Design of photographic lens

1
Design of photographic lens

• Shinsaku Hiura
• Osaka University

2
Depth of field

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

3
Defocus
Focused at infinity

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

4
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?

5
Aperture and Defocus
Focused at infinity

• The smaller aperture, we have smaller defocus

6
Amount of defocus

• Circle of Confusion is the radius of defocus on
  the image plane
• Depends on F-no and d

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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,
• 1/10001/1500 of diagonal length
• permissible circle of confusion(e)

8
Permissible circle of confusion
35mm camera(135 format) 36mm x 24mm Diagonal
length 43.3mm

• For 35mm camera,e1/30mm is commonly used
• 1/1300 of diagonal length
• For digital camera, pitch of pixel decides
• For 1/3inch 2Mega Pixel, approx. 3µm

Digital camera (2/3 inch 1/3 inch) 8.8x6.6mm
4.8x3.6mm Diagonal length 11mm 6mm
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depth of focus
e 1/30mm
Depth of focus

• Depth of focusdepth of the focus point within
  permissible circle of confusion
• Approximately 2Fe
• Because eltltf

10
Effective F-no.
radD
Focal length f
b
a

• If the object is close to the object, we have to
  use effective F-no.
• We can not assume b?f

11
depth of field
Depth of field

• Depth of fieldrange of in focus at the object
  area

12
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?

13
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 0.3140.133mm
• Focused range is 5.6m13.9m
• Depth of field is 8.3m

14
Depth of focus indicator

• For F4 , depth of focus is 5m 10m

15
Depth of focus

• Old Carl Zeiss lens(Germany) for
  Hasselblad(Sweden)

16
Depth of focus scale

• Underwater camera Nikonos

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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.

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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
• 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)

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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?

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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 - 1025mm
• 25mm 477mm - 525mm
• Depth of field is same when F-no and
  magnification ratio are same

21
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)

22
Practice (7)

• Permissible circle of confusion is 1/30mm. What
  is the hyperfocal distance of 50mm F4 lens?

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Practice (7)answer

• Depth of image of 50mm F4 is 4/30mm for one side
• This is good for lens displacementfocused
  distance is 18.8m
• Nearest object in focus is at 9.4m
• Approximately half of the distance of just
  focused object

24
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

25
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?

26
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

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Scaled Design

• Same field of view, F-no
• Focal length, depth of field, depth of focus are
  different

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Why digital camera

• Scaled design of ratio 1/41/8
• Depth of field is 4 8 times deeper
• Easy to take small objects
• If life size, object is 1/41/8
• 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 1/161/64