Diffractive interferometer for visualization and measurement of optical inhomogeneities Irina G. Palchikova,2, Ivan А. Yurlagin 2 Technological Design Institute of Scientific Instrument Engineering (TDI SIE) Siberian Branch of the Russian Academy of Sciences (SB RAS) 4, Russkaya str., Novosibirsk, 630058, Russia Tel.: + 7 [383] 333-27-60 Fax: +7 [383] 332-93-42 E-mail: palchikova@tdisie.nsc.ru 2 Novosibirsk State University 2, Pirogova str., Novosibirsk, 630090, Russia Abstract New optical arrangements of two beam diffractive interferometer with the inverted wave fronts and the combined optical branches based on zone plates are proposed. Diffractive interferometers allow effectively influencing characteristics of an interference field and to carry out both immediate visualization, and measuring the optical inhomogeneities of the transparent samples. Keywords: Diffractive interferometer, zone plates, Talbot effect, optical inhomogeneity. Introduction Interferometry is usually used as a method of measuring the shape of the wavefront created by an optical system, and, hence, as a means of testing the optical quality of components in that system. The interference pattern between the test and reference wavefronts is easily interpreted, if their relative inclination and curvature are adjusted so that to result the pattern in a simple form, such as a few straight fringes. The deviation from straightness or from equality of spacing characterizes the difference in the shape of two wave fronts. This can in turn be used to determine optical inhomogeneities in the optical path of the test wavefront. Interferometry of this type is a valuable tool in precise metrology of variations of an optical depth or a refractive index of sample placed in an optical path of the test beam. The purpose of the given paper is to consider potentials and peculiarities of the diffractive interferometer (DI) for such applications. Three optical arrangements of DI with the inverted wave fronts and the combined branches are proposed. DI allows effectively influencing characteristics of an interference field. Comparison of DI characteristics is carried out and results of an experimental research in real time of the dynamics of photomodifications of the holographic photopolymeric materials (HPPM) are given. 2. Zone plate as a basic element of the diffractive interferometer Zone plate (ZP) acts as a set of т lenses [] with the coincided principal planes and the 2 0 focal distances f m, where 0 0F is the radius of the first Fresnel zone for an 0m operating wavelength 0 and a focal length F, m is the number of the diffraction order. One of the fundamental ZP properties [] is a formation in image space of the non-local interference fringes owing to intersection of the diffraction orders, if ZP is irradiated by the point light source. In any section of image space the fringes of multibeam interference which are easily interpreted [] as the sum of fringes of a paired interference of the diffraction orders are observed. The contrast of two-beam fringes depends on the relative intensity of orders and -287
the coherence of the light, depends on the relative arrangement of the recording plane, the light source and ZP. Palchikova I.G. [2] introduced two-beam DI based on single ZP. As proved in [2], the influence of the non-operating orders can be weak for three reasons: the non-operating orders have a weak intensity, or the non-operating fringes have a low contrast, or the widths of fringes strongly differ from the operating, and consequently their influence is shown in a brightness modulation of operating fringes with the frequency of non-operating. ZP interferometer application for the study of thermal inhomogeneities in the optical depth of a laser active element has revealed changes of the refractive index of the crystal of potassium gadolinium tungstate, arising after the pumping lamp flare. The magnitude of this changes was equal to 0.5 0-6. These measurements became possible only because the influence of mechanical vibrations and temperature fluctuations of an environment at the indications of DI is weaker, than in classical interferometers. The ZP interferometer arrangements for testing the optical surfaces shape is described in paper [3], where variety means for obtaining the interference field, generated by the different diffraction orders, were covered. 3. Diffractive interferometers based on two zone plates To make the improvement of the interference pattern, we propose to use the Talbot effect in light field, diffracted by ZP [4]. Complementary ZP2 is applied in arrangement for practical use the Talbot effect. The diffraction structure of ZP2 is negative one in relation to the structure of ZP. ZP2 is placed into the self-imaging plane spaced at the double focal length ( 2F ) from the first ZP. The arrangement of DI based on two zone plates is shown in Fig.. Fig.. First type diffractive interferometer based on two zone plates. It incorporates a light source, a collimator, first ZP, the complementary ZP2, the spatial frequency filter of the non-operating orders and the matrix photo receiver, which optical axes are coaxial with the principal one. To smooth away the speckles, the moving ground glass is placed directly behind the laser, or in the operating interference field at the photo receiver. The new element of the two beams DI arrangement is the spatial frequency filter, in which the pinhole define both the interference pattern quality and DI sensitivity. The pinhole passes the operating diffraction orders ([+, +], [0, 0]) and attenuates others beams. It is easy to verify that the pinhole size a D must satisfy the inequality: F ad Fd f, where is the peak angle for which the sample declines incident rays, F is the focal length of objective O, and d is the operating aperture of ZP2. Objective O2 produces both the interference field and the image of the front-focal plane of ZP2 at the photo receiver together. If a sample is placed in the test light beam (in the position S or S2), the extra phase difference is arisen and it is equal to kl( n ), where -288
k 2 0 is the wave number, L is the sample depth, n=n 0 +dn is the refractive index of sample, dn is its inhomogeneity. Then changes of the interference pattern are appeared in the image plane on the photoreceiver, which permits the quantity of inhomogeneities to be found at any point of the sample aperture. Within the single interference fringe it is possible to visualize the inhomogeneities and to define its position. Automated data analysis of interferograms is carried out by means of the computer. The appearance of the interference pattern is strictly defined by a mutual disposition of zone plates. In the optical arrangement of the first type (DI) (see Fig. ) ZP and ZP2 are located confocally with high precision. The test and reference beams ([+, +] and [0, 0]) are parallel to the principal optical axis. These beams are focused into the point F 2 of optical axis by the objective O, so that two images of the source coincide. Objective O2 converts the divergent lights beams into the parallel ones and there is an interference of two axially directed plane waves at the photoreceiver, i.e. the interference fringe of the infinite width is observed (uniformly irradiated image of sample in the operating field). All inhomogeneities of the optical depth of a sample will be visible as changes of intensity in the image of sample on the photo receiver. That is a direct visualization of inhomogeneities occurs in real time, and the measurement of the light intensity distribution in the operating field allows estimating their quantity. At such arrangement of zone plates the interference will be observed with a light source of any type, even in a white light. In the arrangement of second type (DI2) the displacement of ZP2 from the confocal configuration along the principal optical axis leads to that the reference beam [+, +] becomes spherical (or cylindrical, according to what modification of ZP was used) one while the test beam [0, 0] remains parallel to the optical axis after passing through ZP2. The test beam is focused into the point F 2 of optical axis by the objective O, while the reference beam is focused into another point of the optical axis so that two images of the source are not coinciding. In the interference field the fringes of variable width are observed. The structure of interference pattern is similar to the diffraction structure of ZP. In the arrangement of third type (DI3) the displacement of ZP2 from the confocal configuration across the principal optical axis leads to inclining the reference beam [+, +] about the optical axis while the test beam [0, 0] remains parallel to axis after passing through ZP2. The test beam is focused into the point F 2 of optical axis by the objective O, while the reference beam is focused into another point of the focal plane, which properly displaced from the axis so that again two images of the source don t coincide. In the interference field the equidistant fringes of the limited width are observed. The consideration reveals, that in proposed DI arrangements the two images of light source in the focal plane of objective O is created, and the operating field in the plane of registration is formed owing to the interference of the light beams which are originated from these two apparent light sources, actually, under double slit scheme of T. Young. The calculation of interference fringes in the operating field is a trivial problem. 4. Interferogram processing For calculation of the optical depth of a sample it is necessary to determine the true coordinates of points with equal intensity on an interferogram. The experimental interference pattern contains various impairments of fringes, namely: disruptions, erosions, the noise random contortions, etc. The restitution of garbled interferogram [5] from the stage of recording and up to the stage of fringe tracking and fringe skeletonizing consists of the following steps: gaining the contrast, reducing binary noise by median filter, Gaussian filter, the repeated processing with the nonlinear adaptive transformation, and the final gain of contrast. The special software is designed. In the computer-aided interferogram processing the -289
restitution of an interference pattern is performed; the fringes skeleton is selected; the graphic visualization of optical inhomogeneities in the aperture of a sample is built. The onedimensional sections of a frame are saved as the CSV-file. Illustrations of a final part of the interferogram processing script are given in Fig. 2. In consequence of running the software the results of processing the interference pattern are output. Figure 3 presents the graphics window, the graphic a b c d e Fig. 2. Illustrations of the interferogram processing script: experimental pattern - (2a) : the binarization with auto selecting the threshold - (2b); dilatation filling of enclosures and discontinuities - (2c); eroding the noise aggregates - (2d); fringe tracking and skeletonizing - (2e). visualization of optical inhomogeneities as two-dimensional representation is shown at the right side, at the left side there is the one-dimensional section. Approval of the program was fulfilled with the help of test images and the interferogram of the test sample. Fig. 3. Software graphics window. 5. Experimental results All three proposed arrangements of DI are approved at TDISIE SB RAS. On the basis of these arrangements the experimental mounting for studying the dynamic of HPPM films photomodification during exposure is created. DI has been fulfilled on the basis of the third type arrangement and provides sensitivity to changing the refractive index about ~0-3 for the depth of sample about ~0 00 microns. The explored samples are the dried up polymeric films with the colorings agents dissolved in it, applied on a glass base plate. In experiment the sample is continuously lit by monochromatic actinic light and interferograms are recorded through particular time intervals. The experimental results illustrating the process of changing the refractive index of a HPPM film during the exposure by actinic light appear in Fig. 4. The interval between pictures is equal to 60 seconds. In the processing area the boundary of an exposed spot and the shift of the fringes, carrying the information on changes of refractive index, become precisely visible as time goes on. The interferograms processing allows building diagrams for the changes of the refractive index during the exposure of a sample. These changes are the key parameters for optimization of a qualitative and quantitative chemistry of a photopolymeric composition. -290
Fig. 4. The evolution of interferograms of HPPM film during the exposure. Testing of interferometers has revealed that arrangements are easily adjusted and can effectively work both with high and with partly coherent light sources. Interference fringes have high contrast. The accuracy of the computer-aided interferogram processing has averaged ~0,05 fraction of the fringe width. 6. Conclusion Metrological advantages of proposed optical arrangements for two beams DI based on zone plates, achievable as a result of combining the optical branches are experimentally confirmed. The recombination of interfering beams is carried out without additional optical elements, the optical branches are combined and interfering beams have the common optical path that provides the improved parameters regarding chatter stability and noise immunity. DI allows carrying out both immediate visualization, and measuring the optical inhomogeneities of the transparent samples. References. V.P. Koronkevitch, I.G. Palchikova. Interference properties of zone plates. Optoelectronics. Instrumentation & Data Processing. 994, No. 3, pp. 85-00. 2. I.G. Palchikova, S.L. Mikerin, V.D. Ugozhayev, A.A. Klyuchnikov. Visualization of the thermal distortions in KGW lasers crystal by means of interferometer with zone plates. In: 9th Congress of the International Commission for Optics: Optics for the Quality of Life. Proc. SPIE. 2003, vol. 4829, part, pp. 257-258. 3. R.N. Smart. Zone plate interferometer. Appl. Opt. 974, vol. 3, pp. 093-099. 4. I.G. Palchikova, S.S. Popova, S.V. Smirnov. Research for the Talbot effect in light fields behind zone plates. Optoelectronics, Instrumentation & Data Processing. 200, No., pp. 84-99. 5. D. Malacara. Interferogramm Analysis for Optical Testing. CRC. 2005, 568 p. -29