NASA's Satellite Laser Ranging Systems for the 21st Century.

For over 40 years, NASA's global network of satellite laser ranging (SLR) stations has provided a significant percentage of the global orbital data used to define the International Terrestrial Reference Frame (ITRF). The current NASA legacy network is reaching its end-of-life and a new generation of systems must be ready to take its place. Scientific demands of sub-millimeter precision ranging and the ever-increasing number of tracking targets give aggressive performance requirements to this new generation of systems. Using lessons learned from the legacy systems and the successful development of a prototype station, a new network of SLR stations, called the Space Geodesy Satellite Laser Ranging (SGSLR) systems, is being developed. These will be the state-of-the-art SLR component of NASA's Space Geodesy Project (SGP). Each of SGSLR's nine subsystems has been designed to produce a robust, kilohertz laser ranging system with 24/7 operational capability and with minimal human intervention. SGSLR's data must support the aggressive goals of the Global Geodetic Observing System (GGOS), which are 1 millimeter (mm) position accuracy and 0.1 mm per year stability of the ITRF. This paper will describe the major requirements and accompanying design of the new SGSLR systems, how the systems will be tested, and the expected system performance.

Optical antenna gain. 3: The effect of secondary element support struts on transmitter gain.

The effect of a secondary element spider support structure on optical antenna transmitter gain is analyzed. An expression describing the influence of the struts on the axial gain, in both the near and far fields, is derived as a function of the number of struts and their width. It is found that, for typical systems, the struts degrade the on-axis gain by less than 0.4 dB, and the first side-lobe level is not increased significantly. Contour plots have also been included to show the symmetry of the far-field distributions for three and four support members.

Optical antenna gain. 1: transmitting antennas.

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.

Optical antenna gain. 2: receiving antennas.

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.

Minimization of the prime power consumption of a coupling-modulated gas laser transmitter.

The present article addresses itself to the prime power requirements of a coupling-modulated gas laser transmitter. The latter consists of a gas discharge tube and electrooptic modulator inside a laser resonator. In performing the calculations, the laser discharge length and the modulator voltage are simultaneously varied so that the transmitted power remains constant. In this way, tradeoffs can be made between the prime power supplied individually to the discharge tube and to the modulator driver to obtain a transmitter configuration that minimizes the total prime power consumption. An analytical expression is derived that describes the effects of information bandwidth and transmitter output power on the prime power requirements. Specific numerical results are obtained for a CO(2) laser transmitter based on presently available experimental data.

Waveguide laser mode patterns in the near and far field.

The difference in notations used by researchers in the dielectric waveguide field and those primarily interested in waveguide lasers is discussed, and the equations for the field components of the various modes in large radius hollow dielectric waveguides are rederived in terms of the more widely used notation. Certain linear combinations of these modes that give linearly polarized field distributions are then considered to be launched into free-space at a waveguide termination. The resultant Fresnel and Fraunhofer field distributions are useful in identifying the modes of oscillation and in choosing mirror apertures that will restrict oscillation on the fundamental waveguide mode.

A ray analysis of optical resonators formed by two spherical mirrors.

A paraxial resonance equation is derived. This gives the mirror separation as a function of the radii of curvature of the mirrors and an integer N which is the number of return transits necessary to form a closed path of rays. Differentiating the paraxial resonance equation gives a formula for the relative mode density as a function of mirror separation. It is shown that the output power from a laser incorporating solid mirrors is inversely proportional to the mode density. In the case of hole coupling, the output power follows the same general profile but dips in power occur at the mirror separations corresponding to the resonance configurations of modes characterized by low values of N. Further confirmation of the paraxial resonance equation is obtained from passive resonators in which conic interference fringes and sudden increases in transmitted intensity are found to occur at the predicted mirror separations for low values of N corresponding to mode-degenerate configurations. The positions of the vertices of the ray traces are found to correspond to the patterns of discrete spots which are obtained in the output of a CO(2) laser incorporating Brewster angle windows and a solid germanium mirror. The laser configurations which give maximum output power are plotted as a cliff of constant height above the g(1)g(2) plane of the stability diagram, where g(1) and g(2) are the configuration coordinates. The relative merits of all possible cavity configurations having one mirror in common are shown as a set of equipower contours, and the hyperbolic curves of constant N are also superimposed on the stability diagram. The advantages of simplicity and directness in using the ray model are made clear.