Lecture 9.2 Fall 2023: Imaging and Detection by the Eye PDF

IMAGING AND DETECTION BY THE EYE Dr. Anastasia Hadjiconstanti Aknowledgements: Dr C.Zervides  LECTURE LOB’S 66. Explain how the cornea and crystalline lens image light on the retina. 67. Develop optic...

IMAGING AND DETECTION BY THE EYE Dr. Anastasia Hadjiconstanti Aknowledgements: Dr C.Zervides  LECTURE LOB’S 66. Explain how the cornea and crystalline lens image light on the retina. 67. Develop optical models of the eye. 68. Link image formation and eye properties to vision and visual perception. 69. Outline the physics of the perception of colour. 3  STRUCTURE OF THE EYE I The parts of the eye The eye has an average radius of 12 mm.  STRUCTURE OF THE EYE II The cornea is transparent because it is uniform in structure, avascular except in the extreme periphery, and relatively dehydrated. It is covered by a 7–10 µm thick layer of tears, which smoothens over optical irregularities and supplies the cornea with oxygen.  STRUCTURE OF THE EYE III The average radius of curvature of the anterior surface of the cornea is about 7.8 mm in the central region, with a variation among people of about ±0.4 mm, and is flatter in the periphery. The pupil in the iris can vary from 1.5 to 10 mm in diameter. The diameter of the pupil is controlled by an opposing pair of smooth muscles.  STRUCTURE OF THE EYE IV The crystalline lens is suspended and rests on the posterior surface of the iris. This crystalline lens is about 4 mm thick and 9 mm in diameter. It continues to grow as we age, with new layers growing over older layers (onion like).  STRUCTURE OF THE EYE V The formation of an image on the retina is determined by: 1. the indices of refraction of each eye component that the light passes through and 2. by the shapes of the surfaces of these elements. The cornea and crystalline lens are the focusing elements in the eye. The cornea performs about two-thirds of the focusing and the crystalline lens the remaining one-third.  STRUCTURE OF THE EYE VI There are about 120 million rod cells per retina. They have high sensitivity, low spatial acuity (detection of shapes), and are relatively more numerous in the periphery of the retina. The sensitivity of rods peaks near 500 nm. Vision using only rods results in various shades of gray. NIGHT VISION AND PERIPHERAL VISION ARE MOSTLY DUE TO RODS. Rods are about 2 µm in diameter, and far from the fovea they become more widely spaced and many rods are connected to the same nerve fiber.  STRUCTURE OF THE EYE VII Both factors decrease visual acuity in the outer portions of the retina. There are about 6.5 million cone cells per retina. They have low sensitivity—about 1000 × lower than rods—high spatial awareness and are concentrated in the fovea.  STRUCTURE OF THE EYE VIII There are three types of cone cells, with spectral sensitivities peaking near: 1. 445 nm (blue cones), 2. 535 nm (green cones) and 3. 670 nm (red cones). The overall spectral sensitivity due to the rods and cones of humans closely matches the spectrum of solar light reaching land. Sharp vision and color vision are due to cones, thus damage to the fovea leads to visual images that are fuzzy.  STRUCTURE OF THE EYE IX Light acts like light packets, called photons. 𝒉𝒄 The energy of a photon is: 𝑬 = 𝒉𝒇 = where h is the 𝝀 Plank’s constant, f is the frequency of the light, c is the speed of light in vacuum and λ is the light wavelength. Absorption occurs when the photons have energy in ranges that can be absorbed by the photosensitive molecules (rhodopsin) in these cells.  TRANSMISSION OF LIGHT IN THE EYE I Only about 50% of visible light (400–700 nm) incident on the eye reaches the retina to form an image. Losses are due to reflection of light, absorption and scattering. Much of this loss is due to scattering in the eye.  TRANSMISSION OF LIGHT IN THE EYE II This scattered light does not contribute to the desired image even if it hits the retina. Also due to transmission through the retina, there is loss due to absorption and scattering within the retina before light hits the rods and cones. The expression for the portion of light that reflects from an interface between two media with refractive indices n1 and n2 is: 𝒏𝟐 −𝒏𝟏 𝟐 𝑹=. 𝒏𝟐 +𝒏𝟏 The reflected fraction at the air/cornea interface is ≈ 2%.  TRANSMISSION OF LIGHT IN THE EYE III Most of the light from 300 to 400 nm is absorbed by the crystalline lens. There are no important sources of absorption in the visible spectrum.  THE EYE AS A COMPOUND LENS I Several schematic models for the imaging of rays in the eye exist. The most complete model is the Gullstrand exact eye, which has six refractive surfaces and the variation of the refractive index within the lens is included.  THE EYE AS A COMPOUND LENS II The simplest model is the Reduced eye. It has only one refractive interface at the cornea. For this eye, all distances are relative to the single refractive interface.  THE EYE AS A COMPOUND LENS III The next model is called Schematic eye 1. In this model, the refractive index within the crystalline lens is uniform. The figure showing the locations of the four interfaces, the refractive indices of the five media and the radii of the four surfaces.  THIN LENS APPROXIMATION OF THE SCHEMATIC EYE I Consider Schematic eye 1 with four interfaces. The refractive power of each interface is given by: 𝒏𝒊+𝟏 −𝒏𝒊 𝑷𝒊,𝒊+𝟏 =. 𝑹𝒊,𝒊+𝟏 Ignore the distance the rays propagate between the refractive interfaces.  THIN LENS APPROXIMATION OF THE SCHEMATIC EYE II 𝑛2 −𝑛1 1.3771−1.0 For the air/anterior cornea interface: 𝑃12 = = = 48.35 𝐷. 𝑅12 0.0078 𝑛3 −𝑛2 1.3374−1.3771 For the posterior cornea/aqueous humor interface: 𝑃23 = = = −6.11 𝐷. 𝑅23 0.0065 𝑛4 −𝑛3 1.42−1.3374 For the aqueous humor/anterior crystalline lens interface: 𝑃34 = = = 𝑅34 0.0102 8.10 𝐷.  THIN LENS APPROXIMATION OF THE SCHEMATIC EYE III 𝑛5 −𝑛4 1.336−1.42 For the posterior crystalline lens/vitreous humor interface: 𝑃45 = = = 𝑅45 −0.006 14.00 𝐷. The refractive power of the cornea, ignoring its thickness is: Pcornea= P12+P23 = 48.35D-6.11D = 42.24 D. The refractive power of the crystalline lens, again ignoring its thickness, is: Plens= P34+P45 = 8.10D+14.00D = 22.10 D.  THIN LENS APPROXIMATION OF THE SCHEMATIC EYE IV This shows that two-thirds of the refractive power is due to the cornea and one-third is due to the lens. The total refractive power of the eye is: Peye = Pcornea + Plens = 42.24D + 22.10D = 64.34 D. The focal length is found using: 𝒏𝒋 1.336 𝒇=σ = = 0.0208𝐷 = 20.8 𝑚𝑚. 𝒊=𝟏 𝒕𝒐 𝒋−𝒊 𝑷𝒊,𝒊+𝟏 64.34𝐷 The image from this lens falls on the retina, which is 24.20 mm from the anterior surface of the cornea and so this calculated focal length is not exactly correct. But, the lens is 7.6 mm long (anterior cornea surface to posterior surface of crystalline lens).  THIN LENS APPROXIMATION OF THE SCHEMATIC EYE V Thus the focal length is really measured for this type of lens from somewhere between the cornea and crystalline lens. Assuming that it is from the middle (position 3.8 mm), we would expect the image to fall 3.8 mm + 20.8 mm = 24.6 mm from the anterior surface of the cornea, compared to 24.20 mm. What happens when you swim in water? The refractive power of the first (air/anterior cornea) interface changes to: 𝑃12 = 1.3771−1.331 = 5.91𝐷. 0.0078 This is a loss of 42.44 D of refractive power.  THIN LENS APPROXIMATION OF THE SCHEMATIC EYE VI The refractive power of the cornea is 5.91D + (−6.11D) = −0.2D, which means the cornea has essentially no refractive power under water. The total refractive power of the eye is only −0.2D + 22.10D = 21.90D, and the eye sees very blurred images because the focused image would be beyond the retina. Why can we see much better in water when wearing goggles? The images in water are made even blurrier when the water is not perfectly still, because the movement of water causes local variations in the index of refraction.  ACCOMMODATION I The ability to control the focal length of the crystalline lens is called accommodation. The crystalline lens is suspended by ligaments. The tension in these ligaments controls the curvature of the crystalline lens surfaces and thus its focal length. When the tension in ligaments is at a maximum, the crystalline lens flattens and the focal length is at a maximum. The lens equation shows that this flatter lens will produce clear images of distant objects.  ACCOMMODATION II When the ligaments are relaxed, the crystalline lens assumes its more normal spherical shape. The larger curvature of the crystalline lens surfaces produces a shorter focal length, which produces clear images of nearby objects. Such tunability in the eye focal length should allow people to see objects clearly both far and near. The maximum distance from the eye where objects form sharp images is called the far point (FP)—and we would like our FP to be ∞. The nearest distance where objects are clear is the near point (NP)—and we would like our NP to be 25 cm for convenient reading and such.  ACCOMMODATION III Lack of appropriate accommodation is called presbyopia (“old eyes” or “old age vision”). Most of the loss of accommodation with age can be explained by: 1. increase in crystalline lens Young’s modulus, 2. flattening of the lens and 3. decrease in the lens capsule Young’s modulus. CLASS EXAMPLE 1: Beth noticed that in order to read the newspaper in the morning she must hold it further away from herself. She has recently bought a set of reading glasses. In order to read the paper without them, she must hold the newspaper at arm's length. With her glasses on, she can hold the paper as close as 30 cm from her and still read it clearly. If Beth's arms are 55 cm long and she wears her glasses such that they are 2.5 cm in front of her eyes, what is the optical power of her new reading glasses? A. 0.033 D B. 1.73 D C. 3.64 D 28 CLASS EXAMPLE 1 - SOLUTION: We can calculate the optical power of her new glasses by using the known object and image distances. Beth holds the newspaper 0.3 m away from her eye to read it using her new glasses. Given that her glasses sit 0.025 m in front of her eye, the object distance must be do = 0.275 m. Similarly the image distance must be di =(0.025-0.55)=-0.525 m. The negative image distance is quite important, as this indicates the corrective lenses are producing the required virtual image. Sign Convention for Lenses All figures are drawn with light initially travelling from left to right, so the object is to the left of the lens. The distance from the object to a lens is positive. The distance from a lens to a real image is positive. (Image is located to the right of the lens.) The distance from a lens to a virtual image is negative. (Image is located to the left of the lens.) For a convex (converging) lens, f is positive. For a concave (diverging) lens, f is negative. CLASS EXAMPLE 1 - SOLUTION: The thin-lens equation will enable us to calculate the optical power of Beth’s new reading glasses: 1 1 1 1 1 𝑃𝐺𝑙𝑎𝑠𝑠𝑒𝑠 = = + = + = 1.73 𝐷 𝑓𝑔𝑙𝑎𝑠𝑠𝑒𝑠 𝑑0 𝑑1 0.275 −0.525 The optical power of the corrective lenses in Beth’s new glasses is 1.73 D.  IMPERFECT HUMAN VISION I Hyperopia The first eye shown suffers from farsightedness, which is also known as hyperopia. This is due to a focal length that is too long, causing the image to be focused behind the retina, making it difficult for the person to see close up Formation of image behind things. the retina in a hyperopic eye. The second eye is being helped with a convex lens. The convex lens helps the eye refract the light and decrease the Convex lens correction image distance so it is once again focused on the retina. for hyperopic eye. Hyperopia usually occurs among adults due to weakened ciliary muscles or decreased lens flexibility. Farsighted means “can see far” and the rays focus too far from the lens. 33 IMPERFECT HUMAN VISION II Myopia The first eye suffers from nearsightedness, or myopia. This is a result of a focal length that is too short, causing the images of distant objects to be focused in front of the retina. Formation of image in front of the retina in a myopic eye. The second eye’s vision is being corrected with a concave lens. The concave lens diverges the light rays, increasing the image distance so that it is focused on the retina. Concave lens correction for myopic eye. Nearsightedness is common among young people, sometimes the result of a bulging cornea (which will refract light more than normal) or an elongated eyeball. Nearsighted means “can see near” and the rays focus too near the lens. 34 IMPERFECT HUMAN VISION III Near point: closest distance at which eye can focus clearly. Normal is about 25 cm. Far point: farthest distance at which object can be seen clearly. Normal is at infinity. Nearsightedness: far point is too close. Farsightedness: near point is too far away. CLASS EXAMPLE 2: A man with refractive myopia cannot see objects clearly if they are further away than 10 m. In order to be able to drive safely and obtain his driving licence he needs to be able to clearly see objects up to 100 m away. What is the minimum optical power of the corrective lenses he needs? Assume that his eye is of normal size and the lens–retina distance is 20 mm. A. -0.09 D B. 0.09 D C. 50.01 D D. 50.10 D 35  IMPERFECT HUMAN VISION IV CLASS EXAMPLE 2 - SOLUTION: A man with refractive myopia cannot see objects clearly if they are further away than 10 m. In order to be able to drive safely and obtain his driving licence he needs to be able to clearly see objects up to 100 m away. What is the minimum optical power of the corrective lenses he needs? Assume that his eye is of normal size and the lens–retina distance is 20 mm. 𝑃𝑐𝑜𝑚𝑏𝑜 = 𝑃𝑒𝑦𝑒 + 𝑃𝑔𝑙𝑎𝑠𝑠 ⇒ 𝑃𝑔𝑙𝑎𝑠𝑠 = 𝑃𝑐𝑜𝑚𝑏𝑜 − 𝑃𝑒𝑦𝑒 ⇒ 1 1 𝑃𝑔𝑙𝑎𝑠𝑠 = − ⇒ 𝑓𝑐𝑜𝑚𝑏𝑜,𝑚𝑎𝑥 𝑓𝑒𝑦𝑒,𝑚𝑎𝑥 1 1 1 1 𝑃𝑔𝑙𝑎𝑠𝑠 = + − + = 50.01 − 50.10 = −0.09 𝐷 100 0.02 10 0.02  COLOUR VISION I The human eye has two types of light-sensing photoreceptors in the retina. Rods and cones. The intensity-sensing rods are far more numerous than the colour-sensing cones. Rods are responsible for night vision and peripheral vision. They are about a thousand times more sensitive to light than the cones, but take longer to adapt to changing light conditions.  COLOUR VISION II The cones show some peculiarities in distribution and sensitivity. The long-wavelength cones and medium-wavelength cones make up about 95 % of the total cones. The short-wavelength cones are found scattered slightly further out than the other types. These blue-sensitive cones are much more sensitive than the others, but not enough to compensate for the reduced number. Graphic arts experts suggest caution when putting red and blue in close proximity, particularly for text. The difference in accommodation in the eye needed to focus on the different colours is tiring for the viewer (Is it??)!! COLOUR VISION III The cones in the retina come in three varieties, which have peak responses in different areas of the visible spectrum. When light of all wavelengths enters the eye, all the receptors are stimulated, and the brain interprets this as close to white. If only some wavelengths are present, the receptors are stimulated different amounts and this is interpreted as a particular colour. A chromaticity diagram, is a way of showing how any mixture of wavelengths of visible light will appear to the eye.  COLOUR VISION IV Because the eye responds primarily to red, green and blue light, these are known as the primary colours. Almost any colours that the brain can differentiate between can be produced with mixtures of monochromatic red, green and blue light. Three secondary colours are defined also, these being cyan, magenta and yellow. These secondary colours can be thought of a mixtures of pairs of the primary colours of light, or the absence of one of the colours from white light. CLASS EXAMPLE 3: A beam of red light has a frequency of 5 x 10^14 Hz while a beam of green light has a frequency of 6 x 10^14 Hz. Which has greater energy? A. A photon of the red light B. A photon of the green light 41 CLASS EXAMPLE 3 - SOLUTION: A beam of red light has a frequency of 5 x 10^14 Hz while a beam of green light has a frequency of 6 x 10^14 Hz. Which has greater energy? A. A photon of the red light B. A photon of the green light The energy of a photon is: 𝑬 = 𝒉𝒇 42 EXERCISES FOR HOME 1. Something that with usual lighting looks white and opaque has yellow light shine on it. What colour will it appear? A. Yellow B. White C. Black 2. Light is absorbed at the front of the eye.  True  False 1. For an in-focus image to be detected at the retina, light rays from one point on an object should meet at one point on the retina.  True  False 43 EXERCISES FOR HOME 1. Something that with usual lighting looks white and opaque has yellow light shine on it. What colour will it appear? A. Yellow B. White C. Black 2. Light is absorbed at the front of the eye.  True  False 1. For an in-focus image to be detected at the retina, light rays from one point on an object should meet at one point on the retina.  True  False 44  SUMMARY I The cornea is transparent because it is uniform in structure, avascular except in the extreme periphery, and relatively dehydrated. It is covered by a 7–10 µm thick layer of tears, which smoothens over optical irregularities and supplies the cornea with oxygen. The diameter of the pupil is controlled by an opposing pair of smooth muscles. The crystalline lens is suspended and rests on the posterior surface of the iris. The crystalline lens is avascular and almost completely transparent. The shape and thus the focal length of the crystalline lens are adjustable.  SUMMARY II Only about 50% of visible light (400–700 nm) incident on the eye actually reaches the retina as direct light. The formation of an image on the retina is determined by: 1. the indices of refraction of each eye component that the light passes through and 2. by the shapes of the surfaces of these elements. The cornea and crystalline lens are the focusing elements in the eye. The cornea performs about two-thirds of the focusing and the crystalline lens the remaining one-third.  SUMMARY III The fovea or fovea centralis is the central region of the retina, and the REGION OF SHARPEST VISION because it has the highest density of cone cells on the retina. The optic nerve leaves the eyeball at a blind spot, a region with no rods or cones. We are usually not aware of the blind spot when we use both eyes. There are about 120 million rod cells per retina. They have high sensitivity, low spatial acuity and are relatively more numerous in the periphery of the retina. The sensitivity of rods peaks near 500 nm and vision using only rods results in various shades of gray.  SUMMARY IV NIGHT VISION AND PERIPHERAL VISION ARE MOSTLY DUE TO RODS. There are about 6.5 million cone cells per retina. They have low sensitivity—about 1.000× lower than rods—high spatial awareness and are concentrated in the fovea. There are three types of cone cells, with spectral sensitivities peaking near: 1. 445 nm (blue cones), 2. 535 nm (green cones) and 3. 570 nm (red cones).  SUMMARY V Only about 50% of visible light (400–700 nm) incident on the eye reaches the retina to form an image. Losses are due to reflection of light, absorption and scattering. The expression for the portion of light that reflects from an interface between two media with refractive indices n1 and n2 is: 𝒏𝟐 −𝒏𝟏 𝟐 𝑹=. 𝒏𝟐 +𝒏𝟏 Most of the light from 300 to 400 nm is absorbed by the crystalline lens. The ability to control the focal length of the crystalline lens is called accommodation.  SUMMARY VI People with myopia are “near-sighted,” meaning that their vision 25 cm away is fine, but it needs correction for objects near infinity. Myopia is corrected with a diverging lens. People with hyperopia are “far-sighted” meaning that their vision at infinity is fine, but it needs correction with objects that are near. Converging lenses are needed to correct hyperopia.  SUMMARY VII The human eye has two types of light-sensing photoreceptors in the retina. Rods and cones. Rods are responsible for night vision and peripheral vision. The cones in the retina come in three varieties, which have peak responses in different areas of the visible spectrum. When light of all wavelengths enters the eye, all the receptors are stimulated, and the brain interprets this as close to white. If only some wavelengths are present, the receptors are stimulated different amounts and this is interpreted as a particular colour.  SUMMARY VIII Because the eye responds primarily to red, green and blue light, these are known as the primary colours. Almost any colours that the brain can differentiate between can be produced with mixtures of monochromatic red, green and blue light. Three secondary colours are defined also, these being cyan, magenta and yellow. These secondary colours can be thought of a mixtures of pairs of the primary colours of light, or the absence of one of the colours from white light.  REFERENCES Authors Title Edition Publisher Year ISBN Kirsten Franklin, Paul Introduction to Biological John Wiley & Muir, Terry Physics for the Health and 1st Edition 2010 9780470665930 Sons Scott and Paul Life Sciences Yates I.P. Herman Physics of the Human Body 2nd Edition Springer 2016 978331923930 Martin Zinke Cengage Physics of the Life Sciences 3rd Edition 2016 9780176558697 Allmag Learning Physics in Biology and Academic P. Davidovits 4th Edition 2012 9780763730406 Medicine Press OpenStax College Physics 1st Edition OpenStax 2012 9781938168000