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

MIT 2.71/2.710 09/22/04 wk3-b-2

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

MIT 2.71/2.710 09/22/04 wk3-b-3

The significance of principal planes /1

thin lensof the same power

located at the 2nd PS for rays passing through 2nd FP

optical system

MIT 2.71/2.710 09/22/04 wk3-b-4

The significance of principal planes /2

thin lensof the same power

located at the 1st PS for rays passing through 1st FP

optical system

MIT 2.71/2.710 09/22/04 wk3-b-5

Reminder: imaging condition (thin lens)

object image

chief ray

MIT 2.71/2.710 09/22/04 wk3-b-6

The significance of principal planes /3

object

multi-elementoptical system

image?magnification?

MIT 2.71/2.710 09/22/04 wk3-b-7

The significance of principal planes /4

object

multi-elementoptical system

lateral hold, where f= (EFL)

MIT 2.71/2.710 09/22/04 wk3-b-8

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

MIT 2.71/2.710 09/22/04 wk3-b-9

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

MIT 2.71/2.710 09/22/04 wk3-b-10

Entrance & exit pupils

multi-elementoptical system

image throughpreceding elements

image throughsucceeding elements

entrancepupil

exit pupil

MIT 2.71/2.710 09/22/04 wk3-b-11

The Chief Ray

Starts from off-axis object,Goes through the center of the Aperture

MIT 2.71/2.710 09/22/04 wk3-b-12

The Field Stop

Limits the angular acceptanceof Chief Rays

MIT 2.71/2.710 09/22/04 wk3-b-13

Entrance & Exit Windows

multi-elementoptical system

image throughpreceding elements

image throughsucceeding elements

entrancewindow

exit window

MIT 2.71/2.710 09/22/04 wk3-b-14

All together

entrancewindow

exit window

entrancepupil

exit pupil

field stop

aperture stop

MIT 2.71/2.710 09/22/04 wk3-b-15

All together

entrancewindow

exit window

entrancepupil

exit pupil

field stop

aperture stop

MIT 2.71/2.710 09/22/04 wk3-b-16

Example: single-lens camera

objectplan

eimage

plane

size of film

or digital detector

array

MIT 2.71/2.710 09/22/04 wk3-b-17

Example: single-lens camera

objectplan

e Aperture Stop

& Entrance Pupil

imageplan

e

MIT 2.71/2.710 09/22/04 wk3-b-18

Example: single-lens camera

objectplan

e

imageplan

e

ExitPupil

(virtual)

Aperture Stop

& Entrance Pupil

MIT 2.71/2.710 09/22/04 wk3-b-19

Example: single-lens camera

chief ray

Field Stop& Exit Window

objectplan

e

MIT 2.71/2.710 09/22/04 wk3-b-20

Example: single-lens camera

Entrancewindow

Field Stop& Exit Window

chief ray

MIT 2.71/2.710 09/22/04 wk3-b-21

Example: single-lens camera

Entrancewindow

Field Stop& Exit Window

ExitPupil

(virtual)

Aperture Stop

& Entrance Pupil

MIT 2.71/2.710 09/22/04 wk3-b-22

Example: single-lens camera

Entrancewindow

Field Stop& Exit Window

ExitPupil

(virtual)

Aperture Stop

& Entrance Pupil

MIT 2.71/2.710 09/22/04 wk3-b-23

Example: single-lens camera

Aperture Stop

vignetting

MIT 2.71/2.710 09/22/04 wk3-b-24

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)

MIT 2.71/2.710 09/22/04 wk3-b-25

Anatomy of the human eye

Images removed due to copyright concerns

W. J. Smith, “Modern Optical Engineering,” McGraw-Hill

MIT 2.71/2.710 09/22/04 wk3-b-26

Images removed due to copyright concerns

Eye schematic with typical dimensions

Photographic camera concerns

Images removed due to copyright concerns

MIT 2.71/2.710 09/22/04 wk3-b-27

Accommodation (focusing)

Remote object (unaccommodated eye)

Proximal object (accommodated eye)Comfortable viewing up to 2.5cm away from the cornea

MIT 2.71/2.710 09/22/04 wk3-b-28

Eye defects and their correction

Images removed due to copyright concerns

from Fundamentals of Opticsby F. Jenkins & H. White

MIT 2.71/2.710 09/22/04 wk3-b-29

The eye’s “digital camera”: retina

Images removed due to copyright concerns

http://www.mdsupport.org

MIT 2.71/2.710 09/22/04 wk3-b-30

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/

MIT 2.71/2.710 09/22/04 wk3-b-31

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)

MIT 2.71/2.710 09/22/04 wk3-b-32

Retina vs your digital camera

Retina:blind spot not noticeable

Digital camera:bad pixels destructive

MIT 2.71/2.710 09/22/04 wk3-b-33

Retina vs your digital camera

Retinal image CCD image

http://www.klab.caltech.edu/~itti/

Images removed due to copyright concerns

MIT 2.71/2.710 09/22/04 wk3-b-34

Spatial response of the retina –lateral connections

http://webvision.med.utah.edu/

Images removed due to copyright concerns

MIT 2.71/2.710 09/22/04 wk3-b-35

http://www.phys.ufl.edu/~avery/

Spatial response of the retina –lateral connections

MIT 2.71/2.710 09/22/04 wk3-b-36

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

MIT 2.71/2.710 09/22/04 wk3-b-37

Temporal response: after-images

http://dragon.uml.edu/psych/

MIT 2.71/2.710 09/22/04 wk3-b-38

Seeing 3D

http://www.ccom.unh.edu/vislab/VisCourse

Images removed due to copyright concerns

MIT 2.71/2.710 09/22/04 wk3-b-39

VIEWING POINT

MIT 2.71/2.710 09/22/04 wk3-b-40

The compound eye

Images removed due to copyright concerns

MIT 2.71/2.710 09/22/04 wk3-b-41

Elements of the compound eye:ommatidia (=little eyes)

“image” formation:blurry, but

computationally efficientfor moving-edge detection

Images removed due to copyright concerns

MIT 2.71/2.710 09/22/04 wk3-b-42

Reflective Optics

Example:imaging by a spherical mirror

MIT 2.71/2.710 09/22/04 wk3-b-43

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

MIT 2.71/2.710 09/22/04 wk3-b-44

Reflective optics formulae

Imaging condition

Focal length

Magnification

MIT 2.71/2.710 09/22/04 wk3-b-45

The Cassegrain telescope

MIT 2.71/2.710 09/22/04 wk3-b-46

The Scheimpflug condition

The object plane and the image planeintersect at the plane of the lens.

OBJECT PLANE

OPTICAL AXIS

LENS PLANE

IMAGE PLANE