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  • 2020–2021 BCSC Basic and Clinical Science Course™

    Go to Academy Store Learn more and Purchase.

    3 Clinical Optics

    Chapter 2: Physical Optics

    Phenomena of Light

    Coherence and Interference

    Fundamentals

    Coherence describes the ability of light to produce interference phenomena. Interference reveals the correlation between light waves and occurs when 2 light waves are brought together (superposition of waves), reinforcing each other and resulting in a wave of greater amplitude (ie, constructive or additive interference), or subtracting from each other and resulting in a wave of lower amplitude (ie, destructive or subtractive interference), depending on their relative phase (Fig 2-4). Figures 2-5 and 2-6 illustrate the concepts of coherence and interference of light.

    Figure 2-4 Superposition of waves of identical frequency and amplitude produces stable interference patterns. A, Waves overlap in phase—peaks coincide with peaks and troughs with troughs—producing a resultant wave of twice the amplitude. B, Waves overlap out of phase—the peak of one wave coincides with the trough of the other—and the waves cancel. C, Waves partially overlap—neither completely in nor out of phase—producing a wave of intermediate amplitude (between zero and twice the amplitude).

    (Illustration developed by Edmond H. Thall, MD, and redrawn by C. H. Wooley.)

    Figure 2-5 Pictorial explanation of coherence. A white light source produces incoherent light, emitting wavefronts of diverse wavelengths and arrangements. If incoherent light is passed through a pinhole aperture, spatial coherence is improved; that is, the resulting wavefronts are more regularly arranged. If spatially coherent light is passed through a narrow-band filter, selecting a narrow band of wavelengths, temporal coherence is improved; that is, the resulting wavefronts also have the same wavelength.

    (Illustration developed by Kristina Irsch, PhD.)

    Figure 2-6 Pictorial explanation of interference. Coherent light strikes a double slit or 2 pinhole apertures from which new wavefronts emanate, which are then superimposed on a screen, creating an interference pattern of a series of bright and dark fringes. (A) represents constructive interference. (B) indicates destructive interference.

    (Illustration by Jonathan Clark, modified by Kristina Irsch, PhD.)

    In Figure 2-5, a white light source produces incoherent light, emitting wavefronts of diverse wavelengths and arrangements. However, if incoherent light is passed through a pinhole aperture, spatial coherence of the light is improved, that is, the resulting wavefronts are more regularly arranged. If spatially coherent light is passed through a narrow-band filter, selecting a narrow band of wavelengths (we will discuss later how these filters work), temporal coherence of the light is improved, that is, the resulting wavefronts have the same wavelength, thereby making the light monochromatic. Laser light is highly coherent. However, as shown here, coherent light can be produced even without a laser, but at the expense of discarding a large amount of the light.

    Figure 2-6 illustrates the basic concept of Young’s double-slit experiment, discussed earlier. If coherent light strikes a double slit or 2 pinhole apertures, new wavefronts emanate, which then are superimposed on a screen. Note that the curved lines represent the crests of the waves at a particular instant. Where the crests coincide (eg, at A), a maximum of intensity is produced (constructive interference); where the crest of one wave coincides with the trough of the other wave (B) intensity is minimized (destructive interference). An interference pattern of a series of bright and dark fringes is observed on the screen, representing areas of constructive and destructive interference respectively.

    The concepts of coherence length and coherence time, which are essential in the understanding of the basic principle of optical coherence tomography (OCT; see Chapter 8), can be best understood in the example of interferometry. In interferometry, as illustrated in Figure 2-7, light is split into 2 beams, and the beam backscattered from a sample is then compared (superimposed) with the beam that has traveled a known time from a reference mirror. Interference between the 2 light beams occurs only when the optical distances traveled by the light in both the sample and reference paths (arms) match to within the coherence length of the light. In other words, coherence length is the maximum path difference for good visibility of interference fringes. Likewise, coherence time is the maximum transit time difference for which interference fringes are still observable.

    Figure 2-7 Basic concept of interferometry. Light is split into 2 beams, and the beam that has traveled an unknown time and distance (d2) from a sample is compared (interfered) with the beam that has traveled a known time and distance (d1) from a reference mirror. An interference pattern is detected only when the optical distances traveled by the light in both the sample and reference paths match to within the coherence length of the light (∆L).

    (Illustration developed by Kristina Irsch, PhD.)

    Both coherence time and length are inversely proportional to the spectral bandwidth of the light source (ie, the frequency or wavelength range over which sources emit light). Note that a source with a narrow spectral bandwidth (light of nearly a single wavelength or wholly monochromatic; eg, laser light) has a high temporal coherence, whereas a source with a broad bandwidth (light of multiple wavelengths; eg, white light) has a low temporal coherence (Fig 2-8).

    Hence, when a narrow-bandwidth source is used to perform interferometry (eg, conventional laser interferometry), interference fringes will occur over a long range of path length differences between the 2 beams (Video 2-1). In low-coherence interferometry—using a broadband light source—on the other hand, interference occurs only when the time traveled by the light in the reference and sample arms is nearly equal, within the coherence length of the source. Low-coherence interferometry therefore enables greater sensitivity in separating out reflections, especially when from a sample with multiple, closely spaced reflecting surfaces (Video 2-2).

    VIDEO 2-1 Concept of conventional (laser) interferometry.

    Animation developed by Kristina Irsch, PhD.

    Access all Section 3 videos at www.aao.org/bcscvideo_section03.

    Figure 2-8 Inverse relationship between spectral bandwidth of a light source and its coherence length. A source with a broad bandwidth (light of multiple wavelengths; eg, white light) has a short coherence length (upper panel), whereas a source with a narrow spectral bandwidth (light of nearly a single wavelength or wholly monochromatic; eg, laser light) has a long coherence length (lower panel).

    (Illustration developed by Kristina Irsch, PhD.)

    VIDEO 2-2 Concept of low-coherence interferometry.

    Animation developed by Kristina Irsch, PhD.

    Applications and clinical relevance

    One familiar application of interference in ophthalmic optics is the use of antireflection coatings on spectacle lenses (Fig 2-9). To decrease unwanted reflections from the surfaces of spectacle lenses, a thin film of a transparent material with a refractive index that is different from the lens is deposited on the lens surface, so that some light will be reflected from the back surface and an equal amount will be reflected at the front surface. These reflected waves—if the thickness of this deposited film is chosen such that it is one-quarter of a specified wavelength of light—will be one-half wavelength out of phase, resulting in complete destructive interference and therefore eliminating the reflections.

    The use of narrow-band interference filters, such as in fluorescein and indocyanine green angiography, as well as autofluorescence imaging (discussed in Chapter 8), is another application of interference in ophthalmology. To produce very sharp boundaries and separate excitation from fluorescent light, a thin film of a transparent material is deposited on a glass substrate, similar to the previous example but this time with a thickness that is a multiple of the desired wavelength and surfaces that are partially reflecting. Multiple reflections of light with the desired wavelength, from the front and back surfaces of this deposited film, will exit in phase and reinforce each other, whereas light of other wavelengths will exit out of phase and cancel each other (Fig 2-10). Modern narrow-band filters exist that consist of several thin layers of transparent materials allowing only light of wavelengths within a few nanometers to get transmitted while blocking everything else.

    Figure 2-9 Antireflection coating on a spectacle lens. The thickness of the thin film deposition is chosen such that it is one-quarter of a specified wavelength of light, which results in complete destructive interference and therefore eliminates the reflections.

    (Redrawn by C. H. Wooley.)

    Figure 2-10 Interference filter. Multiple reflections from the front and back surfaces of the deposited film (multiple of a specified light wavelength thick) exit in phase and reinforce each other, whereas light of other wavelengths exits out of phase and cancels each other.

    (Redrawn by C. H. Wooley.)

    Excerpted from BCSC 2020-2021 series : Section 3 - Clinical Optics. For more information and to purchase the entire series, please visit https://www.aao.org/bcsc.

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