Imaging Instruments (part I)dspace.mit.edu/bitstream/handle/1721.1/74610/2-71-fall... · 2019. 9....
Transcript of Imaging Instruments (part I)dspace.mit.edu/bitstream/handle/1721.1/74610/2-71-fall... · 2019. 9....
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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
MIT 2.71/2.71009/22/04 wk3-b-1
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Focal Lengths & Principal Planes
generalized optical system(e.g. thick lens,
multi-element system)
2nd PS
2nd FP
1st FP
1st PS
EFL
BFL
EFL
FFL
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
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generalizedoptical system
thin lensof the same power
located at the 2nd PSfor rays passing through 2nd FP
1st PS
2nd PS
2nd FP
1st FP
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The significance of principal planes /2
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generalizedoptical system
thin lensof the same power
located at the 1st PPfor rays passing through 1st FP
1st PS
2nd PS
2nd FP
1st FP
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Reminder: imaging condition (thin lens)
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2nd FP
object
image
chief ray1st FP
n=1 n=1
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The significance of principal planes /3
1st PS 2nd PS
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image?magnification?
multi-elementoptical system
2nd FP
1st FP
object
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The significance of principal planes /4
1st PS 2nd PS
multi-elementoptical system
2nd FP
1st FP
object
s s’
,111fss
=′
+ssm′
−=lateral hold, where f = (EFL)MIT 2.71/2.71009/22/04 wk3-b-7
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Numerical Aperture
medium ofrefr. index n
θ
θ: half-angle subtended by the imaging system from an axial object
Numerical Aperture(NA) = n sinθ
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
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medium ofrefr. index n
θ
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 exitpupil
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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
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entrancewindow
exitwindow
image throughsucceeding elements
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All together
entrancepupil
exitpupil
exitwindow
entrancewindow
aperturestopfield
stop
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All together
entrancepupil
exitwindow
entrancewindow
aperturestopfield
stopexit
pupil
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Example: single-lens camera
2nd FP
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objectplane
imageplane
1st FPsize offilm
or digitaldetector
array
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Example: single-lens camera
2nd FP
objectplane
1st FP
ApertureStop
& EntrancePupil
imageplane
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Example: single-lens camera
2nd FP
1st FP
Exitpupil
(virtual)
ApertureStop
& EntrancePupil
objectplane
imageplane
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Example: single-lens camera
2nd FP
objectplane
1st FP
chief ray
Field Stop& Exit Window
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Example: single-lens camera
Field Stop& Exit Window
2nd FP
1st FP
chief ray
EntranceWindow
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Example: single-lens camera
2nd FP
1st FP
Exitpupil
(virtual)
ApertureStop
& EntrancePupilEntrance
Window
Field Stop& Exit Window
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Example: single-lens camera
Field Stop& Exit Window
2nd FP
1st FP
Exitpupil
(virtual)
ApertureStop
& EntrancePupilEntrance
WindowMIT 2.71/2.71009/22/04 wk3-b-22
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Example: single-lens camera
vignettingvignetting
2nd FP
1st FP
ApertureStop
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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 much simpler processor (human brain = ~1011 neurons; insect brain = ~104 neurons)
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Anatomy of the human eye
Images removed due to copyright concerns
W. J. Smith, “Modern Optical Engineering,” McGraw-HillMIT 2.71/2.71009/22/04 wk3-b-25
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Image removed due to copyright concerns
Eye schematic with typical dimensions
Photographic camera
Image 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 corneaMIT 2.71/2.71009/22/04 wk3-b-27
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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
rods: intensity (grayscale) cones: color (R/G/B)
Images removed due to copyright concerns
http://www.phys.ufl.edu/~avery/MIT 2.71/2.71009/22/04 wk3-b-30
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Retina vs your digital cameraRetina:
variant sampling rateDigital camera:
fixed sampling rate
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(grossly exaggerated; in actual retinatransition from dense to sparse sampling
is much smoother)
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Retina vs your digital cameraRetina:
blind spot not noticeableDigital camera:
bad pixels destructive
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Retina vs your digital camera
Images removed due to copyright concerns
Retinal image CCD image
http://www.klab.caltech.edu/~itti/MIT 2.71/2.71009/22/04 wk3-b-33
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Spatial response of the retina –lateral connections
Image removed due to copyright concerns
http://webvision.med.utah.edu/MIT 2.71/2.71009/22/04 wk3-b-34
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Spatial response of the retina –lateral connections
http://www.phys.ufl.edu/~avery/MIT 2.71/2.71009/22/04 wk3-b-35
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Spatial response of the retina –lateral connections
Explanation of the “flipping dot” illusion: the Mexican hat response
Image removed due to copyright concerns
MIT 2.71/2.71009/22/04 wk3-b-36
http://faculty.washington.edu/wcalvin
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Temporal response: after-images
http://dragon.uml.edu/psych/MIT 2.71/2.71009/22/04 wk3-b-37
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Seeing 3D
Images removed due to copyright concerns
http://www.ccom.unh.edu/vislab/VisCourseMIT 2.71/2.71009/22/04 wk3-b-38
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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)
Images removed due to copyright concerns
“image” formation:blurry, but
computationally efficientfor moving-edge detection
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Reflective Optics
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s
s’
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 reflection are 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
Rss211
−=′
+Imaging condition
2Rf −=Focal length
ssmx′
−=ssm′
−=αMagnification
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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.
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Imaging Instruments (part I)Focal Lengths & Principal PlanesThe significance of principal planes /1The significance of principal planes /2Reminder: imaging condition (thin lens)The significance of principal planes /3The significance of principal planes /4Numerical ApertureAperture / NA: physical meaningEntrance & exit pupilsThe Chief RayThe Field StopEntrance & Exit WindowsAll togetherAll togetherExample: single-lens cameraExample: single-lens cameraExample: single-lens cameraExample: single-lens cameraExample: single-lens cameraExample: single-lens cameraExample: single-lens cameraExample: single-lens cameraImaging systems in natureThe eye’s “digital camera”: retinaThe eye’s “digital camera”: retinaRetina vs your digital cameraRetina vs your digital cameraRetina vs your digital cameraSpatial response of the retina – lateral connectionsSpatial response of the retina – lateral connectionsSpatial response of the retina – lateral connectionsTemporal response: after-imagesSeeing 3DThe compound eyeElements of the compound eye:ommatidia (=little eyes)Reflective OpticsSign conventions for reflective opticsReflective optics formulaeThe Cassegrain telescopeThe Scheimpflug condition