7. The Form Sense III 2223.pptx

The Form Sense III Introduction. Objectives and Readings. Theories of spatial resolution. SFO1004 Dr Sarah J Waugh© Objectives and readings The student should be able to: • Understand the potential optical limitations of the eye effecting spatial resolution including diffraction. • Describe what...

The Form Sense III Introduction. Objectives and Readings. Theories of spatial resolution. SFO1004 Dr Sarah J Waugh© Objectives and readings The student should be able to: • Understand the potential optical limitations of the eye effecting spatial resolution including diffraction. • Describe what is meant by the terms point and line spread functions. • Describe how retinal factors can limit spatial resolution. SFO1004 Optometry: Science, Techniques and clinical management. Rosenfield and Logan. • Chapter 1. • Chapter 12. • Adler’s Physiology of the Eye. L. Levin (Ed) ebook: Chapter 33 Visual Acuity. – available through the library https://webvision.med.utah.edu/ • Part VIII: Visual acuity Dr Sarah J Waugh© Theories of spatial resolution • The ability to resolve detail, as in a task of resolution acuity, depends on a number of different possible factors. SFO1004 1. The optics of the eye and the quality of the retinal image. 2. The structure and function of the retina. 3. The capacity of the neural pathways. Dr Sarah J Waugh© Optics of the eye • Imagine a small point source of light that is imaged onto the retina. • The image of the point source is not another point. • Even with a perfectly focused eye, the image of a point of light ‘spreads’ on the retina. • This spreading in the point image creates what is called a point spread function (PSF). • For a thin line object, the image spread is called the line spread function. • The spread can be represented on SFO1004 a graph of brightness versus Dr Sarah J Waugh© Optics of the eye • The figure shows the light spread of a thin line imaged onto the retina. • Relative brightness is on the ‘y’ axis and retinal distance on the ‘x’. • The spread function can be effected by a number of factors: • including diffraction, aberrations, light scatter, absorption and focus factors. From Adler’s Physiology of the Eye, 10th edition: Chapter 17; Visual Acuity, G Westheimer SFO1004 Dr Sarah J Waugh© Optics of the eye – diffraction • According to the wave theory of light the limitations of an aperture (such as the eye’s pupil) will cause a spread of light even when the system is fully and properly focussed. This phenomenon is called diffraction. • Diffraction occurs as the result of light ‘bending’ around an SFO1004 edge or through an • The diffraction image of a point source (e.g. a star or distance light) through a circular aperture comprises a bright central area (Airy disc) containing most of the light energy, surrounded by concentric rings. Dr Sarah J Waugh© Optics of the eye – diffractionAiry disc with • The size of the Airy disc is given by the equation: • r = 1.22 * λ/ d – r = angular radius of disk, λ = wavelength of light used and d = pupil diameter • Whenever the eye’s pupil is 2mm or less in diameter, the image spread (i.e. point spread function) is equal to the SFO1004 diffraction image. concentric rings Airy disc and diffraction pattern for a point object Dr Sarah J Waugh© Optics of the eye – diffraction and aberrations • Almost all optical systems have aberrations that degrade the quality of the optical image. • For light rays that enter a larger pupil at the periphery (or edge), they may not converge to a single point, thus contributing to the spread of light beyond that due to diffraction. • SFO1004 Effects of aberrations become more prominent Small pupil (2mm) diffraction limited As pupil size increases, aberrations cause more spread of the image Dr Sarah J Waugh© Optics of the eye – diffraction and aberrations • What if the line spread function was measured and compared to the calculated function for different pupils. • This is what Campbell and Gubisch did in their 1966 paper. • The figure shows line spread functions that were measured (thicker curves) and the calculated (thinner curves) for the 2 pupil sizes shown. • Notice the measured ‘spread’ of the image is greater than the calculated spread based only on diffraction. SFO1004 • This shows the influence of other Campbell and Gubisch 1966 Dr Sarah J Waugh© Optics of the eye – diffraction and aberrations • As pupil size decreases (down to 3 and 2.4mm), notice how the measured ‘spread’ of the image is coming closer to the calculated diffraction limited spread. • This shows that as pupil size decreases ocular aberrations also decrease. SFO1004 Campbell and Gubisch 1966 Dr Sarah J Waugh© • As pupil size decreases to about 2mm, the measured line spread function is the same as the calculated line spread function. • In other words, the eye is now diffraction limited. • Thus – Pupil size < ~2 mm diffraction important. – Pupil size > ~ 2-3 mm aberrations important. SFO1004 Diffraction limited Optics of the eye – diffraction and aberrations Campbell and Gubisch 1966 Dr Sarah J Waugh© Optics of the eye – diffraction and aberrations • Consider three images of a light bulb filament. • In image (a) through a relatively large pinhole, the light rays do not converge properly and the image is blurred. • As the pinhole is reduced the focus improves and the image becomes clearer (b) until, • Through a very small pupil, the image is now SFO1004 diffraction limited and https:// foundationsofvision.stanford.edu/ chapter-2-image-formation/ Dr Sarah J Waugh© Optics of the eye – other factors • Light scatter may also be important in determining the quality of the retinal image. • As the eye comprises various structures, light can be scattered as it passes through the media to the retina. • Light scatter is often worse with the aging eye and can be a SFO1004 • Light may also be absorbed by the various media. The amount of light absorbed varies with wavelength. Shorter wavelengths tend to be absorb more. • Factors relating to how the eye focusses will also impact on the quality of the image – this will be discussed in future lectures. Dr Sarah J Waugh© Interval • If you need a break you can pause here SFO1004 Dr Sarah J Waugh© Minimum visible acuity (detection) • Consider a thin line seen against a plain background. Its image forms a line spread function on the retina. • As the line increases in size (e.g. by moving nearer) the height of the line spread function increases, thus increasing in contrast. • In order to be ‘seen’ the threshold is achieved when the light increment (retinal illuminance) ΔI is reached. SFO1004 • So the task of detecting a line From Adler’s Physiology of the Eye, 10th edition: Chapter 17; Visual Acuity, G Westheimer Dr Sarah J Waugh© Minimum resolvable acuity (resolution) • Consider two adjacent lines closely spaced. • Their images form two line spread functions on the retina. If the lines are very close together the line spread functions will overlap almost completely. • As the lines are separated, the overlap in their respective line spread functions is less. This creates a pattern of light, two peaks with a ‘trough’. • Resolution is possible when the SFO1004 visual system can distinguish ΔI/I https:// webvision.med.utah.edu/ book/part-viiipsychophysics-of-vision/ visual-acuity/ Dr Sarah J Waugh© Minimum resolvable acuity (resolution) • This type of resolution is sometimes referred to as achieving the Rayleigh criterion. • 2 lines will be resolved if the separation between their respective line spread functions is sufficiently wide (at least the width of the PSF i.e. the radius of the respective Airy disc). • Equates to about 1 cone SFO1004 separation at the fovea. https://webvision.med.utah.edu/ book/part-viii-psychophysics-ofvision/visual-acuity/ Dr Sarah J Waugh© Retinal mosaic (cone density) • Although diffraction can limit spatial resolution, the retinal photoreceptors also place a limit on the processing of spatial information. • Recall that the cone and rod density varies across the retina (data from Osterberg). • In the rod-free fovea the cones are packed very closely, approximately 2 SFO1004 cones per minute of arc of https:// webvision.med.utah.edu Dr Sarah J Waugh© Retinal mosaic • Shown is an image of the human foveal photoreceptor Cone ‘mosaic’ for 3 individual retinas. • Note the close packing of cones at the centre of the Cone fovea. • Note also the variability between the individuals. • Range of cone density in the Cone rod free area (about 1 degree of angle) ranges from 98000 to 324000 cones per Curcio, Christine A., et al. "Human photoreceptor topography." Journal of comparative neurology 292.4 mm. SFO1004 (1990): 497-523. Dr Sarah J Waugh© Retinal mosaic • Variation in cone/rod density as a function of retinal location. • Rods peak in density ~18° or 5 mm out from the center of the fovea, in a ring around the fovea at 160,000 rods/mm2 Nasal retina 1.35 mm Rod Cone 5 mm Rod Cone 8 mm Rod Cone Rod 16 mm Cone SFO1004 Curcio, Christine A., et al. "Human photoreceptor topography." Journal of comparative neurology 292.4 (1990): 497-523. Dr Sarah J Waugh© Retinal mosaic • Assuming the optics are correct, the resolution limit at the fovea is defined by the separation of the cone photoreceptors. • Resolution of two lines (or the stroke in the tumbling E) will occur if the images of the lines fall on 2 independent cones separated by a single cone. • This corresponds to a separation of approximately 0.5 arc mins. SFO1004 • Foveal cones Dr Sarah J Waugh© Retinal mosaic • For optimal visual acuity at the fovea, the signal from a single cone must be processed through a single ganglion cell. • For cones further from the fovea, the 1:1 connection is lost and more that one photoreceptor connects to a ganglion cell – this is what is referred as spatial pooling of cone signals. GGG SFO1004 Dr Sarah J Waugh© Summary • For foveal vision, the optical resolution is closely matched to the cone density. • Visual acuity at the fovea is limited primarily by the photoreceptor density (assuming pupil size of 2mm or more). • So it is a neural limitation. • For peripheral vision retinal limits increase and visual acuity becomes limited by spatial pooling. SFO1004 Dr Sarah J Waugh© Questions? • Remember you can ask questions via module Teams site. SFO1004 Dr Sarah J Waugh©