Measurement Techniques, Vol. 53, No. 3, 2010

PRINCIPLES FOR THE DESIGN OF MODERN INTERFEROMETERS

N. G. Vlasov*

UDC 531.7

Principles for the development of modern interferometers are discussed. Key words: interferometry, lasers, coherence, types of interferometers. Interferometry has been one of the most intensively developed areas in physical and applied optics over the course of the last several decades. In addition to classical methods, methods of holographic and speckle- and low-coherence interferometry, enhanced by the capabilities of digital optics methods of obtaining and processing interferometric patterns, have been proposed and developed. Simultaneous with the development of new physical principles of interferometry, the circuit engineering of interference measurements has been developed and transformed. The present article will discuss the modern state and trends for further development of the circuit engineering underlying interference measurements. Let us first consider and then attempt to systematize the basic principles in the construction of modern interferometers. The first of these principles is that several functions must be implemented by one and the same element of the interferometer. Thus, in speckle photography witth carrier spatial frequency [1, 2] the surface of the diffusely reflecting object that is the focus of study simultaneously implements the function of semi-transparent mirror that separates the illuminating radiation and guides it to the interferometer’s two arms. At the same time, the objective, which focuses the image of the object in the recording medium, combines the radiation that has traversed both of the interferometer’s arms. In contrast, in speckle photography with bilateral illumination of the object [3], the object’s surface coincides with both of the interferometer’s arms. Finally, in speckle interferometry [4] both of these optical circuits [1–3], which are used to increase sensitivity, are combined into a single circuit and the object’s surfaces functions as a special spatial frequency heterodyne. The next technique, which is also encountered quite often, involves the use of holographic (diffraction) optics. Compensation of the aberrations of optical elements that are components of the interferometer by means of a hologram is often discussed in the literature. Note, too, that in addition, holographic engineering makes it possible to write several optical elements in one and the same area of the recording medium. Thus, a shift interferometer that is written entirely in a single hologram was considered in the first study on the subject of diffraction optics [5]. One possible approach in the development of interferometers involves the use of the analogy between time and space frequencies. For example, an analogy between classical, holographic, and speckle interferometers and laser Doppler anemometers was drawn in [6]. It turns out that, in principle, the circuits of interferometers and those of anemometers are practically identical and each new type of device belonging to one class may be considered a prototype in the development of devices belonging to the other class. Modern microcircuitry, particularly CCD arrays, provide broad opportunities for the creation of new types of interferometers. Their appearance has made it possible to avoid the use of photographic recording media and photographic processes. CCD arrays and the phase step method has become basic for the development of digital optical interferometers [7, 8]. The optical flow charts of nearly all classical interferometers were developed even before the current century. At the same time, only thermal radiation has been used as the sources of the illuminating radiation, with the coherence length of this *

Deceased.

Stankin State Technical University, Moscow, Russia. Translated from Izmeritel’naya Tekhnika, No. 3, pp. 27–29, March, 2010. Original article submitted December 14, 2009. 0543-1972/10/5303-0277 ©2010 Springer Science+Business Media, Inc.

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Fig. 1. Optical flow chart of interferometer designed for motion measurements: 1) laser; 2) prism cube; 3) semitransparent coating; 4) mirror; 5) photodetector.

Fig. 2. Optical flow chart of digital optical speckle interferometer: 1) laser; 2) prism cube; 3) semitransparent coating; 4) study object; 5) CCD array; 6) lens; 7) diaphragm.

a

b

Fig. 3. Flow chart for producing an optical diffraction element (a) and interference distance gauge (b): 1) laser beam; 2) micro-objective; 3) point; 4, 9) spherical waves; 5) photographic plate; 6, 7) directions of propagation of reference wave field; 8) hologram; 9) spherical wave; 10) study object; 11, 13) directions of propagation of spherical waves; 12) photographic plate.

radiation even artificially increased through the use of light filters up to several dozen micrometers. The domain of spatial coherence, both transverse and longitudinal, is also significantly limited for such sources. Therefore, equalization of the lengths of the optical beams in both arms of the interferometer to render their difference equal to zero is a mandatory condition for the formation and observation of the interference pattern [9–14]. This feature has significantly complicated the design of interferometers as well as their assembly, adjustment, and operation. The situation changed slightly in the first decade after the appearance of lasers. Lasers functioning in the single-mode regime, a feature that is necessary for interference measure278

ments, were quite cumbersome and expensive, and the physical principles underlying the construction of interferometers and their optical circuits were not reviewed. In the course of last several decades, small-size and inexpensive lasers have been developed and offered for sale. The radiation emitted by these lasers possess coherent properties sufficient to avoid the need for equalization of the optical paths in the different arms of an interferometer. Thus, the HL6512MG semiconductor laser diode from the firm of Optnext has a coherence length of several meters. We will consider the new capabilities which developers of interferometers now have available below, using as an example the optical circuts presented in Figs. 1 and 2. The flow chart of an interferometer intended for use in motion measurement is shown in Fig. 1. It is similar to a Michaelson interferometer, two of whose arms are combined into a single arm. The beam from laser 1 is directed at a beam splitter, or prism cube 2, on the right face of which a semitransparent coating 3 has been applied. The beams from the laser that have been reflected by the coating 3 and the moving mirror 4 of the prism cube 2 are shifted and directed at the photodetector 5. As in a Michaelson interferometer, the movement of the mirror 4 is determined from the number of interference bands that are recorded by photodetector 5; the latter is linked to a computer for automatic processing of the experimental data. The flow chart may be considered a starting chart, based on which interferometers to be used for other purposes may be created. Thus, if the beam from laser 1 is enlarged by a collimator and if photodetector 5 is replaced by the CCD array of the digital device, the moving mirror 4 may be replaced by a fixed mirror placed in the interferometer for the purpose of controlling the planeness of its surface by means of a comparison with the reference surface 3. The optical part shown in Fig. 2 of a digital speckle interferometer designed for the study of mechanical, thermal, and other types of deformations of a diffusely reflecting object 4 is slightly more complicated than the previous flow chart. Collimated radiation from the laser 1 is directed at the cubic prism 2 described above with an additional semiconductor coating 3. The image of the study object 4 produced by the lens 6 is focused on the surface of the CCD array 5. The reference wave field reflected by the coating 3 is also incident on this surface. The mean dimension of the elements of the speckle structure sufficient for resolution by the speckle array is established by the diaphragm 7. The image of the study object is input into the computer twice, before and after a deformable load has been applied to it. A digital analog of an interference pattern is then obtained and output in a display using well-known methods of computer processing [13], making it possible to calculate the deformation of the study object. The examples that have been presented here demonstrate the value of and possibility of developing a new class of double-beam interferometers with combined reference and object arms. These interferometers will differ from their classical analogs in a positive way in terms of simplicity, reliability, and vibration immunity. The ideas that have been set forth in the present article have been verified experimentally with the use of the HL6512MG semiconductor laser diode from the firm of Optnext, which possesses a certified power of 60 mW and coherence length of around 10 m. The optical circuit has been assembled in accordance with Fig. 1. The contrast interference bands are observed up to a difference of the optical beams of 1.5 m (a greater difference cannot be achieved because of the length of the vibration-immune bench). Thus, modern lasers in fact make it possible to realize the new type of interferometer proposed in the present article. Let us present one more example, that of an interference gauge to measure the distance from a reference plane to a study object, an example that demonstrates the value of simultaneous use of diffraction optics and high-coherence laser radiation [15]. The gauge consiss of a source of coherent radiation and a diffraction optical element, or hologram, and a multielement photodetector designed for input of interference patterns into a computer. An optical flow chart for obtaining a diffraction optical element is shown in Fig. 3a. A hologram is created by directing the undivided beam of laser 1 at the micro-objective 2, in this case forming a spherical wave 4 that diverges from point 3 and is transmitted to the doubly exposed photographic plate 5. In the course of the first exposure, the collimated reference wave field is transmitted to the photosensitive medium, or plate 5, along direction 6, while in the course of the second exposure the direction of exposure 7 of the reference wave field is rendered opposite to its initial direction. Following photographic processing, the plate 5 becomes a diffraction optical element 8 (Fig. 3b). An optical flow chart of an interference distance gauge is presented in Fig. 3b. Once the hologram 8 is illuminated by means of collimated radiation traveling in the direction 7 in a first diffraction order transit, there occurs a reconstruction 279

of the converging spherical wave 9 incident on the study object 10. The surface of the study object is situated near the center of curvature of the wave 9. The divergent spherical wave 11 reflected by the study object enters the multi-element photodetector 12 through the hologram 8. Reconstruction of the divergent reference spherical wave 13 traveling in direction 7 occurs simultaneously with the illumination of the hologram by means of reflection. Suppose that the distance between the object 10 and the reference plane, i.e., holograph plane 8, coincides with the distance from the point source 3 (cf. Fig. 3a) to the hologram 5 while it is being created. Then the wave reflected by the object and the reference wave reconstructed by the hologram will coincide in terms of curvature, which corresponds to tuning of the interferometer to a band of infinite width. If these distances differ, an interference band in the form of rings (or fragments of rings) will appear in the interference pattern. The desired distance is then found by means of computer-based digital processing of the interference pattern, In conclusion, let us consider one more interesting feature. The use of the analogy between the length of a pulse of laser radiation and the coherence length of continuous radiation was noted in [16]. In recent years, methods of dilation and shrinkage of femtosecond pulses have been developed for the purpose of amplification of these pulses. By analogy with these methods, it is also possible to develop methods for controlling the coherence length of continuous radiation without any change in the spectral composition of the radiation itself. Such methods could find use in different areas in interference measurements. Thus, an increase in the coherence length would be required for measurements of distance and motion, whereas a decrease in the coherence length would be necessary in the case of low-coherence and correlation interferometry. The present study was completed with the support of the Russian Foundation for Basic Research (Grant No. 0907-00502A).

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