Light as a stimulus for vision The physics of light: Light is considered both as a propagating electromagnetic wave and as a stream of individual particles (photons). In Vision Science, both of these aspects are important. Light as rays help us trace the path of light through optical systems. Light as waves help us understand refraction, diffraction and interference phenomena. Wave front measurement is a common tool for describing the optics of the eye. Light as photons helps us understand the detection of light by photoreceptors and its conversion to electrical activity. Electromagnetic spectrum Radiant Energy (Electromagnetic) Spectrum Solar Radiation Spectrum Nanometer (10-9 m): most common units for wavelength UV c b a
Black Body Radiators Spectral radiance of some artificial lights The spectrum of a light source depends on how energy is converted to photons. Incandescence produces a broad, continuous spectrum that depends on temperature. Fluorescence produces a peaked, discontinuous spectrum that depends on the chemicals being electrically excited. Lasers produce extremely narrow spectra. Hot objects like a stove, an incandescent bulb, or the sun give off light in a characteristic way. At 700 F they start to glow a dull red, as they heat more they get bright red, then white, then bluish. The surface of the sun is about 10,340 F (6000 K) Black body spectra vs. Temp Color appearance Spectra of the sun and sky Light directly from the sun ( noon sunlight 5500K ) appears yellow and peaks at around 500 nm Light from the sky ( north sky light ) appears blue, and peaks around 400-450 nm Light falling on the ground ( noon daylight 6500K ) is a mixture of yellow sunlight and blue sky light. At sunset, ( sunset sky + sunlight <4000K ) the sky is reddish, and peaks at around 650 nm. These curves have all been adjusted to intersect at 580 nm, for easier comparison of the shapes. Absorption of short wavelengths in the eye Each curve here shows the spectrum of light as it passes through the eye. The light hitting the cornea is assumed to be a flat, white light spectrum ( light at surface of cornea ) Light that gets through the cornea is less blue, because the cornea absorbs short wavelengths. Light that gets through the lens is even more filtered, especially the shortest wavelengths. The lens removes light less than 400 nm. Light that gets through the macular pigment is further reduced in short wavelengths up to 500 nm. The light that finally reaches the cones has almost no UV in it and much less blue. As the lens ages, it absorbs more blue light and begins to look yellow. Artificial lenses implanted after cataract surgery are clear, so patients notice a sudden increase in blues. They still absorb UV, though!
Absorption of light by Rods and Cones Rods are 100 times more sensitive than cones in the middle of the spectrum. Cones are a little more sensitive for very long wavelengths (deep red). Vision with rods is called scotopic and with cones is called photopic. Photopic & scotopic spectral sensitivity functions: CIE 1951 scotopic luminous efficiency CIE 1964 wide field (10 ) photopic luminous efficiency, Normalized to peak photopic sensitivity on log vertical scale; From Kaiser & Boynton Human Color Vision (1996) Luminous Efficiency Functions Rods Cones The cone curve is called Vλ ( Vee lambda ) The rod curve is called V λ, ( Vee Prime lambda.) The same curves from the previous figure are shown now with a linear (not log) vertical scale. Each curve is adjusted so it s peak is at 1, to show the relative sensitivity to light. The term efficiency is referring to how likely it is that a photon will be absorbed. They let you predict the relatively sensitivity of the eye to lights of various wavelength. These are standardized curves, based on lots and lots of people with normal vision. Radiometric and photometric units Radiometric units measure the total energy of light from a source, or falling on a surface. Photometric units are similar, but they are compensated by the human spectral luminous efficiency curves Vλ or V λ. Photometric units predict how visible a light should be to a human. Retinal illuminance T Troland = cd/m 2 x pupil area mm 2 Sun s surface at noon 10 9 10 8 10 7 Tungsten filament 10 6 10 5 White paper in sunlight 10 4 10 3 10 2 Comfortable Reading 10 1 10 0 10-1 White paper in moonlight 10-2 10-3 White paper in starlight 10-4 10-5 Absolute Threshold 10-6 -----Scotopic--- ---photopic-------------- Luminance of everyday scenes Our eyes are able to adjust to a very large range of luminance levels in the environment, spanning more than ten orders of magnitude from dim to dazzling. Units are approximate cd/m 2 Adapted from Vision and Visual Perception, C.H. Graham, Ed.
Candelas/m 2, Trolands, and Photons compared Recall that the Troland is a photometric unit of retinal illumination, found by multiplying luminance with pupil area (cd/m 2 * pupil area). For a pupil diameter of 3.5 mm, a surface with luminance of 1 cd/m 2 will produce about 10 Trolands on the retina. Recall that the area of a circle is π * r 2 Pupil area in this example is π * (3.5/2) 2 = 9.6 mm 2 so 1 cd/m 2 is 9.6 td. A photon has a very very small amount of energy. In this table, Troland values are compared with the number of photons hitting a small patch of the retina each second, assuming a white piece of paper in white light. Cone Threshold 0.1 td 10 6 photons/sec/deg 2 Comfortable reading light 1,000 td 10 10 photons/sec/deg 2 Bright Sunlight 100,000 td 10 12 photons/sec/deg 2 From Kaiser & Boynton Human Color Vision 1996 Energy of one photon The energy of a photon depends on its frequency. Higher frequency, shorter wavelength photons have higher energy. Energy and frequency are related through Plank s constant: E = h * ν Where E is energy in joules ν (Greek letter Nu ) is frequency in cycles / second (aka Hertz) And h is Planck s constant = 6.626 10-34 joule - seconds. Alternatively we can write E = h * c / λ Where c is the speed of light in a vacuum 3 x 10 8 meters / second And λ (Greek letter lambda ) is the wavelength of light in meters Example: What is the energy of one quantum of 500 nanometer light? E = 6.626 x 10-34 * 3 x 10 8 / 500 x 10-9 = about 4 x 10-19 joules For comparison, one joule is the energy required to lift an apple one meter. Just sitting there you are generating 100 joules of heat every second. Photons from the sun How light interacts with a medium Solar energy reaching the Earth s surface is about 1000 Watts per square meter on a sunny day. 1 Watt = 1 joule/sec. Based on the previous calculation, the number of photons falling on one square meter of Earth each second is about 10 22 Or 10,000,000,000,000,000,000,000 Or 10 thousand billion billion The pupil is around 1 * 10-5 m 2, so 10 17 photons per second enter your pupil from the sun when you look up at the sky. Compare this to Niagara Falls: Each second, there are 5 x 10 10 drops of water that pass over the falls. So the photons entering your eye from the sun is like 2 million Niagaras!
How light interacts with the eye Scattered light forming haze Light speed and wavelength change with different media The index of refraction n describes the ratio of light speed in vacuum compared to a given medium, such as glass. The frequency of light and the energy of the photons do not change as light passes from one medium to another, but wavelength does. Focused light forming image Courtesy of Dr. Ray Applegate RAA Refraction at a surface Refraction occurs when light is transmitted from one medium to another with a different index. The change in direction depends on factors such as index change and wavelength. Diffraction of light at an aperture A planar wavefront entering from the left interacts with the pupil margin, producing a diffraction pattern on the retina. Diffraction occurs where light hits the edges of an aperture, such as the pupil of the eye. In this example, light entering from the left is diffracted, resulting in a ripple interference pattern at the imaging surface. Diffraction limits the ability of the eye to focus points sharply, especially when the pupil is small.
Diffraction of light at an aperture The spread of a focused point is called the Airy disk. In order to resolve two points, they must be separated so that their peaks are distinct. Because diffraction spreads out the points, it limits our ability to resolve them. Mie and Rayleigh scattering Particles smaller than the wavelength of light scatter by diffraction, in proportion to 1/λ4 (Rayleigh) Larger particles scatter by reflection primarily (Mie). Mie Mie and Rayleigh scattering Rayleigh Reflection at a surface Reflection occurs when light passes from one index of refraction to another. The amount reflected depends on factors such as the index change, the angle of incidence, the wavelength, and the polarization angle of the light. Rayleigh scattering is strongly wavelength dependent (1/λ4) and gives us the blue color of the sky. Mie scattering is not strongly wavelength dependent and produces the almost white glare around the sun when a lot of particulate material is present in the air. It also gives us the white light from mist and fog. Mie scattering in the eye produces haze from cataracts and other particles clouding the ocular media. The direction of scatter depends somewhat on the size of particles.
Absorption of photons Once light reaches the photoreceptors of the eye, it is absorbed by a particular molecule called a photopigment. The energy of the photon causes the molecule to change shape (isomerize) and this starts a cascade of activity that results in electrical signals through the nervous system. Two important characteristics of this photon absorption are: 1) There is an inherent randomness to the process. When and where a photon gets absorbed is a matter of probability, following a Poisson statistical distribution. 2) Once a photon is absorbed, the photoreceptor responds the same way, regardless of the wavelength. This is the Principle of Univariance. Example of damage from laser exposure A 15 year old bought a laser pointer through the internet. He stood in front of a mirror and looked right into it. The laser was 50 X more powerful than most laser pointers. NEJM september 9, 2010 Light exposure damage Intense light exposure can damage the eye through three principle mechanisms: Thermal Damage: proteins in the eye are denatured by tissue heating, especially in the retinal pigment epithelium (RPE) which absorbs light over a broad spectrum. Photochemical Damage: particular pigments, such as photoreceptor photopigments, or lipofuscin in the RPE, are altered by absorbed light resulting in damaging byproducts such as free radicals. ThermoAcoustic Damage: extremely intense pulses of light can produce vibrations that damage tissue. As light intensity increases, usually either thermal or photochemical damage will occur first. With very brief pulses of light, thermoacoustic damage might be the first to occur. To determine safe levels, we make sure none of the three will occur! Maximum Permissible Exposures (MPEs) MPEs refer to the highest intensity of light exposure that is considered safe: that is, a level that is not likely to cause damage to the eye. MPEs are established through animal experiments and through accidental damage in humans. The MPE for a particular situation is 1/10th the intensity of light that would produce damage in half the cases. MPE values are published by the American National Standards Institute in their document ANSI Z136.1-2007. Other organizations have similar standards.
Calculating MPEs is not simple Determining light exposure safety limits is complicated. It depends on wavelength (nm), power (Watts), exposure time (sec), area of retina exposed (mm 2 ), pupil size (mm 2 ), eye motion (deg/sec). We have to answer: How much energy in Joules was delivered to one retinal location? Does the wavelength(s) used produce thermal or photochemical damage first? If it is thermal damage, was the exposure long enough that some of the heat could dissipate away? A significant problem is that some eyes may be more susceptible to damage than others, for example in retinal disease. Laser Classes and Safety Lasers are sorted into Classes based on their potential to do damage. (The old system used Roman numerals and A/B designations. The classes shown here are the new system.) Class 1 lasers do not exceed MPE level even for very long exposures. Class 1M is a special case: they are safe as sold, but could be hazardous if optics were used to focus the beam to a point. Class 2 lasers are visible (400 700 nm) lasers that do not exceed MPE level for exposure durations less than 0.25 sec. The assumption here is that you will blink or look away (aversion reflex). Power is less than 1 mwatt. A Class 2M laser is safe unless optics are used to focus it down. Class 3R lasers (firearm sights, laser pointers) have power less than 5 mwatt and generally won t do damage unless they are focused. Class 3B lasers have power from 5 to 500 mwatt and will damage the eye if viewed directly even with short exposures. Diffusely reflected light from the spot they make is not hazardous. Class 4 lasers have power over 500 mwatt, will burn the skin, start fires, etc. Surgical lasers are in this category. Comparing direct vs. indirect view of a laser The damage calculations assume that all the laser light goes into the eye. When you look at a laser dot on the wall, only a very small fraction of the light goes into your eye. The screen scatters light from laser dot in all directions At a distance of 7 meters, the light has spread out into a hemisphere that is 308 square meters in area Effects of time and wavelength on exposure damage a 4 mm pupil has an area of.000025 square meters so pupil gets just 1 part in 12,254,000 of the light! From Delori et al. JOSA 2007
Apparent Brightness is not a measure of safety! The curves show the luminance of light at the threshold for damage across the visible spectrum. The heavy curve is for 300 seconds continuous exposure, the lighter curve is for 30 seconds exposure. The vertical axis plots log Trolands, a photometric unit. Damaging light at 800 nm will appear 10,000 times less bright than equally damaging light at 550 nm. Notice that the curves are different in the blue, but the same in the red. In the blue, damage is photochemical and accumulates over longer time periods. The longer the flash lasts, the lower the power must be to avoid damage. The vertical axis here is radiometric, showing power in Watts entering the pupil for a 2 arc minute spot at 488 nm. For brief flashes thermal damage is more likely. Time and damage threshold do not trade off perfectly, because heat can dissipate away if exposures are long. For very long exposures (e.g. 10 3 seconds) photochemical damage becomes more likely. MPE calculation for ophthalmic instruments The sloping blue line shows the MPE calculated for photochemical damage across a large range of exposure times. The horizontal lines show the power output of various instruments. The point where each line intersects the MPE shows the maximum safe exposure time for that instrument. Dong Chen 2016 Masters thesis: Safety Evaluation of Light Levels in Ophthalmic Instruments and Devices.