Abstract: An optical system includes an optical element defining an optical axis and a focal plane and a defocus element disposed between the optical element and the focal plane. The defocus element includes at least one first lens for producing a positive defocus image of a light beam passing through the optical element, irrespective of a position of the first lens along the optical axis, and at least one second lens for producing a negative defocus image of the light beam passing through the optical element, irrespective of a position of the second lens along the optical axis.

Abstract: A method of recovering unknown aberrations in an optical system includes collecting intensity data produced by the optical system, generating an initial estimate of a phase of the optical system, iteratively performing a phase retrieval on the intensity data to generate a phase estimate using an initial diversity function corresponding to the intensity data, generating a phase map from the phase retrieval phase estimate, decomposing the phase map to generate a decomposition vector, generating an updated diversity function by combining the initial diversity function with the decomposition vector, generating an updated estimate of the phase of the optical system by removing the initial diversity function from the phase map.

Abstract: Systems, methods and apparatus are provided through which, in some embodiments, a formal specification is pattern-matched from scenarios, the formal specification is analyzed, and flaws in the formal specification are corrected. The systems, methods and apparatus may include pattern-matching an equivalent formal model from an informal specification. Such a model can be analyzed for contradictions, conflicts, use of resources before the resources are available, competition for resources, and so forth. From such a formal model, an implementation can be automatically generated in a variety of notations. The approach can improve the resulting implementation, which, in some embodiments, is provably equivalent to the procedures described at the outset, which in turn can improve confidence that the system reflects the requirements, and in turn reduces system development time and reduces the amount of testing required of a new system.

Abstract: Systems, methods and apparatus are provided through which in some embodiments self health/urgency data and environment health/urgency data may be transmitted externally from an autonomic element. Other embodiments may include transmitting the self health/urgency data and environment health/urgency data together on a regular basis similar to the lub-dub of a heartbeat. Yet other embodiments may include a method for managing a system based on the functioning state and operating status of the system, wherein the method may include processing received signals from the system indicative of the functioning state and the operating status to obtain an analysis of the condition of the system, generating one or more stay alive signals based on the functioning status and the operating state of the system, transmitting the stay-alive signal, transmitting self health/urgency data, and transmitting environment health/urgency data.