Chapter 5 – Physical Optics for Clinicians
EDMOND H. THALL
• Whereas geometrical optics considers light to be a series of rays, physical optics approaches problems in optics by treating light as a waveform.
• Interference of light waves.
• Polarization of light waves.
• Diffraction effects of light waves.
• Scattering of light waves (effects on glare and contrast sensitivity).
• Understanding the quantum model of light waves.
• Lasers and light waves.
• Interaction of tissue and light waves (i.e., laser light).
Geometrical optics ignores the basic nature of light yet remarkably is able to explain many aspects of image formation, such as image location and magnification, based on the geometry of the paths that light follows when moving from object to image. However, many clinical phenomena can be understood only through knowledge of light’s physical nature.
ELECTROMAGNETIC AND SCALAR WAVE MODELS OF LIGHT
Certain phenomena are best explained by modeling light as a wave. Maxwell showed that light behaved as an electromagnetic wave consisting of an electric field oscillating perpendicular to an oscillating magnetic field, with both fields perpendicular to the direction of propagation ( Fig. 5-1 ). Since the magnetic field oscillates in lockstep with the electric field, it is often sufficient to consider only the electric field. In the scalar wave model, light is modeled as a single transverse wave ( Fig. 5-2 ).
In both the electromagnetic and the scalar wave models, light is a transverse wave. In such waves, the direction of oscillation is always perpendicular to the direction of propagation. Nevertheless, the wave may oscillate in many different directions. A linearly polarized wave oscillates in a single plane (see Fig. 5-2 ).
Polarization may be achieved in several ways. If light is reflected specularly from a plane surface, it is polarized partially—the direction of polarization is parallel to the reflecting surface. If light is reflected at a specific angle (discovered by Brewster and named in his honor), the reflected light is polarized totally. The Brewster angle can be calculated using the following equation:
Figure 5-1 Electromagnetic wave. An electromagnetic wave consists of an oscillating electric field perpendicular to an oscillating magnetic field. The direction of propagation is perpendicular to both the electric and the magnetic fields.
Fresnel took Brewster’s discovery further and calculated the degree of (partial) polarization produced by a reflecting surface at any angle of incidence. Fresnel’s equations are somewhat complicated but can be found in any standard treatment of optics.
Some materials have different refractive indices, depending on the direction of polarization; they are called birefringent because they have two different refractive indices. Light incident on such birefringent materials travels in different directions, depending on its polarization. Such materials separate a beam of light into two beams, each linearly polarized at right angles to each other. 
Dichroic materials absorb light linearly polarized in one direction and transmit light linearly polarized at right angles to this. These materials are commonly used in polarized sunglasses. Most reflecting surfaces in human surroundings are horizontally oriented, such as floors, automobile hoods, and so forth. Light reflected from a surface (and consequently at least partially polarized) is absorbed by dichroic materials in the lenses of polarized sunglasses. In sunglasses, the dichroic material is oriented to transmit vertically polarized light and absorb horizontally polarized light. Polarizing sunglasses reduce only reflected glare, and only when the reflecting surface is horizontal. Despite these limitations, polarization is a popular feature in sunglasses.
Several ocular structures are birefringent; these include collagen fibers in the cornea and iris and nerve fibers of the inner retina. A number of attempts have been made to capitalize on this. An instrument is now available for clinical use that measures birefringence in the retinal nerve fiber layer as an indicator of thickness of that layer. However, the accuracy of nerve fiber
Figure 5-2 Polarization. Both transverse waves propagate in the same direction but oscillate in different planes. Here, only the scalar wave approximation is adopted, and only the electric field is shown.
layer measurements may be affected by birefringence in other ocular tissues, especially the cornea.
The potential for changes in other ocular structures to produce apparent changes in the nerve fiber layer should always be considered when interpreting data based on birefringence measurements. Recently, changes in nerve fiber layer thickness measured by birefringence were reported following LASIK. Whether the change in birefringence is the result of a decrease in nerve fiber layer thickness or a change in corneal birefringence is an open question, but one that can be easily resolved using laser keratectomy. Intraocular pressure increases only to 30?mmHg during laser keratectomy. It is extremely unlikely that this would produce a change in the nerve fiber layer, so any apparent change would be an artifact.
Birefringence in the anterior segment is demonstrated easily using the circular polarizer furnished in some direct ophthalmoscopes to eliminate annoying corneal reflections. In circularly polarized light, the plane of polarization rotates uniformly ( Fig. 5-3 ). If the anterior segment is focused on, instead of the retina, a dark Maltese-style cross is seen, with bright, iridescent colors between the arms of the cross. The dark cross is produced by Fresnel reflection at the corneal surface. The colors are probably produced by birefringence of the corneal and iris collagen.
Several attempts have been made to measure corneal topography using Fresnel reflection by the anterior corneal surface. When light is reflected from a surface, it is at least partially polarized. The degree of polarization is related to the angle between the light and the reflecting surface. In theory, it is possible to calculate corneal shape from measurements of the degree and direction of polarization of light reflected from the corneal surface. In practice, this has proved exceedingly difficult.
Birefringence has been used to detect defects in intraocular lenses. The birefringence is detected by placing the lens between two linear polarizers at right angles to each other. Any light transmitted appears as a readily recognizable bright spot that indicates a possible defect in the strength of the lens. These defects arise from various causes, such as heat produced when the haptics of a three-piece lens are inserted, or from heat generated during lathe cutting or polishing.
Polarization is the basis of the “Fly test” for stereopsis.  Two images are superimposed and slightly displaced. Each image linearly polarizes light, and the axes of polarization are perpendicular. The patient wears polarizing glasses so that each eye sees only one of the images. Because each image is slightly displaced, the observer perceives the image in front of the page. By wearing
Figure 5-3 Circularly polarized light. In circularly polarized light, the electric field has a constant amplitude, and the plane of polarization rotates at a constant speed. The plane of polarization follows a corkscrew path as the wave travels.
the polarizing glasses upside down, each eye sees the opposite image, and the perception is that the image is below the page.
Projector charts and polarization can also be used to detect malingering in patients claiming unilateral vision loss. Again, the patient wears polarizers over each eye so that each eye sees only some of the letters on a line. The patient is instructed to keep both eyes open and read the chart. If the patient identifies all the letters on the 20/20 line, the unilateral vision loss is factitious.
When two different light waves overlap, their amplitudes add. If two waves of equal amplitude are 180° out of phase, the amplitudes cancel out, and the net result is zero ( Fig. 5-4 ). If the waves are perfectly in phase, the amplitudes double, and the intensity (square of the amplitude) is four times greater than that of a single wave. Interference refers to the summation of amplitudes that always occurs when two waves overlap. When the waves are in phase, the interference is constructive, and when the waves are out of phase, the interference is destructive.
Imagine shining two identical flashlights illuminating the same spot on a wall. You would expect to see twice as much light, but if the waves from each light were perfectly out of phase, you would actually see no light at all. In practice, in order to observe interference effects, the waves must be coherent and polarized in similar directions. The light from two different sources always interferes either constructively or destructively, but you cannot observe the interference because the light from one source is not coherent with the other light.
Because of coherence requirements, interference can be observed only under certain conditions. An interference phenomenon widely used in clinical practice, but not widely appreciated, is the basis for antireflection coatings. When light travels from one medium to another, a small amount of light is reflected at the interface between the two media. Anyone who has used a direct ophthalmoscope has experienced the annoying reflection from the corneal surface. In indirect ophthalmoscopy, reflection from the handheld lens may interfere with fundus visualization, particularly when the slit lamp is used. Patients often complain of reflections associated with spectacle lenses.
One way to reduce reflected light is to coat lenses with thin films. One type of antireflective coating consists of a thin film (one half wavelength thick, approximately 250?nm) of material with a refractive index in between those of air and glass. Light is reflected from both the front and back surfaces of the film, but because the film is half a wavelength thick, the two reflections interfere destructively and reduce the amount of back-scattered light.
In practice, thin film coatings are much more complicated and usually consist of multiple layers of different materials. A simple one-layer antireflective coating may eliminate reflection
Figure 5-4 Constructive and destructive interference. When two or more light waves are superimposed, the amplitudes sum. If two identical waves are in phase, the resulting amplitude doubles (bottom). If the waves are perfectly out of phase, the waves cancel out (top).
for only one wavelength of light. Multilayer coatings may reduce reflection significantly over a range of wavelengths. Single-layer coatings also are scratched easily and can be removed by routine lens cleaning. Additional layers are used to make the coatings more durable.
Thin films also occur clinically. The tear film consists of three layers: an outer oil layer, a middle aqueous layer, and an inner mucin layer. The oil layer constitutes a thin film that produces a colored interference pattern visible on slit-lamp examination. The appearance of the interference pattern is similar to the iridescent colors produced by a layer of oil or gasoline on the surface of a puddle of water. Inability to elicit the interference pattern suggests a specific defect in the oil layer.
Sometimes a nearly transparent layer of inflammatory cells grows on the surface of an intraocular lens implant. It may be difficult to see this layer with conventional slit-lamp illumination, but with placement of the slit beam at a slight angle to the visual axis, a rainbow of color caused by thin film interference may be appreciated. Cortical cells growing on the posterior capsule can produce a similar effect.
Interference is used to assess retinal function in patients with media opacity, especially cataract. A laser light source is split into two narrow beams that presumably pass through small, clear regions of the lens. Because the beams are coherent, they form interference fringes on the retina. The arrangement is essentially a modification of Young’s two-slit experiment. The greater the separation of beams in the pupil, the narrower the interference fringes on the retina. The patient reports when he or she can see the fringes; the narrower the fringes the patient can detect, the better the potential acuity. To avoid a falsely low estimate of potential acuity, the patient must have a sufficiently large pupil to produce narrow fringes on the retina. Unfortunately, a falsely optimistic estimate of acuity can also be obtained in patients with macular edema or degeneration, because the test uses coherent light.
The most recent innovative clinical application of interference is optical coherence tomography (OCT). The OCT scanner is basically a Michaelson interferometer ( Fig. 5-5 ). The light source is a superluminescent diode, which has more coherence than white light but less than a laser diode. The limited coherence allows detection of interference effects over only a small optical path difference. By scanning the reference mirror, the optical path difference between various tissue layers can be measured.
When interpreting OCT images, it is important to realize that OCT measures optical path length, not physical length. Optical path length is physical length multiplied by refractive index.
Figure 5-5 Michaelson interferometer is the basis of optical coherence tomography. A beam splitter divides one light beam into two, which travel different paths and then are recombined. If the light source has low coherence, interference fringes are observed only when the optical path length of each arm is nearly identical. Placing the eye in one path of the interferometer and varying the length of the other arm can measure the optical path length to various ocular tissues.
OCT has also been used to measure axial length and corneal thickness. Just as the accuracy of ultrasound biometry depends on assumptions about the speed of light in ocular media, the accuracy of OCT measurements depends on assumptions about the refractive index of ocular tissues. Two corneas of identical thickness but with small differences in refractive index will appear to have different lengths when measured by OCT.
Diffraction refers to the bending of light as it passes through an aperture; it was first observed independently by Hooke and Grimaldi in the mid-1600s.   Ultimately, diffraction limits the resolution of optical images. If an imaging system is well corrected, the image of a point source is an airy disc, and the radius of the central maximum is :
For the average eye, the exit pupil diameter is about 3?mm, and it is 18.5?mm from the retina. Thus, for an eye of these dimensions, the airy disc has a radius of about 2?µm or a diameter of 4?µm. This corresponds roughly to the diameter of a photoreceptor. If the airy disc were considerably larger than a photoreceptor, the optics of the eye would limit vision, and the retina would have an unnecessarily large number of photoreceptors. Conversely, if the airy disc were much smaller than the diameter of a photoreceptor, the imaging capabilities of the eye would far exceed the retinal resolution. So it is not surprising that the resolution of the ocular media correlates with the retinal anatomy.
The calculation of ocular resolution assumes that the eye is essentially aberration free. Aberrations can be decreased by miosis,
but this increases diffraction and the size of the airy disc, decreasing resolution. Conversely, mydriasis decreases diffraction and theoretically would improve resolution. However, the retina cannot make use of the increased resolution, and aberrations increase as the pupil dilates. This may explain the physiological purpose of the Stiles-Crawford effect. Rays that traverse the edge of the pupil are not as effective at stimulating the retina as central rays are.
The visual symptoms of glare and haloes may be the result of diffraction.  In corneal epithelial edema, fluid collects between epithelial cells and has a refractive index different from that of the cells. From an optical standpoint, a cornea that has epithelial edema is effectively a diffraction grating. Diffraction of white light produces a rainbow of colors.
When a patient complains of seeing haloes, they are typically seen around streetlights, automobile headlights, or the moon. A distant, discrete light source produces nearly spatially coherent light; haloes from such light are especially prominent. It may be helpful to inquire specifically whether the patient sees a colored halo or a series of black and white rings. It is this author’s personal experience that the haloes produced by the subepithelial infiltrates of epidemic keratoconjunctivitis are not colored but rather are white-light interference fringes. These occur even in the absence of corneal edema and can be seen even when visual acuity is 20/20 (6/6).
The haloes produced by epithelial edema are colored when white-light objects are viewed. Epithelial edema may be caused by a variety of conditions, some of the most common being glaucoma (with very high intraocular pressure), corneal abrasion, and contact lens overwear. The colored halo also is a useful sign in vitreoretinal surgery. The surgeon’s view may be diminished markedly by corneal epithelial edema or many other causes. Shining the light pipe on the working instrument gives a specular reflection that invariably has a colored halo around it if epithelial edema is present. A diminished view from epithelial edema can be overcome by removing the epithelium, but this can lead to postoperative complications such as corneal ulcer, especially in diabetics, who tend to re-epithelialize slowly. In the absence of a colored halo, the surgeon should consider other possible causes for the decreased view before removing the epithelium, perhaps unnecessarily.
Binary optical lenses combine refractive and diffractive effects. Some multifocal intraocular lenses use binary optical designs. In the early 1990s there was considerable interest in the use of diffractive optics for the correction of presbyopia. The diffractive part of the lens produced two images at different focal lengths. Some patients can tolerate the monocular diplopia and decreased image contrast. However, currently there is greater interest in more physiological approaches.
GLARE AND LIGHT SCATTER
In an ideal world, light would travel straight through a material, but in reality, a small amount of light is scattered in all directions. Glare occurs when a defect in the ocular media scatters light, which decreases the contrast of the retinal image ( Fig. 5-6 ).
Light scatter generally is caused by particles in the medium. There are two types of scatter: Rayleigh scatter is caused by particles smaller than the wavelength of incident light, and Mie scatter is caused by particles larger than the wavelength of light. In Rayleigh scatter, the amount of scatter is proportional to the fourth power of the wavelength of the incident light. In Mie scatter, the amount of scatter is directly proportional to the wavelength of the incident light.
Molecules of air result in Rayleigh scatter of sunlight. In Rayleigh scatter, blue light is scattered about 16-fold more than red. Consequently, the atmosphere acts as a blue-light filter. When the sun is overhead, sunlight traverses relatively little atmosphere, and the sun appears yellow. When the sun is low over the horizon, light must travel through more of the atmosphere, and more blue light is scattered, which gives the sun a red appearance.
Figure 5-6 Glare. Without light scatter, light from an off-axis glare source does not overlap with the central retinal image. Light scatter by the ocular media, such as an early cataract, may decrease contrast in the central retinal image.
The same applies to scatter by the ocular media, especially the crystalline lens. As a person ages, light scatter by the lens increases, and fundus features appear more yellow and red. After cataract extraction, fundus details appear whiter. If a patient has had a cataract removed from one eye but has a cataract in the other eye, the optic nerve in the operated eye may appear atrophic by comparison to that in the phakic eye. This appearance may result from the difference in light scatter between the two eyes.
For several reasons, attempts have been made to measure the amount of light scattered by the crystalline lens. Such measurements may be able to verify whether a cataract is bad enough to explain a patient’s visual loss or whether another cause is present. A fundamental problem is that only back-scattered light can be measured clinically. Back-scattered light is light that hits the lens and is scattered through the pupil and out of the eye. Back-scattered light does not reach the retina and therefore does not affect vision. Forward-scattered light hits the lens and is scattered, but it continues through the crystalline lens to reach the retina (and decrease vision). No definite relationship exists between forward- and back-scattered light.
Some investigators hoped that objective measurements of light scatter by the crystalline lens would provide a guideline for cataract surgery. However, the appropriateness of cataract surgery depends on the effect of a visual deficit on the patient’s lifestyle, not on the degree of visual loss per se. A better use for light scatter measurements is to evaluate the efficacy of drugs intended to slow or prevent cataract formation.
The difficulty in performing useful light scatter measurements cannot be overstated. Generally, to be of value, the amount of light scattered in all directions must be measured for every possible direction of incident beam. The results of such measurements
constitute the bidirectional reflection distribution function. No current commercial instrument can measure the bidirectional reflection distribution of crystalline lens light scatter.
A device that measures both Mie and Rayleigh scatter has been introduced to quantify both cells and flare in the anterior chamber. To date, the principal value of such measurements is to compare the efficacy of different treatment regimens.
QUANTUM MODEL OF LIGHT
Although the wave model is very useful, some phenomena can be explained only on the basis of a quantum or discrete model of light. When electrons change energy levels, they often absorb or emit a photon. An electron in an elevated energy level may drop to a lower energy level spontaneously or as a result of stimulated emission. If a photon of appropriate energy passes by an electron in a high-energy state, the photon induces the electron to drop to a lower energy level and give off a second photon. The two photons are identical in energy and phase.
BASIC LASER PHYSICS
Stimulated emission is the basis of the laser. The word laser was originally an acronym for light amplification by stimulated emission of radiation. In any laser there is a working medium. Normally, in any working material there are more electrons in lower energy levels than in higher levels. By some means, which can vary depending on the type of laser, energy is added to the working material so that a preponderance of electrons are in a high-energy state, a condition referred to as a population inversion. Eventually, one electron spontaneously decays, producing a photon that passes by other electrons and stimulates them to emit more identical photons. Partially reflecting mirrors placed at the ends of the medium cause the photons to pass through the working material multiple times, yielding a chain reaction that produces a beam.
Depending on the working material, photons of various wavelengths can be produced. To understand the clinical use of lasers, it is necessary to understand the various ways light interacts with tissue.
In photocoagulation, light energy is absorbed by tissue generating heat. The heat denatures proteins, producing coagulation, much as the white of an egg coagulates when it is fried. To produce thermal effects, a tissue must absorb light; the more pigmented the tissue, the greater its absorption. The retina is largely transparent and does not absorb much light. However, the retinal pigment epithelium (RPE) and choroid do absorb light and produce heat that coagulates the adjacent retina. It can be difficult to photocoagulate the retina in patients with a blond fundus, because the choroid and RPE absorb less light. For similar reasons, producing a peripheral iridectomy using a thermal laser is more difficult in blue irides.
In photodisruption, a shock wave is generated by optical breakdown. Photodisruption is essentially a miniature lightning bolt. In lightning, high electric fields literally tear the electrons away from the molecules of air, generating an expanding plasma. When the lightning stops, the electrons recombine, and the contraction of the air produces an acoustic shock wave commonly called thunder. In photodisruption, a very high power density is produced in a very small region, causing the material in that region to break down into a plasma. A small spark is seen at the site of optical breakdown. Recombination of electrons with ions in the plasma produces an acoustic shock wave that can alter ocular tissues.
Because the posterior capsule is largely transparent, photocoagulation cannot reliably produce a capsulotomy, so photodisruption is used instead. When performing a capsulotomy, the goal is to produce an optical breakdown behind the lens implant and capsule and let the acoustic shock wave tear the capsule. It is more difficult to perform a capsulotomy in patients with silicone implants, because optical breakdown of silicone occurs at lower power densities than does breakdown of polymethylmethacrylate. Often the optical breakdown occurs in the lens and not posterior to it. Optical breakdown in the lens implant produces a small pit that by itself is usually not visually significant, but severe pitting of the lens can decrease vision.
In photoablation, high power densities break chemical bonds and vaporize tissue, but with minimal thermal or acoustic effects. LASIK and photorefractive keratectomy are based on photoablation. It is often stated that each excimer laser pulse removes a precise amount of tissue. This, of course, is nonsense. Many factors affect the amount of tissue removed. The amount of energy delivered in each pulse varies, depending on factors associated with the laser and atmospheric conditions. The amount of tissue removed also varies with corneal hydration and probably other patient-specific factors.
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