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勞埃德鏡（Lloyd's mirror）是愛爾蘭物理學家漢弗萊·勞埃德在1834年和1837年發表的一個經典光學實驗。在這個實驗中，從狹縫發出的單色光波，一部分掠射（即入射角接近90°）到平面鏡上，經平面鏡反射到達屏上，另一部分直接射到屏上，這兩部分光在屏上發生干涉，形成干涉條紋[1][2]。

裝置

 
圖1. 勞埃德鏡
 
圖2. 楊氏雙縫實驗中，觀察到的是單縫衍射圖樣與雙縫干涉圖樣的疊加

勞埃德鏡用於產生雙光源干涉圖樣，其圖樣與楊氏雙縫實驗中的圖樣顯著不同。

現代勞埃德鏡實驗用的光源是發散激光束，光源發出的光一部分掠到平面鏡上，經平面鏡反射到達屏上（圖1. 中的紅線），一部分直接射到屏上（圖1. 中的藍線）。反射光可看成是由虛光源發出的，與實光源發出的光相干。

在楊氏雙縫實驗中，觀察到的是單縫衍射圖樣與雙縫干涉圖樣的疊加（見圖2.），而勞埃德鏡實驗中，不採用狹縫光源，因此顯示的是沒疊加單縫衍射圖樣的雙光源干涉圖樣。

在楊氏雙縫實驗中，中心條紋是亮條紋，因為兩束相干光等光程，發生相長干涉。而在勞埃德鏡實驗中，到達屏上最下端的兩束光等光程，但卻是暗條紋，這是因為反射光在平面鏡上發生半波損失，相位有180°的躍變，因此發生相消干涉。

應用

干涉光刻

勞埃德鏡最常見的應用是紫外光刻和圖案成形。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.[3]

勞埃德鏡光刻的典型應用包括製造用於表面編碼器的衍射光柵[4] 和製作醫學植入物的表面圖案，以提高生物功能[5]。

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.[6]

光學測量

勞埃德鏡的輸出通過CCD光電二極管陣列分析，可產生傅里葉變換波長計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.[7]

射電天文學

主條目：Sea interferometry
 
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.[8][9]

水聲學

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.[10]

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.[11]

See also

References

  1. ^ Fresnel's and Lloyd's Mirrors
  2. ^ Interference by the Division of the Wavefront (PDF). University of Arkansas. [20 May 2012]. 
  3. ^ Application Note 49: Theory of Lloyd's Mirror Interferometer (PDF). Newport Corporation. [16 February 2014]. 
  4. ^ Li, X.; Shimizu, Y.; Ito, S.; Gao, W.; Zeng, L. Fabrication of diffraction gratings for surface encoders by using a Lloyd's mirror interferometer with a 405 nm laser diode. International Symposium on Precision Engineering Measurement and Instrumentation. 2013: 87594Q–87594Q. 
  5. ^ Domanski, M. 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. 2010: 3–7. 
  6. ^ Hochberg, E. B.; Chrien, N. L. Lloyd's mirror for MTF testing of MIRS CCD (PDF). Jet Propulsion Laboratory. [16 February 2014]. 
  7. ^ Kielkopf, J.; Portaro, L. Lloyd's mirror as a laser wavemeter. Applied Optics. 1992, 31 (33): 7083–7088. Bibcode:1992ApOpt..31.7083K. doi:10.1364/AO.31.007083. 
  8. ^ Bolton, J. G.; Stanley, G. J.; Slee, O. B. Positions of Three Discrete Sources of Galactic Radio-Frequency Radiation. Nature. 1949, 164: 101–102. Bibcode:1949Natur.164..101B. doi:10.1038/164101b0. 
  9. ^ Edwards, Philip. Interferometry (PDF). National Astronomical Observatory of Japan (NAOJ). [11 February 2014]. 
  10. ^ doi:10.1121/1.3182842
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  11. ^ Gerstein, Edmund. Manatees, Bioacoustics and Boats. American Scientist. 2002, 90 (2): 154–163 [13 February 2014]. Bibcode:2002AmSci..90..154G. doi:10.1511/2002.2.154. 

Further reading

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