MIT 2.71/2.710 09/22/04 wk3-b-1 Imaging Instruments (part I) Principal Planes and Focal Lengths...

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