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All sourcesNASA NTRSDOE OSTI
NASA NTRS1993

Software to model AXAF image quality

This draft final report describes the work performed under this delivery order from May 1992 through June 1993. The purpose of this contract was to enhance and develop an integrated optical performance modeling software for complex x-ray optical systems such as AXAF. The GRAZTRACE program developed by the MSFC Optical Systems Branch for modeling VETA-I was used as the starting baseline program. The original program was a large single file program and, therefore, could not be modified very efficiently. The original source code has been reorganized, and a 'Make Utility' has been written to update the original program. The new version of the source code consists of 36 small source files to make it easier for the code developer to manage and modify the program. A user library has also been built and a 'Makelib' utility has been furnished to update the library. With the user library, the users can easily access the GRAZTRACE source files and build a custom library. A user manual for the new version of GRAZTRACE has been compiled. The plotting capability for the 3-D point spread functions and contour plots has been provided in the GRAZTRACE using the graphics package DISPLAY. The Graphics emulator over the network has been set up for programming the graphics routine. The point spread function and the contour plot routines have also been modified to display the plot centroid, and to allow the user to specify the plot range, and the viewing angle options. A Command Mode version of GRAZTRACE has also been developed. More than 60 commands have been implemented in a Code-V like format. The functions covered in this version include data manipulation, performance evaluation, and inquiry and setting of internal parameters. The user manual for these commands has been formatted as in Code-V, showing the command syntax, synopsis, and options. An interactive on-line help system for the command mode has also been accomplished to allow the user to find valid commands, command syntax, and command function. A translation program has been written to convert FEA output from structural analysis to GRAZTRACE surface deformation file (.dfm file). The program can accept standard output files and list files from COSMOS/M and NASTRAN finite analysis programs. Some interactive options are also provided, such as Cartesian or cylindrical coordinate transformation, coordinate shift and scale, and axial length change. A computerized database for technical documents relating to the AXAF project has been established. Over 5000 technical documents have been entered into the master database. A user can now rapidly retrieve the desired documents relating to the AXAF project. The summary of the work performed under this contract is shown.

Ahmad, Anees↗
NASA NTRS1978

Body-fitted coordinates systems transformations

Two computer programs generate two-dimensional body-fitted coordinate systems and coordinate transformation. Programs are useful in fields requiring accurate numerical representation of boundary conditions and accurate numerical solutions of partial differential equations.

Mastin, C. W.↗
NASA NTRS1974

THREED: A computer program for three dimensional transformation of coordinates

Program THREED was developed for the purpose of a research study on the treatment of control data in lunar phototriangulation. THREED is the code name of a computer program for performing absolute orientation by the method of three-dimensional projective transformation. It has the capability of performing complete error analysis on the computed transformation parameters as well as the transformed coordinates.

Wong, K. W.↗
NASA NTRSDate not supplied

NASA CARA Tools

The NASA Conjunction Assessment Risk Analysis (CARA) team has created and posted to GitHub a set of MATLAB software tools for collision assessment (CA) analysis. The software is provided to the public under a NASA Open-Source Software Agreement and is maintained/updated by the CARA Analysis team. Capabilities provided within the toolset include algorithms in assessing probability of collision (Pc), collision consequence, covariance realism, Orbit Determination (OD) quality assessment, and single covariance max Pc. Additionally, a set of utilities are provided for astrodynamics topics closely related to CA, such as: Conjunction Data Message (CDM) parsing, covariance transformations, coordinate system transformations, etc. The repository is regularly updated on a monthly basis and new functionality will be added as algorithms are approved for public release. This presentation will provide a brief introduction to the toolset, highlight some of the key components which can be used in operations, and will present information on algorithms that are in the release pipeline and can be expected soon. This software will enable operators to independently perform CA calculations using the same core algorithms that CARA uses in operations.

L. Baars↗
NASA NTRSDate not supplied

NASA CARA Tools

The NASA Conjunction Assessment Risk Analysis (CARA) team has created and posted to GitHub a set of MATLAB software tools for collision assessment (CA) analysis. The software is provided to the public under a NASA Open-Source Software Agreement and is maintained/updated by the CARA Analysis team. Capabilities provided within the toolset include algorithms in assessing probability of collision (Pc), collision consequence, covariance realism, Orbit Determination (OD) quality assessment, and single covariance max Pc. Additionally, a set of utilities are provided for astrodynamics topics closely related to CA, such as: Conjunction Data Message (CDM) parsing, covariance transformations, coordinate system transformations, etc. The repository is regularly updated on a monthly basis and new functionality will be added as algorithms are approved for public release. This presentation will provide a brief introduction to the toolset, highlight some of the key components which can be used in operations, and will present information on algorithms that are in the release pipeline and can be expected soon. This software will enable operators to independently perform CA calculations using the same core algorithms that CARA uses in operations.

Luis Baars↗
NASA NTRS1990

Hybrid vision activities at NASA Johnson Space Center

NASA's Johnson Space Center in Houston, Texas, is active in several aspects of hybrid image processing. (The term hybrid image processing refers to a system that combines digital and photonic processing). The major thrusts are autonomous space operations such as planetary landing, servicing, and rendezvous and docking. By processing images in non-Cartesian geometries to achieve shift invariance to canonical distortions, researchers use certain aspects of the human visual system for machine vision. That technology flow is bidirectional; researchers are investigating the possible utility of video-rate coordinate transformations for human low-vision patients. Man-in-the-loop teleoperations are also supported by the use of video-rate image-coordinate transformations, as researchers plan to use bandwidth compression tailored to the varying spatial acuity of the human operator. Technological elements being developed in the program include upgraded spatial light modulators, real-time coordinate transformations in video imagery, synthetic filters that robustly allow estimation of object pose parameters, convolutionally blurred filters that have continuously selectable invariance to such image changes as magnification and rotation, and optimization of optical correlation done with spatial light modulators that have limited range and couple both phase and amplitude in their response.

Juday, Richard D.↗
NASA NTRS1977

TOMCAT - A code for numerical generation of boundary-fitted curvilinear coordinate systems on fields containing any number of arbitrary two-dimensional bodies

A method for automatic generation of boundary-fitted curvilinear coordinate systems, where the transformed coordinates are solutions of an elliptic differential system in the physical plane, and where the coordinate lines are coincident with all boundaries of a general multiply-connected, two-dimensional region containing any number of arbitrarily shaped bodies, and is described along with a suitable computer code for implementing the method. Any partial differential system can be solved on the boundary-fitted coordinate system by appropriate transformations. The transformed equations are approximated by finite differences and solved numerically in the transformed plane. All computations, whether for generating coordinate system or then solving the transformed equations, can be done on a rectangular field with square mesh with no interpolation required on the boundaries. The physical boundaries may even be time-dependent.

Thompson, J. F.↗
NASA NTRS1989

Correcting Distortions In Optical Correlators

Coordinate transformation maps object space to correlation space. Theory developed to predict and correct typical anamorphic coordinate-transformation errors in off-axis Vander Lugt optical correlators.

Chrien, Thomas G.↗
NASA NTRS1992

An off-center point explosion in a radially stratified medium - Kompaneets approximation

The Kompaneets (1960) approximation is applied to a blast in a medium that is radially stratified according to a power law. The basic equation is derived that gives the location of the shock front as a function of time. This equation is transformed by means of a conformal coordinate transformation into an equation in which the density variation of the medium does not appear. In the new coordinates, and the problem is reduced to that of a blast in a uniform medium, the solution of which is a set of concentric circles about the initial explosion point; in the transformed coordinates, the paths followed by points on the shock front are radial, making it possible to find the paths in the original coordinates. Using the new solution, the effect of the explosion is considered for a solid core embedded at the origin, and the extent of the core's surface that is affected by the blast is calculated.

Korycansky, D. G.↗
NASA NTRS1989

Jacobi-Bessel Analysis Of Antennas With Elliptical Apertures.

Coordinate transformation improves convergence pattern analysis of elliptical-aperture antennas. Modified version of Jacobi-Bessel expansion for vector diffraction analysis of reflector antennas uses coordinate transformation to improve convergence with elliptical apertures. Expansion converges rapidly for antennas with circular apertures, but less rapidly for elliptical apertures. Difference in convergence behavior between circular and elliptical Jacobi-Bessel algorithms indicated by highest values of indices m, n, and p required to achieve same accuracy in computed radiation pattern of offset paraboloidal antenna with elliptical aperture.

Rahmat-Samii, Y.↗
NASA NTRS1975

Calculation of unsteady transonic aerodynamics for oscillating wings with thickness

An analytical approach is presented to account for some of the nonlinear characteristics of the transonic flow equation for finite thickness wings undergoing harmonic oscillation at sonic flight speed in an inviscid, shock-free fluid. The thickness effect is accounted for in the analysis through use of the steady local Mach number distribution over the wing at its mean position by employing the local linearization concept and a coordinate transformation. Computed results are compared with that of the linearized theory and experiments. Based on the local linearization concept, an alternate formulation avoiding the limitations of the coordinate transformation method is presented.

Ruo, S. Y.↗
NASA NTRS1994

A simple suboptimal least-squares algorithm for attitude determination with multiple sensors

Three-axis attitude determination is equivalent to finding a coordinate transformation matrix which transforms a set of reference vectors fixed in inertial space to a set of measurement vectors fixed in the spacecraft. The attitude determination problem can be expressed as a constrained optimization problem. The constraint is that a coordinate transformation matrix must be proper, real, and orthogonal. A transformation matrix can be thought of as optimal in the least-squares sense if it maps the measurement vectors to the reference vectors with minimal 2-norm errors and meets the above constraint. This constrained optimization problem is known as Wahba's problem. Several algorithms which solve Wahba's problem exactly have been developed and used. These algorithms, while steadily improving, are all rather complicated. Furthermore, they involve such numerically unstable or sensitive operations as matrix determinant, matrix adjoint, and Newton-Raphson iterations. This paper describes an algorithm which minimizes Wahba's loss function, but without the constraint. When the constraint is ignored, the problem can be solved by a straightforward, numerically stable least-squares algorithm such as QR decomposition. Even though the algorithm does not explicitly take the constraint into account, it still yields a nearly orthogonal matrix for most practical cases; orthogonality only becomes corrupted when the sensor measurements are very noisy, on the same order of magnitude as the attitude rotations. The algorithm can be simplified if the attitude rotations are small enough so that the approximation sin(theta) approximately equals theta holds. We then compare the computational requirements for several well-known algorithms. For the general large-angle case, the QR least-squares algorithm is competitive with all other know algorithms and faster than most. If attitude rotations are small, the least-squares algorithm can be modified to run faster, and this modified algorithm is faster than all but a similarly specialized version of the QUEST algorithm. We also introduce a novel measurement averaging technique which reduces the n-measurement case to the two measurement case for our particular application, a star tracker and earth sensor mounted on an earth-pointed geosynchronous communications satellite. Using this technique, many n-measurement problems reduce to less than or equal to 3 measurements; this reduces the amount of required calculation without significant degradation in accuracy. Finally, we present the results of some tests which compare the least-squares algorithm with the QUEST and FOAM algorithms in the two-measurement case. For our example case, all three algorithms performed with similar accuracy.

Brozenec, Thomas F.↗
NASA NTRS1992

Spacecraft nonlinear control

The feedback linearization technique is applied to the problem of spacecraft attitude control and momentum management with control moment gyros (CMGs). The feedback linearization consists of a coordinate transformation, which transforms the system to a companion form, and a nonlinear feedback control law to cancel the nonlinear dynamics resulting in a linear equivalent model. Pole placement techniques are then used to place the closed-loop poles. The coordinate transformation proposed here evolves from three output functions of relative degree four, three, and two, respectively. The nonlinear feedback control law is presented. Stability in a neighborhood of a controllable torque equilibrium attitude (TEA) is guaranteed and this fact is demonstrated by the simulation results. An investigation of the nonlinear control law shows that singularities exist in the state space outside the neighborhood of the controllable TEA. The nonlinear control law is simplified by a standard linearization technique and it is shown that the linearized nonlinear controller provides a natural way to select control gains for the multiple-input, multiple-output system. Simulation results using the linearized nonlinear controller show good performance relative to the nonlinear controller in the neighborhood of the TEA.

Sheen, Jyh-Jong↗
NASA NTRS1985

Rapid estimation of frequency response functions by close-range photogrammetry

The accuracy of a rapid method which estimates the frequency response function from stereoscopic dynamic data is computed. It is shown that reversal of the order of the operations of coordinate transformation and Fourier transformation, which provides a significant increase in computational speed, introduces error. A portion of the error, proportional to the perturbation components normal to the camera focal planes, cannot be eliminated. The remaining error may be eliminated by proper scaling of frequency data prior to coordinate transformation. Methods are developed for least squares estimation of the full 3x3 frequency response matrix for a three dimensional structure.

Tripp, J. S.↗