Principles of Interference
Introduction to Light Interference
The formation of an image in the microscope relies on the complex interplay between two critical optical phenomena: diffraction and interference. Light passing through the specimen is scattered and diffracted into divergent waves by tiny details and features present in the specimen. Some of the divergent light scattered by the specimen is captured by the objective and focused onto the intermediate image plane, where the superimposed light waves are recombined or summed through the process of interference to produce a magnified image of the specimen.
The seemingly close relationship between diffraction and interference occurs because they are actually manifestations of the same physical process and produce ostensibly reciprocal effects. Most of us observe some type of optical interference almost every day, but usually do not realize the events in play behind the often-kaleidoscopic display of color produced when light waves interfere with each other. One of the best examples of interference is demonstrated by the light reflected from a film of oil floating on water. Another example is the thin film of a soap bubble (illustrated in Figure 1), which reflects a spectrum of beautiful colors when illuminated by natural or artificial light sources.
The dynamic interplay of colors in a soap bubble derives from simultaneous reflection of light from both the inside and outside surfaces of the exceedingly thin soap film. The two surfaces are very close together (separated by only a few micrometers) and light reflected from the inner surface interferes both constructively and destructively with light reflected from the outer surface. The interference effect is observed because light reflected from the inner surface of the bubble must travel farther than light reflected from the outer surface, and variations in the soap film thickness produce corresponding differences in the distances light waves must travel to reach our eyes.
When the waves reflected from the inner and outer surfaces of the soap film recombine, they will interfere with each other to either remove or reinforce some wavelengths of white light by destructive or constructive interference (as illustrated in Figure 2). The result is a dazzling display of color that seems to gyrate along the surface of the bubble as it expands and contracts with wind currents. Simply turning the soap bubble, or moving it closer or farther away, causes the colors to change, or even disappear altogether. If the extra distance traveled by the light waves reflected from the inner surface is exactly equal to the wavelength of those bouncing away from the outer surface, then the light waves will recombine constructively to form bright colors. In areas where the waves are out of step with each other, even by some fractional portion of a wavelength, destructive interference effects will begin to occur, attenuating or canceling the reflected light (and the color).
Music, movie, and computer enthusiasts are also exposed to the interference phenomenon each time they load a compact disk into the audio player or a CD-ROM drive. The closely spaced spiral tracks on a compact or digital videodisk contain a series of pits and lands that are utilized to encode the digital profile of the audio and/or video sequences contained on the disk. The very close spacing of these tracks mimics the ultra-fine lines present on a diffraction grating to produce a spectacular rainbow-like effect of color when ordinary white light is reflected from the surface. Like the soap bubble, the color is derived from interference between reflected light waves bouncing from neighboring tracks on the disk.
Interference is responsible for the often-brilliant iridescent coloring displayed by hummingbirds, a variety of beetles and other insects whose wings cast a metallic luster, and several species of magnificent butterflies. For example, the wings of the diamond beetle are covered with a microscopic crisscrossed diffraction grating having approximately 2,000 lines per inch. White light reflected from the wings of the beetle produces a stunning spectral display of interference patterns similar to that originating from the surface of a compact disk. A similar effect is created by the tortoise beetle, which has wing casings composed of multiple chitin layers, rendering them iridescent in reflected light. Interestingly, this insect can vary the moisture content of the thin films to produce thickness variations, changing the predominant reflected interference color from gold to reddish-copper.
Another spectacular example of naturally occurring interference, the Morpho didius butterfly thrives in the Amazon rain forest and exhibits one of the most beautiful forms of iridescence seen in the insect world. The intense blue wing color is the consequence of color-producing structures fastened to the scales layering the butterfly's wings. Each scale is composed of two sheet-like, extremely thin lamella, an upper and lower, which are separated by a void held apart with vertical rods. The lamellae support an even smaller network of Christmas tree-shaped ridges containing plates or branches projecting laterally from a central stalk. Plates on the ridges arising from thin layers of chitin that are separated by air spaces at distances equal to one-half the wavelength of blue light mimic a natural diffraction grating. The ridges have evolved with spacing at the correct intervals for light waves reflecting from the plates to undergo constructive and destructive interference. The result is a deep iridescent blue color that covers almost the entire wing structure, although no blue light is actually reflected from the wing scales.
The classical method of describing interference includes presentations (see Figure 4) that depict the graphical recombination of two or more sinusoidal light waves in a plot of amplitude, wavelength, and relative phase displacement. In effect, when two waves are added together, the resulting wave has an amplitude value that is either increased through constructive interference, or diminished through destructive interference. To illustrate the effect, consider a pair of light waves from the same source that are coherent (having an identical phase relationship) and traveling together in parallel (presented on the left-hand side of Figure 4).
If the vibrations produced by the electric field vectors (which are perpendicular to the propagation direction) from each wave are parallel to each other (in effect, the vectors vibrate in the same plane), then the light waves may combine and undergo interference. If the vectors do not lie in the same plane, and are vibrating at some angle between 90 and 180 degrees with respect to each other, then the waves cannot interfere with one another. The light waves illustrated in Figure 4 are all considered to have electric field vectors vibrating in the plane of the page. In addition, the waves all have the same wavelength, and are coherent, but vary with respect to amplitude. The waves on the right-hand side of Figure 4 have a phase displacement of 180 degrees with respect to each other.
Assuming all of the criteria listed above are met, then the waves can interfere either constructively or destructively to produce a resultant wave that has either increased or decreased amplitude. If the crests of one of the waves coincide with the crests of the other, the amplitudes are determined by the arithmetic sum of the amplitudes from the two original waves. For example, if the amplitudes of both waves are equal, the resultant amplitude is doubled. In Figure 4, light wave A can interfere constructively with light wave B, because the two coherent waves are in the same phase, differing only in relative amplitudes. Bear in mind that light intensity varies directly as the square of the amplitude. Thus, if the amplitude is doubled, intensity is quadrupled. Such additive interference is called constructive interference and results in a new wave having increased amplitude.
If the crests of one wave coincide with the troughs of the other wave (in effect, the waves are 180-degrees, or half a wavelength, out of phase with each other), the resultant amplitude is decreased or may even be completely canceled, as illustrated for wave A and wave C on the right-hand side of Figure 4. This is termed destructive interference, and generally results in a decrease of amplitude (or intensity). In cases where the amplitudes are equal, but 180-degrees out of phase, the waves eliminate each other to produce a total lack of color, or complete blackness. All of the examples presented in Figure 4 portray waves propagating in the same direction, but in many cases, light waves traveling in different directions can briefly meet and undergo interference. After the waves have passed each other, however, they will resume their original course, having the same amplitude, wavelength, and phase that they had before meeting.
Real-world interference phenomena are not as clearly defined as the simple case depicted in Figure 4. For example, the large spectrum of color exhibited by a soap bubble results from both constructive and destructive interference of light waves that vary in amplitude, wavelength, and relative phase displacement. A combination of waves having amplitudes that are approximately equal, but with differing wavelengths and phases, can produce a wide spectrum of resultant colors and amplitudes. In addition, when two waves of equal amplitude and wavelength that are 180-degrees (half a wavelength) out of phase with each other meet, they are not actually destroyed, as suggested in Figure 4. All of the photon energy present in these waves must somehow be recovered or redistributed in a new direction, according to the law of energy conservation (photons are not capable of self-annihilation). Instead, upon meeting, the photons are redistributed to regions that permit constructive interference, so the effect should be considered as a redistribution of light waves and photon energy rather than the spontaneous construction or destruction of light. Therefore, simple diagrams, such as the one illustrated in Figure 4, should only be considered as tools that assist with the calculation of light energy traveling in a specific direction.
Thomas Young's Double Slit Experiment
Among the pioneers in early physics was a nineteenth century English scientist named Thomas Young, who convincingly demonstrated the wave-like character of light through the phenomenon of interference using diffraction techniques. Young's experiments provided evidence in contrast to the popular scientific opinion of the period, which was based on Newton's corpuscular (particle) theory for the nature of light. In addition, he is also responsible for concluding that different colors of light are made from waves having different lengths, and that any color can be obtained by mixing together various quantities of light from only three primary colors: red, green, and blue.
In 1801, Young conducted a classical and often-cited double-slit experiment providing important evidence that visible light has wave-like properties. His experiment was based on the hypothesis that if light were wave-like in nature, then it should behave in a manner similar to ripples or waves on a pond of water. Where two opposing water waves meet, they should react in a specific manner to either reinforce or destroy each other. If the two waves are in step (the crests meet), then they should combine to make a larger wave. In contrast, when two waves meet that are out of step (the crest of one meets the trough of another), the waves should cancel and produce a flat surface in that area.
In order to test his hypothesis, Young devised an ingenious experiment. Using sunlight diffracted through a small slit as a source of semi-coherent illumination, he projected the light rays emanating from the slit onto another screen containing two slits placed side by side. Light passing through the slits was then allowed to fall onto a third screen (the detector). Young observed that when the slits were large, spaced far apart and close to the detection screen, then two overlapping patches of light formed on the screen. However, when he reduced the size of the slits and brought them closer together, the light passing through the slits and onto the screen produced distinct bands of color separated by dark regions in a serial order. Young coined the term interference fringes to describe the bands and realized that these colored bands could only be produced if light were acting like a wave.
The basic setup of the double slit experiment is illustrated in Figure 5. Red filtered light derived from sunlight is first passed through a slit to achieve a semi-coherent state. Light waves exiting the first slit are then made incident on a pair of slits positioned close together on a second barrier. A detector screen is placed in the region behind the slits to capture overlapped light rays that have passed through the twin slits, and a pattern of bright red and dark interference bands becomes visible on the screen. The key to this type of experiment is the mutual coherence of the light diffracted from the two slits at the barrier. Although Young achieved this coherence through the diffraction of sunlight from the first slit, any source of coherent light (such as a laser) can be substituted for light passing through the single slit.
The coherent wavefront of light impacting on the twin slits is divided into two new wavefronts that are perfectly in step with each other. Light waves from each of the slits must travel an equal distance to reach point A on the screen illustrated in Figure 5, and should reach that point still in step or with the same phase displacement. Because the two waves reaching point A possess the necessary requirements for constructive interference, they should add together to produce a bright red interference fringe on the screen.
In contrast, neither of the points B on the screen is positioned equidistant from the two slits, so light must travel a greater distance from one slit to reach point B than from the other. The wave emanating from the slit closer to point B (take for example the slit and point B on the left-hand side of Figure 5) does not have as far to travel to reach its destination, as does a wave traveling from the other slit. As a consequence, the wave from the closest slit should arrive at point B slightly ahead of the wave from the farthest slit. Because these waves will not arrive at point B in phase (or in step with each other), they will undergo destructive interference to produce a dark region (interference fringe) on the screen. Interference fringe patterns are not restricted to experiments having the double slit configuration, but can be produced by any event that results in the splitting of light into waves that can be canceled or added together.
The success of Young's experiment was strong testimony in favor of the wave theory, but was not immediately accepted by his peers. The events in place behind phenomena such as the rainbow of colors observed in soap bubbles and Newton's rings (to be discussed below), although explained by this work, were not immediately obvious to those scientists who firmly believed that light propagated as a stream of particles. Other types of experiments were later devised and conducted to demonstrate the wave-like nature of light and interference effects. Most notable are the single mirror experiment of Humphrey Lloyd, and the double mirror and bi-prism experiments devised by Augustin Fresnel for polarized light in uniaxial birefringent crystals. Fresnel concluded that interference between beams of polarized light could only be obtained with beams having the same polarization direction. In effect, polarized light waves having their vibration directions oriented parallel to each other can combine to produce interference, whereas those that are perpendicular do not interfere.
Sir Isaac Newton, the famous seventeenth century English mathematician and physicist, was one of the first scientists to study interference phenomena. He was curious about how the brilliant display of color on the surfaces of soap bubbles arose, especially considering the bubbles were composed of a colorless liquid soap solution. Newton correctly speculated that the color might be attributed to the close proximity of the inner and outer surfaces of the bubbles, and devised an experimental approach designed to mimic the colored patterns observed. In his famous Newton's Rings experiment (see Figure 6), Newton placed a convex lens having a large curvature radius on a flat glass plate and applied pressure through a brass frame to hold the lens and glass plate together, but still separated by a very thin void filled with air and having the same dimensions as visible light. When he viewed the plates by reflected sunlight, he observed a series of concentric bands having both light and dark colored regions.
The orderly progression of the rings surprised Newton. Near the center of the contact point, the rings were larger and had ordered color patterns starting with black, then progressing through faint blue, white, orange, red, purple, blue, green and yellow. The bands had greater intensity and were thicker at the center, grew thinner as they progressed outward, and finally trailed off at the edges of the brass frame. Newton also discovered that if he illuminated the glass with red light, the colors changed to produce alternating red and black lines. In a similar manner, blue light produced blue and black rings, while green light generated green and black rings. Furthermore, Newton found that the spacing between the rings depended upon the color. Blue rings were closer together than green rings, which were closer together than the red rings (an identical effect would be observed for interference fringe spacing in the double slit experiment if different colored filters were employed).
Newton recognized that the rings indicated the presence of some degree of periodicity, but was puzzled over the results of the experiment. In fact, the physical basis for the formation of the rings became a mystery that endured for over 75 years after Newton's death. It wasn't until Young conducted the double slit experiment that scientists realized light reflected from the top and bottom surfaces of the glass becomes superimposed, or combined, and produces interference patterns that appear as the colored rings. Today, this principle is often used by lens manufacturers to test the uniformity of large polished surfaces.
Interference distribution fringes (such as those observed in Young's double slit experiment or the Newton's ring device) vary in intensity when they are presented on a uniform background. The visibility (V) of the intensity was defined by Albert Michelson, an early twentieth century physicist, as the difference between the maximum and minimum intensity of a fringe divided by their sum:
where I(max) represents the measured maximum intensity and I(min) is the corresponding minimum intensity. In this equation, idealized fringe intensity always lies between zero and one, however in practice fringe visibility is dependent upon the geometrical design of the experiment and the spectral range utilized.
The explosive interest in fluorescence microscopy, using classical widefield observation alone or in combination with scanning confocal and multiphoton laser techniques, has led to the rapid development of new filter technology designed to enable the microscopist to selectively excite fluorophores and observe their secondary fluorescence with a minimum of background noise. For these applications, filters having multiple thin coatings of dielectric materials, commonly termed interference filters, have become the mechanism of choice for wavelength selection.
In general, interference filters are constructed of planar optical glass coated with dielectric materials in layers either one-half or one-quarter wavelength thick, which act by selectively blocking and/or reinforcing the transmission of specific wavelength bands through a combination of constructive and destructive interference (illustrated in Figure 7). The filters are designed to transmit a limited range of wavelengths that are reinforced through constructive interference between the transmitted and reflected light waves. Wavelengths not selected by the filter do not reinforce each other, and are removed by destructive interference or reflected away from the filter.
The dielectric materials commonly employed for interference filters are electrically nonconductive metallic salts and true metals having specific refractive index values. Salts such as zinc sulfide, sodium aluminum fluoride, and magnesium fluoride, as well as metals such as aluminum, are several of the materials of choice for designing and building filters of this type. Interference filters, much like the thin chitin structures in iridescent insects or the soap thin films discussed above, rely on the physical properties existing at the interface between two very thin dielectric materials of different refractive index to reflect, transmit, and promote interference between incident light waves. Wavelength selection is dependent upon the dielectric thickness and refractive index of the thin-layer coatings used to build the filters.
Coatings on interference filters are fabricated in units termed cavities, with each cavity containing four or five alternating layers of dielectric salts, which are separated from other cavities by a spacer layer. The number of cavities determines the overall precision of wavelength selection. Filter performance and wavelength selection can be dramatically enhanced by increasing the number of cavities, as exemplified by the current high-performance filters having up to 10-15 cavities and being able to produce bandwidths of a single wavelength. These extremely selective filters have stimulated research in the quest for new fluorophore dyes, and have dramatically boosted the search for mutation variants of the popular biologically active green fluorescent protein (GFP).
Holograms Produced by Interference
The principles and theory behind interference holograms were outlined by Dennis Gabor in the late 1940s, but he lacked the sophisticated coherent laser sources necessary to produce these pseudo three-dimensional images. Lasers appeared on the scene in 1960 and two years later, University of Michigan graduate students Juris Upatnieks and Emmet Leith were successful in producing the first hologram. Holograms are essentially photographic records that are made with two sets of coherent light waves. One set of waves is reflected onto photographic film by the object being imaged (similar to the mechanism employed in traditional photography), while the other set of waves arrives at the film without reflecting from, or passing through, the object. When the two sets of laser waves finally meet at the film plane, they produce interference patterns (fringes) that are recorded as a three-dimensional image.
In reflection holograms, both a reference and object-illuminating laser beam (usually a helium-neon laser is employed for this duty) are reflected onto a thick film from opposite sides. These beams interfere to yield light and dark areas, which interact to produce an image that appears three-dimensional. Reflection holograms are finding increasing application as identity markers on driver licenses, credit cards, and identification badges, to prevent forgery. Typically they display color images of logos, identification numbers, or specific images produced using laser light of the three primary colors. Each laser produces a unique interference pattern, and the patterns add together to form the final image. Because they are virtually impossible to copy, reflection holograms are valuable security devices.
Transmission holograms use both the reference and object-illuminating beams on the same side of the film to produce an effect that is similar to the one from reflection holograms (Figure 8). One set of laser waves is utilized to illuminate the object being imaged, which reflects the waves and scatters them in a manner similar to ordinary illumination. In addition, a polarized reference laser beam is applied in a direction that is parallel to the hologram film plane. Scattered (reflected) light waves reach the film emulsion simultaneously with the reference waves, where they interfere to create the image from fringe patterns. Transmission holograms have a number of applications, but one of the most interesting is the heads-up display utilized by pilots. In a traditional aircraft cockpit the pilot must constantly shift his attention between the windows and the control panel. With the holographic display, a three-dimensional transmission hologram of the aircraft controls is reflected onto a disk positioned close to the pilot's eye, so the pilot can view both the controls and the horizon simultaneously.
In addition to soap bubbles, beautiful iridescent insects, and the many other examples discussed above, the phenomenon of visible light interference occurs quite frequently in nature and is often utilized to man's advantage in a wide variety of applications. For example, the rainbow-like color spectrum observed on the inside of abalone shells (Figure 9) is generated by very thin layers of a hard mineral termed nacre or mother of pearl. Light reflected from successive layers undergoes interference to produce the display of color in a manner similar to that observed from multiple layers of chitin on the exoskeleton of several beetle insects. In the same fashion, silvery scales on some fish produce colored interference patterns due to multiple layers having varying thickness.
The iridescent eyes of the peacock feather are another example of interference in action (Figure 9). Tiny rod-shaped structures composed of the protein pigment melanin are arranged in an orderly fashion that produces unique interference colors when observed from different angles. In the mineral world, iridescent opal is composed of microscopic silicate spheres that are stacked in regular layers. Each sphere reflects incident light that interferes with reflected light from neighboring spheres to produce an exquisite array of color that changes as the stone is turned.
Significant and very useful applications of the interference effect are the measurements made over long distances with precision laser instrumentation. The laser systems can be used to measure very small distances over a range of many miles, a task that is accomplished by splitting the laser beam and reflecting it back from adjacent surfaces that are very close together. Upon recombining the separated laser beams, analysis of the resulting interference fringes will yield a remarkably accurate calculation of the distance between the two surfaces. This technique is also commonly utilized in the laser guidance systems designed to control the flight path of manned and unmanned airplanes, rockets, and bombs.
Interference also occurs in other media, such as sound waves (in air) and ripples or waves induced in a standing pool of water. A very concise and easy interference experiment can be performed at home using a sink full of water and two marbles. First, let the water become very still, then simultaneously drop the marbles into the water (about 10-14 inches apart) from a height of about a foot. Just as with light waves, the two marbles will induce a series of waves in the water emanating in all directions. Waves formed in the area between the points where the marbles entered the water will eventually collide. Where they collide in step, they will constructively add together to make a bigger wave, and where they collide out of step they will destructively cancel each other out.
Interference works in many ways to influence the things we see in our everyday lives. The interaction between light waves that are very close together occurs so often that the phenomenon is often neglected and taken for granted. However, from its fundamental contributions to the physics of image formation and a myriad of sensational insect disguises, to the beautiful color patterns of halos and coronas in the atmosphere, interference of light waves helps to bring color to the world around us.
Douglas B. Murphy - Department of Cell Biology and Microscope Facility, Johns Hopkins University School of Medicine, 725 N. Wolfe Street, 107 WBSB, Baltimore, Maryland 21205.
Kenneth R. Spring - Scientific Consultant, Lusby, Maryland, 20657.
Thomas J. Fellers and Michael W. Davidson - National High Magnetic Field Laboratory, 1800 East Paul Dirac Dr., The Florida State University, Tallahassee, Florida, 32310.