depth of field
Depth of field

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

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?

For digital camera, pitch of pixel decides
For 1/3inch 2Mega Pixel, approx. ３μm
depth of focus
ε= 1/30mm
Depth of focus

Depth of focus=depth of the focus point within permissible circle of confusion
Focusing and Defocus
Focused at infinity
Focused at finite distance

It is impossible to focus at different distance at a same time

So, what is “approximately in focus”?
Hyper-focal Distance
Hyper-focal Distance

Depth of focus which just includes infinity

Used for fixed focus camera (lens with film, very cheap digital camera, cellphone camera)

Approximately ２・F・ε
• Because ε<<f
Effective F-no.
f F D b F D

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

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 35mm camera，ε=1/30mm is commonly used

1/1300 of diagonal length
Digital camera (2/3 inch ～1/3 inch） 8.8x6.6mm ～4.8x3.6mm Diagonal length : 11mm ～6mm
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 (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 (9)answer

Permissible circle of confusion：

40mm : 0.04mm, 10mm : 0.01mm 40mm : 10m, 10mm : 2.5m

Hyperfocal distance


Hyperfocal distance is proportional to the image size

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
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, (1.282 + 0.251)/2 = 0.767mm
Aperture and Defocus Focused at infinity

The smaller aperture, we have smaller defocus
Amount of defocus
d
d


F

“Circle of Confusion” is the radius of defocus on the image plane
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
Design of photographic lens
Shinsaku Hiura Osaka University
Depth of field

Practically, sufficient small defocus could be ignored

Approximately in focus

In this case, lens is focused at 3.3m
Depth of focus is (1.282-0.251) = 1.031mm, so, F-no is decided by 1.031 = 2 * F * 1/30

F = 15.5 （approx. F16）

Several important concepts
Depth of field Depth of image Hyperfocal distance

Defocus
Focused at infinity

Finite tickness (Radius) of entering ray bundle is the source of defocus

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?
• 50mm : 977mm - 1025mm • 25mm : 477mm - 525mm

Lens displacement


Depth of field（F2, circle = 1/30mm）


Depth of field is same when F-no and magnification ratio are same
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