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We discuss time-optimal path planning for a Dubins vehicle operating in a planar environment required to investigate a series of static objects of interest. The objects are obscured such that they can be viewed only from a specified direction. The vehicle is equipped with an arbitrary number of sensors projecting circle sector viewing areas of arbitrary size and offset angle from the vehicle's heading, allowing for a range of vehicle orientations at which the objects can be viewed. Our objective is to minimize the total path distance the vehicle must travel while ensuring that the vehicle views all targets once from their respective required viewing direction. We discretize the sensors' area and examine the resulting possible solutions with an exhaustive search algorithm and show Monte Carlo simulation results of the exhaustive search algorithm compared to a standard Dubins algorithm.