In a variety of scientific applications we are interested in imaging 3D objects at very fine resolutions. However,
we typically can not measure the object or its footprint directly.
Rather restricted by fundamental laws governing the propagation
of light we have access to 2D magnitude-only measurements of
the 3D object through highly nonlinear projection mappings.
Therefore, reconstructing the object requires inverting highly
nonlinear and seemingly non-invertible mappings. In this paper
we discuss some of the challenges that arises in such three dimensional phaseless imaging problems and offer possible solutions for
3D reconstruction. In particular we demonstrate how variants
of the recently proposed Accelerated Wirtinger Flow (AWF)
algorithm can enable precise 3D reconstruction at unprecedented
resolutions
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3D PHASE RETRIEVAL AT NANO-SCALE VIA ACCELERATED WIRTINGER FLOW
Imaging 3D nano-structures at very high resolution is crucial in a variety of scientific fields. However,
due to fundamental limitations of light propagation we can only measure the object indirectly via 2D
intensity measurements of the 3D specimen through highly nonlinear projection mappings where a
variety of information (including phase) is lost. Reconstruction therefore involves inverting highly nonlinear and seemingly non-invertible mappings. In this paper, we introduce a novel technique where
the 3D object is directly reconstructed from an accurate non-linear propagation model. Furthermore,
we characterize the ambiguities of this model and leverage a priori knowledge to mitigate their effect
and also significantly reduce the required number of measurements and hence the acquisition time.
We demonstrate the performance of our algorithm via numerical experiments aimed at nano-scale
reconstruction of 3D integrated circuits. Moreover, we provide rigorous theoretical guarantees for
convergence to stationarity.
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- NSF-PAR ID:
- 10159507
- Date Published:
- Journal Name:
- EUSIPCO
- ISSN:
- 2076-1465
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Accepted Manuscript1.0
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