Many satellite applications require a model that represents a surface as it deforms over time. Yet, space applications demand a precise, low-weight, low-volume, and easy to implement solution. A metrology sensing system is presented in this thesis, consisting of a series of cameras and laser dot projectors positioned along the length of the antenna. This system accurately models the geometry of the surface to meet the demands of a space based radar. Each laser dot projector casts a matrix of points onto the antenna surface. The points are then imaged simultaneously by a pair of cameras, each having a different, but overlapping, viewpoint. Given the two overlapping images, a Gaussian nonlinear least squares algorithm solves the stereo-triangulation problem which provides the coordinates of the projected points and thereby maps the surface. There are three different strategies discussed in this thesis. The first strategy assumes the positions and orientations of the cameras are absolutely known. This produces an extremely accurate result; yet it is unrealistic to assume absolute knowledge of cameras locations and orientations for the application. The next strategy assumes the positions and orientations of the cameras are completely unknown in addition to the unknown surface. This program produces a less accurate, but more realistic, result considering the dynamic nature of rigid structures in space. To increase the accuracy and improve the robustness of these results, the third method employs a global metrology sensing system to reduce the uncertainty in the location and orientation of the outboard cameras relative to the center camera. This approach estimates the surface extremely accurately and, although more complex, offers advantages and addresses the desire for a family of designs wherein higher accuracy is achievable by further optimization.
Many satellite applications require a model that represents a surface as it deforms over time. Yet, space applications demand a precise, low-weight, low-volume, and easy to implement solution. A metrology sensing system is presented in this thesis, consisting of a series of cameras and laser dot projectors positioned along the length of the antenna. This system accurately models the geometry of the surface to meet the demands of a space based radar. Each laser dot projector casts a matrix of points onto the antenna surface. The points are then imaged simultaneously by a pair of cameras, each having a different, but overlapping, viewpoint. Given the two overlapping images, a Gaussian nonlinear least squares algorithm solves the stereo-triangulation problem which provides the coordinates of the projected points and thereby maps the surface. There are three different strategies discussed in this thesis. The first strategy assumes the positions and orientations of the cameras are absolutely known. This produces an extremely accurate result; yet it is unrealistic to assume absolute knowledge of cameras locations and orientations for the application. The next strategy assumes the positions and orientations of the cameras are completely unknown in addition to the unknown surface. This program produces a less accurate, but more realistic, result considering the dynamic nature of rigid structures in space. To increase the accuracy and improve the robustness of these results, the third method employs a global metrology sensing system to reduce the uncertainty in the location and orientation of the outboard cameras relative to the center camera. This approach estimates the surface extremely accurately and, although more complex, offers advantages and addresses the desire for a family of designs wherein higher accuracy is achievable by further optimization.