Interferometric Image Acquisition and Reconstruction
- Paper number
IAC-06-A3.P.1.02
- Author
Dr. Haithem Altwaijry, King Abdulaziz City for Science & Technology (KACST), Saudi Arabia
- Coauthor
Prof. David Hyland, Texas A&M University, United States
- Year
2006
- Abstract
We begin by giving a brief but self-contained account of the underlying mathematics of image synthesis for a formation of free-flying telescopes in which a continuous sequence of mutual intensity measurements are carried out via interferometry using the collected light beams from selected pairs of telescopes. For this situation, we determine the least-square-error estimate of the image given the set of mutual intensity measurements obtained from the start of the imaging maneuver until the current time. This image estimation algorithm produces an increment to the estimated image, following the acquisition of each new mutual intensity measurement. In addition, the estimated image depends on the past history of the relative locations of the various telescopes from which interferometric data were gathered.
A measure of image quality is adopted that incorporates the estimated image and takes into account the optical performance and geometry of the telescopes. The Modulation Transfer Function (MTF) of the entire formation with all its evolutions up to the current time as an equivalent optical instrument is determined as a function of the two-dimensional wave number vector (the Fourier transform variables associated with the coordinates of the image plane).
Qualitatively, we can say that in the absence of a priori image information, and given a stipulated angular resolution requirement, acceptable image quality is achieved when the MTF assumes sufficient magnitudes everywhere within the resolution disc in the spatial resolution plane. Further, using a derived model of the noise variance, we can define a de-convolution operator which provides, at each point in the spatial resolution plane, a de-convolved image of the required signal-to-noise ratio (SNR). Finally, we define a ratio Γ that represents the ratio of the MTF to the de-convolution operator, the function Γ starts at zero and accumulates to unity, whereupon, it increases no further. Therefore, we can say that values of Γ near unity indicate good image quality and, further, overall quality is acceptable (the desired image is in fact attained) when Γ achieves the value unity within the entire resolution disc.
The problem is then defined as a coverage problem, in which the resolution disc in the spatial resolution plane must be entirely covered via coverage discs associated with the spacecraft (in the physical plane). We formulate and find the necessary conditions for optimality using Lagrange multipliers. Finally, we specialize the developed necessary conditions of optimality to distinct cases and formulated a short-time horizon version of the optimal maneuvering problem and deduced a short-time horizon control law that governed the motion of the coverage discs.
- Abstract document
- Manuscript document
IAC-06-A3.P.1.02.pdf (🔒 authorized access only).
To get the manuscript, please contact IAF Secretariat.