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Chapter 8 – Light Units

Chapter 8 – Light Units

DAVID MILLER
JEROME S. SARMIENTO
STEPHEN K. BURNS

DEFINITIONS
• Light intensity can be defined either in general energy units or in operational terms, that is, in units that relate to the amount of light from optical and electronic images, as well the amount of light needed to damage the eye.
• Candles, candelas, watts, and joules are units that describe the intensity of light emitted from a light source.
• Illuminance is the blanket term covering luxes, phots, foot-candles, and lumens, which are light units describing the amount of light falling onto a surface.
• Luminance is the blanket term covering luxes, nits, stilbs, foot-lamberts, and candelas/area, which are units describing the amount of light coming from a surface.
• Joules and watts are the units used to describe the amount of light that causes eye damage (e.g., in laser treatment).

KEY FEATURES
• Lighting levels that damage the eye.
• Lighting levels used in laser treatment.

ASSOCIATED FEATURES
• Lighting levels needed for patients with cataracts and macular degeneration.

INTRODUCTION
A cursory attempt to understand light units may result in a high level of frustration. Candles, candelas, watts, and joules are all used to describe the intensity of light sources; luxes, phots, and foot-candles are used to measure light that falls on a surface (i.e., illumination); and light that comes off a surface is measured in luxes, nits, stilbs, foot-lamberts, and candelas/cm2 .
It was much simpler in 1760, when Lambert wrote his essay on photometry and the only standard source of artificial light was the candle. In the mid-1880s, John Herschel and his sister compared one star with another to measure the brightness of both. Using two telescopes, they kept the control star in focus and placed layers of muslin over the second telescope, until the star in question became as dim as the control; a star’s brightness was thus given by its muslin index.
As science developed, more was learned about new light sources, new light sensors, and the wavelength composition of these new light sources. Thus, terms such as candles and the muslin index were used less. With each passing generation of light scientists, new units were developed to replace the older ones. Unfortunately, the new units were not accepted universally, and older books with older units continue to be used.
DEFINING LIGHT OPERATIONALLY
As clinicians, we must use the units that manufacturers and standards committees use to describe light levels that damage, comfortable reading light levels, or projector chart light levels. In other words, the definitions are divided into operational categories.
Light Used to Produce Damage
Lasers or conventional light sources damage the eye if the density of energy (i.e., the energy distributed per unit area) exceeds a threshold level.
Light is a form of energy that is emitted as photons from a light source. The energy in an individual photon is given by Planck’s equation, E = hc/?. Light energy depends on the wavelength, ?. Short wavelengths (blue) contain more energy than long wavelengths (red). The basic unit of light energy is the lumen, which measures the total flow of photons or light energy produced by a light source. One lumen represents a power of 1/683 joule per second at a wavelength of 555?nm (yellow–green). Energy is measured in joules or calories. One joule is approximately 0.24 calorie. One joule raises the temperature of 1?g of water 0.24°C. Power is the flow of energy. One joule per second is 1 watt of power, so a lumen is 1/683 watt. A lumen measures the total light (the sum of energy from all the photons) emanating from a source. The luminous intensity of a real light source is measured in candles or candelas. The standard states: “The candela is the luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 540 × 1012 hertz and that has a radiant intensity in that direction of 1/683 watt per steradian.”[1] The candela measures the luminous intensity/steradian of light originating from a specific direction of a real source as if it were emerging from a point source at that origin. The number of candelas from a real source varies with direction but not with distance. The number of photons per second emitted does not change with distance from the source. The same number strikes a 1?m radius sphere that completely surrounds the source as strikes a 2?m radius sphere. The solid angle is independent of the distance. Light power from a 1 candela source is 1/683 watt/steradian. The total power is 1/683 watt × 4p = 4p lumens = 12.566 lumens. The total amount of light (photons/sec) emitted from a point source is constant, but the spatial density (photons/sec per unit area) decreases with the square of the distance. Light flux is measured in luxes, where 1 lux = 1 lumen/m2 . If you were to enclose a 1-lumen light source in a 1?m radius sphere, the total amount of light striking the surface of the sphere would still be 1 lumen, but the density of the light at the surface would be 1 lumen divided by the area of the sphere (4pR2 = 12.566?m2 ). So the illumination of the surface would be 1 lumen/12.566?m2 = 1/12.566 lux = 0.0796 lux. A 2?m radius sphere would still receive 1 lumen of light, but this light would now be distributed over 50.265?m2 . The surface illumination of the 2?m radius sphere would be 0.0199 lux. The candela specifies light coming from a particular direction, measured as if it were coming from a point source in that direction. The lumen specifies the total amount of light. The lux specifies the amount of light illuminating a surface.
To create damage, the power from the light source needs to be concentrated in a small area and develop heat. Thus, it is the power density—power or work per unit area—that gives the best indication of the damage done. Another term for the power density

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that falls on a surface is irradiance. In terms of damage from laser light, it is the light incident on a surface (irradiance, or illumination) that is important, not the light reflected from the surface (radiance, or luminance).
For example, in panretinal photocoagulation for diabetic retinopathy, the irradiance or power density of the argon laser is about 22?mW/0.04?mm2 , or 22?mW/0.0004?cm2 (spot size of 200?µm), delivered in bursts of 0.1-second duration each. Energy densities from this laser are very high: 22?mW/0.0004?cm2 = 55,000 watts/m2 = 378,565,000 lumens/m2 = 378,565,000 luxes. The damage is restricted to the area of the spot. A 200?µm cube of tissue is essentially 8?µg of water. The laser delivers 2.2 millijoules = 0.53 millicalorie to 8?µg of tissue. If isolated, this would raise the temperature of 8?µg of the water by 275°C, vaporizing it.
The indirect ophthalmoscope can produce retinal damage after a few minutes of steady illumination at its power density of 70?mW/cm2 = 700?w/m2 = 478,100 luxes. This is 70?mW/sec = 70 millijoules or 16.8 millicalories delivered to a 1?cm2 area in 1 second. A 1?cm2 area 200?µm deep contains about 20?mg of tissue, and 16.8 millicalories would raise the temperature of 20?mg of isolated water 0.84°C. Of course, the heated volume is not isolated, and some heat would be conducted away to the underlying tissue and circulating blood. But a substantial temperature rise would be expected in 10s of seconds from such an exposure. The slit lamp can produce the same damage in less time if the light is focused on the retina, because it emits 200?mW/cm2 (2000?w/m2 = 1,366,000 luxes).
The operating microscope emits 1000?mW/cm2 = 10,000?w/m2 = 6,830,000 luxes. Compare this with the argon laser (55,000?w/m2 ), which is on for 0.1 second. With a moist, smooth corneal surface and clear crystalline lens in place, it may produce retinal damage in a short time. Fortunately, during cataract surgery, the cornea dries and becomes distorted once the eye has been entered via an incision. This, along with the presence of a cataract, diffuses the power density of the light on to the retina. However, once the implant is seated and the incision closed, the eye’s focusing elements can concentrate the enormous light energy of the microscope light on to the retina. At that time, either an opaque disc must be placed on the corneal surface to obstruct the light, or an air bubble must be placed in the anterior chamber to defocus the light.
The yttrium-aluminum-garnet (YAG) laser delivers bursts of energy measured in millijoules. The unique effect of the YAG laser is achieved because a burst of one or more pulses is delivered in a billionth or a trillionth of a second and because the energy is concentrated at a point. The power levels of the YAG laser light are immense, since all the energy is delivered in a very short time and concentrated in a very small region. One millijoule delivered in 10-9 seconds corresponds to 1,000,000 watts/beam area. The focused beam further increases the power density. The beam power is so large that any material at the focal point of the laser breaks down, absorbs the energy, and is vaporized. These exceedingly high power levels affect transparent materials and even air.

TABLE 8-1 — SIMPLIFIED CATEGORIES OF LIGHT
Light Category
Description
Units
Light source
Total light from source
Lumens (lm)
Light source
Light/per unit solid angle from source
Candles, candelas (cd) 1 candle = 1.02 candelas
Illuminance (see Box 8-1 )
Light incident on a surface
Luxes (lx;lm/m2 )
Luminance (see Box 8-2 )
Light reflected from a surface
Luxes (lx;lm/m2 ); lamberts; candelas (cd/m2 ); nits; stilbs 1 cd/m2 = 1 nit = 10-4 stilbs

Light Used to See
Since eyes see certain wavelengths of light better than others, light also can be described in terms relevant to the physiology of the eye. The devices used to describe indoor lighting are calibrated only for visible light and are further calibrated to the most sensitive wavelengths (i.e., green–yellow) to the retina. The lighting engineer divides the analysis of any lighting system into four categories:

1.
Light source, described in watts or lumens; dimensions in watts.

2.
Luminous intensity of a point source, described in candles or candelas; dimensions in watts/steradian.

3.
Illumination, or light falling on a surface, described in luxes or lumens/m2 , foot-candles, or phots; dimensions in watts/unit area.

4.
Light reflected from the surface, described in candelas/m2 , foot-lamberts, meter-lamberts, or nits; dimensions in watts/unit area.
Table 8-1 summarizes the categories, and illuminance and luminance are described in Boxes 8-1 and 8-2 .
Electronic Vision
Television cameras have illumination requirements that are comparable to those of the human eye, typically between 10 and 200 luxes. Television and computer displays typically produce a maximal luminance of 250 candelas/m2 , or 250 nits. The dynamic range (the ratio of brightest to dimmest perceivable objects) of human vision is very large, around 108 :1. Our environment commonly provides wide ranges of illumination. The ratio

ESSENTIAL COMPONENTS OF ILLUMINANCE
Illuminance is defined as the luminous flux on a surface per unit area.
Illumination decreases as the distance from the source increases. For a point source, illumination decreases as the square of the distance from the source increases. The precise formulation for the decrease in illumination from a finite source is dependent on the nature of the source.
The inverse square law applies when:
• Illuminance is the luminous flux incident on a surface per unit area at the surface being illuminated without regard to the direction from which the light approaches.
• Use of the cosine correction to correct for changes in the illuminated area of a surface as a function of angle incidence guarantees that the measured value of illuminance is independent of the direction from which the light approaches the sensor.[1] [4] [8]
Units are foot-candles or lumens:
• 1?lm/m2 = 1 lx = 1 meter-candle = 0.0929 foot-candle = .3183 cd/m2
• 1?lm/ft2 = 1 foot-candle = 10.764 lx
• 1?lm/cm2 = 1 phot

ESSENTIAL COMPONENTS OF LUMINANCE
Luminance is defined as a luminuous flux per unit area per unit solid angle from a surface, whether reflected or emitted.
Luminance refers to light that emanates from a source or is reflected from a surface.
The inverse square law does not apply because it is the luminous intensity per unit area in a given direction.
1 foot-lambert is the luminance of a perfectly diffusing and reflecting surface illuminated by 1 candle at a distance of 1 foot.
Unit conversions:
• 1 lambert (L) = 1 candle/ft2
• 1 foot-lambert = (1/p)lm/steradian/ft2 = (1/p)candle/ft2 = 0.00003426 candle/cm2
• 1 candle/ft2 = 1?lm/steradian/ft2 = 0.001076 candle/cm2
• 1?lm/W/m2 = 1 candle/m2 = 0.3142 millilambert = 0.2919 foot-lambert
• 1?lm/W/m2 = 1 lambert

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of light available on a sunny noon to moonlight can be 107 :1. Television and computer images, like photography, have much more limited dynamic ranges. The contrast ratio of a modern liquid-crystal display is around 200–400.
ILLUMINANCE
Illuminance (E) is the light flux (lumens) incident on a surface and is measured in luxes (1 lux = 1 lumen/m2 = 1 foot-candle/10.764). For example, a visual acuity wall chart is calibrated by measurement of the light that falls on it and should have an illumination in the range 480–600 luxes, or 44.6–55.74 foot-candles. A well-lit desk is illuminated by 20 foot-candles, or 215 luxes.
In the relationship between the point light source and the light incident on a surface, the intensity of the illuminance diminishes as the light is positioned farther away, according to Newton’s inverse square law (the intensity of light is related inversely to the square of the distance from its source). The total amount of light from a source falling on a closed surface is the same no matter what the shape or distance of the surface. For example, consider a source of 1 lumen of light. The total light striking the surface of a 1?m diameter sphere enclosing the 1-lumen source is the same as the total light striking the inside of a 2?m sphere. But the density, measured in luxes, would be four times larger on the surface of the 1?m sphere (1 lumen/pm2 = 0.318 lux) than on the surface of the 2?m sphere (1 lumen/4pm2 = 0.0796 lux). The amount of light (candelas, lumens) is given by the density of light (nits or candles/m2 ; luxes or lumens/m2 ) multiplied by the total surface area it falls on. Thus, if E is the illuminance, I the point light source intensity, and d the distance, then E = I/d2 , where E is measured in luxes (lumens/m2 ), I in lumens, and d in meters.
LUMINANCE
Luminance refers to light that leaves, is reflected, or is back-scattered from a surface. Reflected light requires a few extra considerations, as different surfaces reflect light differently. Thus, white paper may reflect more than 90% of the incident light, and red paper much less. Of course, the amount of reflection also depends on the angle of incidence of the light and on the angle of observation. All combine to determine the luminance of the light that reaches the eye.
Photographers are particularly interested in reflected light, because they must adjust their camera lenses according to the light that is reflected from the subject and enters the camera. Since lighting engineers must be most rigorous, they use units such as nits, stilbs, and lamberts, which are direction dependent. Photographers use the lux (lumens/m2 ), which has no directional consideration.
Ophthalmologists may want to calibrate the light of a visual acuity chart that is projected onto a screen, for which a light meter that measures reflected light in foot-lamberts may be used. The conversion factor for foot-lamberts into candelas/m2 is 0.291. For example, the British standard for minimal luminance for an internally illuminated acuity chart (projected chart) is 411.1 foot-lamberts,2 which is 411.1 × 0.291 = 120 candelas/m2 .
People who have normal sight need a luminance of about 70 candelas/m2 (220 luxes), which is produced by varying the wattage of the lamp or adjusting the distance of the light from the printed page.
LIGHTING LEVELS FOR PATIENTS WITH EYE DISEASE
Cataracts
Opacity that results from cataracts may reduce the amount of light incident on the retina by 10–90%. Therefore, such patients require an increased luminance to read or do work. To read efficiently, a patient who has a cataract may (on average) need about double or triple the luminance required by a person of normal sight (about 70 candelas/m2 ), which may be achieved by using a 75- or 100-watt incandescent bulb held at a distance of 1?ft (0.3?m) or less from the reading material.[3] A 100-watt bulb typically produces 1570 lumens, or 125 candelas, when new.
A patient who has a cataract may need about double or triple the average illuminance level (750 luxes) for a reading task, which would be 1500–2500 luxes (477–795 candelas/m2 ).
Age-Related Macular Degeneration
Patients who have age-related macular degeneration have either a diminished number of photoreceptors within the macular area or photoreceptors that need higher levels of light energy to be stimulated. Logically, the luminance of reading material for these patients must be greater than 200 foot-candles (64 candelas/m2 , or 2152 luxes).
In the literature, the recommended illuminance on the printed page is in the range of 400–4000 luxes.[4] Understandably, the more serious the level of damage, the greater the illuminance needed. Also, the coefficient of reflectance and the color of the page both influence the amount of light (luminance) that finally reaches the patient. [5] [6] [7] [8]

REFERENCES

1. Ferris FL, Sperduto RD. Standardized illumination for visual acuity testing clinical research. Am J Ophthalmol. 1982;94:97–8.

2. Bergem-Jansen PM. Ergonomic workplace design for a visually impaired person. In: Kooijman AC, Looijestijn PL, Welling JA, van der Wildt GJ, eds. Low vision. Washington DC: IOS Press; 1994:183–90.

3. Com AL, Koenig AJ. Foundations of low vision: clinical and functional perspectives. New York: American Foundation of Blind; 1996:137–8.

4. Faye EE, Hood CM. Low vision. Springfield: CC Thomas; 1975:42–5.

5. Cornelissen FW, Kooijman AC, School AJ, et al. Optimizing illumination for visually impaired persons; comparing subjective and objective criteria. In: Kooijman AC, Looijestijn PL, Welling JA, van der Wildt GJ, eds. Low vision. Washington DC: IOS Press; 1994:68–77.

6. Lagrow SJ. Assessing optimal illumination for visual response accuracy in visually impaired adults. J Vis Impairment Blindness. 1986;8:888–95.

7. Lehon LH. Development of lighting standards for the visually impaired. J Vis Impairment Blindness. 1980;74:249–53.

8. Taylor BN, ed. The international system of units. Special publication 330 (2001). Gaithersburg: National Institute of Standard and Technology; 2001:8.

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