OPT 331 - Physiological Optics II_L1 PDF

2023 – 2024 OPT 331 – PHYSIOLOGICAL OPTICS VISUAL ANGLE In vision science, the size of objects/stimuli is measured in degrees and/or minutes of visual angle that the object/stimulus occupies on the retina. 1 degree (o)= 60 minutes (‘)...

2023 – 2024 OPT 331 – PHYSIOLOGICAL OPTICS VISUAL ANGLE In vision science, the size of objects/stimuli is measured in degrees and/or minutes of visual angle that the object/stimulus occupies on the retina. 1 degree (o)= 60 minutes (‘) 1 minute (‘) = 60 seconds (“) Visual angles are calculated using trigonometry for a stimulus using its known size and distance from the eye. 𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒 tan 𝛉 = 𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡 Opposite 𝛉 Adjacent  NOTE: MOST CALCULATIONS INVOLVING VISUAL ANGLES ARE BASED ON THE DIMENSIONS OF EMSLEY’S REDUCED EYE Emsley’s Reduced Eye Key Features 1 refracting surface located 1.67 mm behind cornea (approx. in the pupil space) Emmetropic (D = +60 D) Constants Cornea, r = 5.55 mm Refractive index = 4/3 or 1.333 VISUAL ANGLE The ability to see a scene/object depends directly on the size of the image on the retina and not necessarily the physical size of the object. A large distant object, e.g. a tanker, may be difficult or impossible to see when far away, while a pin head held close to the eye appears large. A small nearby object might cast an image of the same size as a more distant larger one. To illustrate, let us try the “rule of thumb” game  VISUAL ANGLE Here’s an example of how the angular size of a 7cm x 7cm, square 6 meters away from the observer’s eye would be calculated. Tan (0.5 * 𝛉) = (0.5 x 7cm)/(6 x 100cm) = 3.5/600 = 0.0058 7cm 0.5 * 𝛉 = tan –1 (0.0058) 6m = 0.3323 degrees 𝛉 = 2 x 0.3323 = 0.665 degrees ( or 0.665 x 60 ) = 39.9 minutes VISUAL ANGLE Now your turn: Calculate the visual angle size of an 8cm feature at a 100-cm viewing distance. Leave your answer in degrees Calculate the visual angle of a 48 cm target feature that is viewed from 6 meters. Leave your answer in minutes of arc. IT ALL BEGAN WITH THE WORDS…  VISUAL ACUITY Vision is the process by which an organism sees and includes all the stages from the physical stimulus reaching the eye to the mental perception. The tasks of the visual system in order of complexity are:  Light perception  Discrimination (contrast)  Form vision (recognition)  Resolution (seeing details)*  Localisation  Higher tasks of stimulating other responses VISUAL ACUITY: RESOLUTION Every optical instrument has a limit to which it can resolve progressively smaller details. In the emmetropic eye, two theories are used to explain the limit of resolution  The receptor theory and  The wave theory  RESOLUTION: THE RECEPTOR THEORY Applied Anatomy of the Retina  RESOLUTION: THE RECEPTOR THEORY 22.2mm 16.7 mm The eye can distinguish between two closely adjacent point sources of the light if the eye can detect a gap between them The fovea is the part of the retina that provides the highest acuity. Foveal cones have a diameter of 1.5um and are Figure 1. Receptor theory of resolution separated by an edge to edge distance of 0.5um Let α be the minimum angle of separation 𝛼 𝑂𝑝𝑝𝑜𝑠𝑖𝑡𝑒 tan( ) = If each foveal cone can transmit a 2 𝐴𝑑𝑗𝑎𝑐𝑒𝑛𝑡 separate impulse, then in theory, the 𝛼 2 × 10−6 minimum separation distance between the tan( ) = 2 16.7 × 10−3 images is 4um (α = 0.0136o) 𝛼 = 6.8718 × 10−3 𝑑𝑒𝑔 2 α = 0.0137o  RESOLUTION: THE WAVE THEORY The wave theory predicts that, even with a perfect optical system, the image of a point object cannot be a point, but must spread to cover a finite area due to diffraction of light at the margins of the optical system. 2.44λ θ 𝜔= , Equation 1 𝑑 ω Modified from: https://commons.wikimedia.org/w/index.php?curid=16981639 The central disc (brightest spot) is called the Airy disc. In the eye, its angular subtense (diameter), ω, in radians at the nodal point is given in equation 1. Where λ is the wavelength in nm, and d is the diameter of the aperture (i.e. pupil)  RESOLUTION: THE WAVE THEORY a b c When 2 point light sources are viewed through the pupil, two diffraction patterns are produced on the retina (Fig 1a). As points approach each other, their images reach a point where they are barely resolved (Fig 1b). Beyond this point, the two Figure 1. Diffraction pattern of two approaching points will not be resolved and the observer point sources sees only one point (Fig 1c). The minimum separation required for the 2 1.22λ 𝜃= , Equation 2 𝑑 points to be resolved occurs when the peak of one Airy discs falls on the extreme edge 𝜔 NB: 𝜃 = of the other. This is known as Rayleigh’s 2 Criterion Figure 2. Rayleigh’s Criterion  RESOLUTION: THE WAVE THEORY Worked example. Calculate the angular size of the airy disc produced by a beam of light (wavelength = 555nm) passing through a 3mm pupil. Give the final answer in degrees. 2.44λ 𝜔= , 𝑑 2.44 × 555 × 10−9 𝜔= 3 × 10−3 𝜔 = 4.514 × 10−4 𝑟𝑎𝑑 180 Converting to degrees, ω = × 4.514 × 10−4 𝑟𝑎𝑑 𝜋 = 0.0259o  RESOLUTION: THE WAVE THEORY Worked example: Calculate the minimum angle of separation between two points of light (wavelength = 555nm) viewed through a 3mm pupil. Give the final answer in degrees. 1.22λ 𝜃= , 𝑑 1.22 × 555 × 10−9 𝜃= 3 × 10−3 𝜃 = 2.257 × 10−4 𝑟𝑎𝑑 180 Converting to degrees, 𝜃 = × 2.257 × 10−4 𝑟𝑎𝑑 𝜋 = 0.0129o  RESOLUTION IN THE REAL EYE In the real emmetropic eye, the theoretical minimum angle of resolution (i.e. 47 sec of arc = 0.013o) cannot be obtained. The best results obtained are ~90 sec (=0.025o) (Ogle 1951) The reasons include the following  Light is normally chromatic  Photoreceptor density varies across the retina  The normal eye has 3 types of cones which are tiled randomly in the retina  Pupil size varies constantly with illumination  Aberrations in the ocular media  Modulation transfer function RESOLUTION IN THE REAL EYE Critical Thinking Questions  What is the effect of pupil size on resolution? (Hint – Calculate the minimum separation for light passing through a 2mm, 3mm and 5mm pupil.) Diffraction through a small aperture  What is the effect of pupil size on retinal illumination?  Further info available at http://cnx.org/contents/9ANhisjh@5/Limits-of-Resolution- The-Rayle Diffraction through a large aperture VISUAL ACUITY: IN CLINICAL PRACTICE Visual acuity – ability of the visual system to detect spatial changes It has three clinical components  Detection acuity – patient detects presence or absence of a target  Resolution – patient resolves a critical element of a target (e.g. the orientation of the gap in the Landolt C  Recognition – patient identifies a particle symbol (e.g. the letter “A”)  VISUAL ACUITY: IN CLINICAL PRACTICE In the clinic, visual acuity takes the form of character recognition recognition A letter chart is often used, but numbers and symbols are also used. ^ The chart is designed so that smaller symbols are seen by people with better vision, while point resolution patients with poorer sight will see larger characters The testing distance should be large enough not to stimulate accommodation (6m or 20ft) VISUAL ACUITY: IN CLINICAL PRACTICE The Snellen Chart  Introduced by Snellen in 1862  Most commonly used and one of the first  Contains 10 lines of letters in progressive sizes. Each is designated at the distance at which the overall height of the letter subtends 5 minutes, and the detail size or limb width subtends 1 minute of arc. OTHER CLINICAL TESTS OF VISUAL ACUITY The Landolt Ring (or C) The Tumbling E OTHER CLINICAL TESTS OF VISUAL ACUITY Ffooks Test The Sheridan-Gardiner Test Lea Symbols Test OTHER CLINICAL TESTS OF VISUAL ACUITY Pictorial Charts Checkerboard Test BLUR CIRCLES AND VISUAL ACUITY The requirement for a sharp retinal image is that after refraction by the eye, the image vergence, L’, is equal to the dioptric length of the eye, K’. A point source forms a point image on the retina if positioned at the far point of the eye. However, if the point source is positioned elsewhere then a blur circle will be formed. The size of the blur circle depends on:  the amount of defocus  diameter of the pupil BLUR CIRCLES AND VISUAL ACUITY Consider an optotype E on a visual acuity chart located 6 m away from an emmetropic eye. The optotype can be considered as an infinite number of point sources projected onto the retina. The optical image is limited only by the resolving power of the eye diffraction  BLUR CIRCLES AND VISUAL ACUITY The blur circle and the pinhole effect Image point Object rays from infinity Blur circle Credits: http://www.eyeapps.com.au/vision-test---self-testing.html Figure 1. Blur circle formation and pinhole effect in a myopic eye BLUR CIRCLES AND VISUAL ACUITY Pinhole as a diagnostic tool If an uncorrected ametrope views an optotype through a pinhole, it reduces the size of the blur circles constituting the optotype enabling a better resolution. Hence, an improvement in acuity with the pinhole suggests that the reduction in acuity is due to optical blur caused by ametropia. BLUR CIRCLES AND VISUAL ACUITY The image produced by a point source, is not a point but a blur circle. The blur circle is the area or spatial extent covered by the image of a point source. Alternatively, the blur circle can be thought of as a cross section of a bundle of focused rays originating from a point source. BLUR CIRCLES AND VISUAL ACUITY The size of a blur circle depends on the amount of defocus as well as pupil size Defocus is an aberration in which the image is out of focus. Other factors affecting the blur circle are  Accommodation  Illuminance  Media scattering END OF SECTION NEXT WEEK Depth of Focus and Depth of Field Hyperfocal Distance Stiles-Crawford Effect  SPATIAL FREQUENCY Spatial frequency refers to the level of detail present in a stimulus per degree of visual angle. Spatial frequency is expressed in the number of cycles of alternating dark and light bars per degree of visual angle. A cycle refers to one complete light and dark bar repetition. E.g. a grating with SF of 1 cyc/deg (cpd) has 1 dark http://webvision.med.utah.edu/book/part-viii-gabac-receptors/visual-acuity/ and 1 light bar occupying 1 deg of visual angle  SPATIAL FREQUENCY Since the visual angle of a stimulus/object becomes smaller with increasing viewing distance, moving away from a particular stimulus increases its high spatial frequency content. Thus the advantage of specifying spatial frequency in cpd of visual angle is that it accounts for both the size of the stimulus and its viewing http://webvision.med.utah.edu/book/part-viii-gabac-receptors/visual-acuity/ distance from the eye. FOVEAL IMAGE QUALITY Every optical system can be thought of as having a “resolving power”, an ability to faithfully transfer the details of an object through to its image. An optical system with a high resolving power will produce high quality images while an optical system with a low resolving power will produce poor quality or degraded images. This function of an optical system can be measured using a sine- wave grating as the object and measuring the intensity distribution in the image plane FOVEAL IMAGE QUALITY Optical systems, including the In the eye, the degradation is human eye, are not perfect. brought about by  Diffraction As a result every image produced by any optical system  Spherical aberration undergoes some sort of  Chromatic aberration degradation; some more than  Light scatter others The overall quality of an image can be summarised in a number of ways, two of which are  Line spread function  Modulation transfer function FOVEAL IMAGE QUALITY LINE SPREAD FUNCTION Remember: A point object does not produce a point image. What you get is a diffraction pattern or Airy disc Also remember that a line can also be thought of as an arrangement of closely packed points. The LSF is simply the distribution of light intensity in the image of a line Line spread function illustrated using gratings. a. Square wave grating with light and dark areas as measured in the direction sharply demarcated perpendicular to its length. b. Sine wave grating showing the gradual increase and decrease in light intensity FOVEAL IMAGE QUALITY MODULATION TRANSFER FUNCTION  First, what is “modulation”?  In simple English it means to alter/change something to make it less strong  In visual optics it means to change the amplitude, intensity, frequency or other property of light during transmission  It can be measured and given by the formula: 𝐿𝑚𝑎𝑥 − 𝐿𝑚𝑖𝑛 𝑀𝑜𝑑𝑢𝑙𝑎𝑡𝑖𝑜𝑛, 𝑀 = 𝐿𝑚𝑎𝑥 + 𝐿𝑚𝑖𝑛 (This equation is also known as the Michelson contrast equation) FOVEAL IMAGE QUALITY SAMPLE QUESTIONS Calculate the modulation of a square grating which has a luminance of 80 cd/m2 in the white spaces and 8 cd/m2 in the black stripes. (0.82) If viewed through an optical produces an image with a modulation of 0.7, what is the modulation transfer function of the optical system  FOVEAL IMAGE QUALITY MODULATION TRANSFER FUNCTION  Second, what is modulation transfer?  It is the way in which (or the factor by which) an optical system degrades the modulation (or contrast) in the image of a sinusoidal grating of a particular spatial frequency  It is given by the formula 𝑀𝑖 𝑀𝑜𝑑𝑢𝑙𝑎𝑡𝑖𝑜𝑛 𝑡𝑟𝑎𝑛𝑠𝑓𝑒𝑟, 𝑀 = 𝑀𝑜  FOVEAL IMAGE QUALITY MODULATION TRANSFER FUNCTION  Finally, what is modulation transfer function?  It is the plot of the modulation transfer as a function of the spatial frequency of the sinusoidal grating  It indicates the ability of an optical system to reproduce (transfer) various levels of detail (spatial frequencies) from the object to the image  To illustrate the point, see the next slide  Increasing spatial frequency Decreasing contrast due to SMTF  FOVEAL IMAGE QUALITY MODULATION TRANSFER FUNCTION  Why is the MTF important?  It represents the optical component of the contrast sensitivity function (more of that in a little moment)  As spatial frequency of the object increases, the image become progressively poorer until at a certain frequency the image loses all contrast and a uniform field results. CONTRAST SENSITIVITY Contrast is measured using the Michelson formula 𝐿𝑚𝑎𝑥 − 𝐿𝑚𝑖𝑛 𝐶𝑜𝑛𝑡𝑟𝑎𝑠𝑡 = 𝐿𝑚𝑎𝑥 + 𝐿𝑚𝑖𝑛 Where Lmax and Lmin represent the maximum and minimum luminance of the grating respectively. The contrast threshold is the minimum contrast of a sine-wave grating of a specified spatial frequency, that an observer can detect Contrast sensitivity is the inverse of the contrast threshold  CONTRAST SENSITIVITY It is the ability of the eye to differentiate between an object (foreground) and its background It measures the ability to discern between different luminosities in a static image. It is measured as the reciprocal of contrast threshold Commonly measured in clinic using a Pelli-Robson chart  CONTRAST SENSITIVITY Contrast or luminance Spatial frequency IMAGE QUALITY IN THE EYE Subtitle or catch phrase for the presentation INTRODUCTION In the absence of refractive errors, the eye produces a remarkably good image. However, when the eye is in good working condition would produce high quality images. These images are produced in the presence of several aberrations that degrade the optical image. However the design of the eye (often thought to be imperfect) efficiently eliminates or minimises the aberrations when the eye is operating under optimum conditions FACTORS AFFECTING IMAGE QUALITY IN THE EYE In the absence of ametropia and accommodation the quality of the foveal image is affected by Diffraction Spherical aberration Chromatic aberration Light scatter DIFFRACTION Source of diffraction: pupil Diffraction (related to size airy disc) increases with decreasing (smaller) pupil size How is it dealt with: the pupil diameter at optimum levels is between 2.5 – 3 mm in diameter (this produces the best compromise between aberrations and diffraction. More of this later) The 2.5 – 3.0 mm produce a Rayleigh’s criterion of ~49 sec of arc, comparable to the theoretical limit of resolution imposed by the photoreceptor arrangement SPHERICAL ABERRATION In spherical aberration (SA) light rays that strike close to the centre of the lens (paraxial region of the lens) are focused in a different plane than light rays that strike the periphery of the lens (i.e. non-paraxial region of the lens) In the eye, SA increases as more of the paraxial regions of the cornea and lens are allowed to transmit light rays. SPHERICAL ABERRATION Two forms  Positive (under-corrected) (Fig b)  Negative (over-corrected) (Fig c) The unaccommodated eye typically (but not always) exhibits positive SA, which tends to increase with age (Guirao et al, 2000) SA is minimised when the eye accommodates to about 1.50 D, further accommodation results in increasing amounts of negative SA https://www.researchgate.net/figure/228843892_fig13_Schematic-drawing-of the-spherical-aberrations-of-a-positive-lens-a-An-aberration-free SPHERICAL ABERRATION Control of SA in the eye Primary achieved by the pupil. In daylight conditions, the pupil is 3 mm or less and the eye manifests insignificant SA (usually