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AIMS: We aim to investigate the physical and chemical properties of the molecular envelope of the oxygen-rich AGB star IK Tau. METHODS: We carried out a millimeter wavelength line survey between ~79 and 356 GHz with the IRAM-30 m telescope. We analysed the molecular lines detected in IK Tau using the population diagram technique to derive rotational temperatures and column densities. We conducted a radiative transfer analysis of the SO2 lines, which also helped us to verify the validity of the approximated method of the population diagram for the rest of the molecules. RESULTS: For the first time in this source we detected rotational lines in the ground vibrational state of HCO+, NS, NO, and H2CO, as well as several isotopologues of molecules previously identified, namely, C18O, Si17O, Si18O, 29SiS, 30SiS, Si34S, H13CN, 13CS, C34S, H234S, 34SO, and 34SO2. We also detected several rotational lines in vibrationally excited states of SiS and SiO isotopologues, as well as rotational lines of H2O in the vibrationally excited state ν2=2. We have also increased the number of rotational lines detected of molecules that were previously identified toward IK Tau, including vibrationally excited states, enabling a detailed study of the molecular abundances and excitation temperatures. In particular, we highlight the detection of NS and H2CO with fractional abundances of f(NS)~10-8 and f(H2CO)~[10-7-10-8 ]. Most of the molecules display rotational temperatures between 15 and 40 K. NaCl and SiS isotopologues display rotational temperatures higher than the average (~65 K). In the case of SO2 a warm component with Trot~290 K is also detected. CONCLUSIONS: With a total of ~350 lines detected of 34 different molecular species (including different isotopologues), IK Tau displays a rich chemistry for an oxygen-rich circumstellar envelope. The detection of carbon bearing molecules like H2CO, as well as the discrepancies found between our derived abundances and the predictions from chemical models for some molecules, highlight the need for a revision of standard chemical models. We were able to identify at least two different emission components in terms of rotational temperatures. The warm component, which is mainly traced out by SO2, is probably arising from the inner regions of the envelope (at â²8R∗) where SO2 has a fractional abundance of f(SO2)~10-6. This result should be considered for future investigation of the main formation channels of this, and other, parent species in the inner winds of O-rich AGB stars, which at present are not well reproduced by current chemistry models.
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The local plane-interface approximation (LPIA) is a method for propagating electromagnetic fields through the inhomogeneous regions (e.g., elements) of an optical system. The LPIA is the superclass of all approximations that replace the usually curved optical interfaces with local tangential planes. Therefore the LPIA is restricted to smooth optical surfaces. A maximum radius of curvature of the optical interface of the order of a few wavelengths is a rough estimate for the validity of the LPIA. Two important approximation levels of the LPIA are the thin-element approximation (TEA) and a geometric-optical version of the LPIA (LPIA(ray)). The latter combines the wave-optical propagation of an electromagnetic field in the homogeneous region of an optical system with a ray-tracing step in the inhomogeneous region. We discuss the regions of validity of the LPIA in general and the approximation levels LPIA(ray) and TEA in detail.
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The spatial shaping of laser beams is a subject of research in modern optics. Recently the introduction of diffractive elements in laser resonators has offered an alternative to external beam-shaping optics by mode shaping within the resonator. We describe the specification of the laser resonator mirrors to obtain by means of internal mode shaping a desired beam outside the resonator. Modal discrimination of the modified resonator and the mirror alignment sensitivity is discussed. Basic features of resonator-originated and external beam shaping are compared.
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Diffractive elements with polarization multiplexing for the visible spectral region are demonstrated. The polarization-multiplexing property of the element is based on the polarization-dependent transmission characteristics of metal-stripe subwavelength period gratings. The proper dimensions of these gratings are estimated by rigorous calculations. The principle of polarization multiplexing by use of metal-stripe subwavelength period gratings is described for a diffractive element that has a binary amplitude transmission per polarization channel and is demonstrated by experimental results.
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The implementation of a two-stage design process for the design of diffractive optical elements for array illumination is described. Results are presented for on-axis two-dimensional array illuminators for which this method is used. The final designs are theoretically within 5% of the calculated diffraction efficiency upper bound, and theoretical signal reconstruction error is below 1%. Experimental verification of the design theory is given, with experimental diffraction efficiencies within 4% of design values and signal reconstruction error below 6%.
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Optical coherent Fourier correlators are applicable in real-time image analysis such as image classification. The functionality of Fourier correlators can be increased by use of multifunctional filters, which have many spatially multiplexed impulse responses. The concept of multiresolution analysis on the basis of wavelet theory offers profitable methods to design multifunctional filters for image analysis. The applicability of such filters is demonstrated by an example in which different characteristic textures of medical images are extracted. The physical implementation of multiwavelet filters is restricted by modulation-domain constraints imposed by the use of spatial-light-modulator or of diffractive-element fabrication technology. Coding methods of diffractive optics are shown to be helpful to transform the original complex-valued distributions of multiwavelet filters into light-efficient quantized phase-only distributions by preservation of the original filter functionality. The quality of the designed diffractive phase filters is documented by computer experiments.
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Beam splitters are used to couple the light of high-power Nd:YAG lasers into a fiber bundle. By the fibers the light is delivered to the workstations in the factory. This technique is used to reduce the costs of the light and to simplify the logistics within the fabrication process. Typically, dielectric beam splitters are used. However, they suffer from a polarization-sensitive splitting ratio. Because the polarization content of a high-power Nd:YAG-laser is not constant in time, polarization-independent beam splitters are of concern. The feasibility of diffractive beam splitters is investigated.
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The treatment of phase synthesis and retrieval with the help of projection algorithms often suffers from a stagnation problem. A bandwidth constraint introduces undesired first-order zeros. From the incorporation of error diffusion the stagnation can be avoided.
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An analysis of the error diffusion procedure is presented that is based on the terminology of filter theory. It is demonstrated that the error diffusion procedure is a powerful means to avoid signal error caused by a nonlinear system. An appropriate filter design method is described. The theoretical results are applied to treat picture binarization as well as quantization and coding in diffractive optics-digital holography.
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An error diffusion and an iterative concept that is based on the Fourier-transform algorithm are applied to binarize nonperiodic diffractive elements that generate speckle-free diffraction patterns. These methods are used successfully to calculate periodic elements and are adapted to specific constraints in the case of nonperiodic elements. Techniques to avoid stagnation are described, and optical experiments are presented.
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An upper bound of the diffraction efficiency of diffractive elements that only influence the phase of the illumination wave is derived. The derivation only utilizes the specification of the desired diffraction pattern. It is independent of the technique to design and fabricate the diffractive element. The theory is based on the transmittance approach to describe the effect of the element on the illumination wave.
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Generally, a diffractive optical element/digital hologram is used as a component in a system. For a specific system output, an appropriate signal must be realized as a diffraction pattern. We present methods to determine such signals, whereby the characteristics of the system are considered. In particular, we calculate signals and corresponding digital amplitude holograms for the generation of a special binary data set in a holographic storage system and a special binary surface relief in a microlithographic production process.
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Diffractive optics allows the incorporation of several optical functions, e.g., wave shaping and focusing, in one element. A method suitable to calculate a diffractive phase element with this feature is described. Coding and quantization effects are analyzed. As an example an array generator with integrated focal power is designed.
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Optical pattern recognition can profit from the progress in coding theory and technology that has been made in digital holography. The calculation of a phase-encoded inverse filter is described. This filter allows compromises between discrimination capability and diffraction efficiency. Phase quantization facilitates the materialization of the filter.
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An iterative concept is suggested to quantize digital amplitude holograms. It is based on an iterative Fourier transform algorithm. A stepwise introduction of the quantization constraint results in a convergent algorithm. The production of holograms is described and their optical reconstructions are presented.