Sampling the Radon transform with beams of finite width

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Abstract
It is shown that a common method of taking data, based on a star shaped pattern in the sampling space, leads to a loss of as much at 50% of the information available to the experimenter, regardless of how many views are taken. An alternative method of taking data with parallel beams which samples all of the available information is proposed. For this method it is shown that the number of the independent pieces of information obtainable in the absence of noise is precisely n(k+1/2), where n is the number of views and k is the diameter of the object measured in units of the width of the beam. For large n this is at most n2/ pi +n/2.