The first imaging devices of optical interferometry are likely to be of weak phase, typically: a set of three-element arrays independently observing the same object. The study of their imaging capabilities refers to appropriate optimization methods, which essentially address the self-calibration process and its stability. A general survey of these techniques is given, and it is shown, in particular, how the related algorithms can be used for examining the imaging capabilities of weak-phase interferometric devices. The phase-calibration algorithm involved in the self-calibration cycles is based on the principle underlying the trust-region methods. It benefits from certain remarkable properties, the analysis of which appeals to algebraic graph theory. The Fourier synthesis operation, which is also involved in these cycles, is performed by means of Wipe, a methodology recently introduced in radio imaging and optical interferometry. (Wipe is reminiscent of Clean, a widely used technique in astronomy). In the related theoretical framework the stability of the image-reconstruction process is controlled by considering certain elements of the singular-value decomposition of the derivative of the self-calibration operator. For example, the largest singular value of this derivative, which depends on the interferometric configuration and on the object thus imaged, provides a key indication of the observational limits of these experimental devices.
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