Design of photographic lens Shinsaku Hiura Osaka University

Depth of field Practically, sufficient small defocus could be ignored Approximately in focus Several important concepts Depth of field Depth of image Hyperfocal distance

Defocus Finite tickness (Radius) of entering ray bundle is the source of defocus Focused at infinity

Focusing and Defocus It is impossible to focus at different distance at a same time So, what is “approximately in focus”? Focused at infinity Focused at finite distance

Aperture and Defocus The smaller aperture, we have smaller defocus Focused at infinity

Amount of defocus “Circle of Confusion” is the radius of defocus on the image plane Depends on F-no and δ

Approximately in focus Resolution of human vision 5’, 1’, 40’’, etc. (depends on the condition) If 2’, 0.17mm at 30cm distance is resolved For a photograph with 300mm width, 1/1700 For usual photographs, 1/1000~1/1500 of diagonal length permissible circle of confusion （ ε ）

Permissible circle of confusion For 35mm camera ， ε=1/30mm is commonly used 1/1300 of diagonal length For digital camera, pitch of pixel decides For 1/3inch 2Mega Pixel, approx. ３ μm 35mm camera （ 135 format ） 36mm x 24mm Diagonal length : 43.3mm Digital camera (2/3 inch ～ 1/3 inch ） 8.8x6.6mm ～ 4.8x3.6mm Diagonal length : 11mm ～ 6mm

depth of focus Depth of focus=depth of the focus point within permissible circle of confusion Approximately ２・ F ・ ε Because ε<<f ε= 1/30mm Depth of focus

Effective F-no. If the object is close to the object, we have to use effective F-no. We can not assume b ≒ f Focal length = ｆ ba rad=D

depth of field Depth of field ＝ range of in focus at the object area Depth of field

Practice (4) Let us assume that the permissible circle of confusion is 1/30mm. If we set the focus a 50mm F4 lens to the object 8m away, what is the range of depth of field?

Practice (4)answer For F4 lens, depth of focus at one side is 4/30 [mm] = 0.133mm 50mm lens, focused at 8m, the forward displacement of the lens is 0.314mm Therefore, depth of field is 0.314±0.133mm Focused range is 5.6m ～ 13.9m Depth of field is 8.3m

Depth of focus indicator For F:4, depth of focus is 5m+ ～ 10m+

Depth of focus Old Carl Zeiss lens(Germany) for Hasselblad(Sweden)

Depth of focus scale Underwater camera “Nikonos”

Practice (5) Permissible circle of confusion is 1/30mm, we use 50mm lens. Set the focus of the lens and the F-number, to focus to the object from 2m to 10m.

Practice (5) answer Lens displacement for 2m object with 50mm lens is 1.282mm lens displacement for 10m object with 50mm lens is 0.251mm Ideal displacement of the lens is the center of two plance, therefore, ( )/2 = 0.767mm In this case, lens is focused at 3.3m Depth of focus is ( ) = 1.031mm, so, F-no is decided by = 2 * F * 1/30 F = 15.5 （ approx. F16 ）

Practice (6) Permissible circle of confusion is 1/30mm. If we set same magnification ratio 1/20 for both 50mm F2 and 25mm F2, are the depth of field different or not?

Practice (6)answer Object distance （ magnification = 1/20 ） 50mm : 1000mm, 25mm : 500mm Lens displacement 50mm : 2.63mm, 25mm : 1.316mm Depth of field （ F2, circle = 1/30mm ） Depth of focus is 2/30mm for each side 50mm : 977mm mm 25mm : 477mm - 525mm Depth of field is same when F-no and magnification ratio are same

Hyper-focal Distance Depth of focus which just includes infinity Used for fixed focus camera (lens with film, very cheap digital camera, cellphone camera) Hyper-focal Distance

Practice (7) Permissible circle of confusion is 1/30mm. What is the hyperfocal distance of 50mm F4 lens?

Practice (7)answer Depth of image of 50mm F4 is 4/30mm for one side This is good for lens displacement focused distance is 18.8m Nearest object in focus is at 9.4m Approximately half of the distance of “just focused object”

Practice (8) Same permissible circle of confusion 1/30mm, same F-no F4 hyperfocal distances of 50mm, 25mm, 12.5mm lenses? 50mm : 18.8m 25mm : 4.7m 12.5mm : 1.18m Depth of field is rapidly (quadratic) deepen for short focal length

Practice (9) Permissible circle of confusion is 1/1000 of diagonal length of image. We have to image sensors with diagonal length 40mm and 10mm Same field of view (ex. Focal length is same as the diagonal length of image), same F-no Hyperfocal distance?

Practice (9)answer Permissible circle of confusion ： 40mm : 0.04mm, 10mm : 0.01mm Hyperfocal distance 40mm : 10m, 10mm : 2.5m Hyperfocal distance is proportional to the image size Small camera has deeper depth of field

Scaled Design Same field of view, F-no Focal length, depth of field, depth of focus are different Hyper-focal distance

Why digital camera Scaled design of ratio 1/4~1/8 Depth of field is 4 – 8 times deeper Easy to take small objects If life size, object is 1/4 ～ 1/8 Easy to focus at close object Lens displacement is 1/4, focused distance is 1/4 If the object is at the same distance, lens displacement is 1/16 ～ 1/64