The gain of centrally obscured optical transmitting antennas is analyzed in detail. The calculations, resulting in near- and far-field antenna gain patterns, assume a circular antenna illuminated by a laser operating in the TEM(00) mode. A simple polynomial equation is derived for matching the incident source distribution to a general antenna configuration for maximum on-axis gain. An interpretation of the resultant gain curves allows a number of auxiliary design curves to be drawn that display the losses in antenna gain due to pointing errors and the cone angle of the beam in the far field as a function of antenna aperture size and its central obscuration. The results are presented in a series of graphs that allow the rapid and accurate evaluation of the antenna gain which may then be substituted into the conventional range equation.
Expressions are derived for the gain of a centrally obscured, circular optical antenna when used as the collecting and focusing optics in a laser receiver which include losses due to (1) blockage of the incoming light by the central obscuration, (2) the spillover of energy at the detector, and (3) the effect of local oscillator distribution in the case of heterodyne or homodyne detection. Numerical results are presented for direct detection and for three types of local oscillator distributions (uniform, Gaussian, and matched) in the case of heterodyne or homodyne detection. The results are presented in several graphs that allow the rapid evaluation of receiver gain for an arbitrary set of telescope and detector parameters. It is found that, for uniform illumination by the LO, the optimum SNR is obtained when the detector radius is approximately 0.74 times the Airy disk radius. The use of an optimized Gaussian (spot size = 0.46 times the Airy disk radius) improves the receiver gain by less than 1 dB. Theuse results are insensitive to the size of the central obscuration.
The crystal and molecular structure of tris(nitrato)( 1,4,7,10,13-pentaoxacyclopentadecane)europium(III), Eu(N03),(C,&,05), has been determined from single-crystal X-ray diffraction. The complex crystallizes in the trigonal space group P3] with Z = 3. Lattice parameters are a = 8.845 (3) A, c = 20.330 (4) A, and y = 120O. The structure was solved by Patterson and Fourier techniques and refined by least squares to a final conventional R value of 0.037. The europium(II1) ion is 1 laordinate and bonded to three bidentate nitrate groups and to the five oxygen atoms of the crown ether. The Eu-O(nitrate) and Eu-O(ether) distances lie in the ranges 2.43-2.65 and 2.55-2.69 A, respectively. The nitrate groups are planar with N-0 bond lengths between 1.21 and 1.31 A. The five CHzCH2 moieties of the macrocycle have a slight fluxional motion at room temperature. The coordination polyhedron of the Eu(II1) ion is discussed. The ionic radius of the 1 1-coordinate Eu(II1) ion is 1.25 A. Crystal field splittings, obtained from the high-resolution fluorescence spectrum at 77 K, are reported for the 5D1, 5Dz, 7FI, 7Fz, and 7F4 electronic levels. Interpretation of these splittings leads to the conclusion that the 1 l-coordinate polyhedron of the Eu(II1) ion can be viewed as a distortion of either a pentagonal or a hexagonal symmetry.
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