MIT 2.71/2.710 09/22/04 wk3-b-1
Imaging Instruments (part I)
• Principal Planes and Focal Lengths (Effective, Back, Front)• Multi-element systems• Pupils & Windows; Apertures & Stops• the Numerical Aperture and f/#• Single-Lens Camera• Human Eye• Reflective optics• Scheimpflug condition
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Focal Lengths & Principal Planes
generalized optical system(e.g. thick lens,
multi-element system)
EFL: Effective Focal Length (or simply “focal length”)FFL: Front Focal LengthBFL: Back Focal LengthFP: Focal Point/Plane PS: Principal Surface/Plane
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The significance of principal planes /1
thin lensof the same power
located at the 2nd PS for rays passing through 2nd FP
optical system
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The significance of principal planes /2
thin lensof the same power
located at the 1st PS for rays passing through 1st FP
optical system
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Reminder: imaging condition (thin lens)
object image
chief ray
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The significance of principal planes /3
object
multi-elementoptical system
image?magnification?
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The significance of principal planes /4
object
multi-elementoptical system
lateral hold, where f= (EFL)
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Numerical Aperture
medium of refr. index n
half-angle subtended by the imaging system from an axial object
Numerical Aperture
Speed (f/#)=1/2(NA)pronounced f-number, e.g.f/8 means (f/#)=8.
Aperture stopthe physical element whichlimits the angle of acceptance of the imaging system
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Aperture / NA: physical meaning
medium of refr. index n
The Numerical Aperturelimits the optical energythat can flow through the system
Later we will also learn that the NA also defines the resolution (or resolving power) of the optical system
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Entrance & exit pupils
multi-elementoptical system
image throughpreceding elements
image throughsucceeding elements
entrancepupil
exit pupil
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The Chief Ray
Starts from off-axis object,Goes through the center of the Aperture
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The Field Stop
Limits the angular acceptanceof Chief Rays
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Entrance & Exit Windows
multi-elementoptical system
image throughpreceding elements
image throughsucceeding elements
entrancewindow
exit window
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All together
entrancewindow
exit window
entrancepupil
exit pupil
field stop
aperture stop
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All together
entrancewindow
exit window
entrancepupil
exit pupil
field stop
aperture stop
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Example: single-lens camera
objectplan
eimage
plane
size of film
or digital detector
array
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Example: single-lens camera
objectplan
e Aperture Stop
& Entrance Pupil
imageplan
e
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Example: single-lens camera
objectplan
e
imageplan
e
ExitPupil
(virtual)
Aperture Stop
& Entrance Pupil
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Example: single-lens camera
chief ray
Field Stop& Exit Window
objectplan
e
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Example: single-lens camera
Entrancewindow
Field Stop& Exit Window
chief ray
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Example: single-lens camera
Entrancewindow
Field Stop& Exit Window
ExitPupil
(virtual)
Aperture Stop
& Entrance Pupil
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Example: single-lens camera
Entrancewindow
Field Stop& Exit Window
ExitPupil
(virtual)
Aperture Stop
& Entrance Pupil
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Example: single-lens camera
Aperture Stop
vignetting
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Imaging systems in nature
• “Physical” architecture matches survival requirements and processing capabilities
• Human eye: evolved for – adaptivity (e.g. brightness adjustment) – transmission efficiency (e.g. mexican hat response) – bypass structural defects (e.g. blind spot) – other functional requirements (e.g. stereo vision)
• Insect eye: similar, but muchsimpler processor (human brain = ~1011neurons; insect brain = ~104neurons)
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Anatomy of the human eye
Images removed due to copyright concerns
W. J. Smith, “Modern Optical Engineering,” McGraw-Hill
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Images removed due to copyright concerns
Eye schematic with typical dimensions
Photographic camera concerns
Images removed due to copyright concerns
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Accommodation (focusing)
Remote object (unaccommodated eye)
Proximal object (accommodated eye)Comfortable viewing up to 2.5cm away from the cornea
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Eye defects and their correction
Images removed due to copyright concerns
from Fundamentals of Opticsby F. Jenkins & H. White
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The eye’s “digital camera”: retina
Images removed due to copyright concerns
http://www.mdsupport.org
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The eye’s “digital camera”: retina
Images removed due to copyright concerns
rods: intensity (grayscale) cones: color (R/G/B)
http://www.phys.ufl.edu/~avery/
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Retina vs your digital camera
Retina:variant sampling rate
Digital camera:fixed sampling rate
(grossly exaggerated; in actual retinatransition from dense to sparse sampling
is much smoother)
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Retina vs your digital camera
Retina:blind spot not noticeable
Digital camera:bad pixels destructive
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Retina vs your digital camera
Retinal image CCD image
http://www.klab.caltech.edu/~itti/
Images removed due to copyright concerns
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Spatial response of the retina –lateral connections
http://webvision.med.utah.edu/
Images removed due to copyright concerns
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http://www.phys.ufl.edu/~avery/
Spatial response of the retina –lateral connections
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Explanation of the “flipping dot” illusion: the Mexican hat response
Spatial response of the retina –lateral connections
http://faculty.washington.edu/wcalvin
Images removed due to copyright concerns
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Temporal response: after-images
http://dragon.uml.edu/psych/
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Seeing 3D
http://www.ccom.unh.edu/vislab/VisCourse
Images removed due to copyright concerns
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VIEWING POINT
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The compound eye
Images removed due to copyright concerns
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Elements of the compound eye:ommatidia (=little eyes)
“image” formation:blurry, but
computationally efficientfor moving-edge detection
Images removed due to copyright concerns
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Reflective Optics
Example:imaging by a spherical mirror
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Sign conventions for reflective optics
• Light travels from left to right before reflection and from right to left after reflection• A radius of curvature is positive if the surface is convex towards the left• Longitudinal distances before reflectionare positive if pointing to the right; longitudinal distances after reflection are positive if pointing to the left• Longitudinal distances are positive if pointing up• Ray angles are positive if the ray direction is obtained by rotating the +z axis counterclockwise through an acute angle
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Reflective optics formulae
Imaging condition
Focal length
Magnification
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The Cassegrain telescope
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The Scheimpflug condition
The object plane and the image planeintersect at the plane of the lens.
OBJECT PLANE
OPTICAL AXIS
LENS PLANE
IMAGE PLANE
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