MIT 2.71/ /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/ /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 Length BFL: Back Focal Length FP: Focal Point/Plane PS: Principal Surface/Plane

MIT 2.71/ /22/04 wk3-b-3 The significance of principal planes /1 thin lens of the same power located at the 2 nd PS for rays passing through 2 nd FP optical system

MIT 2.71/ /22/04 wk3-b-4 The significance of principal planes /2 thin lens of the same power located at the 1 st PS for rays passing through 1 st FP optical system

MIT 2.71/ /22/04 wk3-b-5 Reminder: imaging condition (thin lens) object image chief ray

MIT 2.71/ /22/04 wk3-b-6 The significance of principal planes /3 object multi-element optical system image? magnification?

MIT 2.71/ /22/04 wk3-b-7 The significance of principal planes /4 object multi-element optical system lateral hold, where f= (EFL)

MIT 2.71/ /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 stop the physical element which limits the angle of acceptance of the imaging system

MIT 2.71/ /22/04 wk3-b-9 Aperture / NA: physical meaning medium of refr. index n 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

MIT 2.71/ /22/04 wk3-b-10 Entrance & exit pupils multi-element optical system image through preceding elements image through succeeding elements entrance pupil exit pupil

MIT 2.71/ /22/04 wk3-b-11 The Chief Ray Starts from off-axis object, Goes through the center of the Aperture

MIT 2.71/ /22/04 wk3-b-12 The Field Stop Limits the angular acceptance of Chief Rays

MIT 2.71/ /22/04 wk3-b-13 Entrance & Exit Windows multi-element optical system image through preceding elements image through succeeding elements entrance window exit window

MIT 2.71/ /22/04 wk3-b-14 All together entrance window exit window entrance pupil exit pupil field stop aperture stop

MIT 2.71/ /22/04 wk3-b-15 All together entrance window exit window entrance pupil exit pupil field stop aperture stop

MIT 2.71/ /22/04 wk3-b-16 Example: single-lens camera object plan e image plan e size of film or digital detector array

MIT 2.71/ /22/04 wk3-b-17 Example: single-lens camera object plan e Aperture Stop & Entrance Pupil image plan e

MIT 2.71/ /22/04 wk3-b-18 Example: single-lens camera object plan e image plan e Exit Pupil (virtual) Aperture Stop & Entrance Pupil

MIT 2.71/ /22/04 wk3-b-19 Example: single-lens camera chief ray Field Stop & Exit Window object plan e

MIT 2.71/ /22/04 wk3-b-20 Example: single-lens camera Entrance window Field Stop & Exit Window chief ray

MIT 2.71/ /22/04 wk3-b-21 Example: single-lens camera Entrance window Field Stop & Exit Window Exit Pupil (virtual) Aperture Stop & Entrance Pupil

MIT 2.71/ /22/04 wk3-b-22 Example: single-lens camera Entrance window Field Stop & Exit Window Exit Pupil (virtual) Aperture Stop & Entrance Pupil

MIT 2.71/ /22/04 wk3-b-23 Example: single-lens camera Aperture Stop vignetting

MIT 2.71/ /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 = ~10 11 neurons; insect brain = ~10 4 neurons)

MIT 2.71/ /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/ /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/ /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/ /22/04 wk3-b-28 Eye defects and their correction Images removed due to copyright concerns from Fundamentals of Optics by F. Jenkins & H. White

MIT 2.71/ /22/04 wk3-b-29 The eye’s “digital camera”: retina Images removed due to copyright concerns

MIT 2.71/ /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)

MIT 2.71/ /22/04 wk3-b-31 Retina vs your digital camera Retina: variant sampling rate Digital camera: fixed sampling rate (grossly exaggerated; in actual retina transition from dense to sparse sampling is much smoother)

MIT 2.71/ /22/04 wk3-b-32 Retina vs your digital camera Retina: blind spot not noticeable Digital camera: bad pixels destructive

MIT 2.71/ /22/04 wk3-b-33 Retina vs your digital camera Retinal imageCCD image Images removed due to copyright concerns

MIT 2.71/ /22/04 wk3-b-34 Spatial response of the retina – lateral connections Images removed due to copyright concerns

MIT 2.71/ /22/04 wk3-b-35 Spatial response of the retina – lateral connections

MIT 2.71/ /22/04 wk3-b-36 Explanation of the “flipping dot” illusion: the Mexican hat response Spatial response of the retina – lateral connections Images removed due to copyright concerns

MIT 2.71/ /22/04 wk3-b-37 Temporal response: after-images

MIT 2.71/ /22/04 wk3-b-38 Seeing 3D Images removed due to copyright concerns

MIT 2.71/ /22/04 wk3-b-39 VIEWING POINT

MIT 2.71/ /22/04 wk3-b-40 The compound eye Images removed due to copyright concerns

MIT 2.71/ /22/04 wk3-b-41 Elements of the compound eye: ommatidia (=little eyes) “image” formation: blurry, but computationally efficient for moving-edge detection Images removed due to copyright concerns

MIT 2.71/ /22/04 wk3-b-42 Reflective Optics Example: imaging by a spherical mirror

MIT 2.71/ /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/ /22/04 wk3-b-44 Reflective optics formulae Imaging condition Focal length Magnification

MIT 2.71/ /22/04 wk3-b-45 The Cassegrain telescope

MIT 2.71/ /22/04 wk3-b-46 The Scheimpflug condition The object plane and the image plane intersect at the plane of the lens. OBJECT PLANE OPTICAL AXIS LENS PLANE IMAGE PLANE