Key Features
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The selection of a prescription for corrective lenses that balances optical clarity with other important physical and psychological factors, such as equality of magnification, single vision, and comfort.
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The determination of the most appropriate form of optical correction based on the patient’s visual needs and on environmental factors.
Introduction
Many people equate an eye examination with a refraction test for glasses. The confusion is understandable because for the vast majority, especially those in the preretirement age group, eyeglasses or contact lenses resolve the main complaints they have about their eyes. Also, refraction is almost always part of a comprehensive eye examination, not only to provide a prescription for corrective lenses but also to determine the best acuity that an eye can achieve.
Refraction is only one of the many methods used to determine the function and health of the visual system. Because of the value of the results, it is important to develop an efficient and accurate basic refractive technique that can be modified when unusual variations present themselves.
Although often relegated as a purely technical task in the spectrum of high-technology examination and treatment procedures that characterize contemporary ophthalmic practice, refraction provides relief for one of the world’s most common physical defects. An understanding of the concepts used to identify and measure refractive errors is the basis for prescribing individual corrections that offer patients improved quality of life.
History
Spectacles were first described during the Middle Ages. In 1266 Roger Bacon magnified print in a book using a segment of a glass sphere. A painting completed in 1352 shows a prelate wearing lenses in a mounting. In the late fifteenth century, merchants sold spectacles to buyers who chose them on the basis of their own judgment of how vision improved. As the trade of lens-making proliferated throughout Europe, it became organized into a guild. Although cylindrical lenses had been manufactured since 1827, it was not until Donders published his methods of refraction that correcting astigmatism became an exact science. In 1893 when American Optical developed the trial case of lenses, opticians—rather than spectacle peddlers—became the primary providers of eye examinations. Although instrument-makers have dramatically improved the ability of examiners to provide accurate and repeatable lens prescriptions, most subjective techniques still rely on a comparison of views through different lenses.
Visual Acuity
The idea that the minimal separation between two point sources of light was a measure of vision dates back to Hooke in 1679, when he noted, “tis hardly possible for any animal eye well to distinguish an angle much smaller than that of a minute: and where two objects are not farther distant than a minute, if they are bright objects, they coalesce and appear as one.” In the early nineteenth century, Purkinje and Young used letters of various sizes for “judging the extent of the power of distinguishing objects too near or too remote for perfect vision.” Finally, in 1863, Professor Hermann Snellen of Utrecht developed his classic test letters. He quantitated the lines by comparison of the visual acuity of a patient with that of his assistant, who had perfect vision. Thus 20/200 (6/60) vision meant that the patient could see at 20 ft (6 m) what Snellen’s assistant could see at 200 ft (60 m).
The essence of correct identification of the letters on the Snellen chart is to see the clear spaces between the black elements of the letter. Thus in Fig. 2.3.1 , the angular spacing between the bars of the C is 1 minute for the 20/20 (6/6) letter. The entire letter has an angular height of 5 minutes. To calculate the height, x, of a 20/20 (6/6) letter, use Eq. 2.3.1 .
tan(5minutes)=xfeet20
From Eq. 2.3.1 , x = 0.0291 ft (0.349 in). In like manner, the 20/200 (6/60) letter is 10 times taller, or 3.49 in (8.87 cm) high.
Testing Distance
The Snellen acuity test traditionally is done at a distance of 20 feet (6 m). At this distance, very little accommodation is required by the patient. For hospital patients, testing must often be carried out in a smaller room. If the doctor stands at the foot of the bed and the patient sits propped up at the head of the bed, the distance between them is about 5 feet (1.5 m). Thus the classic Snellen chart, with its conventional notations, may be used if the chart is reduced to one-fourth its original size. Admittedly, a test at 5 ft (1.5 m) requires the emmetropic patient to accommodate 0.67 diopters (D).
Other Considerations
Over the years, it has become apparent that projection of the Snellen chart onto a screen in a darkened examination room does not give an accurate replication of “everyday” visual function. For example, the high contrast black-on-white letters do not represent the contrast of most objects seen in everyday life. The dark examination room, which is devoid of glare sources, also is not representative of most daytime visual tasks.
As the projector bulb ages or collects dirt, and as the projection lens becomes dusty, the contrast of the letters projected on the chart decreases. Thus a change in readings between patient visits may not always arise from a significant change in the visual status of the patient. At present, British standards require 480 to 600 lux to illuminate distant wall charts and 1200 lux to illuminate projected charts.
As the letters become smaller on the Snellen chart, the number of letters per line increases. Thus one error per line means a different degree of impairment for each line. It is necessary, therefore, to establish criteria by which it can be agreed that a patient has seen the line. Some clinicians credit a patient if more than one-half the letters are identified correctly. Others require identification of all the letters before credit is given. Also remember that no orderly progression of size change exists from line to line. Thus a two-line change on the Snellen chart going from the 20/200 (6/60) line to the 20/80 (6/24) line represents an improvement of visual acuity by a factor of 2.5, whereas a two-line change going from the 20/30 (6/9) line to the 20/20 (6/6) line represents an improvement by only a factor of 1.5.
Another problem is that the identification of different letters of the same size has been shown to vary in difficulty. Thus A and L are easier to identify than E. The Bailey–Lovie chart ( Fig. 2.3.2 ), designed by two Australian optometrists and modified by Ferris et al. in 1982, uses 10 letters of similar difficulty with five different letters per line and has uniform proportional size change between neighboring lines. Another approach is to use the Landolt ring test in which circles of decreasing size, each with an open gap, are used in successive lines, with the orientation of the gaps in the circles randomly changing.
The 20/20 (6/6) Snellen line represents the ability to resolve 1 minute of arc, which is close to the theoretical diffraction limit, but the occasional patient can see the 20/15 (6/4.5) or, rarely, 20/10 (6/3) line. Four explanations suggest themselves. First, some individuals may have cone outer segment diameters of less than 1.5 µm, which would give a finer-grain mosaic having cone separations of less than 1 minute of arc. Second, longer eyes provide slightly magnified retinal images, thereby tending to yield better acuities. Third, some eyes may have less aberration than others, which would allow them to function optimally with larger pupils having, consequently, better diffraction-limited performance. Finally, our experience with a small aperture corneal inlay has taught us that brain processing cancels much of the diffraction noise for apertures between 1.5 mm to 2.0 mm (US PATENT # 4955904, Atebara, Miller. US PATENT #5245367, Miller/Meshel. US PATENT #6899424, Miller, Blanco).
Contrast Sensitivity
Visual acuity testing is relatively inexpensive, takes little time to perform, and describes visual function with one notation, such as 20/40 (6/12). Best of all, for more than 150 years it has provided an end point for the correction of a patient’s refractive error. Yet contrast sensitivity testing, a time-consuming test born in the laboratory of the visual physiologist and described by a graph rather than a simple notation, has become a popular clinical test recently. It describes a number of subtle alterations of vision not accounted for by the visual acuity test. Thus it more accurately quantifies the loss of vision in cataracts, corneal edema, neuro-ophthalmic diseases, and certain retinal diseases. Although these advantages have been known for a long time, the recent enhanced popularity has arisen because of patients with cataracts. As lifespan increases, more patients who have cataracts request medical help. Very often, their complaints of objects that appear faded or objects that are more difficult to see in bright light are not described accurately by their Snellen acuity scores. Contrast sensitivity tests and glare sensitivity tests do quantitate many of these complaints.
Contrast sensitivity testing is similar to Snellen visual acuity testing in that it tests using several different sized letters or grid patterns. However, it is different from visual acuity testing because the letters (or grid patterns) are displayed in six or more shades of gray instead of the standard black letters of the Snellen chart. Thus contrast sensitivity testing reports show a contrast threshold (i.e., lightest shade of gray just perceived) for each of several letter (or grid pattern) sizes.
Contrast
The components of a conventional newspaper photo consist of various regions associated with the scene where each region is filled in with a definite density of black dots depicting that region’s contrast or level of gray. Such newspaper photos may have over 100 half-tone levels (i.e., densities of black dots) to represent the different contrast levels in the scene.
Whereas a black letter on a white background is a scene of high contrast, a child crossing the road at dusk and a car looming in a fog are scenes of low contrast. The contrast of a target on a background is defined by Eq. 2.3.2 .
contrast=target luminance−background luminancetarget luminance+background luminance
As an example, suppose a photometer measures the luminance of a target at 100 units of light and the luminance of the background at 50 units of light. Substitution into Eq. 2.3.2 gives Eq. 2.3.3 .
contrast=100−50100+50=0.33(or33%)
Suppose the contrast of a target of a certain size is 0.33, which also may represent a particular older patient’s threshold, which means that this patient cannot detect similar-sized targets of lower contrast. The older patient’s contrast sensitivity (CS) is the reciprocal of the contrast, namely CS = 3.0. On the other hand, a young, healthy subject viewing a target of the same size may have a contrast threshold of 0.01 with a corresponding CS = 100. Occasionally subjects (for certain-size targets) have even better contrast thresholds. A subject could have a contrast threshold of 0.003, which converts into a CS of 333. In the visual psychology literature, CS often is described in logarithmic terms. For example, associated with CS = 10 is log(CS) = 1, with CS = 100 is log(CS) = 2, and with CS = 1000 is log(CS) = 3, and so on.
Targets
Both the visual scientist and the optical engineer use a series of alternating black and white bars as targets. The optical engineer describes the fineness of a target by the number of line pairs per millimeter (a line pair consists of a dark bar with a white space next to it). The higher the number of line pairs per millimeter, the finer is the target. For example, about 82 line pairs per millimeter imaged on the retina of an eye with a focal length of 21 mm is equivalent to a periodic black–white target in object space, where the white space between two black spaces subtends approximately a minute of arc (like the letter E of the Snellen chart viewed at 20 ft). Equivalently, with a Snellen chart viewed at 20 ft, 109 line pairs per millimeter on the retina is equivalent to the 20/15 (6/4.5) letters.
The vision scientist generally describes a periodic bar pattern in terms of its spatial frequency as perceived at the test distance—the units are cycles per degree (cpd). A cycle is a black bar and a white space. To convert Snellen units into cpd at the 20 ft (6 m) testing distance, the Snellen denominator is divided into 600 (180). For example, 20/20 (6/6) converts into 30 cpd. Likewise, 20/200 (6/60) converts into 3 cpd.
Sine Waves
So far, targets have been described as high-contrast dark bars of different spatial frequency against a white background. These also are known as square waves or Foucault gratings. However, in optics very few images can be described as perfect square waves with perfectly sharp edges. Diffraction tends to make most edges slightly fuzzy, as do spherical aberration and oblique astigmatism, particularly in the case of the optics of the eye. If the light intensity is plotted across a strongly blurred image of a Foucault grating, a sine wave pattern results. Sine wave patterns have great appeal because they can be considered the essential elements from which any pattern can be constructed. The mathematician can break down any alternating pattern, be it an electrocardiogram or a trumpet’s sound wave, into a unique sum of sine waves. This mathematical decomposition of patterns into sinusoidal components is known as a Fourier transformation. Fourier’s theorem describes the way that any pattern may be written as a sum of sine waves that have various spatial frequencies, amplitudes, and phases.
Also, it is thought that the visual system of the brain may operate by breaking down observed patterns and scenes into sine waves of different frequencies. The brain then adds them up again to produce the mental impression of a complete picture. Fourier transformations may be the method the visual system uses to encode and record retinal images. It has been shown that different cells or “channels” occur in the retina, lateral geniculate body, and cortex that selectively carry different spatial frequencies. So far, six to eight channels have been identified. It also has been shown that all channels respond to contrast—the cortex shows a linear relationship between the amplitude of the neuronal discharge and the logarithm of the grating contrast. Consequently, many contrast sensitivity tests are based on sine wave patterns rather than square wave patterns.
Recording Contrast Sensitivity
Fig. 2.3.3 shows a number of functions, including the contrast sensitivity testing function for a normal subject. The shape of the human eye’s contrast sensitivity function is different from that of an inanimate optical imaging systems in which the function generally decreases continuously from very low to very high spatial frequencies. For the normal human eye, the contrast sensitivity generally increases from very low frequencies to about 6 cpd and then decreases with increasing frequency beyond 6 cpd. The decrease of the contrast sensitivity with frequency above 6 cpd is due to the influence of diffraction and aberrations, which make the detection of finer details more difficult. The increase of the contrast sensitivity with frequency up to 6 cpd is due to the retina–brain processing system, which is programmed to enhance our contrast sensitivity in the range of 2 to 6 cpd. Receptor fields, on–off systems, and lateral inhibition are the well-known physiological mechanisms that influence the different spatial frequency channels and are responsible for such enhancement. In Fig. 2.3.3 , the plot labeled retinal testing function (RTF) represents the retinal–neural system’s contrast sensitivity performance. A striking proof of brain enhancement of contrast is given in Fig. 2.3.4 .
Also shown in Fig. 2.3.3 is the plot labeled modulation transfer function (MTF), which represents the sinusoidal components of the object-to-image transfer function for the purely optical portion of the visual system (cornea, lens). The MTF is described more completely in the next section. A significant mathematical relationship exists among the three functions, which is expressed by Eq. 2.3.4 , the so-called Campbell–Green relation, and is illustrated in Fig. 2.3.3 . The Campbell–Green relation has been demonstrated in clinical studies.
CS=RTF×MTF for all frequencies
Differences in the contrast sensitivity function are expected among different subject groups. For example, contrast sensitivity decreases with age, for which two factors appear to be responsible. First, the normal crystalline lens scatters more light with increasing age, which thus blurs the edges of targets and degrades the contrast. Second, the retina–brain processing system itself loses its ability to enhance contrast with increasing age.
The contrast sensitivity function also is an accurate method by which to follow certain disease states. For example, the contrast sensitivity function of a patient who has a cataract is diminished, as it is in another light-scattering lesion, corneal edema. Because the contrast sensitivity function is dependent on central nervous system processing, it is not surprising that conditions such as optic neuritis and pituitary tumors also characteristically have diminished contrast sensitivity functions.
The contrast sensitivity of patients also decreases as the illumination decreases. Thus contrast sensitivity for a spatial frequency of 3 cpd typically drops from 300 to 150 to 10 as the retinal luminance drops from 9 trolands to 0.09 trolands to 0.0009 trolands. (The troland is a psychophysical unit. One troland is the retinal luminance produced by the image of an object, the luminance of which is 1 lumen/m 2 (1 lux) for an area of the entrance pupil of 1 mm 2 .) Therefore, when careful contrast sensitivity function comparisons are made, the illuminance of the test targets must be kept at the recommended value.
Testing Distance
The Snellen acuity test traditionally is done at a distance of 20 feet (6 m). At this distance, very little accommodation is required by the patient. For hospital patients, testing must often be carried out in a smaller room. If the doctor stands at the foot of the bed and the patient sits propped up at the head of the bed, the distance between them is about 5 feet (1.5 m). Thus the classic Snellen chart, with its conventional notations, may be used if the chart is reduced to one-fourth its original size. Admittedly, a test at 5 ft (1.5 m) requires the emmetropic patient to accommodate 0.67 diopters (D).
Other Considerations
Over the years, it has become apparent that projection of the Snellen chart onto a screen in a darkened examination room does not give an accurate replication of “everyday” visual function. For example, the high contrast black-on-white letters do not represent the contrast of most objects seen in everyday life. The dark examination room, which is devoid of glare sources, also is not representative of most daytime visual tasks.
As the projector bulb ages or collects dirt, and as the projection lens becomes dusty, the contrast of the letters projected on the chart decreases. Thus a change in readings between patient visits may not always arise from a significant change in the visual status of the patient. At present, British standards require 480 to 600 lux to illuminate distant wall charts and 1200 lux to illuminate projected charts.
As the letters become smaller on the Snellen chart, the number of letters per line increases. Thus one error per line means a different degree of impairment for each line. It is necessary, therefore, to establish criteria by which it can be agreed that a patient has seen the line. Some clinicians credit a patient if more than one-half the letters are identified correctly. Others require identification of all the letters before credit is given. Also remember that no orderly progression of size change exists from line to line. Thus a two-line change on the Snellen chart going from the 20/200 (6/60) line to the 20/80 (6/24) line represents an improvement of visual acuity by a factor of 2.5, whereas a two-line change going from the 20/30 (6/9) line to the 20/20 (6/6) line represents an improvement by only a factor of 1.5.
Another problem is that the identification of different letters of the same size has been shown to vary in difficulty. Thus A and L are easier to identify than E. The Bailey–Lovie chart ( Fig. 2.3.2 ), designed by two Australian optometrists and modified by Ferris et al. in 1982, uses 10 letters of similar difficulty with five different letters per line and has uniform proportional size change between neighboring lines. Another approach is to use the Landolt ring test in which circles of decreasing size, each with an open gap, are used in successive lines, with the orientation of the gaps in the circles randomly changing.
The 20/20 (6/6) Snellen line represents the ability to resolve 1 minute of arc, which is close to the theoretical diffraction limit, but the occasional patient can see the 20/15 (6/4.5) or, rarely, 20/10 (6/3) line. Four explanations suggest themselves. First, some individuals may have cone outer segment diameters of less than 1.5 µm, which would give a finer-grain mosaic having cone separations of less than 1 minute of arc. Second, longer eyes provide slightly magnified retinal images, thereby tending to yield better acuities. Third, some eyes may have less aberration than others, which would allow them to function optimally with larger pupils having, consequently, better diffraction-limited performance. Finally, our experience with a small aperture corneal inlay has taught us that brain processing cancels much of the diffraction noise for apertures between 1.5 mm to 2.0 mm (US PATENT # 4955904, Atebara, Miller. US PATENT #5245367, Miller/Meshel. US PATENT #6899424, Miller, Blanco).
Contrast Sensitivity
Visual acuity testing is relatively inexpensive, takes little time to perform, and describes visual function with one notation, such as 20/40 (6/12). Best of all, for more than 150 years it has provided an end point for the correction of a patient’s refractive error. Yet contrast sensitivity testing, a time-consuming test born in the laboratory of the visual physiologist and described by a graph rather than a simple notation, has become a popular clinical test recently. It describes a number of subtle alterations of vision not accounted for by the visual acuity test. Thus it more accurately quantifies the loss of vision in cataracts, corneal edema, neuro-ophthalmic diseases, and certain retinal diseases. Although these advantages have been known for a long time, the recent enhanced popularity has arisen because of patients with cataracts. As lifespan increases, more patients who have cataracts request medical help. Very often, their complaints of objects that appear faded or objects that are more difficult to see in bright light are not described accurately by their Snellen acuity scores. Contrast sensitivity tests and glare sensitivity tests do quantitate many of these complaints.
Contrast sensitivity testing is similar to Snellen visual acuity testing in that it tests using several different sized letters or grid patterns. However, it is different from visual acuity testing because the letters (or grid patterns) are displayed in six or more shades of gray instead of the standard black letters of the Snellen chart. Thus contrast sensitivity testing reports show a contrast threshold (i.e., lightest shade of gray just perceived) for each of several letter (or grid pattern) sizes.
Contrast
The components of a conventional newspaper photo consist of various regions associated with the scene where each region is filled in with a definite density of black dots depicting that region’s contrast or level of gray. Such newspaper photos may have over 100 half-tone levels (i.e., densities of black dots) to represent the different contrast levels in the scene.
Whereas a black letter on a white background is a scene of high contrast, a child crossing the road at dusk and a car looming in a fog are scenes of low contrast. The contrast of a target on a background is defined by Eq. 2.3.2 .
contrast=target luminance−background luminancetarget luminance+background luminance
As an example, suppose a photometer measures the luminance of a target at 100 units of light and the luminance of the background at 50 units of light. Substitution into Eq. 2.3.2 gives Eq. 2.3.3 .
contrast=100−50100+50=0.33(or33%)
Suppose the contrast of a target of a certain size is 0.33, which also may represent a particular older patient’s threshold, which means that this patient cannot detect similar-sized targets of lower contrast. The older patient’s contrast sensitivity (CS) is the reciprocal of the contrast, namely CS = 3.0. On the other hand, a young, healthy subject viewing a target of the same size may have a contrast threshold of 0.01 with a corresponding CS = 100. Occasionally subjects (for certain-size targets) have even better contrast thresholds. A subject could have a contrast threshold of 0.003, which converts into a CS of 333. In the visual psychology literature, CS often is described in logarithmic terms. For example, associated with CS = 10 is log(CS) = 1, with CS = 100 is log(CS) = 2, and with CS = 1000 is log(CS) = 3, and so on.
Targets
Both the visual scientist and the optical engineer use a series of alternating black and white bars as targets. The optical engineer describes the fineness of a target by the number of line pairs per millimeter (a line pair consists of a dark bar with a white space next to it). The higher the number of line pairs per millimeter, the finer is the target. For example, about 82 line pairs per millimeter imaged on the retina of an eye with a focal length of 21 mm is equivalent to a periodic black–white target in object space, where the white space between two black spaces subtends approximately a minute of arc (like the letter E of the Snellen chart viewed at 20 ft). Equivalently, with a Snellen chart viewed at 20 ft, 109 line pairs per millimeter on the retina is equivalent to the 20/15 (6/4.5) letters.
The vision scientist generally describes a periodic bar pattern in terms of its spatial frequency as perceived at the test distance—the units are cycles per degree (cpd). A cycle is a black bar and a white space. To convert Snellen units into cpd at the 20 ft (6 m) testing distance, the Snellen denominator is divided into 600 (180). For example, 20/20 (6/6) converts into 30 cpd. Likewise, 20/200 (6/60) converts into 3 cpd.
Sine Waves
So far, targets have been described as high-contrast dark bars of different spatial frequency against a white background. These also are known as square waves or Foucault gratings. However, in optics very few images can be described as perfect square waves with perfectly sharp edges. Diffraction tends to make most edges slightly fuzzy, as do spherical aberration and oblique astigmatism, particularly in the case of the optics of the eye. If the light intensity is plotted across a strongly blurred image of a Foucault grating, a sine wave pattern results. Sine wave patterns have great appeal because they can be considered the essential elements from which any pattern can be constructed. The mathematician can break down any alternating pattern, be it an electrocardiogram or a trumpet’s sound wave, into a unique sum of sine waves. This mathematical decomposition of patterns into sinusoidal components is known as a Fourier transformation. Fourier’s theorem describes the way that any pattern may be written as a sum of sine waves that have various spatial frequencies, amplitudes, and phases.
Also, it is thought that the visual system of the brain may operate by breaking down observed patterns and scenes into sine waves of different frequencies. The brain then adds them up again to produce the mental impression of a complete picture. Fourier transformations may be the method the visual system uses to encode and record retinal images. It has been shown that different cells or “channels” occur in the retina, lateral geniculate body, and cortex that selectively carry different spatial frequencies. So far, six to eight channels have been identified. It also has been shown that all channels respond to contrast—the cortex shows a linear relationship between the amplitude of the neuronal discharge and the logarithm of the grating contrast. Consequently, many contrast sensitivity tests are based on sine wave patterns rather than square wave patterns.
Recording Contrast Sensitivity
Fig. 2.3.3 shows a number of functions, including the contrast sensitivity testing function for a normal subject. The shape of the human eye’s contrast sensitivity function is different from that of an inanimate optical imaging systems in which the function generally decreases continuously from very low to very high spatial frequencies. For the normal human eye, the contrast sensitivity generally increases from very low frequencies to about 6 cpd and then decreases with increasing frequency beyond 6 cpd. The decrease of the contrast sensitivity with frequency above 6 cpd is due to the influence of diffraction and aberrations, which make the detection of finer details more difficult. The increase of the contrast sensitivity with frequency up to 6 cpd is due to the retina–brain processing system, which is programmed to enhance our contrast sensitivity in the range of 2 to 6 cpd. Receptor fields, on–off systems, and lateral inhibition are the well-known physiological mechanisms that influence the different spatial frequency channels and are responsible for such enhancement. In Fig. 2.3.3 , the plot labeled retinal testing function (RTF) represents the retinal–neural system’s contrast sensitivity performance. A striking proof of brain enhancement of contrast is given in Fig. 2.3.4 .
Also shown in Fig. 2.3.3 is the plot labeled modulation transfer function (MTF), which represents the sinusoidal components of the object-to-image transfer function for the purely optical portion of the visual system (cornea, lens). The MTF is described more completely in the next section. A significant mathematical relationship exists among the three functions, which is expressed by Eq. 2.3.4 , the so-called Campbell–Green relation, and is illustrated in Fig. 2.3.3 . The Campbell–Green relation has been demonstrated in clinical studies.
CS=RTF×MTF for all frequencies
Differences in the contrast sensitivity function are expected among different subject groups. For example, contrast sensitivity decreases with age, for which two factors appear to be responsible. First, the normal crystalline lens scatters more light with increasing age, which thus blurs the edges of targets and degrades the contrast. Second, the retina–brain processing system itself loses its ability to enhance contrast with increasing age.
The contrast sensitivity function also is an accurate method by which to follow certain disease states. For example, the contrast sensitivity function of a patient who has a cataract is diminished, as it is in another light-scattering lesion, corneal edema. Because the contrast sensitivity function is dependent on central nervous system processing, it is not surprising that conditions such as optic neuritis and pituitary tumors also characteristically have diminished contrast sensitivity functions.
The contrast sensitivity of patients also decreases as the illumination decreases. Thus contrast sensitivity for a spatial frequency of 3 cpd typically drops from 300 to 150 to 10 as the retinal luminance drops from 9 trolands to 0.09 trolands to 0.0009 trolands. (The troland is a psychophysical unit. One troland is the retinal luminance produced by the image of an object, the luminance of which is 1 lumen/m 2 (1 lux) for an area of the entrance pupil of 1 mm 2 .) Therefore, when careful contrast sensitivity function comparisons are made, the illuminance of the test targets must be kept at the recommended value.
Contrast
The components of a conventional newspaper photo consist of various regions associated with the scene where each region is filled in with a definite density of black dots depicting that region’s contrast or level of gray. Such newspaper photos may have over 100 half-tone levels (i.e., densities of black dots) to represent the different contrast levels in the scene.
Whereas a black letter on a white background is a scene of high contrast, a child crossing the road at dusk and a car looming in a fog are scenes of low contrast. The contrast of a target on a background is defined by Eq. 2.3.2 .
contrast=target luminance−background luminancetarget luminance+background luminance
As an example, suppose a photometer measures the luminance of a target at 100 units of light and the luminance of the background at 50 units of light. Substitution into Eq. 2.3.2 gives Eq. 2.3.3 .
contrast=100−50100+50=0.33(or33%)
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