Lloyd's mirror

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Lloyd's mirror is an optics experiment that was first described in 1834 by Humphrey Lloyd in the Transactions of the Royal Irish Academy . [1] Its original goal was to provide further evidence for the wave nature of light, beyond those provided by Thomas Young and Augustin-Jean Fresnel. In the experiment, light from a monochromatic slit source reflects from a glass surface at a small angle and appears to come from a virtual source as a result. The reflected light interferes with the direct light from the source, forming interference fringes. [2] [3] It is the optical wave analogue to a sea interferometer. [4]

Contents

Setup

Figure 1. Lloyd's mirror Zerkalo Lloida.png
Figure 1. Lloyd's mirror
Figure 2. Young's two-slit experiment displays a single-slit diffraction pattern on top of the two-slit interference fringes. Single slit and double slit3.jpg
Figure 2. Young's two-slit experiment displays a single-slit diffraction pattern on top of the two-slit interference fringes.

Lloyd’s Mirror is used to produce two-source interference patterns that have important differences from the interference patterns seen in Young's experiment.

In a modern implementation of Lloyd's mirror, a diverging laser beam strikes a front-surface mirror at a grazing angle, so that some of the light travels directly to the screen (blue lines in Fig. 1), and some of the light reflects off the mirror to the screen (red lines). The reflected light forms a virtual second source that interferes with the direct light.

In Young's experiment, the individual slits display a diffraction pattern on top of which is overlaid interference fringes from the two slits (Fig. 2). In contrast, the Lloyd's mirror experiment does not use slits and displays two-source interference without the complications of an overlaid single-slit diffraction pattern.

In Young's experiment, the central fringe representing equal path length is bright because of constructive interference. In contrast, in Lloyd's mirror, the fringe nearest the mirror representing equal path length is dark rather than bright. This is because the light reflecting off the mirror undergoes a 180° phase shift, and so causes destructive interference when the path lengths are equal or when they differ by an integer number of wavelengths.

Applications

Interference lithography

The most common application of Lloyd's mirror is in UV photolithography and nanopatterning. Lloyd's mirror has important advantages over double-slit interferometers.

If one wishes to create a series of closely spaced interference fringes using a double-slit interferometer, the spacing d between the slits must be increased. Increasing the slit spacing, however, requires that the input beam be broadened to cover both slits. This results in a large loss of power. In contrast, increasing d in the Lloyd's mirror technique does not result in power loss, since the second "slit" is just the reflected virtual image of the source. Hence, Lloyd's mirror enables the generation of finely detailed interference patterns of sufficient brightness for applications such as photolithography. [5]

Typical uses of Lloyd's mirror photolithography would include fabrication of diffraction gratings for surface encoders [6] and patterning the surfaces of medical implants for improved biofunctionality. [7]

Test pattern generation

High visibility cos2-modulated fringes of constant spatial frequency can be generated in a Lloyd's mirror arrangement using parallel collimated monochromatic light rather than a point or slit source. The uniform fringes generated by this arrangement can be used to measure the modulation transfer functions of optical detectors such as CCD arrays to characterize their performance as a function of spatial frequency, wavelength, intensity, and so forth. [8]

Optical measurement

The output of a Lloyd's mirror was analyzed with a CCD photodiode array to produce a compact, broad range, high accuracy Fourier transform wavemeter that could be used to analyze the spectral output of pulsed lasers. [9]

Radio astronomy

Figure 3. Determining the position of galactic radio sources using Lloyd's mirror Locating galactic radio-frequency sources using Lloyd's mirror.svg
Figure 3. Determining the position of galactic radio sources using Lloyd's mirror

In the late 1940s and early 1950s, CSIRO scientists used a technique based on Lloyd's mirror to make accurate measurements of the position of various galactic radio sources from coastal sites in New Zealand and Australia. As illustrated in Fig. 3, the technique was to observe the sources combining direct and reflected rays from high cliffs overlooking the sea. After correcting for atmospheric refraction, these observations allowed the paths of the sources above the horizon to be plotted and their celestial coordinates to be determined. [10] [11]

Underwater acoustics

An acoustic source just below the water surface generates constructive and destructive interference between the direct path and reflected paths. This can have a major impact on sonar operations. [12]

The Lloyd mirror effect has been implicated as having an important role in explaining why marine animals such as manatees and whales have been repeatedly hit by boats and ships. Interference due to Lloyd's mirror results in low frequency propeller sounds not being discernible near the surface, where most accidents occur. This is because at the surface, sound reflections are nearly 180 degrees out of phase with the incident waves. Combined with spreading and acoustic shadowing effects, the result is that the marine animal is unable to hear an approaching vessel before it has been run over or entrapped by the hydrodynamic forces of the vessel's passage. [13]

See also

Related Research Articles

<span class="mw-page-title-main">Double-slit experiment</span> Physics experiment, showing light and matter can be modelled by both waves and particles

In modern physics, the double-slit experiment demonstrates that light and matter can satisfy the seemingly incongruous classical definitions for both waves and particles. This ambiguity is considered evidence for the fundamentally probabilistic nature of quantum mechanics. This type of experiment was first performed by Thomas Young in 1801, as a demonstration of the wave behavior of visible light. In 1927, Davisson and Germer and, independently George Paget Thomson and his research student Alexander Reid demonstrated that electrons show the same behavior, which was later extended to atoms and molecules. Thomas Young's experiment with light was part of classical physics long before the development of quantum mechanics and the concept of wave–particle duality. He believed it demonstrated that Christiaan Huygens' wave theory of light was correct, and his experiment is sometimes referred to as Young's experiment or Young's slits.

<span class="mw-page-title-main">Wave interference</span> Phenomenon resulting from the superposition of two waves

In physics, interference is a phenomenon in which two coherent waves are combined by adding their intensities or displacements with due consideration for their phase difference. The resultant wave may have greater intensity or lower amplitude if the two waves are in phase or out of phase, respectively. Interference effects can be observed with all types of waves, for example, light, radio, acoustic, surface water waves, gravity waves, or matter waves as well as in loudspeakers as electrical waves.

Wave-particle duality is the concept in quantum mechanics that quantum entities exhibit particle or wave properties according to the experimental circumstances. It expresses the inability of the classical concepts such as particle or wave to fully describe the behavior of quantum objects. During the 19th and early 20th centuries, light was found to behave as a wave then later discovered to have a particulate behavior, whereas electrons behaved like particles in early experiments then later discovered to have wavelike behavior. The concept of duality arose to name these seeming contradictions.

<span class="mw-page-title-main">Diffraction grating</span> Optical component which splits light into several beams

In optics, a diffraction grating is an optical grating with a periodic structure that diffracts light, or another type of electromagnetic radiation, into several beams traveling in different directions. The emerging coloration is a form of structural coloration. The directions or diffraction angles of these beams depend on the wave (light) incident angle to the diffraction grating, the spacing or periodic distance between adjacent diffracting elements on the grating, and the wavelength of the incident light. The grating acts as a dispersive element. Because of this, diffraction gratings are commonly used in monochromators and spectrometers, but other applications are also possible such as optical encoders for high-precision motion control and wavefront measurement.

<span class="mw-page-title-main">Interferometry</span> Measurement method using interference of waves

Interferometry is a technique which uses the interference of superimposed waves to extract information. Interferometry typically uses electromagnetic waves and is an important investigative technique in the fields of astronomy, fiber optics, engineering metrology, optical metrology, oceanography, seismology, spectroscopy, quantum mechanics, nuclear and particle physics, plasma physics, biomolecular interactions, surface profiling, microfluidics, mechanical stress/strain measurement, velocimetry, optometry, and making holograms.

Coherence expresses the potential for two waves to interfere. Two monochromatic beams from a single source always interfere. Wave sources are not strictly monochromatic: they may be partly coherent. Beams from different sources are mutually incoherent.

<span class="mw-page-title-main">Mach–Zehnder interferometer</span> Device to determine relative phase shift

The Mach–Zehnder interferometer is a device used to determine the relative phase shift variations between two collimated beams derived by splitting light from a single source. The interferometer has been used, among other things, to measure phase shifts between the two beams caused by a sample or a change in length of one of the paths. The apparatus is named after the physicists Ludwig Mach and Ludwig Zehnder; Zehnder's proposal in an 1891 article was refined by Mach in an 1892 article. Mach–Zehnder interferometry with electrons as well as with light has been demonstrated. The versatility of the Mach–Zehnder configuration has led to its being used in a range of research topics efforts especially in fundamental quantum mechanics.

<span class="mw-page-title-main">Michelson interferometer</span> Common configuration for optical interferometry

The Michelson interferometer is a common configuration for optical interferometry and was invented by the 19/20th-century American physicist Albert Abraham Michelson. Using a beam splitter, a light source is split into two arms. Each of those light beams is reflected back toward the beamsplitter which then combines their amplitudes using the superposition principle. The resulting interference pattern that is not directed back toward the source is typically directed to some type of photoelectric detector or camera. For different applications of the interferometer, the two light paths can be with different lengths or incorporate optical elements or even materials under test.

<span class="mw-page-title-main">Sagnac effect</span> Relativistic effect due to rotation

The Sagnac effect, also called Sagnac interference, named after French physicist Georges Sagnac, is a phenomenon encountered in interferometry that is elicited by rotation. The Sagnac effect manifests itself in a setup called a ring interferometer or Sagnac interferometer. A beam of light is split and the two beams are made to follow the same path but in opposite directions. On return to the point of entry the two light beams are allowed to exit the ring and undergo interference. The relative phases of the two exiting beams, and thus the position of the interference fringes, are shifted according to the angular velocity of the apparatus. In other words, when the interferometer is at rest with respect to a nonrotating frame, the light takes the same amount of time to traverse the ring in either direction. However, when the interferometer system is spun, one beam of light has a longer path to travel than the other in order to complete one circuit of the mechanical frame, and so takes longer, resulting in a phase difference between the two beams. Georges Sagnac set up this experiment in 1913 in an attempt to prove the existence of the aether that Einstein's theory of special relativity makes superfluous.

An atom interferometer uses the wave-like nature of atoms in order to produce interference. In atom interferometers, the roles of matter and light are reversed compared to the laser based interferometers, i.e. the beam splitter and mirrors are lasers while the source emits matter waves rather than light. Atom interferometers measure the difference in phase between atomic matter waves along different paths. Matter waves are controlled an manipulated using systems of lasers. Atom interferometers have been used in tests of fundamental physics, including measurements of the gravitational constant, the fine-structure constant, and universality of free fall. Applied uses of atom interferometers include accelerometers, rotation sensors, and gravity gradiometers.

A delayed-choice quantum eraser experiment, first performed by Yoon-Ho Kim, R. Yu, S. P. Kulik, Y. H. Shih and Marlan O. Scully, and reported in early 1998, is an elaboration on the quantum eraser experiment that incorporates concepts considered in John Archibald Wheeler's delayed-choice experiment. The experiment was designed to investigate peculiar consequences of the well-known double-slit experiment in quantum mechanics, as well as the consequences of quantum entanglement.

Interference lithography is a technique for patterning regular arrays of fine features, without the use of complex optical systems or photomasks.

<span class="mw-page-title-main">Fizeau interferometer</span>

A Fizeau interferometer is an interferometric arrangement whereby two reflecting surfaces are placed facing each other. As seen in Fig 1, the rear-surface reflected light from the transparent first reflector is combined with front-surface reflected light from the second reflector to form interference fringes.

The N-slit interferometer is an extension of the double-slit interferometer also known as Young's double-slit interferometer. One of the first known uses of N-slit arrays in optics was illustrated by Newton. In the first part of the twentieth century, Michelson described various cases of N-slit diffraction.

<span class="mw-page-title-main">White light scanner</span>

A white light scanner (WLS) is a device for performing surface height measurements of an object using coherence scanning interferometry (CSI) with spectrally-broadband, "white light" illumination. Different configurations of scanning interferometer may be used to measure macroscopic objects with surface profiles measuring in the centimeter range, to microscopic objects with surface profiles measuring in the micrometer range. For large-scale non-interferometric measurement systems, see structured-light 3D scanner.

Sea interferometry, also known as sea-cliff interferometry, is a form of radio astronomy that uses radio waves reflected off the sea to produce an interference pattern. It is the radio wave analogue to Lloyd's mirror. The technique was invented and exploited in Australia between 1945 and 1948.

Young's interference experiment, also called Young's double-slit interferometer, was the original version of the modern double-slit experiment, performed at the beginning of the nineteenth century by Thomas Young. This experiment played a major role in the general acceptance of the wave theory of light. In Young's own judgement, this was the most important of his many achievements.

A common-path interferometer is a class of interferometers in which the reference beam and sample beams travel along the same path. Examples include the Sagnac interferometer, Zernike phase-contrast interferometer, and the point diffraction interferometer. A common-path interferometer is generally more robust to environmental vibrations than a "double-path interferometer" such as the Michelson interferometer or the Mach–Zehnder interferometer. Although travelling along the same path, the reference and sample beams may travel along opposite directions, or they may travel along the same direction but with the same or different polarization.

<span class="mw-page-title-main">White light interferometry</span> Measurement technique

As described here, white light interferometry is a non-contact optical method for surface height measurement on 3D structures with surface profiles varying between tens of nanometers and a few centimeters. It is often used as an alternative name for coherence scanning interferometry in the context of areal surface topography instrumentation that relies on spectrally-broadband, visible-wavelength light.

References

  1. Lloyd, Humphrey (1831). "On a New Case of Interference of the Rays of Light". The Transactions of the Royal Irish Academy. 17. Royal Irish Academy: 171–177. ISSN   0790-8113. JSTOR   30078788 . Retrieved 2021-05-29.
  2. Fresnel's and Lloyd's Mirrors
  3. "Interference by the Division of the Wavefront" (PDF). University of Arkansas. Archived from the original (PDF) on 7 September 2012. Retrieved 20 May 2012.
  4. Bolton, J. G.; Slee, O. B. (1953). "Galactic Radiation at Radio Frequencies V. The Sea Interferometer". Australian Journal of Physics. 6: 420–433. Bibcode:1953AuJPh...6..420B. doi: 10.1071/PH530420 .
  5. "Application Note 49: Theory of Lloyd's Mirror Interferometer" (PDF). Newport Corporation. Retrieved 16 February 2014.
  6. Li, X.; Shimizu, Y.; Ito, S.; Gao, W.; Zeng, L. (2013). "Fabrication of diffraction gratings for surface encoders by using a Lloyd's mirror interferometer with a 405 nm laser diode". In Lin, Jie (ed.). Eighth International Symposium on Precision Engineering Measurement and Instrumentation. Vol. 8759. pp. 87594Q. Bibcode:2013SPIE.8759E..4QL. doi:10.1117/12.2014467. S2CID   136994909.
  7. Domanski, M. (2010). "Novel approach to produce nanopatterned titanium implants by combining nanoimprint lithography and reactive ion etching" (PDF). 14th International Conference on Miniaturized Systems for Chemistry and Life Sciences. pp. 3–7. ISBN   978-0-9798064-3-8.
  8. Hochberg, E. B.; Chrien, N. L. "Lloyd's mirror for MTF testing of MIRS CCD" (PDF). Jet Propulsion Laboratory. Archived from the original (PDF) on 22 February 2014. Retrieved 16 February 2014.
  9. Kielkopf, J.; Portaro, L. (1992). "Lloyd's mirror as a laser wavemeter". Applied Optics. 31 (33): 7083–7088. Bibcode:1992ApOpt..31.7083K. doi:10.1364/AO.31.007083. PMID   20802569.
  10. Bolton, J. G.; Stanley, G. J.; Slee, O. B. (1949). "Positions of Three Discrete Sources of Galactic Radio-Frequency Radiation". Nature. 164 (4159): 101–102. Bibcode:1949Natur.164..101B. doi:10.1038/164101b0. S2CID   4073162.
  11. Edwards, Philip. "Interferometry" (PDF). National Astronomical Observatory of Japan (NAOJ). Archived from the original (PDF) on 21 February 2014. Retrieved 11 February 2014.
  12. Carey, W. M. (2009). "Lloyd's Mirror—Image Interference Effects". Acoustics Today. 5 (2): 14. doi:10.1121/1.3182842.
  13. Gerstein, Edmund (2002). "Manatees, Bioacoustics and Boats". American Scientist. 90 (2): 154–163. Bibcode:2002AmSci..90..154G. doi:10.1511/2002.2.154. S2CID   121310274 . Retrieved 13 February 2014.

Further reading