Ecole Supérieure de Chimie Physique Electronique de Lyon, F-69616 Lyon, France.
Opt Lett. 2009 Nov 15;34(22):3475-7. doi: 10.1364/OL.34.003475.
Inline digital holograms are classically reconstructed using linear operators to model diffraction. It has long been recognized that such reconstruction operators do not invert the hologram formation operator. Classical linear reconstructions yield images with artifacts such as distortions near the field-of-view boundaries or twin images. When objects located at different depths are reconstructed from a hologram, in-focus and out-of-focus images of all objects superimpose upon each other. Additional processing, such as maximum-of-focus detection, is thus unavoidable for any successful use of the reconstructed volume. In this Letter, we consider inverting the hologram formation model in a Bayesian framework. We suggest the use of a sparsity-promoting prior, verified in many inline holography applications, and present a simple iterative algorithm for 3D object reconstruction under sparsity and positivity constraints. Preliminary results with both simulated and experimental holograms are highly promising.
内联数字全息图通常使用线性算子进行经典重建，以模拟衍射。长期以来，人们一直认识到，这种重建算子并没有反转全息图形成算子。经典的线性重建会产生具有失真的图像，例如在视场边界附近或孪生图像附近的失真。当从全息图中重建位于不同深度的物体时，所有物体的聚焦和离焦图像都会相互叠加。因此，对于任何成功使用重建体积的情况，都需要进行最大聚焦检测等额外处理。在这封信中，我们考虑在贝叶斯框架中反转全息图形成模型。我们建议使用在许多内联全息术应用中得到验证的稀疏促进先验，并提出了一种用于在稀疏性和正定性约束下进行 3D 物体重建的简单迭代算法。使用模拟和实验全息图的初步结果非常有希望。
