Compressed digital holograms: snapshot optical imaging and inspection

Since the invention of Gabor in 1948, holography has provided a means of observing light wave phase information, which can quantitatively analyze the interaction between light and matter, and has been widely used in biomedical imaging, defect detection, morphology measurement and other fields. Digital holographic imaging directly records the diffraction image of the sample through the image sensor, and then uses the algorithm numerical inversion to achieve image reconstruction, which has once again attracted the attention of the academic community with the development of computational optical imaging technology in recent years.

Figure 1: Schematic diagram of a digital holographic imaging system

Since image sensors such as CCD and CMOS can only respond to the intensity of light waves, phase information is lost during acquisition, and light field inversion becomes an unstable problem, resulting in twins in the reconstructed image, which seriously affects the quality of holographic reconstruction. The existing holographic reconstruction algorithm faces the problem of difficulty between robustness and reconstruction quality: the iterative projection method uses physical constraints to limit the solution space, which has high robustness and universality, but the reconstruction quality is poor; The regularization method combines the prior characteristics such as the sparsity of the signal, and optimizes the objective function, which can achieve a high reconstruction quality in specific situations, but often sacrifices a certain generalization.


Figure 2: Schematic diagram of alternating projection and regularization algorithm

In view of this, Professor Cao Liangcai’s research group of Tsinghua University proposed a compressed digital holographic algorithm framework, which combines the respective advantages of alternating projection and sparse regularization methods, and only needs to collect a hologram to achieve quantitative phase imaging with high robustness and reconstruction quality.

The study, titled “Iterative projection meets sparsity regularization: towards practical single-shot quantitative phase imaging with in-line holography,” was published online in the latest issue of Light: Advanced Manufacturing。

In this work, the author takes the combination of non-negative absorption physical constraints and gradient domain sparse priori as an example, establishes an image reconstruction non-convex optimization model, and uses the proximal gradient algorithm to iteratively solve the problem, and finally reconstructs the amplitude and phase distribution of the sample from a hologram.


Figure 3: Holographic reconstruction of muscle tissue sections

By comparing the standard test samples, it is verified that the method has high accuracy in the reconstruction of amplitude and phase information. Therefore, this method can be widely applied to absorbent samples (such as histopathological detection, etc.) and transparent samples (such as live-cell imaging, optical element surface type characterization, etc.).


Figure 4: Amplitude pattern discrimination plate reconstruction results


Figure 5: Phase type identification plate reconstruction results

Since the phase reflects the optical path difference as light propagates through the sample, the surface topography distribution of the sample can be solved from the phase information. The figure below shows the phase and surface height reconstruction of a Fresnel bandpiece with a surface etching bath approximately 500 nm deep.

Figure 6: Phase and surface reconstruction results of transparent structures

This work also solves the problem of convergence of the traditional algorithm. In this paper, the author reveals the local convergence of the algorithm through the analysis of the geometric properties of the optimization problem, and provides theoretical guidance for parameter selection in practical applications.

In conclusion, a digital holographic algorithm framework with high robustness and reconstruction quality is proposed, which realizes snapshot-based quantitative phase imaging, and has been applied in biological tissue imaging and device surface characterization. The algorithm model and the corresponding convergence theory can be applied to different digital holographic imaging systems, and can be extended to a variety of physical constraints and sparse transformations.

The relevant program and experimental data have also been open sourced on GitHub (。

In the future, the characterization capabilities of nonlinear transformation and implicit signal priors will be further explored, and extended to application scenarios such as far-field coherent diffraction imaging. (Source: Advanced Manufacturing WeChat public account)

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