• Spectrally flat from 400-700nm
• Homogeneous Glass: Blocks by absorption or by reflection
• Light/Exposure Control for Imaging
• Transmittance = 10^(-optical density) * 100
Variable Neutral Density Filters
Variable Neutral Density Filters
Color Filters
Filter Book
Linear Variable Interference Filters
Mirrors
Cold Mirrors
• Reflect VIS
• Transmit IR
Hot Mirrors
• Reflect IR
• Transmit VIS
Prisms
Image Reflection
Right Angle Prism
Penta Prism
Image Rotation
Dove Prism
Single Lens Reflex Cameras
•
•
What you see is what you get
Single Light Pathway for viewfinder
and image
1 - Front-mount Lens (4 element Tessar design)
2 - Reflex Mirror at 45 degree angle
3 - Focal Plane Shutter
4 - 35 mm Film or Sensor
5 - Focusing Screen
6 - Condenser Lens
7 - Optical Glass Pentaprism (or Pentamirror)
8 - Eyepiece (can have diopter correction ability)
Canon.com