Design of photographic lens Shinsaku Hiura Osaka University

Vignetting Sensitivity is not uniform For photographic lenses, 50% is still permissible 製品例

cos 4 law Without vignetting, irradiance of peripheral is still very small, cos 4 θ (θ is the half of angle of view) Distance from the film to the lens 1/cosθ (effects square) The aperture of the lens seems ellipse (1) Incoming ray to the film is oblique(1)  totally, cos 4 θ 1 1/cosθ Lens is far from the lens (square) Lens is tilted from the film Incoming ray is oblique

Telephoto lens Rear principal point is in front of the lens. Front part of the lens has converging effect, and rear is diverging. (definition of telephoto lens)

Wide-angle (retro-focus) It is used if the back-focus (mechanical clearance behind of the lens) must be long For SLR or 3CCD cameras Rear principle point is behind of the lens. Front part of the lens has diverging power, and the rear elements is converging.

３ＣＣＤ camera Prism for color separation is placed between the lens and the image sensors Little loss of energy Lens design is limited

SLR Focusing screen (ground glass)

AF SLR （１） Contrast method Two images are captured for different distances Lens is moved to maximize the contrast Pentax ME-F (1981)

Phase detection AF Taking lens AF sensor (1-D image sensor)

AF SLR(2) Phase difference detection Minolta Maxxum-7000

Symmetric type lens Standard lens (normal angle of view) Wide angle lens without the requirement of long back focus Compact cameras “range finder” camera Distortion-sensitive applications Scan lens of Copy machine, FAX

Symmetric lens(2) Design is almost symmetric to the aperture Perfect symmetric lens is not so common for photographic lens, but used for scanners Transversal aberration can be cancelled out Distortion coma Transversal chromatic aberration 2.1cm F4 2.5cm F4 2.8cm F cm F2.5

Zoom lens Order and distance of diverging and converging power much affects to the focal length  Moving the elements to change f Telephoto lens Retrofocus lens

Example of zoom lens Aberration of each group must be conpensated independently Canon zoom lens 35-70mm F (1972)

Zoom lens (2) Getting more complex  aspherical, etc.

Teleconverter(1) Diverging lens begind the master lens extends the focal length Aperture is same  larger F no. The principle of the rear-converter rear-converter Master lens

Teleconverter(2) Inserted between the lens and SLR camera Master lens rear converter

Front converter Attached in front of the lens Popular for video cameras (lens is fixed to the body) Ｆ no. is not changed Converter itself has no diverging / converging effect Called “afocal” tele wide Master lens Front converter

Optics not for cameras

Telescope(1) – opera glasses Attaching front tele-converter for eyeball  Galilerian (= Galileo type) terescope f1f1 f2f2 Lens of the eye eyepiece Objective lens

Telescope(2) Both objective and eyepiece is converging lens Keplerian (=Kepler type) telesclope Image is inverted Maginification ratio : (both Galilean / Keplerian) (focal length of objective)/(focal length of eyepiece) f1f1 f2f2 Lens of the eye eyepiece Objective lens

Keplerian Telescope

Loupe Transfer near object to far In general, image is supposed to be at 250mm (distance of distinct vision) Magnification (using thin lens law) 1/x – 1/250 = 1/f, M= 250/x  M = /f 250 x Lens of the eye Loupe

Microscope Magnified image by objective lens is observed using loupe Image is inverted Magnification ratio : Magnification ratio of objective lens x magnification ratio of eyepiece Lens of the eye eyepiece Objective lens

HMD Optics of MHD is a loupe Lens of the eye lens display

HMD Concave mirror works as converging lens off-axis optics is difficult to design  Aspherical curve, combination with lens, etc. Lens of the eye Curved mirror display