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| title | chunk | source | category | tags | date_saved | instance |
|---|---|---|---|---|---|---|
| Interferometry | 7/10 | https://en.wikipedia.org/wiki/Interferometry | reference | science, encyclopedia | 2026-05-05T09:43:15.174742+00:00 | kb-cron |
Optical heterodyne detection is an essential technique used in high-accuracy measurements of the frequencies of optical sources, as well as in the stabilization of their frequencies. Until relatively few years ago, lengthy frequency chains were needed to connect the microwave frequency of a cesium or other atomic time source to optical frequencies. At each step of the chain, a frequency multiplier would be used to produce a harmonic of the frequency of that step, which would be compared by heterodyne detection with the next step (the output of a microwave source, far infrared laser, infrared laser, or visible laser). Each measurement of a single spectral line required several years of effort in the construction of a custom frequency chain. Currently, optical frequency combs have provided a much simpler method of measuring optical frequencies. If a mode-locked laser is modulated to form a train of pulses, its spectrum is seen to consist of the carrier frequency surrounded by a closely spaced comb of optical sideband frequencies with a spacing equal to the pulse repetition frequency (Fig. 16). The pulse repetition frequency is locked to that of the frequency standard, and the frequencies of the comb elements at the red end of the spectrum are doubled and heterodyned with the frequencies of the comb elements at the blue end of the spectrum, thus allowing the comb to serve as its own reference. In this manner, locking of the frequency comb output to an atomic standard can be performed in a single step. To measure an unknown frequency, the frequency comb output is dispersed into a spectrum. The unknown frequency is overlapped with the appropriate spectral segment of the comb and the frequency of the resultant heterodyne beats is measured. One of the most common industrial applications of optical interferometry is as a versatile measurement tool for the high precision examination of surface topography. Popular interferometric measurement techniques include phase shifting interferometry (PSI), and vertical scanning interferometry (VSI), also known as scanning white light interferometry (SWLI) or by the ISO term coherence scanning interferometry (CSI), CSI exploits coherence to extend the range of capabilities for interference microscopy. These techniques are widely used in micro-electronic and micro-optic fabrication. PSI uses monochromatic light and provides very precise measurements; however it is only usable for surfaces that are very smooth. CSI often uses white light and high numerical apertures, and rather than looking at the phase of the fringes, as does PSI, looks for best position of maximum fringe contrast or some other feature of the overall fringe pattern. In its simplest form, CSI provides less precise measurements than PSI but can be used on rough surfaces. Some configurations of CSI, variously known as Enhanced VSI (EVSI), high-resolution SWLI or Frequency Domain Analysis (FDA), use coherence effects in combination with interference phase to enhance precision.
Phase Shifting Interferometry addresses several issues associated with the classical analysis of static interferograms. Classically, one measures the positions of the fringe centers. As seen in Fig. 13, fringe deviations from straightness and equal spacing provide a measure of the aberration. Errors in determining the location of the fringe centers provide the inherent limit to precision of the classical analysis, and any intensity variations across the interferogram will also introduce error. There is a trade-off between precision and number of data points: closely spaced fringes provide many data points of low precision, while widely spaced fringes provide a low number of high precision data points. Since fringe center data is all that one uses in the classical analysis, all of the other information that might theoretically be obtained by detailed analysis of the intensity variations in an interferogram is thrown away. Finally, with static interferograms, additional information is needed to determine the polarity of the wavefront: In Fig. 13, one can see that the tested surface on the right deviates from flatness, but one cannot tell from this single image whether this deviation from flatness is concave or convex. Traditionally, this information would be obtained using non-automated means, such as by observing the direction that the fringes move when the reference surface is pushed. Phase shifting interferometry overcomes these limitations by not relying on finding fringe centers, but rather by collecting intensity data from every point of the CCD image sensor. As seen in Fig. 17, multiple interferograms (at least three) are analyzed with the reference optical surface shifted by a precise fraction of a wavelength between each exposure using a piezoelectric transducer (PZT). Alternatively, precise phase shifts can be introduced by modulating the laser frequency. The captured images are processed by a computer to calculate the optical wavefront errors. The precision and reproducibility of PSI is far greater than possible in static interferogram analysis, with measurement repeatabilities of a hundredth of a wavelength being routine. Phase shifting technology has been adapted to a variety of interferometer types such as Twyman–Green, Mach–Zehnder, laser Fizeau, and even common path configurations such as point diffraction and lateral shearing interferometers. More generally, phase shifting techniques can be adapted to almost any system that uses fringes for measurement, such as holographic and speckle interferometry.