We present a holographic imaging approach for the case in which a single source-detector pair is used to scan a sample. The source-detector pair collects intensity-only data at different frequencies and positions. By using an appropriate illumination strategy, we recover field cross correlations over different frequencies for each scan location. The problem is that these field cross correlations are asynchronized, so they have to be aligned first in order to image coherently. This is the main result of the paper: a simple algorithm to synchronize field cross correlations at different locations. Thus, one can recover full field data up to a global phase that is common to all scan locations. The recovered data are, then, coherent over space and frequency so they can be used to form high-resolution three-dimensional images. Imaging with intensity-only data is therefore as good as coherent imaging with full data. In addition, we use an ${\ell _1}$-norm minimization algorithm that promotes the low dimensional structure of the images, allowing for deep high-resolution imaging.

中文翻译：

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从单元素全息数据进行三维成像

对于单个源检测器对用于扫描样品的情况，我们提出了一种全息成像方法。源-探测器对在不同的频率和位置收集仅强度的数据。通过使用适当的照明策略，我们为每个扫描位置恢复了不同频率下的场互相关。问题在于这些场互相关是异步的，因此必须首先对齐它们才能进行相干成像。这是本文的主要结果：一种用于在不同位置同步场互相关的简单算法。因此，人们可以恢复全域数据，直到所有扫描位置共有的全局阶段为止。然后，恢复的数据在空间和频率上是连贯的，因此可以用于形成高分辨率的三维图像。因此，仅具有强度的数据成像与具有完整数据的相干成像一样好。另外，我们使用$ {\ ell _1} $-规范最小化算法，可促进图像的低维结构，从而实现深度的高分辨率成像。