Focus Tues. Jan. 16, 2018 1 Last lecture aperture (and f-number) - - PowerPoint PPT Presentation

β–Ά
focus
SMART_READER_LITE
LIVE PREVIEW

Focus Tues. Jan. 16, 2018 1 Last lecture aperture (and f-number) - - PowerPoint PPT Presentation

Mar 26, 2024 491 likes β€’944 views

COMP 546 Lecture 2 Focus Tues. Jan. 16, 2018 1 Last lecture aperture (and f-number) visual angle binocular disparity and depth Today Image sampling Lenses, blur, focus (accommodation) 2 The ability to see detailed

slide-1
SLIDE 1

1

COMP 546

Lecture 2

Focus

  • Tues. Jan. 16, 2018
slide-2
SLIDE 2

2

Last lecture

  • aperture (and f-number)
  • visual angle
  • binocular disparity and depth

Today

  • Image sampling
  • Lenses, blur, focus (accommodation)
slide-3
SLIDE 3

3

The ability to see detailed patterns is limited by:

  • image sampling (density of photoreceptors/pixels)
  • defocus blur (due to finite size aperture)

small aperture

slide-4
SLIDE 4

Image Sampling

4

What is the density of photoreceptors? What is the angle between samples?

assume pinhole camera

slide-5
SLIDE 5

5

s = distance (mm) between samples f = diameter of eye

slide-6
SLIDE 6

6

s = distance (mm) between samples f = diameter of eye

𝑑 𝑔

= angle (radians) between samples

𝑔 𝑑 𝜌 180

= samples per visual angle (degrees)

slide-7
SLIDE 7

Defocus blur: two ways to think about it

7

Each image pixel receives light from many scene points. Each scene point sends light that reaches many image points.

slide-8
SLIDE 8

8

slide-9
SLIDE 9

Evolution of the Lens of the Eye

http://www.youtube.com/watch?v=mb9_x1wgm7E (Richard Dawkins video)

9

slide-10
SLIDE 10

Focal length and power of a thin lens

parallel rays of light

f f is the focal length 1/f is the β€˜power’.

10

slide-11
SLIDE 11

Focal length f used in two ways

Last lecture:

distance from aperture to sensor plane

11

Today:

distance behind lens where parallel incoming rays converge (It may not coincide exactly with sensor plane.)

slide-12
SLIDE 12

Conjugate points

For every 3D point on one side of a thin lens, the rays diverging from that point will converge at some other 3D point on the

  • pposite side of the lens.

12

slide-13
SLIDE 13

1 focal length of lens = 1

  • bject distance +

1 image distance

Thin lens model

1 meters Units: is called β€œdiopters” (D)

13

slide-14
SLIDE 14

Special case: object at infinity

f

1 focal length of lens = 1

  • bject distance +

1 image distance

14

slide-15
SLIDE 15

focal plane sensor plane

1 focal length of lens = 1 focal plane distance + 1 sensor distance

Which scene points are in focus?

15

slide-16
SLIDE 16

focal plane sensor plane

Image Blur

16

slide-17
SLIDE 17

Blur and depth

beyond focal plane closer than focal plane at focal plane

17

slide-18
SLIDE 18

focal plane sensor plane

Blur width

Blur width is the spread

  • f rays from

a scene point on the sensor plane.

18

slide-19
SLIDE 19

Exercise

Hold up a finger up at arm’s length: 57 cm. Focus at a distance of 10 m. Eye is 2 cm long. Aperture (pupil) is 3 mm. Q: What is the visual angle of the finger blur width w ? w

19

[I am not claiming that the above numbers correspond to this photo.]

slide-20
SLIDE 20

20

thumb

π‘Žπ‘— π‘Žπ‘‘π‘“π‘œπ‘‘π‘π‘  = .02

focal plane

π‘Žπ‘ = 10 m .57

slide-21
SLIDE 21

21

thumb

Solve for π‘Žπ‘—

π‘Žπ‘— π‘Žπ‘‘π‘“π‘œπ‘‘π‘π‘  = .02

focal plane

π‘Žπ‘’β„Žπ‘£π‘›π‘= .57 π‘Žπ‘ = 10

slide-22
SLIDE 22

β†’ π‘₯ β‰ˆ . 0001 𝑛

π‘Žπ‘— = .0207 π‘Žπ‘‘π‘“π‘œπ‘‘π‘π‘  𝐡 = .003

22

slide-23
SLIDE 23

=

π‘₯ π‘Žπ‘‘π‘“π‘œπ‘‘π‘π‘  β‰ˆ 1 200 𝑠𝑏𝑒

π‘Žπ‘‘π‘“π‘œπ‘‘π‘π‘ 

23

blur width angle

β‰ˆ .3 𝑒𝑓𝑕

slide-24
SLIDE 24

24

Exercise: show that blur width (in radians) is:

focal plane

slide-25
SLIDE 25

25

The aperture (pupil) is the hole in the iris. The iris is in front of the lens. For simplicity, I will not draw the iris in the remaining figures.

slide-26
SLIDE 26

Depth of Field

26

Depth of field is the range of depths that are perceived to be in focus. (In fact, only one depth is in perfect focus. )

slide-27
SLIDE 27

focal plane

27

β€œJust noticeable” blur β€œJust noticeable” blur In focus

Depth of Field

slide-28
SLIDE 28

28

Typical depth of field in human vision is said to be about 0.3 diopters (D). But it depends on many factors:

  • pupil diameter
  • variations between people
  • what is the image being judged ?
  • …
slide-29
SLIDE 29

29

Typical depth of field in human vision is said to be about 0.3 diopters (D). But it depends on many factors:

  • pupil diameter
  • variations between people
  • what is the image being judged ?
  • …

NOTE: it does not depend on the depth of focal plane.

slide-30
SLIDE 30

30

1.43 1 m 5 2 m

Examples where depth of field is about 0.3 diopters.

.7 1 D .2 .5 D infinity 3.3 m .3 D

slide-31
SLIDE 31

31

slide-32
SLIDE 32

Thin lens optics

32

( )( ( ) ( ) )

1 𝑔

1 +

1 𝑔

2 +

1 𝑔

3 +

1 𝑔

4 =

1 𝑔

Equivalent power for a single lens

slide-33
SLIDE 33

33

1 𝑔

π‘‘π‘π‘ π‘œπ‘“π‘ +

1 π‘”π‘šπ‘“π‘œπ‘‘ ≑ 1 𝑔

e.g. 40 + 20 = 60 (diopters, D)

typical values

The cornea has more refractive power than the lens.

slide-34
SLIDE 34

Accommodation

focal plane

  • bject

34

The lens shape can change: muscles squeeze the lens and change its curvature (and power).

slide-35
SLIDE 35

35

1 𝑔

π‘‘π‘π‘ π‘œπ‘“π‘ +

1 π‘”π‘šπ‘“π‘œπ‘‘ = 1

π‘Žπ‘”π‘π‘‘π‘π‘šπ‘žπ‘šπ‘π‘œπ‘“ + 1 π‘Žπ‘‘π‘“π‘œπ‘‘π‘π‘ 

focal plane

  • bject

Adjusting power of lens changes the focal plane distance 1 𝑔

slide-36
SLIDE 36

Presbyopia

36

Older lenses resists shape change.

Range of adjustment of lens power (diopters) Age

slide-37
SLIDE 37

Accommodation & presbyopia

37

30 10 50 age

slide-38
SLIDE 38

Myopia

β€œshort sighted”: can’t focus at infinity

cornea power is too high, given size of eye

38

accommodation depth of field

slide-39
SLIDE 39

Hyperopia

β€œfar sighted”: can’t focus on near field

lens + cornea power are too low, given size of eye

39

accommodation

slide-40
SLIDE 40

40

1 π‘”π‘•π‘šπ‘π‘‘π‘‘π‘“π‘‘ + 1 𝑔

π‘‘π‘π‘ π‘œπ‘“π‘ +

1 π‘”π‘šπ‘“π‘œπ‘‘ ≑ 1 𝑔

  • 3 + 40 + 20 D

)(

e.g. I am myopic. My cornea + lens is too strong.

Lens with negative power

ish ish

slide-41
SLIDE 41

Corrected Myopia:

allows distant vision

41

accommodation depth of field

)(

Far enough! Why?

slide-42
SLIDE 42

Corrected Hyperopia:

allows near vision

42

accommodation depth of field

slide-43
SLIDE 43

Open questions

  • How does the visual system determine if an image

is in focus ? (Define blur.)

  • How does the visual system accommodate ?

(Accommodation interacts with binocular vergence)

  • Is defocus blur a β€œdepth cue” ?

43