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2024

Mohamed Hegab, Noor Asir

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clinical optics visual function light properties ophthalmology

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This book, based on Elkington Clinical Optics (3rd edition), covers the properties of light and visual function in ophthalmology. It details reflection, refraction, prisms, and lenses, as well as clinical refraction, refractive surgery, and more.

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CLINICAL OPTICS Mohamed Hegab Noor Asir This book is based on Elkington Clinical Optics (3rd edition) January 2024 Mohamed Hassan Mansour Hegab MBBCh, MRCSEd, FRCOphth Ophthalmology Speciality Trainee (ST5) Northern Deanery Noor...

CLINICAL OPTICS Mohamed Hegab Noor Asir This book is based on Elkington Clinical Optics (3rd edition) January 2024 Mohamed Hassan Mansour Hegab MBBCh, MRCSEd, FRCOphth Ophthalmology Speciality Trainee (ST5) Northern Deanery Noor Asir MBBCh Ophthalmology Trust Doctor Royal Victoria Infirmary, Newcastle 1 Table of contents 1. Properties of light & visual function 3 2. Reflection of light 36 3. Refraction of light 43 4. Prisms 51 5. Spherical lenses 60 6. Astigmatic lenses 68 7. Optical prescriptions & spectacle lenses 75 8. Aberrations of optical systems including the eye 96 9. Refraction by the eye 105 10. Optics of ametropia 121 11. Presbyopia 149 12. Contact lenses 159 13. Optics of low vision aids 169 14. Instruments 173 15. Lasers 225 16. Practical clinical refraction 243 17. Refractive surgery 255 2 Properties of light & Visual function Light may be defined as energy to which the human eye is sensitive. Electromagnetic spectrum Optical radiation: - Lies between X-rays & microwaves, and is subdivided into 7 wavebands (each of these grouped together which elicit similar biological reactions). These seven wavebands are: - Ultraviolet C (UV-C) = 200 – 280 nm. - Ultraviolet B (UV-B) = 280 – 315 nm. - Ultraviolet A (UV-A) = 315 – 400 nm. - Visible light = 400 – 780 nm. - Infrared A (IR-A) = 780 – 1400 nm. - Infrared B (IR-B) = 1400 – 3000 nm. - Infrared C (IR-C) = 3000 – 10,000 nm. The shorter the wavelength, the greater the energy of the individual quanta/photon of optical radiation 3 Absorption of the incident optical radiation by ocular structures: - Front of the eye (cornea & sclera): ✓ Absorb very short wavelengths in the ultraviolet (UV-B and UV-C). ✓ Absorb very long wavelengths in the infrared (IR-B and IR-C). - Crystalline lens: ✓ Absorb wavelengths in the near ultraviolet (UV-A). - Retina: ✓ Absorb wavelengths in the visible light (400-780). ✓ Absorb wavelengths in the near infrared (IR-A). Wavelengths in the range 400–1400 nm (visible light and near infrared), pass through the ocular media to fall on the retina. The visible wavelengths stimulate the retinal photoreceptors giving the sensation of light while the near infrared may give rise to thermal effects (eclipse burns). 4 Colour vision The colour of any object is determined by the wavelengths emitted or reflected from the surface. White light: - Is a mixture of wavelengths of the visible spectrum. Colour is perceived by three populations of cone photoreceptors in the retina which are sensitive to: - Light of short wavelength: blue cones. - Light of middle wavelength: green cones. Light of long wavelength: red cones. Congenital colour vision defect occurs if either: - Cone pigment is absent: ✓ Blue: Tritanopia. ✓ Green: Deuteranopia. ✓ Red: Protanopia. - There is a shift in its spectral sensitivity: ✓ Blue: Tritanomaly. ✓ Green: Deuteranomaly. ✓ Red: Protanomaly. Chromosomes carrying genes encoding for cone pigments: - X-chromosome: Red & Green. - Chromosome 7: Blue. Prevalence of colour vision defects: - 8% of men and 0.5% of women have a defect of the red/green system. - Commonest defect is Dueteranomaly (5% of men and 0.3% of women). - Tritan defects are rare. 5 Congenital colour defects: - Characteristically affect particular parts of the colour spectrum. Acquired colour defects: - Occur throughout the spectrum but may be more pronounced in some regions. Acquired optic nerve disease: - Tends to cause red-green defects. - The following conditions are exceptions which cause a blue-yellow defect: ✓ Glaucoma. ✓ Autosomal dominant optic neuropathy. - It has recently been found that visual field loss in glaucoma is detected earlier if perimetry is performed using a blue light stimulus on a yellow background. Acquired retinal disease: - Tends to cause blue-yellow defects. - The following conditions are exceptions which cause a red–green defect: ✓ Cone dystrophy. ✓ Stargardt’s disease. Causes of red-green defects Causes of blue-yellow defects - Acquired optic nerve disease - Acquired retinal disease - Cone dystrophy - Glaucoma - Stargardt’s disease - Autosomal dominant optic neuropathy 6 Clinical testing of colour vision: - Farnsworth–Munsell (FM) hue 100 test: ✓ Is the most comprehensive method. ✓ It comprises 84 coloured discs, numbered in sequence on the undersurface and divided into four groups of 21, the colours of each group occupy a portion of the colour spectrum. ✓ The colours differ only in hue and have equivalent brightness and saturation. ✓ Each group must be arranged in a row with the reference colours at each end and the intervening discs in order of closest colour match. ✓ The order of placement indicates the nature of the colour defect. - D-15 test : ✓ Uses colours from all parts of the spectrum which must be arranged in order from a single reference colour. ✓ The test does not distinguish mild colour defects, but for most purposes those passing the test are unlikely to have problems with hue discrimination. - Ishihara pseudoisochromatic test : ✓ Plates specifically test for congenital red–green defects, the most common abnormality of colour vision. ✓ The test plates consist of random spots of varying isochromatic density, numbers or wavy lines (for illiterates or children) are represented by spots of different colours. ✓ A patient who is colour blind will see only a random pattern of spots or incorrect numbers. ✓ The figures can only be distinguished from their background by their colour and not by a difference in contrast. - Lanthony New Colour Test: ✓ Tests hue discrimination and can be used by children. 7 Ultraviolet light The retinal photoreceptors are also sensitive to wavelengths between 350-400 nm in the near ultraviolet (UV-A) these wavelengths are normally absorbed by the lens of the eye. In aphakic eyes or pseudophakic eyes with intraocular implants without UV filter, such UV radiation gives rise to the sensation of blue or violet colours. Of greater concern is the recent evidence that wavebands between 350 nm in the UV and 441 nm in the visible spectrum are potentially the most dangerous for causing retinal damage under normal environmental conditions. It is therefore desirable that IOLs filter out these wavelengths and protect the retina, IOL are therefore being produced which incorporate a UVA absorbing substance. The bright illumination employed in modern ophthalmic instruments may also cause retinal damage under some circumstances. Prolonged exposure to high intensity indirect ophthalmoscope illumination, intraocular light pipe illumination and operating microscope light is potentially damaging to the retina, which may in many instances already be unhealthy. Some instruments have yellow filters built into them to reduce exposure to the most damaging wavelengths. 8 Fluorescence Definition: - Property of a molecule to spontaneously emit light of a longer wavelength when stimulated by light of a shorter wavelength. - For example, the orange dye fluorescein sodium when excited by blue light (465–490 nm) emits yellow–green light (520–530 nm). Fluorescein angiography: - Allows the state of retinal and choroidal circulation to be studied by photographing the passage of fluorescein through the vasculature after it has been administered systemically. - White light from the flash unit of a fluorescein camera passes through a blue 'excitation' filter to illuminate the fundus with blue light. - The wavelengths transmitted by the excitation filter approximate to the absorption spectrum of fluorescein. ✓ Most of the light is absorbed. ✓ Some is reflected unchanged. ✓ Some is changed to yellow–green light by fluorescence. - The blue reflected light and yellow–green fluorescent light leaving the eye are separated by a yellow–green 'barrier' filter in the camera, this blocks blue light and exposes the camera film only to yellow–green light from the fluorescein, thereby delineating vascular structures and leakage of dye. 9 The phenomenon of pseudofluorescence: - Occurs if there is an overlap in the spectral transmission of the excitation and barrier filters. - This allows reflected wavelengths at the green end of blue to pass through the barrier filter and appear as fluorescence Other important applications of fluorescein include: - Staining of ocular surface defects. - Anterior segment angiography. - Measurement of aqueous humor production and outflow. - Light microscopy: ✓ The localization of tissue constituents using fluorescein bound to specific immunoglobulin. Indocyanine Green (ICG) dye: - It is a fluorescent substance which absorbs 805 nm and emits 835 nm infrared radiation, so it is better imaged by digital camera. - It has a larger molecule than sodium fluorescein & is more firmly bound to serum proteins. - The retinal pigment epithelium does not absorb these wavelengths, and it is therefore possible to observe fluorescence of the choroidal circulation after ICG is administered intravenously. - Only 4% of 805 nm radiation absorbed by ICG is emitted at 835 nm compared with the total fluorescence of fluorescein. - ICG angiography is not yet in general clinical use, but it has been shown to delineate occult choroidal neovascularisation not visible with fluorescein. - ICG has also been used to photosensitise vascular lesions to diode laser photocoagulation. 10 Wave theory of light The path of light through an optical medium (e.g. glass) is always straight if no obstacle or interface between optical media is encountered. It is now understood that light really travels as waves although its path is often represented as a 'ray'. a = light represented as ray b = light represented as wave motion (viewed from cross section) c = light represented as wave front (viewed from above) Wave motion consists of a disturbance, or energy, passing through a medium. The medium itself does not move, but its constituent particles vibrate at right angles to the direction of travel of the wave (Imagine a ribbon tied to a rope along which a wave is thrown, the crest of the wave moves along the length of the rope, but the ribbon moves up and down at one point on the rope). Wavelength (λ): distance between two symmetrical parts of the wave motion. Cycle (xy): one complete oscillation & occupies one wavelength. Amplitude (a): maximum displacement of an imaginary particle on the wave from the base line. 11 Any portion of a cycle is called a phase. If two waves of equal wavelength (but not necessarily of equal amplitude) are travelling in the same direction but are 'out of step' with each other, the fraction of a cycle or wavelength by which one leads the other is known as the phase difference. “2 waves of equal wavelength which are out of phase by ¼ of a wavelength (phase difference equals 90°, the complete cycle being 360°)” Light waves that are out of phase are called incoherent, while light composed of waves exactly in phase is termed coherent. Interference When two waves of light travel along the same path, the effect produced depends upon whether or not the waves are in phase with one another. The final effect in each case is as if the waves were superimposed and added (in the algebraic sense) to each other. If they are in phase: - The resultant wave will be a summation of the two, and this is called constructive interference. If they are out of phase by half a cycle: - They will cancel each other out, and this is called destructive interference. If they are out of phase by less than half a cycle: - They result in a wave of intermediate amplitude and phase. 12 Destructive interference occurs within the stroma of the cornea: - The collagen bundles of the stroma are so spaced that any light deviated by them is eliminated by destructive interference. Interference phenomena are also utilized in optical instruments: - One example is low reflection coatings which are applied to lens surfaces. - The coating consists of a thin layer of transparent material of appropriate thickness. - Light reflected from the superficial surface of the layer and light reflected from the deep surface of the layer eliminate each other by destructive interference. Diffraction Definition: - When a wave front encounters a narrow opening or the edge of an obstruction, the wave motion spreads out on the far side of the obstruction. - It is as if the edge of the obstruction acts as a new center from which secondary wave fronts are produced which are out of phase with the primary waves. - The intensity of the light falling on zone AB: ✓ Is reduced to some extent by interference between the primary and secondary waves. - The light falling on zone BC: ✓ Is derived from secondary waves alone and is of much lower intensity. 13 When light passes through a circular aperture, a circular diffraction pattern is produced: - This consists of a bright central disc surrounded by alternate dark and light rings. - The central bright zone is known as the Airy disc. Diffraction effects are most marked with small apertures, and occur in all optical systems including lenses, optical instruments and the eye. In the case of lenses and instruments, the diffraction effect at the apertures used is negligible compared with the other errors or aberrations of the system. In the case of the eye, diffraction is the main source of image imperfection when the pupil is small, however the advantage of a large pupil in reducing diffraction is outweighed by the increased effect of the aberrations of the refractive elements of the eye. The principle of diffraction is used in the design of some multifocal intraocular lenses. The longer the wavelength and/or the smaller the gap → the greater the angle through which the wave is diffracted 14 Limit of Resolution (Resolving power) The terms limit of resolution and resolving power refer to the smallest angle of separation (w) between two points which allows the formation of two discernible images by an optical system. The limit of resolution is reached when two Airy discs are separated so that the center of one falls on the first dark ring of the other. Raleigh’s criterion: - It implies on the eye, where airy pattern = point spread function (PSF). 15 Tests of visual acuity (resolving power of the eye) As soon as the child is old enough, tests to which the response is behavioral should be replaced by those requiring matching. Babies: - Are best examined when alert and not hungry. - Fixation with either eye should be central, steady and maintained (CSM). - The best target is a face (especially that of the mother), a toy, or a television cartoon. - A strong preference for one eye is indicated by an aversive response to occlusion of that eye. - Squint, nystagmus, roving gaze, and eye poking, all suggest poor visual acuity. - Visually directed reaching develops between 2-5 months of age (when the vision is poor, the movements are exploratory in nature). - The ability of a child aged 15 months or older to pick up a tiny coloured 'hundreds and thousands' sweet suggests near visual acuity equivalent to 6/24 or better and the absence of a serious visual defect (however, good near visual acuity may develop in the presence of high myopia). The Catford drum: - Comprises a white cylinder marked with black dots of increasing size corresponding to visual acuities ranging from 6/6 to 2/60 when viewed from 60 cm. - The drum is masked by a screen except for a rectangular aperture which exposes a single spot. - This spot is made to oscillate horizontally and stimulates corresponding eye movement if seen by the child. - This test overestimates the acuity both because the target is moving and because the test is conducted at a short working distance. 16 The STYCAR (Screening Test for Young Children And Retards) rolling balls: - Are ten white polystyrene spheres ranging in size from 3.5 mm to 6 cm in diameter. - They are rolled across a well illuminated contrasting floor 3 m from the child. - Pursuit eye movements indicate that they are seen. - The Worth's ivory ball test is similar. Preferential looking: - It can be used to assess the visual acuity of infants based upon their turning their head or eyes towards a patterned rather than a uniform target. - A black and white square wave grating (alternating black and white stripes) is presented simultaneously with a plain grey target of equal size and average luminance. - Children with better vision are able to see a finer grating and turn towards it. Visual evoked potentials: - The electrical responses generated in the occipital cortex by visual stimulation of the eye. - The stimulus used is either a black and white square wave grating or a chequerboard pattern in which the pattern reverses at a set frequency. 17 Optotype: - It is a symbol, the identification of which corresponds to a certain level of visual acuity. - All tests employ black letters or pictures on an opaque or retro illuminated white background in order to maximize contrast. - The requirements of each optotype test correspond to the literary ability of the subject. - Testing of young children requires them to match the optotype letter or symbol on a card shown by the examiner who is 6 m or 3 m away by pointing to one of a group of matching letters on a key card. Children aged 18-24 months may be able to perform picture optotype test: - The Kay's pictures test: ✓ Uses pictures of objects such as a cat, train or house. - The Cardiff cards: ✓ Also use pictures. - The STYCAR letter tests: ✓ Use the letters first recognized by children (H, O, T, V and X) to test children up to the age of approximately 3 years. - The Sheridan–Gardiner test: ✓ Uses seven letters, adding U and A. Kay pictures Cardiff cards STYCAR Sheridan-Gardiner 18 Optotype testing of the literate: - It involves the naming of letters. - The Snellen visual acuity test is the most commonly used. - The test is based on the theory that the smallest object which can be resolved by the eye subtends the same visual angle at the nodal point of the eye as a cone photoreceptor (one minute of arc). - The bars and spaces of each letter subtend an angle of one minute of a degree. - The test chart is normally read from 6 m (20 feet). - Thus, a subject who identifies the letters on the '12' line from 6 m has 6/12 vision (20/40) – the numerator indicates the viewing distance. - Children are sometimes able to perform the test before 5 years of age, and may be able to match the letters to a key card before 4 years of age. - LogMAR (LOGarithm of the Minimal Angle of Resolution) visual acuity charts (e.g. the Bailey–Lovie test) are more precise than the Snellen test because they have a regular progression in the size and spacing of the letters from one line to the next and the same number of letters on every line. 19 Vernier acuity: - It is the smallest offset of a line which can be detected. - It is measured using a square wave grating. - An offset of 3–5 seconds of arc is normally discernible. - This is less than the limit of snellen visual acuity and is therefore also called hyperacuity. Near Visual Acuity Testing The near visual acuity is usually tested at a distance of 25–33 cm. Near acuity charts usually comprise unrelated words or passages of text. Times Roman is used as the standard font because the size of printed text depends on the font chosen. 20 Potential Visual Acuity Testing These tests may be used to assess the potential visual acuity of eyes in which it is not possible to see the macula because of a cataract. Good potential visual acuity indicates that cataract surgery is likely to be of benefit. - Pinhole test: ✓ The simplest clinical test. - Blue field entoptic phenomenon: ✓ It is the ability to see moving white dots when blue light diffusely illuminates the retina. ✓ They are thought to represent light transmitted by white blood cells in the peri-foveal capillaries. ✓ When this phenomenon is present, macular function is grossly intact. - Interferometers: ✓ It projects laser light from two sources on to the retina. ✓ Interference occurs where the two sources meet and this is seen as a sine wave grating if the macula is functioning. - The potential acuity meter: ✓ It projects a letter chart on to the retina through a small aperture. 21 Contrast Sensitivity Tests of visual acuity do not adequately reflect the ability of the eye to see low- contrast objects such as faces. In many conditions, e.g. cataract, glaucoma and optic neuritis, the visual acuity may be almost normal whilst the contrast sensitivity is considerably reduced. Contrast sensitivity: - Is measured using a sine wave grating. - This is a pattern in which there is a gradual transition between alternating light and dark bands, i.e. the edges of the bands appeared blurred. - Narrower bands are described as having a higher spatial frequency. - A contrast sensitivity curve is constructed by plotting a range of different spatial frequencies against the lowest degree of contrast at which the eye can still detect the grating. - Low or very high spatial frequencies must have higher levels of contrast in order to be seen. - In clinical practice, the contrast sensitivity is measured using either a television monitor or a chart. Pelli-Robson contrast test chart: - Displays letters that have decreasing levels of contrast to their background. VISITECH chart: - Has 40 circles with different sine wave gratings and levels of contrast, the subject must indicate the orientation of the circles. Acuity charts provide quantitative assessment, while contrast sensitivity provides qualitative assessment. 22 Scattering of Light When light travels through a medium with many small particles (dusty room), light that hit any of the particles is reflected in a new direction. N.B = vacuum has no particles. Normal ocular scattering: - Cornea: stroma scatters 10% of incident light. - Sclera: scatters by collagen bundles. - Iris: scatters by stromal fibers. - Lens: scatters by faint yellow pigments. - Retina: scatters by muller’s fibers. Sunlight scattering: - Why sky looks blue? ✓ Due to scattering of the most of the blue light of the sunlight. - Why sun appears red at nightfall? ✓ Because the sun is so far at that time, most of the blue light is scattered and only the red light reaches us. Glare Testing: Scattered light which reduces visual function is called glare. Glare may be the predominant symptom of corneal oedema or scarring, cataracts or opacification of the posterior lens capsule. The effect of a glare source depends on its position and intensity and on the light scattering properties of the ocular media. Glare testing refers to the measurement of visual function (e.g. visual acuity, contrast sensitivity, colour vision) in the presence of a source of glare. 23 Polarization of Light The orientation of the plane of the wave motion of rays comprising a beam of light is random unless the light is polarized. Polarized light is produced from ordinary light by: - Polarizing substances (calcite crystals): ✓ Only transmit light rays which are vibrating in one particular plane. ✓ Thus only a proportion of incident light is transmitted onward and the emerging light is polarized. ✓ A polarizing medium reduces radiant intensity but does not affect spectral composition. 24 - Reflection from a plane surface (such as water): ✓ If the angle of incidence is equal to the polarizing angle for the substance. ✓ The polarizing angle is dependent on the refractive index of the substance comprising the reflecting surface. ✓ At other angles of incidence the reflected light is partly polarized, i.e. a mixture of polarized and non-polarized light. ✓ Furthermore, the plane of polarization of the reflected light from such a surface is parallel with the surface. ✓ As most reflecting surfaces encountered in daily life are horizontal, it is possible to prepare polarized sunglasses to exclude selectively the reflected horizontal polarized light. ✓ Such glasses are of great use in reducing glare from the sea or wet roads. 25 Birefringence Some substances have a molecular structure which transmits light waves lying parallel to its structure but which selectively slows and therefore redirects light waves vibrating in a plane perpendicular to its structure. Crystals of quartz have this property, which is known as birefringence. Because they split incident unpolarized light into two polarized beams travelling in different directions, they have two refractive indices. Dichroism The molecular structure of dichroic substances completely blocks transmission of light waves not aligned with its structure by absorption. Thus, only one beam of polarized light emerges, much weakened in intensity compared with the incident non-polarized light. Tourmaline and polaroid (the latter made from fine iodine and quinine sulphate crystals embedded in plastic) are dichroic substances, polaroid being commonly used in sunglasses. Other examples of the use of polarized light in ophthalmology are: - The assessment of binocular vision in which polarizing glasses may be used to dissociate the eyes, e.g. Titmus test. - In pleoptics to produce Haidinger's brushes (usually attributed to the dichroism of the xanthophyll pigment of the macula). In the manufacture of optical lenses to examine them for stress. 26 Stereoscopic vision Stereopsis is the ability to fuse slightly dissimilar images, which stimulate disparate retinal elements within Panum's fusional areas in the two eyes, with the perception of depth. It is graded according to the least horizontal disparity of retinal image that evokes depth of perception, and is measured in seconds of arc. The normal stereoacuity is approximately 60 seconds of arc or better. An individual with very good stereoscopic vision may have a stereoacuity of better than 15 seconds of arc, which is the smallest disparity offered in the Frisby stereotest (range 600–15 seconds of arc). The maximum stereoacuity is achieved when the images fall on the macular area of the retina, where the resolving power of the eye is at its best. Good stereoacuity is therefore a product of central single binocular vision. A stereoacuity of better than 250 seconds of arc is said to exclude significant amblyopia, while a stereoacuity of worse than 250 seconds of arc may be an indicator of amblyopia. Clinical tests of stereoacuity: - Titmus test (3000-40 seconds of arc): ✓ It includes the Wirt fly test, it is in the form of vectographs. ✓ A vectrograph consists of two superimposed views presented in such a way that the light entering each eye is plane polarized, the light from one view being at right angles to that from the other. The composite picture must be viewed through a polarizing visor or spectacles. ✓ The Wirt fly is the largest target in the test, which also includes graded sets of animals & circles, one of which is disparate and appears to stand forward. ✓ The test must be viewed at 40 cm. 27 - Frisby test (600-15 seconds of arc): ✓ It consists of three clear plastic plates of different thicknesses. ✓ On each plate there are four squares filled with small random shapes. ✓ One square on each plate contains a 'hidden' circle, which is printed on the back surface of the plate. ✓ The random shapes give no visual clue to the edge of the 'hidden' circle, and the test is purely three-dimensional and does not require polarizing or colored glasses to be worn. ✓ At a 40 cm viewing distance the plates show a disparity of 340, 170 and 55 seconds of arc, and by adjusting the viewing distance the test can be used to give a disparity range from 600 to 15 seconds of arc. - TNO test (480-15 seconds of arc): ✓ It comprises computer-generated random dot anaglyphs. ✓ An anaglyph is a stereogram in which two disparate views are printed in red and green respectively on a white ground. ✓ Red–green spectacles are worn to view the anaglyph. ✓ The eye looking through the red filter sees only the green picture as black, and the eye looking through the green filter sees the red picture as black, and the two views may be fused to give a stereoscopic effect. 28 - Lang Stereotest (1200-550 seconds of arc): ✓ Targets are made up of fine vertical lines which are seen alternately by each eye when focused through built-in cylindrical lens elements. ✓ The test card must be held parallel to the plane of the patient's face to avoid giving uniocular clues. ✓ The test is viewed at a normal reading distance. 29 Quantitative measurement of light (radiometry-photometry) Radiometry: - Quantifies radiant energy in all parts of the electromagnetic spectrum as an absolute value. Photometry: - Quantifies part of the spectrum in terms of the visual response it produces (the spectral sensitivity of the eye). Photometric measurements are therefore more commonly employed in visual science. Radiometry measures light in terms of: ▪ Amount emitted from a source (radiant flux). ▪ Its intensity (radiant intensity). ▪ Amount falling on a surface (irradiance). ▪ Amount reflected from it (radiance). The equivalent photometric measurements are: ▪ Luminous flux. ▪ Luminous intensity. ▪ Illuminance. ▪ Luminance. 30 Radiometric and photometric units are related by the luminous efficiency of the radiation: a conversion factor specific for each wavelength determined by the sensitivity of the eye to it. The peak photopic sensitivity of the eye: - Is to the wavelength of 555 nm (yellow- green), at which 1 watt of monochromatic light has a photometric equivalent of 685 lumens. - This wavelength is therefore said to have maximum luminous efficiency. The eye is progressively less sensitive to wavelengths towards each end of the visible spectrum: - In other words, the luminous efficiency of the radiation becomes lower and the same energy flux (radiometric unit) is equivalent to a lower luminous flux (photometric unit). The conversion factor falls towards zero outside the range 400–700 nm (visible light). The photometric equivalent of polychromatic light is calculated by summating the photometric equivalents of the constituent wavelengths. 31 The total flow of light emitted in all directions from a source is termed either: - Radiant flux: if measured in watts. - Luminous flux: if measured in lumens. The intensity of light emitted from a source is: - A measurement of the flow of light per unit solid angle of space extending away from it. - It is called either: ✓ Radiant intensity: if measured in watts per steradian. ✓ Luminous intensity: if measured in candelas (lumens per steradian). A steradian: - Is the unit of solid angle (resembling a cone). - It is defined as the angle at the centre of a sphere which subtends an area on the surface of the sphere measuring the square of the radius (r). - Since the surface area of a sphere is 4πr2, it follows that a point source whose luminous intensity is one candela emits a total of 4π lumens. 32 The original unit of luminous intensity was the candle, based on the emission from a wax candle of standard composition, attempts to produce a more uniform and precise source of light by which others could be measured led to the current standard unit, the candela, whereby the luminous intensity per square centimetre of a black body radiator at the freezing point of platinum is defined as 60 candelas because the black body radiator is 60 times brighter than the standard candle. When radiant flux is incident on a surface, the surface is said to be irradiated. The flux incident per unit area at any point is called irradiance and is measured in watts per square metre. The photometric equivalent of irradiance is illuminance, which measures the luminous flux incident on an illuminated surface. The unit of illuminance is the lux (lumen per square metre). The illumination of a surface decreases the further it is from the light source. The surface illumination is inversely related to the square of the distance of the surface from the source (the inverse square law). The illumination of a surface is also dependent upon the angle of the incident light to the surface (the cosine law): I cos 𝑖 E= 𝑑2 ▪ E is the illumination. ▪ I is the luminous intensity. ▪ i is the angle of incidence. ▪ d is the distance between source and surface. A uniformly diffusing surface is one which reflects light equally in all directions, if in addition, it reflects all the light which is incident, it is said to be a perfect diffuser. Each reflecting point on such a surface behaves as a point source of light because it emits light equally in all directions. The luminance at any point on the surface is defined as the luminous intensity per unit projected area in a given direction. Luminance is measured in candelas per square metre. The radiometric equivalent, radiance, is measured in watts per steradian per square metre. It is important to stress that the candela measures light reflected or emitted in only one direction and not the total amount leaving the surface in all directions. For most purposes, the luminance of a surface is measured not in candelas but by comparing it with a uniform diffuser which emits a total flux in all directions of 1 lumen per unit area. 33 A luminous flux of one lumen per square metre corresponds to a luminance of one apostilb. (An alternative definition is 1 apostilb = 1/ π candelas per square metre). Another unit, the troland, is a measure of retinal illumination when a surface luminance of one candela per square metre is viewed through an entrance pupil which measures one square millimetre after correction for the Stiles–Crawford effect. 34 Automated perimetry Perimetry measures the light sensitivity of points on the retina by the ability of the patient to detect light stimuli of varying intensity presented at corresponding points in the visual field. Currently, most perimeters have a standard background luminance of 31.5 apostilbs (asb). The eye to be tested should be positioned at the center of the hemisphere, and the near spectacle correction should be worn whilst the patient maintains steady fixation. Spots of light are projected onto the inner surface of the hemisphere. Light stimuli may vary in intensity between 0.8 and 10,000 asb. This range can be expressed as a logarithmic scale and the log units are termed decibels (dB; 1 log unit equals 10 dB). The range 0.8–10,000 asb used in perimetry corresponds to 51 dB. 35 Reflection of light When light meets an interface between two media, its behavior depends on the nature of the two media involved. Light may be: - Absorbed by the new medium. - Transmitted onward through it. - Bounce back into the first medium (reflection). It occurs, to some degree, at all interfaces even when most of the light is transmitted or absorbed. It is by the small amount of reflected light that we see a glass door and thus avoid walking into it. Laws of Reflection: - The incident ray, the reflected ray and the normal to the reflecting surface all lie in the same plane. - Angle of incidence (i) equals the angle of reflection (r). Reflection at an irregular surface: - When parallel light encounters an irregular surface, it is scattered in many directions, this is called diffuse reflection. - It is by diffuse reflection that most objects (except self-luminous ones) are seen (e.g. furniture) - A perfect reflecting surface (free from irregularities) would itself be invisible, only the image formed by light reflected in it would be seen. 36 Reflection at plane surface (plane mirror): - Light from object O is reflected at the surface according to the laws of reflection. - If the reflected rays are produced behind the surface, they all intersect at point I, the image of object O. - The brain always assumes that an object is situated in the direction from which light enters the eye (Light from object O appears to come from point I, the image of O). - However, if the observer actually goes to point I, there is no real image present, it could not be captured on a screen, such images are called virtual. - Images which can be captured on a screen are called real images. - The image of an object formed by reflection at a plane surface has the following characteristics: ✓ Upright (erect). ✓ Virtual. ✓ Laterally inverted. ✓ It lies along a line perpendicular to the reflecting surface and is as far behind the surface as the object is in front of it. 37 Rotation of a plane mirror: - If a plane mirror is rotated while light is incident upon its center of rotation, the reflected ray is deviated through an angle equal to twice the angle of rotation of the mirror. By the laws of reflection: Angle of incidence = angle of reflection Therefore angle between incident and reflected ray = Angle of incidence + angle of reflection = 2 x angle of incidence With mirror at M1, and it’s normal N1: Angle ICR1 = 2 x i After rotation of the mirror to M2, with normal N2: Angle ICR2 = 2 x (i + a) “a is the angle of rotation” The angle through which the reflected ray is deviated when the mirror rotates from M1 to M2 is angle R1CR2. R1CR2 = ICR2 - ICR1 = 2 (i + a) – 2 (i) = 2a 38 Reflection at spherical reflecting surface: - A reflecting surface having the form of a portion of a sphere is called a spherical mirror. - If the reflecting surface lies on the inside of the curve, it is a concave mirror. - If the reflecting surface lies on the outside of the curve, the mirror is a convex mirror. - Centre of curvature (C): ✓ Is the center of the sphere of which the mirror is a part. - Pole of the mirror (P): ✓ Is the center of the reflecting surface. - CP: ✓ The radius of curvature (r). - An axis: ✓ Is any line passing through the center of curvature and striking the mirror. ✓ That passing through the pole of the mirror is called the principal axis. ✓ Any other is a subsidiary axis. - Rays parallel to the principal axis are reflected towards (concave) or away from (convex) the principal focus (F) of the mirror. - The distance FP is the focal length (f) of the mirror and is equal to half the radius of curvature. - Thus, the image of an object situated on the principal axis an infinite distance away is formed at the principal focus. - The image formed by the concave mirror is real while that formed by the convex mirror is virtual. 39 The following diagrams show the nature and situation of images formed of objects situated at a finite distance from the mirror on the principal axis. In each case the image is constructed using two rays: - A ray parallel to the principal axis and reflected to or away from the principal focus. - A ray from the top of the object, passing through the center of curvature and reflected back along its own path. For any position of the object, the position of the image formed by a spherical mirror can be calculated using the formula: 𝟏 𝟏 𝟏 2 − = = 𝐯 𝐮 𝐟 𝐫 = 𝒑𝒐𝒘𝒆𝒓 𝒐𝒇 𝒕𝒉𝒆 𝒎𝒊𝒓𝒓𝒐𝒓 v = distance of image from the mirror u = distance of object from the mirror f = focal length of the mirror r = radius of curvature of the mirror Also, the magnification produced by a curved mirror can be calculated. Magnification is defined as the ratio of image size to object size: 𝐢 𝐯 𝑴= = − 𝐨 𝐮 M = Magnification i = image size o = object size When using these formulae, the sign convention must be adhered to. All distances are measured from the pole of the mirror (or vertex of the lens) to the point in question. Image size is positive for erect images (above the principal axis) and negative for inverted images (below the principal axis). 40 41 Clinical Application: - The theory of curved mirrors has a major clinical application. - The anterior surface of the cornea acts as a convex mirror and is used as such by the standard instruments employed to measure corneal curvature. - Images formed by the reflecting surfaces of the eye are called catoptric images (Purkinje-Sanson images). 42 Refraction of light Definition: - Change in direction of light when it passes from one transparent medium into another of different optical density. The incident ray, the refracted ray and the normal all lie in the same plane. The velocity of light varies according to the density of the medium through which it travels. The denser the medium the slower the light passes through it. When a beam of light strikes the interface separating a less dense medium from a denser one obliquely, the edge of the beam which arrives first (A) is retarded on entering the denser medium. The opposite side of the beam (B) is meanwhile continuing at its original velocity. The beam is thus deviated as indicated, being bent towards the normal as it enters the denser medium. A comparison of the velocity of light in a vacuum and in another medium gives a measure of the optical density of that medium. This measurement is called the absolute refractive index (n) of the medium: velocity of light in vaccum Absolute refractive index = vaccumnmedium = velocity of light in medium As the optical density of air as a medium is negligible under normal conditions: velocity of light in air Refractive index = airnmedium = 43 Examples of refractive index are: Air =1 Water (Aqueous) = 1.33 Cornea = 1.37 Crystalline lens = 1.386–1.406 Crown glass = 1.52 Flint glass = 1.6 Diamond = 2.5 The absolute refractive index of any material can be determined using a refractometer. On entering an optically dense medium from a less dense medium, light is deviated towards the normal. n1 n2 The incident ray makes an angle (i) the angle of incidence with the normal. The angle between the refracted ray and the normal is called the angle of refraction (r). These angles are governed by the refractive indices of the media involved according to Snell's law. Snell's law states that: - The incident ray, refracted ray and the normal all lie in the same plane. - The angles of incidence (i) and refraction (r) are related to the refractive index (n) of the media, where the first medium is a vacuum (n) is the absolute refractive index, and in air (n) is the refractive index. n1 sin(i) = n2 sin(r) 44 If, however, the interface is between two denser media of differing optical densities, e.g. water and glass, then the value of n for that interface may be calculated as follows: n glass waternglass = n water More generally, on passing from medium1 into medium2, the index of refraction is given by: n2 1n2 = n1 Light passing obliquely through a plate of glass is deviated laterally and the emerging ray is parallel to the incident ray. Thus the direction of the light is unchanged but it is laterally displaced. It should be remembered that some reflection also occurs at every interface. For example, a lens or window with a refractive index of 1.5 in air reflects 4% of light from the anterior surface and transmits the remaining 96% to the posterior surface; a further 4% of this is reflected so that the lens transmits only 92.16% of normally incident light. This illustrates the use of a sheet of glass as an image-splitter (e.g. the teaching mirror of the indirect ophthalmoscope): - Most of the light is refracted across the glass to the examiner's eye. - However, a small proportion is reflected at the anterior surface of the glass and enables an observer to see the same view as the examiner. 45 Refraction of light at a curved interface Light passing across a curved interface between two media of different refractive indices obeys Snell's law. A convex spherical curved surface causes parallel light to either: - Converge to a focus if n2 is greater than n1. - Diverge as from a point focus if n2 is less than n1. The refracting power or vergence power of such a surface is given by the formula: n2−n1 Surface power = r r = radius of curvature of the surface in meters Surface power is measured in diopters Surface power is positive for converging surfaces and negative in sign for diverging surfaces The anterior surface of the cornea is an example of such a refracting surface, and its power accounts for most of the refracting power of the eye. 46 Objects situated in an optically dense medium appear displaced when viewed from a less dense medium. This is due to refraction of the emerging rays which now appear to come from a point I, the virtual image of object O. Objects in water seem less deep than they really are (e.g. one's toes in the bath). This principle applies also to surgical instruments in the anterior chamber of the eye. Rays emerging from a denser medium to a rarer medium suffer a variety of fates, depending on the angle at which they strike the interface: - Ray A: strikes at 90° to the interface and is undeviated. - Ray B: emerges after refraction. - Ray C: As the rays meet the interface more obliquely, a stage is reached where the refracted ray runs parallel with the interface the angle c is called the critical angle. - Ray D: Rays striking more obliquely still fail to emerge from the denser medium and are reflected back into it as from a mirror, this is called total internal reflection. The critical angle is determined by the refractive indices of the media involved and can be calculated using Snell's law. The critical angle for the tear film/air interface is 48.5°, and for a crown glass/air interface the critical angle is 41°. 47 Total internal reflection is used in optical instruments: - Prisms: ✓ They make excellent reflectors by total internal reflection. - Fiber optic cables: ✓ They are used to deliver light from a remote source to the point where it is required. ✓ Examples include the surgical intraocular light source and the transmission of laser light from the laser tube to the delivery system of the laser slit lamp. ✓ Light enters the end of each fiber and is reflected onward by total internal reflection until it emerges from the far end without significant loss of radiant energy. ✓ Bending the optical fiber does not impair its efficiency. Total internal reflection also occurs at surfaces within the eye, notably the cornea:air interface, and prevents visualization of parts of the eye, e.g. the angle of the anterior chamber and peripheral retina. The problem is overcome by applying a contact lens made of material with a higher refractive index than the eye and filling the space between eye and lens with saline, thus destroying the cornea/air refracting surface and allowing visualization of the anterior chamber angle (gonioscopy) and peripheral retina (three-mirror). 48 Dispersion of light So far, this discussion of refraction has overlooked the fact that white light is composed of various wavelengths. In fact, the refractive index of any medium differs slightly for light of different wavelengths. Light of shorter wavelength is deviated more than light of longer wavelength (blue light is deviated more than red). The refractive index of a material is normally taken to mean that for the yellow sodium flame. The angle formed between the red and blue light around the yellow indicates the dispersive power of the medium. This is not related to the refractive index of the material. 49 The Rainbow (Total Internal Reflection and Dispersion) When sunlight enters a raindrop it is dispersed to its constituent spectral colors. Under certain circumstances, the angle of incidence is such that total internal reflection then occurs within the drop. The dispersed light finally emerges, each wavelength or color making a different angle with the horizon. To see the rainbow, the observer must look away from the sun, the observer receives only a narrow pencil of rays from each drop (i.e. only one color). The whole rainbow is the result of rays received from a bank of drops at increasing angle to the observer's eye. Violet: making the smallest angle to the horizon, is received from the lower drops. Red: making the greatest angle with the horizon, is received from the highest drops. Thus the red is on the outside of the primary rainbow. The secondary rainbow is formed by rays that have twice undergone total internal reflection within the raindrops, and the colours are seen in reverse order: violet is on the outside of the bow. 50 Prisms Definition: - It is a portion of a refracting medium bordered by two plane surfaces which are inclined at a finite angle. The angle a between the two surfaces is called the refracting angle or apical angle of the prism. A line bisecting the angle is called the axis of the prism. The opposite surface is called the base of the prism. When prescribing prisms, the orientation is indicated by the position of the base, e.g. 'base-in', 'base-up'. Light passing through a prism obeys Snell's law at each surface. The ray is deviated towards the base of the prism. The net change in direction of the ray, angle D, is called the angle of deviation. For a prism in air, the angle of deviation is determined by three factors: 1) The refractive index of the material of which the prism is made. 2) The refracting angle (a) of the prism. 3) The angle of incidence of the ray considered. 51 For any particular prism, the angle of deviation (D) is least when the angle of incidence equals the angle of emergence. Refraction is then said to be symmetrical and the angle is called the angle of minimum deviation. Under these conditions the angle of deviation is given by the formula: D = (n – 1) α (α=refracting angle) Thus, for a glass prism of refractive index 1.5: 𝛂 D = (1.5 – 1) α = 𝟐 In other words, the angle of deviation equals half the refracting angle for a glass prism. The image formed by a prism is: - Erect. - Virtual. - Displaced towards the apex of the prism. Deviation is reduced to a minimum when light passes through the prism symmetrically. There are two primary positions in which the power of a prism may be specified: 1) Position of minimum deviation. 2) Prentice position. In the Prentice position: - One surface of the prism is normal to the ray of light so that all the deviation takes place at the other surface of the prism. - The deviation of light in the Prentice position is greater than that in the position of minimum deviation, because in the Prentice position the angle of incidence does not equal the angle of emergence. - Therefore the Prentice position power of any prism is greater than its power in the position of minimum deviation. 52 It is the Prentice position power which is normally specified for glass ophthalmic prisms, e.g. trial lens prisms. While it is the power in the position of minimum deviation which is specified for plastic ophthalmic prisms, e.g. prism bars. If a high-power prism is not used in the correct position, a considerable error will result. In practice, plastic prisms may be held in the frontal plane as this is near enough to the position of minimum deviation to avoid significant inaccuracy. For example, a 40 diopter plastic prism held in the frontal plane will have an effective power of 41 diopters, but if it is held in the Prentice position its effective power becomes 72 diopters. Furthermore, it is not satisfactory to stack prisms one on top of another, because the light entering the second and subsequent prisms will not be at the correct angle of incidence. The effective power of such a stack will be significantly different from the sum of the powers of the component prisms. However, it is permissible to place a horizontal and a vertical prism one in front of the other, because their planes of refraction are perpendicular and therefore independent of one another. 53 Notation of prisms The power of any prism can be expressed in various units: Prism diopter (Δ) - A prism of 1 diopter power (1Δ) produces a linear apparent displacement of 1 cm of an object (O) situated at 1 m. Angle of apparent deviation: - The apparent displacement of the object O can also be measured in terms of the angle (θ) the angle of apparent deviation. - Under conditions of ophthalmic usage a prism of 1 prism diopter power produces an angle of apparent deviation of 1/2°. Thus 1 prism diopter = 1/2°. The Centrad (▽): - This unit differs from the prism diopter only in that the image displacement is measured along an arc 1 m from the prism. - The centrad produces a very slightly greater angle of deviation than the prism diopter, but the difference in practice is negligible. Refracting Angle: - A prism may also be described by its refracting angle. - However, unless the refractive index of the prism material is also known, the prism power cannot be deduced. Summary of Prism Units: - Thus a glass prism of refracting angle 10° (a ten-degree prism) deviates light through 5° and has a power of 10 prism diopters (10D), assuming its refractive index is 1.5. 54 Vector addition of prisms Sometimes a patient requires a prismatic correction in both the horizontal and the vertical directions. This can conveniently be achieved by using one stronger prism mounted at an oblique angle. The required power and angle is calculated by vector addition, either graphically or mathematically: 1) Graphically: - The required horizontal and vertical powers are drawn to scale and the rectangle completed. - The diagonal gives the power and the angle ROH the angle required for a single equivalent prism. - The orientation must be specified in terms of the angle, base up/down, and base in/out. 2) Mathematically: - The diagonal power is calculated using Pythagoras' theorem (the square of the diagonal equals the sum of the squares of the vertical and horizontal sides) and tan ROH = RH/OH. - Thus a 5 diopter prism base-up and in, lying in the 37° meridian, is equivalent to a 4 diopter base-in prism plus a 3 diopter base-up prism. 55 Risley prism It consists of two prisms of equal power which are mounted one in front of the other in such a way that they can be rotated with respect to each other and the resulting power is indicated on a scale on the rim of the instrument. A Risley prism may be used in conjunction with a Maddox rod to measure phorias, and is included in the refractor heads used by many optometrists. Interpretation of Orthoptic Reports Armed with the knowledge that 1 prism diopter = 1/2°, orthoptic reports become intelligible to the clinician. The orthoptist measures the angle of squint by two methods: 1) Synoptophore: - Measures the angle between the visual axes of the eyes in degrees. - (+) signifying esotropia and (–) signifying exotropia. - Report reads: Synopt. Without glasses + 20° 2) Prism cover test (PCT): - The alternating cover test is performed, placing prisms of increasing strength before one eye, until movement of the eyes is eliminated. - The result is expressed in prism diopters, eso signifying esotropia and exo signifying exotropia. - Report reads: PCT = distance eso + 40∆ These two statements express the same angle of squint. 56 Uses of prisms Diagnostic prisms 1) Assessment of squint & heterophoria: - Measurement of angle objectively by prism cover test. - Measurement of angle subjectively by Maddox rod. - Assess likelihood of diplopia after proposed squint surgery in adults. - Measurement of fusional reserve: ✓ Increasingly powerful prisms are placed before one eye until fusion breaks down. ✓ This is very useful in assessing the presence of binocular single vision in children under 2 years of age. - 4-diopter prism test: ✓ This is a delicate test for small degrees of esotropia (microtropia). ✓ A 4-diopter prism placed base-out before the deviating eye causes no movement as the image remains within the suppression scotoma. ✓ When placed before the normal (fixing) eye, movement occurs. 2) Assessment of simulated blindness : - If a prims is placed in front of a seeing eye, the eye will move to regain fixation. Forms of prism used in diagnosis: 1) Single unmounted prism. 2) Prisms from the trial lens set. 3) Prism bars. Therapeutic prisms 1) Convergence insufficiency: - The commonest therapeutic use of prisms is building up the fusional reserve of patients with convergence insufficiency. - The prisms are used base-out during the patient’s exercise periods. - They are not worn constantly. 2) Relieving diplopia in certain cases of squint: - Decompensated heterophorias. - Small vertical squints. - Some paralytic squints with diplopia in the primary position. Prisms are reserved for those patients for whom surgery is not indicated. 57 Forms of therapeutic prism: 1) Temporary wear: - Prisms used in treatment include clip-on spectacle prisms for trial wear. - An improvement on these are Fresnel prisms, which are available in all powers employed clinically. - A Fresnel prism consists of a plastic sheet of parallel tiny prisms of identical refracting angle. - The overall prismatic effect is the same as that of a single large prism. - The sheets are lighter than a glass prism and can be stuck on to the patient's glasses. 2) Permanent wear: - Decentering the spherical lens already present. - Alternatively, prisms can be mounted in spectacles. Notes on Prescription of Prisms The apex of the prism must always be placed towards the direction of deviation of the eye. Generally, when prescribing prisms, the correction is split between the two eyes. To correct convergence the prisms must be base-out, e.g. 8D base-out R and L. 58 To correct divergence the prisms must be base-in, e.g. 6D base-in R and L. To correct vertical deviation the orientation of the prisms is opposite for the two eyes, e.g. 2D base-down RE / 2D base-up LE for R hypertropia. Prisms in Optical Instruments Prisms are commonly used in ophthalmic instruments as reflectors of light. The prism is designed and orientated so that total internal reflection occurs within it. It can be seen that prisms give greater flexibility in dealing with an image than do mirrors. Instruments in which prisms are used include the slit lamp microscope, the applanation tonometer and the keratometer. Dove Porro Right angle 59 Spherical lenses A lens is defined as: - A portion of a refracting medium bordered by two curved surfaces which have a common axis. When each surface forms part of a sphere, the lens is called a spherical lens. Various forms of spherical lens are possible, some having one plane surface, this is acceptable because a plane surface can be thought of as part of a sphere of infinite radius. A convex lens: - Cause convergence of incident light. A concave lens: - Cause divergence of incident light. 60 The total vergence power of a spherical lens depends on the: 1) Vergence power of each surface. 2) Thickness of the lens. Most of the lenses used in ophthalmology are thin lenses, and for a thin lens the thickness factor may be ignored. Thus the total power of a thin lens = sum of the two surface powers. Refraction can be thought of as occurring at the principal plane of the lens, and in the following lens diagrams only the principal plane is shown. Note that in ray diagrams the convex or concave nature of a thin lens is shown by the appropriate symbol at each end of the line that indicates the principal plan Principal plane of the lens is shown, AB. The point at which the principal plane and principal axis intersect is called the principal point or nodal point (N) of the lens. Rays of light passing through the nodal point are undeviated. Light parallel to the principal axis is converged to or diverged from the point (F) the principal focus. As the medium on both sides of the lens is the same (air), parallel light incident on the lens from the opposite direction, i.e. from the right, will be refracted in an identical way. 61 There is therefore a principal focus on each side of the lens, equidistant from the nodal point. The two principal foci are by convention distinguished from each other according to the following rules: 1) The first principal focus (F1) is the point of origin of rays which, after refraction by the lens, are parallel to the principal axis. 2) The distance F1N is the first focal length (f1). 3) Incident light parallel to the principal axis is converged to or diverged from the second principal focus (F2). 4) The distance F2N is the second focal length (f2). 5) By the sign convention: ▪ f2 has a positive sign for the convex lens, and a negative sign for the concave lens. 6) Lenses are designated by their second focal length: ▪ Convex or converging lenses are known as 'plus lenses' and are marked with a (+). ▪ Concave or diverging lenses are known as 'minus lenses' and are marked with a (–). 7) If the medium on either side of the lens is the same, e.g. air, then f1 = f2. 8) However, if the second medium differs from the first, e.g. as in the case of a contact lens, then f1 will not equal f2. 62 Thin lens formula As with spherical mirrors, the position and nature of the image formed by a spherical lens depends on the position of the object: 𝟏 𝟏 𝟏 v = distance of image from the principle point − = u = distance of object from the principle point 𝐯 𝐮 𝐟𝟐 f2 = second focal length For an object in any position, the image can be constructed using two rays: 1) A ray from the top of the object which passes through the principal point undeviated. 2) A ray parallel to the principal axis, which after refraction passes through (convex) or away from (concave) the second principal focus. 63 Dioptric power of lenses (Vergence) Lenses of shorter focal length are more powerful than lenses of longer focal length. The reciprocal of the second focal length expressed in meters, gives the vergence power of the lens in diopters (D): 𝟏 F = vergence power of the lens in diopters. 𝐅= 𝐟𝟐 f2 = second focal length in meters. A converging lens of second focal length +5 cm has a power of: 𝟏 = + 20 D 𝟎.𝟎𝟓 A diverging lens of second focal length –25 cm has a power of: 𝟏 - 𝟎.𝟐𝟓 = - 4 D The reciprocal of object and image distances in meters gives a dioptric value which is a measure of the vergence of the rays between object or image and the lens. In other words, it is a measure of the degree of convergence or divergence of the rays in question. 64 Magnification Formulae Linear Magnification: The linear magnification produced by a spherical lens can be calculated from the basic formula: I = image size. 𝐈 𝐯 Linear magnification = = O = object size. 𝐎 𝐮 v = distance of image from principal plane. u = distance of object from principal plane. Angular Magnification: In ophthalmic practice, actual image and object size are of less importance than the angle subtended at the eye, because the angle subtended governs the retinal image size. Objects (A,B,C,D) all subtend angle θ at the eye and produce retinal image xy. They are all therefore of identical apparent size. Apparent size is given by the ratio of object (or image) size divided by its distance from the eye, which is, of course = tan θ. When considering the eye, the angles encountered are small. For small angles the value of tan θ can be taken to be equal to the angles themselves. The concept of apparent size permits the assignment of a definite magnitude to an image at infinity, such as that formed by a convex lens when the object is situated at the first principal focus. The object and its infinitely distant image subtend the same angle, θ, at the lens and also at the eye, if the eye is brought very close to the lens. The angular magnification is therefore unity, i.e. apparent object size and apparent image size are the same. 65 The simple magnifying glass (Loupe) The use of a convex lens enables the eye to view the object at a much shorter distance than would be possible unaided, and to retain a distinct image. As the object approaches the eye it subtends a greater angle at the eye and the retinal image size increases. The magnifying power of the lens under these conditions can be expressed as follows: apparent size of image Magnifying power (M) = at 25 cm from the eye apparent size of object tan θ2 Magnifying power (M) = tan θ1 25 25 Magnifying power (M) = O x = f O f 𝐅 Magnifying power (M) = 𝟒 Thus, the commonly used × 8 loupe has a lens power of +32 diopters. 66 Spherical Lens Decentration and Prism Power Rays of light incident upon a lens outside its axial zone are deviated towards (convex lens) or away from (concave lens) the axis. Thus the peripheral portion of the lens acts as a prism. The refracting angle between the lens surfaces grows larger as the edge of the lens is approached, thus the prismatic effect increases towards the periphery of the lens. Use of a non-axial portion of a lens to gain a prismatic effect is called decentration of the lens. Lens decentration is frequently employed in spectacles where a prism is to be incorporated, on the other hand, poor centration of spectacle lenses, especially high power lenses, may produce an unwanted prismatic effect. This is a frequent cause of spectacle intolerance, especially in patients with aphakia or high myopia. It is thus of importance to be able to predict the prismatic power gained by decentering a spherical lens, this is given by the formula: P=FxD P = prismatic power in prism diopters. F = lens power in diopters. D = decentration in centimeters. The increasing prismatic power of the more peripheral parts of a spherical lens is the underlying mechanism of spherical aberration. Furthermore, it causes the troublesome ring scotoma and jack-in-the-box effect which give rise to great difficulty to those wearing high-power spectacle lenses. 67 Astigmatic lenses All the meridians of each surface of a spherical lens have the same curvature (as parts of a sphere), and refraction is symmetrical about the principal axis. In an astigmatic lens, all meridians do not have the same curvature, and a point image of a point object cannot be formed. There are two types of astigmatic lenses, namely cylindrical and toric lenses. Cylindrical lenses These lenses have one plane surface and the other forms part of a cylinder. Thus, in one meridian the lens has no vergence power and this is called the axis of the cylinder. In the meridian at right angles to the axis, the cylinder acts as a spherical lens. The total effect is the formation of a line image of a point object (focal line). Focal line is parallel to the axis of the cylinder. The Maddox Rod This device used in the diagnosis of extraocular muscle imbalance, consists of a series of powerful convex cylindrical lenses mounted side by side in a trial lens. The patient views a distant white point source of light through the Maddox rod, which is placed close to the eye (in the trial frame). The spotlight must be far enough away for its rays to be parallel on reaching the patient (at least 6 m). 68 Light in the meridian parallel to the axis of each cylinder passes through undeviated and is brought to a focus by the eye. The Maddox rod consists of a row of such cylinders, and thus a row of foci are formed on the retina. These foci join up and are seen as a line of light which lies at 90° to the axis of the Maddox rod. Meanwhile, light incident on the Maddox rod in the meridian at 90° to its axis is converged by each cylinder to a real line focus between the rod and the eye. This focus is too close to the eye for a distinct image to be formed on the retina by the focusing mechanism of the eye. This light is therefore scattered over a wide area of retina and does not confuse the perception of the composite line image described above. Remember that the line seen by the patient lies at 90° to the axis of the Maddox rod and is formed by the focusing mechanism of the eye, it is not the real line image of the Maddox rod. The glass of the Maddox rod is tinted red so the composite line image seen by the patient is also red. 69 Use of the Maddox Rod to Test Muscle Balance To test muscle balance the Maddox rod is placed close in front of the right eye (in the trial frame) and the distant white spotlight is viewed with both eyes. The right eye therefore sees a red line at 90° to the axis of the Maddox rod, while the left eye sees the white spotlight. Thus the two eyes see dissimilar images and are dissociated, allowing any muscle imbalance to become manifest. To test for horizontal imbalance, the rod must be horizontal to give a vertical line and vice versa. Remember that the eye behind the Maddox rod (conventionally the right) is deviating in the opposite direction to that indicated by the red line Any deviation is measured by placing prisms before the left eye until the orthophoric situation is achieved. (Maddox rod before the right eye) patient’s view A = horizontal orthophoria B = Exophoria C = Esophoria D = vertical orthophoria E = right hyperphoria F = right hypophoria (left hyperphoria) 70 Toric Surface Imagine that the cylindrical lens is picked up by its ends and bent so that the axis XY becomes an arc of a circle. The previously cylindrical surface is now curved in both its vertical and horizontal meridians, but not to the same extent, it is now called a toric surface. The meridians of maximum and minimum curvature are called the principal meridians and in ophthalmic lenses these are at 90° to each other. The principal meridian of minimum curvature, and therefore minimum power, is called the base curve. 71 Toric Lenses Lenses with one toric surface are known as toric lenses, or sphero-cylindrical lenses. Such lenses do not produce a single defined image because the principal meridians form separate line foci at right angles to each other. Between the two line foci, the rays of light form a figure known as Sturm's conoid. The distance between the two line foci is called the interval of Sturm. The plane where the two pencils of light intersect is called the circle of least confusion or the circle of least diffusion. Blur circle images only are formed at all other planes lying between 2 line foci. A toric lens can be thought of as a spherical lens with a cylindrical lens superimposed upon it. Toric lenses may be defined numerically as a fraction, the spherical power being the numerator and the cylindrical power the denominator. For example a toric lens with a power of +2 D in one principal meridian and +4 D in the other principal meridian can be regarded as a +2 D sphere with a +2 D cylinder superimposed. This is therefore written as +2.0 DS/+2.0 DC. 72 Spherical Equivalent It is sometimes useful to calculate the power of the spherical lens of closest overall effect to a given toric lens, known as the spherical equivalent. This reveals whether the eye is essentially hypermetropic, emmetropic or myopic. This consideration is especially important in the choice of intraocular lens power for the individual patient. The spherical equivalent power is calculated from the toric lens prescription by addition of the spherical power and half the cylindrical power (S + ½ C) e.g. the spherical equivalent of +2.00 DS/+2.00 DC is +3.00 DS, while that of +2.00 DS/–2.00 DC is +1.00 DS. The focal point of the spherical equivalent would coincide with the circle of least confusion of the toric lens's Sturm's conoid. The Cross-Cylinder In clinical refraction the orientation of the trial cylinder can be checked by superimposing another cylinder with its axis lying obliquely to the axis of the trial cylinder. The power of a cylinder can be checked by superimposing further cylinders of varying power and sign in the same axis as the trial cylinder. These considerations have led to the evolution of the cross-cylinder. The cross-cylinder is a type of toric lens used during refraction. Its use was popularised by Edward Jackson and it is often referred to as 'Jackson's cross-cylinder'. The cross-cylinder is a sphero-cylindrical lens in which the power of the cylinder is twice the power of the sphere and of the opposite sign. The net result is thus the same as superimposing two cylindrical lenses of equal power but opposite sign with their axes at right angles. The lens is mounted on a handle which is placed at 45° to the axes of the cylinders. The axes marked on the lens are the axes of no power of the individual cylinders. The power of each cylinder lies at 90° to the marked axis and coincides with the marked axis (of no power) of the other cylinder (of opposite sign). Cross-cylinders are named by the power of the cylinder, and this is marked on the handle. 73 Cross-cylinders are available in two powers: - The 1.00 D cross-cylinder: ✓ It is used to check the axis of the trial cylinder, and the power in patients with poor visual acuity. - The 0.50 D cross-cylinder: ✓ It is used to check the power of the trial cylinder where the patient has good vision. Clinically the cross-cylinder is used to: - Check the axis of the cylinder prescribed and then its power. - Verify that no cylindrical correction is necessary for the patient if no cylinder was detected on retinoscopy. In practice the patient is asked to look at the line of test type two lines above the smallest he can see, this is because the cross-cylinder blurs the vision and larger letters are used to make discrimination between the positions of the cross-cylinder easier for the patient. To check the axis: ▪ The cross-cylinder is held before the eye with its handle in line with the axis of the trial cylinder. ▪ The cross-cylinder is turned over and the patient asked which position gives a better visual result. ▪ The cross-cylinder is held in the preferred position and the axis of the trial cylinder rotated slightly towards the axis of the same sign on the cross- cylinder. ▪ The process is repeated until the trial cylinder is in the correct axis for the eye, at which time rotation of the cross-cylinder will offer equally unacceptable visual alterations to the patient. To check the power: ▪ The cross-cylinder is held with first one axis and then the other overlying the trial cylinder. ▪ This has the effect of increasing and then decreasing the power of the trial cylinder. To confirm the absence of a cylinder: ▪ The cross-cylinder is offered as an addition to the trial sphere in four different orientations, with its + axis at 90°, 180°, 45°, and 135°. ▪ If the patient prefers one of these options to the sphere alone, a cylindrical correction is necessary. ▪ The exact axis and power can then be determined by the methods described above. To achieve the best results from the test it is important that the patient has the clearest vision possible before the cross-cylinder is used. 74 Optical prescriptions & Spectacle lenses Prescription of lenses When prescribing a spectacle lens, the properties of the lens required are specified in the following way: - A spherical lens alone is written as, for example, +2.00 DS (diopter sphere) or -3.25 DS. - In the case of a cylindrical lens alone, both the dioptric power and the orientation of the axis must be specified. - The axis of the cylinder is marked on each trial lens by a line, and trial frames are marked according to a standard international convention. Thus, a cylinder of –2.0 diopter power, placed with its axis (of no power) vertical is written as –2.0 DC axis 90° (DC = diopter cylinder). Often the correction of a refractive error entails the prescription of both a spherical and a cylindrical component, i.e. a toric astigmatic correction. In such a case, at the end of refraction the trial frame contains a spherical lens (e.g. +2.0 DS) and a cylindrical lens (e.g. +1.0 DC axis 90°). The cylindrical lens is usually placed in front of the spherical lens to allow the axis line to be seen. The prescription is written as +2.00 DS/+1.00 DC axis 90°, and this may be abbreviated to +2.00/+1.0090°. 75 Transposition of Lenses When a lens prescription is changed from one lens form to another optically equivalent form, the process is called transposition of the lens. Simple Transposition of Spheres This applies to the alteration of the lens form of spherical lenses. The lens power is given by the algebraic sum of the surface powers. Simple Transposition of Cylinders This is a change in the description of a toric astigmatic lens so that the cylinder is expressed in the opposite power. Simple transposition of the cylinder is often necessary when the examiner wishes to compare the present refraction with a previous prescription. Consider the following example: +2.00 DS / +1.00 DC axis 90° This lens can be described in two ways: - Let the cylindrical element be at axis 90°: ✓ The lens is now +2.0 DS/+1.0 DC axis 90°. - Let the cylindrical element be of opposite power and at axis 180°: ✓ The lens is now +3.0 DS/–1.0 DC axis 180°. This change in the description of the lens may be easily accomplished for any lens by performing the following steps: a) Sum: ▪ Algebraic addition of sphere and cylinder gives new power of sphere. b) Sign: ▪ Change sign of cylinder, retaining numerical power. c) Axis: ▪ Rotate axis of cylinder through 90°. ▪ Add 90° if the original axis is at or less than 90°. ▪ Subtract 90° from any axis figure greater than 90°. 76 Toric Transposition Toric transposition carries the process one step further and enables a toric astigmatic lens to be exactly defined in terms of its surface powers. A toric astigmatic lens is made with one spherical surface and one toric surface (contributing the cylindrical power). The principal meridian of weaker power of the toric surface is known as the base curve of the lens. The base curve must be specified if toric transposition of a lens prescription is required. +4.0 DS/ -1.0 DC axis 180° with base curve –6 D The toric formula is written in two lines, as a fraction: - The top line (numerator): ✓ Specifies the surface power of the spherical surface. - The bottom line (denominator): ✓ Defines the surface power and axis of the base curve, followed by the surface power and axis of the other principal meridian of the toric surface. For example: +𝟗. 𝟎 𝐃𝐒 −𝟔. 𝟎 𝐃𝐂 𝐚𝐱𝐢𝐬 𝟗𝟎° / −𝟖. 𝟎 𝐃𝐂 𝐚𝐱𝐢𝐬 𝟏𝟖𝟎° 77 The steps of toric transposition are now defined taking the following case as an example: Transpose +3.0 DS / +1.0 DC axis 90° to a toric formula to the base curve -6 D 1. Transpose the prescription so that the cylinder and the base curve are of the same sign: +𝟑.𝟎 𝐃𝐒 +𝟒.𝟎 𝐃𝐒 (a) +𝟏.𝟎 𝐃𝐂 𝐚𝐱𝐢𝐬 𝟗𝟎° to (b) −𝟏.𝟎 𝐃𝐂 𝐚𝐱𝐢𝐬 𝟏𝟖𝟎° 2. Calculate the required power of the spherical surface (the numerator of the final formula): ✓ This is obtained by subtracting the base curve power from the spherical power given in (b) in step 1: +4.0 – (-6 D) = +10 D ✓ Put another way, to obtain an overall power of +4.0 D where one surface of the lens has the power –6 D, the other surface must have the power +10 D (simple transposition of sphere). 3. Specify the axis of the base curve: ✓ As this is the weaker principal meridian of the toric surface, its axis is at 90° to the axis of the required cylinder found in (b) in step 1. ✓ That is: –6 D axis 90° 4. Add the required cylinder to the base curve power with its axis as in (b) in step 1: –6 D + (–1 D) = –7 DC axis 180° ✓ The complete toric formula is thus: +𝟏𝟎. 𝟎 𝐃𝐒 −𝟔. 𝟎 𝐃𝐂 𝐚𝐱𝐢𝐬 𝟗𝟎° / −𝟕. 𝟎 𝐃𝐂 𝐚𝐱𝐢𝐬 𝟏𝟖𝟎° Some further examples for calculation are given below: 1. Transpose +4.0 DS / –2.0 DC axis 180° to the base curve +6 D = −𝟒. 𝟎 𝐃𝐒 +𝟔. 𝟎 𝐃𝐂 𝐚𝐱𝐢𝐬 𝟏𝟖𝟎° / +𝟖. 𝟎 𝐃𝐂 𝐚𝐱𝐢𝐬 𝟗𝟎° 2. Transpose –2.0 DS / +3.0 DC axis 90° to the base curve –6 D = +𝟕. 𝟎 𝐃𝐒 −𝟔. 𝟎 𝐃𝐂 𝐚𝐱𝐢𝐬 𝟗𝟎° / −𝟗. 𝟎 𝐃𝐂 𝐚𝐱𝐢𝐬 𝟏𝟖𝟎° 78 Identification of Lenses In clinical practice it is frequently necessary for the practitioner to identify the type and power of the patient's existing spectacles. This may be done by the following means. Detection of Lens Type It is possible to determine whether a given lens is spherical, astigmatic or a prism by studying the image formed when two lines crossed at 90°, are viewed through the lens. Spherical lenses: - Cause no distortion of the cross. - However, when the lens is moved from side to side and up and down along the arms of the cross, the cross also appears to move. - In the case of a convex lens: ✓ Cross appears to move in the opposite direction to the lens 'against movement'. - In the case of a concave lens: ✓ The movement in the same direction as the lens 'with movement'. (Convex lens “against movement”) (Concave lens “with movement”) 79 Astigmatic lenses: - Cause distortion of the cross unless their axes coincide with the cross lines. - Rotation of the lens thus causes a 'scissors' movement as the crossed lines are progressively displaced. - Rotation of a spherical lens has no effect upon the image of the crossed lines. - Once the principal meridians of an astigmatic lens have been identified & aligned with the cross, each meridian may be examined as for a spherical lens. (Astigmatic lens “scissoring movement”) The optical center of a lens: - It may be found by moving the lens until one cross line is undisplaced. - A line is then drawn on the lens surface, superimposed on the undisplaced cross line. - The process is then repeated for the cross line at 90°. - The point where the lines drawn on the lens intersect is the optical center of the lens. A prism: - Has no optical center and thus displaces one line of the cross regardless of its position with respect to the cross. - Furthermore, the direction of displacement is constant. This test is most effective if the cross lines are placed at the furthest convenient distance and the lens held well away from the eye 80 Neutralization of Power The power of a lens can also be found using the technique described above: - Once the nature of the unknown lens is determined, lenses of opposite type and known power are superimposed upon the unknown lens until a combination is found which gives no movement of the image of the cross lines when the test is performed. - At this point the two lenses are said to 'neutralize' each other, and the dioptric power of the unknown lens must equal that of the trial lens of opposite sign (a +2.0 D lens neutralizes a –2.0 D lens). In the case of astigmatic lenses: - Each meridian must be neutralized separately. Spectacle lenses: - Are named by their back vertex power. - To measure this accurately, the neutralizing lens must be placed in contact with the back surface of the spectacle lens. - However, with many highly curved lenses this is not possible and an air space

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