Precise beam shaping relies on accurate characterisation of deformations in phase and amplitude of a wave as it propagates. We investigate a process where only a priori information about the relative locations of arbitrary source regions in time are known. We use the correlations between each region to obtain information about amplitude and phase to piece together a wavefunction representing the wave. We demonstrate that this method can be used to characterise a singularity in an initially unknown wavefunction and remove it using a beam shaping device. In contrast to some other techniques that assume point correlations, we can use any set of simple connected shapes as correlation regions. This leads us to believe that it has some use to beam shaping applications in multimode-fibres or in turbid media where singularities are present in the scattered light.

精确的光束整形依赖于对波传播时相位和振幅变形的准确表征。我们调查一个过程，其中只有先验关于任意源区域在时间上的相对位置的信息是已知的。我们使用每个区域之间的相关性来获取有关振幅和相位的信息，以拼凑出表示波的波函数。我们证明该方法可用于表征初始未知波函数中的奇点，并使用光束整形设备将其移除。与其他一些假设点相关的技术相比，我们可以使用任何一组简单的连接形状作为相关区域。这使我们相信它对多模光纤中的光束整形应用或在散射光中存在奇点的混浊介质中具有一定的用途。