Design of photographic lens

Shinsaku Hiura

Osaka University

Vignetting

Sensitivity is not uniformFor photographic lenses, 50% is still permissible

製品例

cos4 law

Without vignetting, irradiance of peripheral is still very small, cos4θ (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, cos4

θ

1

1/cosθLens is far fromthe lens (square)

Lens is tiltedfrom the film

Incoming ray is oblique

Telephoto lensRear 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 methodTwo 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 focusCompact cameras“range finder” camera

Distortion-sensitive applicationsScan lens of Copy machine, FAX

Symmetric lens(2)

Design is almost symmetric to the aperturePerfect symmetric lens is not so common for

photographic lens, but used for scannersTransversal aberration can be cancelled out

• Distortion• coma• Transversal chromatic aberration

2.1cm F4

2.5cm F4

2.8cm F3.5

3.5cm 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 lensRetrofocus lens

Example of zoom lens

Aberration of each group must be conpensated independently

Canon zoom lens 35-70mm F2.8-3.5 (1972)

Zoom lens (2)

Getting more complex aspherical, etc.

Teleconverter(1)

Diverging lens begind the master lens extends the focal lengthAperture is same larger F no.

The principle of the rear-converterrear-converter

Master lens

Teleconverter(2)

Inserted between the lens and SLR camera

Master lens rear converter

Front converter Attached in front of

the lensPopular for video

cameras (lens is fixed to the body)

Ｆ no. is not changed

Converter itself has no diverging / converging effectCalled “afocal”

tele

wide

Master lens

Master lens

Front converter

Front converter

Optics not for cameras

Telescope(1) – opera glasses

Attaching front tele-converter for eyeballGalilerian (= Galileo type) terescope

f1

f2

Lens of the eyeeyepiece

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)

f1

f2

Lens of the eyeeyepiece

Objective lens

Keplerian Telescope

Loupe

Transfer near object to farIn 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 = 1 + 250/f

250

x

Lens of the eye

Loupe

Microscope

Magnified image by objective lens is observed using loupeImage is invertedMagnification ratio : Magnification ratio of objective lens

x magnification ratio of eyepiece

Lens of the eyeeyepiece

Objective lens

HMD

Optics of MHD is a loupe

Lens of the eyelens

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