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

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

MIT 2.71/2.71009/22/04 wk3-b-2

The significance of principal planes /1

MIT 2.71/2.71009/22/04 wk3-b-3

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

The significance of principal planes /2

MIT 2.71/2.71009/22/04 wk3-b-4

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

Reminder: imaging condition (thin lens)

MIT 2.71/2.71009/22/04 wk3-b-5

2nd FP

object

image

chief ray1st FP

n=1 n=1

The significance of principal planes /3

1st PS 2nd PS

MIT 2.71/2.71009/22/04 wk3-b-6

image?magnification?

multi-elementoptical system

2nd FP

1st FP

object

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

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

MIT 2.71/2.71009/22/04 wk3-b-8

Aperture / NA: physical meaning

MIT 2.71/2.71009/22/04 wk3-b-9

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

Entrance & exit pupils

multi-elementoptical system

image throughpreceding elements

image throughsucceeding elements

entrancepupil exitpupil

MIT 2.71/2.71009/22/04 wk3-b-10

The Chief Ray

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

MIT 2.71/2.71009/22/04 wk3-b-11

The Field Stop

Limits the angular acceptanceof Chief Rays

MIT 2.71/2.71009/22/04 wk3-b-12

Entrance & Exit Windows

multi-elementoptical system

image throughpreceding elements

MIT 2.71/2.71009/22/04 wk3-b-13

entrancewindow

exitwindow

image throughsucceeding elements

All together

entrancepupil

exitpupil

exitwindow

entrancewindow

aperturestopfield

stop

MIT 2.71/2.71009/22/04 wk3-b-14

All together

entrancepupil

exitwindow

entrancewindow

aperturestopfield

stopexit

pupil

MIT 2.71/2.71009/22/04 wk3-b-15

Example: single-lens camera

2nd FP

MIT 2.71/2.71009/22/04 wk3-b-16

objectplane

imageplane

1st FPsize offilm

or digitaldetector

array

Example: single-lens camera

2nd FP

objectplane

1st FP

ApertureStop

& EntrancePupil

imageplane

MIT 2.71/2.71009/22/04 wk3-b-17

Example: single-lens camera

2nd FP

1st FP

Exitpupil

(virtual)

ApertureStop

& EntrancePupil

objectplane

imageplane

MIT 2.71/2.71009/22/04 wk3-b-18

Example: single-lens camera

2nd FP

objectplane

1st FP

chief ray

Field Stop& Exit Window

MIT 2.71/2.71009/22/04 wk3-b-19

Example: single-lens camera

Field Stop& Exit Window

2nd FP

1st FP

chief ray

EntranceWindow

MIT 2.71/2.71009/22/04 wk3-b-20

Example: single-lens camera

2nd FP

1st FP

Exitpupil

(virtual)

ApertureStop

& EntrancePupilEntrance

Window

Field Stop& Exit Window

MIT 2.71/2.71009/22/04 wk3-b-21

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

Example: single-lens camera

vignettingvignetting

2nd FP

1st FP

ApertureStop

MIT 2.71/2.71009/22/04 wk3-b-23

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)

MIT 2.71/2.71009/22/04 wk3-b-24

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

Image removed due to copyright concerns

Eye schematic with typical dimensions

Photographic camera

Image removed due to copyright concerns

MIT 2.71/2.71009/22/04 wk3-b-26

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

Eye defects and their correction

Images removed due to copyright concerns

from Fundamentals of Opticsby F. Jenkins & H. White

MIT 2.71/2.71009/22/04 wk3-b-28

The eye’s “digital camera”: retina

Images removed due to copyright concerns

http://www.mdsupport.org

MIT 2.71/2.71009/22/04 wk3-b-29

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

Retina vs your digital cameraRetina:

variant sampling rateDigital camera:

fixed sampling rate

MIT 2.71/2.71009/22/04 wk3-b-31

(grossly exaggerated; in actual retinatransition from dense to sparse sampling

is much smoother)

Retina vs your digital cameraRetina:

blind spot not noticeableDigital camera:

bad pixels destructive

MIT 2.71/2.71009/22/04 wk3-b-32

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

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

Spatial response of the retina –lateral connections

http://www.phys.ufl.edu/~avery/MIT 2.71/2.71009/22/04 wk3-b-35

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

Temporal response: after-images

http://dragon.uml.edu/psych/MIT 2.71/2.71009/22/04 wk3-b-37

Seeing 3D

Images removed due to copyright concerns

http://www.ccom.unh.edu/vislab/VisCourseMIT 2.71/2.71009/22/04 wk3-b-38

MIT 2.71/2.71009/22/04 wk3-b-39

The compound eye

Images removed due to copyright concerns

MIT 2.71/2.71009/22/04 wk3-b-40

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

Images removed due to copyright concerns

“image” formation:blurry, but

computationally efficientfor moving-edge detection

MIT 2.71/2.71009/22/04 wk3-b-41

Reflective Optics

MIT 2.71/2.71009/22/04 wk3-b-42

s

s’

Example:imaging by a spherical mirror

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

MIT 2.71/2.71009/22/04 wk3-b-43

Reflective optics formulae

Rss211

−=′

+Imaging condition

2Rf −=Focal length

ssmx′

−=ssm′

−=αMagnification

MIT 2.71/2.71009/22/04 wk3-b-44

The Cassegrain telescope

MIT 2.71/2.71009/22/04 wk3-b-45

The Scheimpflug condition

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

MIT 2.71/2.71009/22/04 wk3-b-46

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