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劳埃德镜（Lloyd's mirror）是爱尔兰物理学家汉弗莱·劳埃德在1834年和1837年发表的一个经典光学实验。在这个实验中，从狭缝发出的单色光波，一部分掠射（即入射角接近90°）到平面镜上，经平面镜反射到达屏上，另一部分直接射到屏上，这两部分光在屏上发生干涉，形成干涉条纹[1][2]。

装置

图1. 劳埃德镜
图2. 杨氏双缝实验中，观察到的是单缝衍射图样与双缝干涉图样的叠加

劳埃德镜用于产生双光源干涉图样，其图样与楊氏雙縫實驗中的图样显著不同。

现代劳埃德镜实验用的光源是发散激光束，光源发出的光一部分掠到平面镜上，经平面镜反射到达屏上（图1. 中的红线），一部分直接射到屏上（图1. 中的蓝线）。反射光可看成是由虚光源发出的，与实光源发出的光相干。

在杨氏双缝实验中，观察到的是单缝衍射图样与双缝干涉图样的叠加（见图2.），而劳埃德镜实验中，不采用狭缝光源，因此显示的是没叠加单缝衍射图样的双光源干涉图样。

在杨氏双缝实验中，中心条纹是亮条纹，因为两束相干光等光程，发生相长干涉。而在劳埃德镜实验中，到达屏上最下端的两束光等光程，但却是暗条纹，这是因为反射光在平面镜上发生半波损失，相位有180°的跃变，因此发生相消干涉。

应用

干涉光刻

劳埃德镜最常见的应用是紫外光刻和图案成形。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]

劳埃德镜光刻的典型应用包括制造用于表面编码器的衍射光栅[4] 和制作医学植入物的表面图案，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]

光学测量

劳埃德镜的输出通过CCD光电二极管阵列分析，可产生傅里叶变换波长计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]

射电天文学

主条目：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]

水声学

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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