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 09/22/04 wk3-b-1
Focal Lengths & Principal Planes 1 st PS 2 nd PS generalized optical system (e.g. thick lens, multi-element system) FFL BFL 2 nd FP 1 st FP EFL EFL 09/22/04 wk3-b-2 EFL: Effective Focal Length (or simply focal length ) FFL: Front Focal Length BFL: Back Focal Length FP: Focal Point/Plane PS: Principal Surface/Plane
The significance of principal planes /1 1 st FP 1 st PS 2 nd FP generalized optical system 2 nd PS thin lens of the same power located at the 2 nd PS for rays passing through 2 nd FP 09/22/04 wk3-b-3
The significance of principal planes /2 1 st FP 1 st PS 2 nd FP generalized optical system 2 nd PS thin lens of the same power located at the 1 st PP for rays passing through 1 st FP 09/22/04 wk3-b-4
Reminder: imaging condition (thin lens) n=1 n=1 object 1 st FP chief ray 2 nd FP image 09/22/04 wk3-b-5
The significance of principal planes /3 object 1 st PS 2 nd PS 1 st FP 2 nd FP multi-element optical system 09/22/04 wk3-b-6 image? magnification?
The significance of principal planes /4 object 1 st PS 2 nd PS 1 st FP 2 nd FP s s multi-element optical system 09/22/04 wk3-b-7 1 s + 1 s = 1 f, m lateral = s s hold, where f = (EFL)
Numerical Aperture medium of refr. 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 stop the physical element which limits the angle of acceptance of the imaging system 09/22/04 wk3-b-8
Aperture / NA: physical meaning medium of refr. index n θ The Numerical Aperture limits the optical energy that can flow through the system Later we will also learn that the NA also defines the resolution (or resolving power) of the optical system 09/22/04 wk3-b-9
Entrance & exit pupils image through preceding elements image through succeeding elements entrance pupil multi-element optical system exit pupil 09/22/04 wk3-b-10
The Chief Ray Starts from off-axis object, Goes through the center of the Aperture 09/22/04 wk3-b-11
The Field Stop Limits the angular acceptance of Chief Rays 09/22/04 wk3-b-12
Entrance & Exit Windows image through preceding elements image through succeeding elements entrance window multi-element optical system exit window 09/22/04 wk3-b-13
All together entrance window entrance pupil field stop aperture stop exit pupil exit window 09/22/04 wk3-b-14
All together entrance window entrance pupil field stop aperture stop exit pupil exit window 09/22/04 wk3-b-15
Example: single-lens camera object plane 1 st FP 2 nd FP size of film or digital detector image array plane 09/22/04 wk3-b-16
Example: single-lens camera 1 st FP 2 nd FP object plane Aperture Stop & Entrance Pupil image plane 09/22/04 wk3-b-17
Example: single-lens camera 1 st FP 2 nd FP object plane Exit pupil (virtual) Aperture Stop & Entrance Pupil image plane 09/22/04 wk3-b-18
Example: single-lens camera chief ray 1 st FP 2 nd FP object plane Field Stop & Exit Window 09/22/04 wk3-b-19
Example: single-lens camera chief ray 1 st FP 2 nd FP Entrance Window Field Stop & Exit Window 09/22/04 wk3-b-20
Example: single-lens camera 2 nd FP 1 st FP Entrance Window Exit pupil (virtual) Aperture Stop & Entrance Pupil Field Stop & Exit Window 09/22/04 wk3-b-21
Example: single-lens camera 2 nd FP 1 st FP Entrance Window Exit pupil (virtual) Aperture Stop & Entrance Pupil Field Stop & Exit Window 09/22/04 wk3-b-22
Example: single-lens camera vignetting 1 st FP 2 nd FP Aperture Stop 09/22/04 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) 09/22/04 wk3-b-24 Insect eye: similar, but much simpler processor (human brain = ~10 11 neurons; insect brain = ~10 4 neurons)
Anatomy of the human eye Images removed due to copyright concerns 09/22/04 wk3-b-25 W. J. Smith, Modern Optical Engineering, McGraw-Hill
Image removed due to copyright concerns Eye schematic with typical dimensions Photographic camera Image removed due to copyright concerns 09/22/04 wk3-b-26
Accommodation (focusing) Remote object (unaccommodated eye) Proximal object (accommodated eye) 09/22/04 wk3-b-27 Comfortable viewing up to 2.5cm away from the cornea
Eye defects and their correction Images removed due to copyright concerns from Fundamentals of Optics by F. Jenkins & H. White 09/22/04 wk3-b-28
The eye s digital camera : retina Images removed due to copyright concerns 09/22/04 wk3-b-29 http://www.mdsupport.org
The eye s digital camera : retina rods: intensity (grayscale) cones: color (R/G/B) Images removed due to copyright concerns 09/22/04 wk3-b-30 http://www.phys.ufl.edu/~avery/
Retina vs your digital camera Retina: variant sampling rate Digital camera: fixed sampling rate 09/22/04 wk3-b-31 (grossly exaggerated; in actual retina transition from dense to sparse sampling is much smoother)
Retina vs your digital camera Retina: blind spot not noticeable Digital camera: bad pixels destructive 09/22/04 wk3-b-32
Retina vs your digital camera Images removed due to copyright concerns Retinal image CCD image 09/22/04 wk3-b-33 http://www.klab.caltech.edu/~itti/
Spatial response of the retina lateral connections Image removed due to copyright concerns 09/22/04 wk3-b-34 http://webvision.med.utah.edu/
Spatial response of the retina lateral connections 09/22/04 wk3-b-35 http://www.phys.ufl.edu/~avery/
Spatial response of the retina lateral connections Explanation of the flipping dot illusion: the Mexican hat response Image removed due to copyright concerns 09/22/04 wk3-b-36 http://faculty.washington.edu/wcalvin
Temporal response: after-images 09/22/04 wk3-b-37 http://dragon.uml.edu/psych/
Seeing 3D Images removed due to copyright concerns 09/22/04 wk3-b-38 http://www.ccom.unh.edu/vislab/viscourse
09/22/04 wk3-b-39
The compound eye Images removed due to copyright concerns 09/22/04 wk3-b-40
Elements of the compound eye: ommatidia (=little eyes) Images removed due to copyright concerns 09/22/04 wk3-b-41 image formation: blurry, but computationally efficient for moving-edge detection
Reflective Optics s s Example: imaging by a spherical mirror 09/22/04 wk3-b-42
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 09/22/04 wk3-b-43
Reflective optics formulae Imaging condition 1 s + 1 s = 2 R Focal length f = R 2 Magnification s m x = s m α = s s 09/22/04 wk3-b-44
09/22/04 wk3-b-45 The Cassegrain telescope
The Scheimpflug condition 09/22/04 wk3-b-46 The object plane and the image plane intersect at the plane of the lens.