Vision 1. Physical Properties of Light. Overview of Topics. Light, Optics, & The Eye Chaudhuri, Chapter 8

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1 Vision 1 Light, Optics, & The Eye Chaudhuri, Chapter Overview of Topics Physical Properties of Light Physical properties of light Interaction of light with objects Anatomy of the eye 2 3

2 Light A form of electromagnetic (EM) radiation (along with gamma rays, UV light, radio, etc.) EM radiation varies by: Wavelength Intensity Polarity Wavelength Abbreviated λ (lambda) Measured in units of distance, such as angstroms or nanometers (nm, 1x10-9 ) Visible light (to humans) ranges from 400 nm to 700 nm Variations in wavelength give rise to colour experience, but relationship is complex. 4 5 Wavelength Wavelength 6 6

Wavelength = 1/Frequency Frequency = 1/Wavelength! Example: Frequency of 10 cycles/meter = 0.

With light we talk mostly in terms of wavelength.

3 Wavelength Wavelength vs. Frequency Long λ (perceived as red) Medium λ (perceived as green) Short λ (perceived as blue) Wavelength = 1/Frequency Frequency = 1/Wavelength! Example: Frequency of 10 cycles/meter = 0.1 meters/cycle of wavelength! Example: Wavelength of.001 seconds/cycle = 1000 cycles/second (i.e., 1000 Hz) With sound we talk mostly in terms of frequency. With light we talk mostly in terms of wavelength. 6 7 Wavelength nm Why is vision limited to such a narrow range? One reason is that this is where most of the energy in sunlight is Some animals do see somewhat outside the human range, however 8 9

Not One λ, But Many Natural lights have a range of λs, each with its own intensity.

part) by its intensity spectrum 10 11 Example Intensity Spectra Intensity Intensity

Human vision can handle between about 10-6 and 10 7 cd/m 2 (beyond this, damage occurs)

4 Not One λ, But Many Natural lights have a range of λs, each with its own intensity. Only laser lights approximate a single λ A light s subjective colour is determined (in part) by its intensity spectrum Example Intensity Spectra Intensity Intensity Measured in units of power per area, such as candela/m 2 (cd/m 2 ) or photons/receptor Human vision can handle between about 10-6 and 10 7 cd/m 2 (beyond this, damage occurs) Variations in intensity give rise to the sensation of brightness, but relationship is nonlinear 12 13

$Intensity Polarity Absolute threshold, under ideal circumstances, 100 photons (!!!) Weber fraction.08 Stephen s Power Law exponent.33 to.$ oscillate orthogo

5 Intensity Polarity Absolute threshold, under ideal circumstances, 100 photons (!!!) Weber fraction.08 Stephen s Power Law exponent.33 to.50, depending on size and duration Light waves are transverse (unlike sound) They consist of an electric field and a magnetic field that oscillate orthogonally Polarity refers to the angle (e.g., in degrees) of the electric component Polarity Light from the sun is of mixed polarity across most of the sky Polarity Light from the sun is highly polarized across a strip of sky that is orthogonal to the direction of the sun Humans cannot perceive this quality of light, but some animals can (e.g., desert ants, bees) and use it to navigate But reflected light becomes plane polarized Some substances can filter out lights of a given polarity (e.g., polarized sunglasses) 16 17

Desert Ant Navigation Questions What are three characteristics of light? What are their units of measurement?

$18 19 Emitted Light Light is emitted from a source and travels in all directions until absorbed, refracted or reflected$ array of linear light beams pointing out in all directions from the source Emitted Light At a sufficient distance

array of linear light beams pointing out in all directions from the source Emitted Light At a sufficient distance

6 Desert Ant Navigation Questions What are three characteristics of light? What are their units of measurement? What is the relationship between physical intensity and subjective intensity of light? Emitted Light Light is emitted from a source and travels in all directions until absorbed, refracted or reflected This can be thought of as either: A series of expanding spherical wavefronts coming out of the light source An spherical array of linear light beams pointing out in all directions from the source Emitted Light At a sufficient distance (called optical infinity),... Spherical wave fronts can be treated as flat Light rays can be treated as parallel By convention, optical infinity is said to be 6 m

Inverse-Square Law (again) Inverse-Square Law (again) Energy from a light source is spread over an area proportional to the square of the distance Energy from a light source is spread over an area

It applies to any form of emitted energy. This is the same rule as we saw with sound. It applies to any form of emitted energy.

7 Inverse-Square Law (again) Inverse-Square Law (again) Energy from a light source is spread over an area proportional to the square of the distance Energy from a light source is spread over an area proportional to the square of the distance 9 rays / square 2.25 rays/square 1 ray/square Intensity = 1/ d 2 Intensity = 1/ d 2 d This is the same rule as we saw with sound. It applies to any form of emitted energy. This is the same rule as we saw with sound. It applies to any form of emitted energy. 2d 3d Light s Journey to the Eye To get to the eye, light must first be emitted by a source (e.g., a lightbulb or the sun) Light then goes through a number of stages, each of which modifies or structures it: Transmission through a medium (e.g., air or water) Interactions with surfaces of objects Transmission through a medium (again) Interactions with outer structure of the eye Interactions with structures of the retina Light s Journey to the Eye At each stage, several things can happen to the particle that make up a light. They can be: Transmitted (also refracted or scattered) Absorbed (re-emitted as heat) Reflected (in one of two different ways) These are not mutually exclusive: Several can happen with the same object or medium 24 25

$medium results in refraction, an organized change in direction (e.g,.$ prescription gl

, fogged glass) Light Absorption Can be selective by wavelength Absorbed photons are re-emitted as

8 Light Transmission Can be selective by wavelength (e.g., rose-coloured glasses) Change in density of medium results in refraction, an organized change in direction (e.g,. prescription glasses) Can result in scatter, a disorganized change in direction (e.g., fogged glass) Light Absorption Can be selective by wavelength Absorbed photons are re-emitted as heat Darker objects absorb more photons, get hotter in the sun Light Reflection Transmission Specular Reflection Diffuse Reflection Any light not absorbed or transmitted is reflected. Usually selective by wavelength. Gives rise to colours of opaque objects (in part). Body Reflection (aka Diffuse): light is scattered in all directions (e.g., matte paper) Specular Reflection: light is reflected at an angle opposite the angle of incidence (e.g., a mirror) 28 29

9 Absorption Reflectance (Specular) Reflectance (Diffuse) Transmission Refraction Scatter Light s Journey to the Eye Light s Journey to the Eye Eye Object Eye Object 31 31

10 Light s Journey to the Eye Light s Journey to the Eye Eye Object Eye Object Light s Journey to the Eye Light s Journey to the Eye Eye Object Eye Object 31 31

Light s Journey to the Eye Light Emitted Transmitted through medium Transmitted through Eye structures Eye Transmitted through medium Reflects

11 Light s Journey to the Eye Light Emitted Transmitted through medium Transmitted through Eye structures Eye Transmitted through medium Reflects off Object Object Eye Object Light s Journey to the Eye Object Object Eye Light s Journey to the Eye Eye Light s Journey to the Eye 32 32

$Object Object Eye Light s Journey to the Eye Eye Light s Journey to the Eye 32 32 Transmitted/Refracted by Object Transmitted through medium Light$

12 Object Object Eye Light s Journey to the Eye Eye Light s Journey to the Eye Transmitted/Refracted by Object Transmitted through medium Light Emitted Object Object Eye Light s Journey to the Eye Transmitted through medium Transmitted through Eye structures Eye Light s Journey to the Eye 32 32

13 Questions Name 6 different things that can happen to light when it encounters and object. What is the difference between specular and lambertian reflection? What is the significance of the fact that light is structured by the environment? Anatomy of The Eye Fovea 34 34

14 Macula Fovea Macula Fovea Optic Disc Anatomy of the Eye Anatomy of the Retina 35 36

point in its field of view to a small point on the imaging surface.

15 Focus An acute imaging system (camera or eye) forms a sharp image on its imaging surface (film or retina) To do so it must direct the light from each point in its field of view to a small point on the imaging surface. This can be accomplished by pin-hole light gathering and/or by using lenses

Pinhole cameras (camera obscura) use this principle, with a hole that is

16 39 39 Pinhole Light Gathering One way to sharpen light is to allow it to reach the imaging surface via only a small opening. Pinhole cameras (camera obscura) use this principle, with a hole that is about.5 mm in diameter. Problem: This allows in only a small amount of light, creating dim images

$41 Lens: Transparent surface that transmits and refracts light: Convex Lens: Gathers light to a focal point Examples: Magnifying glasses, reading glasses, glasses to correct hyperopia.$

17 Lenses Exposure Duration: 20 Minutes! 41 Lens: Transparent surface that transmits and refracts light: Convex Lens: Gathers light to a focal point Examples: Magnifying glasses, reading glasses, glasses to correct hyperopia. Concave Lens: Spreads light beams apart, so no real focal point (but there is a virtual one) Examples: Glasses to correct myopia 42 Lenses Strength measured in diopters (dp). Positive dp = Convex. Focuses light to a point 1/dp meters behind the lens. Negative dp = Concave. Spreads light beams out. Virtual focal point is 1/dp meters in front of lens (i.e. back in direction light came from) F = 1/dp dp = 1/F 43 44

18 dp lens, focal distance = 1 m +1 dp lens, focal distance = 1 m 44 44

19 +1 dp lens, focal distance = 1 m +1 dp lens, focal distance = 1 m +2 dp lens, focal distance =.5 m dp lens, focal distance = 1 m +2 dp lens, focal distance =.5 m Note greater convexity of +2 dp lens vs. +1 dp lens 44 45

20 dp lens, focal distance = -1 m 45 45

21 -1 dp lens, focal distance = -1 m -1 dp lens, focal distance = -1 m dp lens, focal distance = -1 m -1 dp lens, focal distance = -1 m -2 dp lens, Focal Distance = -0.5 m 45 45

22 -1 dp lens, focal distance = -1 m -2 dp lens, Focal Distance = -0.5 m Combining Pinholes & Lenses Combining a convex (+dp) lens with a pinhole allows the pinhole to be bigger ( brighter images) while still having sharp focus. The eye has a quite large pinhole, the pupil, which varies from 2 to 7 mm in diameter. It also has a powerful focusing system in the form of the cornea and crystalline lens Note greater concavity of -2 dp lens vs. -1 dp lens Small Pinhole: Focus is okay, but image dark due to small amount of light allowed to enter Small Pinhole: Focus is okay, but image dark due to small amount of light allowed to enter Large Pinhole: Focus is poor (large representation of each point of light), but image bright due to large amount of light allowed to enter Large Pinhole: Focus is poor (large representation of each point of light), but image bright due to large amount of light allowed to enter Large Pinhole w/ Lens: Focus is excellent, and image bright due to large amount of light allowed to enter Large Pinhole w/ Lens: Focus is excellent, and image bright due to large amount of light allowed to enter 47 47

23 Small Pinhole: Focus is okay, but image dark due to small amount of light allowed to enter Combining Lenses Large Pinhole: Focus is poor (large representation of each point of light), but image bright due to large amount of light allowed to enter Large Pinhole w/ Lens: Focus is excellent, and image bright due to large amount of light allowed to enter For thin lenses placed close together, one can simply add their dioptres to determine the net effect. For instance, putting a +3 dp lens on top of a +5 dp effectively creates a +8 dp lens Likewise, a +3 dp lens and a -3 dp lens would simply cancel each other out Questions What are two principles by which the eye creates a focussed image on the retina? What is the focal distance of a +10 diopter lens? What about -5 diopters? Why is it important that each point in the environment be represented on the retina by a small point? Cornea & Crystalline Lens: Focusing Images on the Retina The cornea is (on average) a +43 dp lens The crystalline lens is also a lens that can vary its shape to +15 to +25 dp Total focussing power is thus = 58 dp when lens is relaxed and 68 dp at maximum accommodation. Eye is about 25 mm in diameter, but distance from lens to retina is about 18 mm ( 1/58 m)

24 Emmetropic eye: light focussed to a point on the retina Focus Light Rays (parallel, from optical infinity) Emmetropic eye: light focussed to a point on the retina Focus Light Rays (parallel, from optical infinity) Emmetropic eye: light focussed to a point on the retina Focus Light Rays (parallel, from optical infinity) Emmetropic eye: light focussed to a point on the retina Focus Light Rays (parallel, from optical infinity) Myopic eye: light focussed in front of retina Myopic eye: light focussed in front of retina 51 51

25 Emmetropic eye: light focussed to a point on the retina Focus Light Rays (parallel, from optical infinity) Emmetropic eye: light focussed to a point on the retina Focus Light Rays (parallel, from optical infinity) Myopic eye: light focussed in front of retina Myopic eye: light focussed in front of retina Myopic eye with corrective artificial lens (-dp) Myopic eye with corrective artificial lens (-dp) Emmetropic eye: light focussed to a point on the retina Myopic eye: light focussed in front of retina Myopic eye with corrective artificial lens (-dp) Focus Light Rays (parallel, from optical infinity) Accommodation When objects are closer than optical infinity, light rays from points are not parallel. Therefore, the same amount of bending as for distant objects would produce blur Luckily, the crystalline lens can change shape to accommodate for this (up to a point) 51 52

26 The Near Point Accommodation & Presbyopia When objects get too close, the crystalline lens can not change its shape enough to accommodate, so image becomes defocussed. The distance at which this happens (about 10 cm for most of you) is called the near point. Presbyopia: As we age, the lens becomes harder and accommodation becomes limited, so the near point gets further away. A convex (+dp) lens can correct for this Accommodation & Presbyopia Accommodation & Presbyopia 54 54

27 Accommodation & Presbyopia Accommodation & Presbyopia Non-accomodated eye: light not focussed to a point on the retina Accommodation & Presbyopia Non-accomodated eye: light not focussed to a point on the retina Accommodation & Presbyopia Non-accomodated eye: light not focussed to a point on the retina Accomodated eye: light focussed to point on the retina (note fatter lens) 54 54

28 Accommodation & Presbyopia Non-accomodated eye: light not focussed to a point on the retina Accomodated eye: light focussed to point on the retina (note fatter lens) Accommodation & Presbyopia Non-accomodated eye: light not focussed to a point on the retina Accomodated eye: light focussed to point on the retina (note fatter lens) Accommodation & Presbyopia Non-accomodated eye: light not focussed to a point on the retina Accomodated eye: light focussed to point on the retina (note fatter lens) Accommodation & Presbyopia Non-accomodated eye: light not focussed to a point on the retina Accomodated eye: light focussed to point on the retina (note fatter lens) Presbyopic eye with corrective artificial lens (+dp) 54 54

Presbyopia The near point becomes more distant with age Hyperopia Lens is not powerful enough for length of eye, so images are blurred In the young, accommodation compensates, but causes eye-strain

29 Presbyopia The near point becomes more distant with age Hyperopia Lens is not powerful enough for length of eye, so images are blurred In the young, accommodation compensates, but causes eye-strain Corrected using convex (+dp) lenses Vocabulary Emmetropia/Emmetropic: An eye whose lightbending power matches its length. 6/6 vision Myopia/Myopic: Eye has too strong a lens for its length. Near-sightedness. Hyperopia/Hyperopic: Eye has too weak a lens for its length. Far-sightedness. Presbyopia/Presbyopic: Older eye s lens unable to change shape to accommodate for near targets. Questions What is emmetropia? When are images defocussed in myopia? What kind of lens corrects for this? When are images defocussed in presbyopia? What kind of lens corrects for this? 57 58

Questions If a child s eye is 10 mm (.01 m) from lens to retina, how powerful (in dp) does her lens system have to be for her to be emmetropic? What if her eye s natural lens system was 95 dp.

30 Questions If a child s eye is 10 mm (.01 m) from lens to retina, how powerful (in dp) does her lens system have to be for her to be emmetropic? What if her eye s natural lens system was 95 dp. What kind of a lens might we prescribe? The Retinal Image So far, we ve largely discussed point sources of light, but what about extended objects? These can be thought of as consisting of a large number of point sources The Retinal Image The Retinal Image Due to the way lenses work, the image on the retina is upside-down and backwards This does not actually pose any problem in terms of analysis of image information Due to the way lenses work, the image on the retina is upside-down and backwards This does not actually pose any problem in terms of analysis of image information 61 61

Retinal Image Objects at distances other than the depth of focus are blurred The degree of blur

31 The Retinal Image Due to lens aberrations, the image on the retina is of higher quality in the centre than at the edges The distribution of receptors in the retina is sparser here too The Retinal Image Objects at distances other than the depth of focus are blurred The degree of blur depends on pupil size Thus, we have greater depth of field under bright conditions than dim ones 62 63

Human Eye and Colourful World Science. Intext Exercise 1

Human Eye and Colourful World Science. Intext Exercise 1 Intext Exercise 1 Question 1: What is meant by power of accommodation of the eye? Solution 1: When the ciliary muscles are relaxed, the eye lens becomes thin, the focal length increases, and the distant