Experimental Holograms Research Articles

Machine learning holography for measuring 3D particle distribution

We propose a learning-based image processing method for particle size measurement based on digital holography in this paper. The proposed approach uses a modified U-net architecture with recorded holograms, hologram reconstructed to each longitudinal location, and minimum intensity projection in longitudinal direction as inputs to produce outputs consisting of in-focus particles at each longitudinal location and their 2D centroids. A soft generalized dice loss is used for the particle size channel and a total variation regularized mean squared error loss is employed for the 2D centroids channel. The proposed method has been assessed using synthetic, manually-labeled experimental, and real experimental holograms. The results demonstrate that our approach have better performance in comparison to the state-of-the-art non-machine-learning methods in terms of particle extraction rate and positioning accuracy. Our learning-based approach can be readily extended to other types of image-based particle size measurement tasks such as shadowgraph imaging and defocusing imaging.

Machine learning holography for 3D particle field imaging

We propose a new learning-based approach for 3D particle field imaging using holography. Our approach uses a U-net architecture incorporating residual connections, Swish activation, hologram preprocessing, and transfer learning to cope with challenges arising in particle holograms where accurate measurement of individual particles is crucial. Assessments on both synthetic and experimental holograms demonstrate a significant improvement in particle extraction rate, localization accuracy and speed compared to prior methods over a wide range of particle concentrations, including highly dense concentrations where other methods are unsuitable. Our approach can be potentially extended to other types of computational imaging tasks with similar features.

From Fienup's phase retrieval techniques to regularized inversion for in-line holography: tutorial.

This paper includes a tutorial on how to reconstruct in-line holograms using an inverse problems approach, starting with modeling the observations, selecting regularizations and constraints, and ending with the design of a reconstruction algorithm. A special focus is placed on the connections between the numerous alternating projections strategies derived from Fienup's phase retrieval technique and the inverse problems framework. In particular, an interpretation of Fienup's algorithm as iterates of a proximal gradient descent for a particular cost function is given. Reconstructions from simulated and experimental holograms of micrometric beads illustrate the theoretical developments. The results show that the transition from alternating projections techniques to the inverse problems formulation is straightforward and advantageous.

Regularized inverse holographic volume reconstruction for 3D particle tracking.

The key limitations of digital inline holography (DIH) for particle tracking applications are poor longitudinal resolution, particle concentration limits, and case-specific processing. We utilize an inverse problem method with fused lasso regularization to perform full volumetric reconstructions of particle fields. By exploiting data sparsity in the solution and utilizing GPU processing, we dramatically reduce the computational cost usually associated with inverse reconstruction approaches. We demonstrate the accuracy of the proposed method using synthetic and experimental holograms. Finally, we present two practical applications (high concentration microorganism swimming and microfiber rotation) to extend the capabilities of DIH beyond what was possible using prior methods.

Holographic representation: Hologram plane vs. object plane

Digital holography allows the recording, storage and subsequent reconstruction of both amplitude and phase of the light field scattered by an object. This is accomplished by recording interference patterns that preserve the properties of the original object field essential for 3D visualization, the so-called holograms.Digital holography refers to the acquisition of holograms with a digital sensor, typically a CCD or a CMOS camera, and to the reconstruction of the 3D object field using numerical methods.In the current work, the different representations of digital holographic information in the hologram and in the object planes are studied. The coding performance of the different complex field representations, notably Amplitude-Phase and Real-Imaginary, in both the hologram plane and the object plane, is assessed using both computer generated and experimental holograms. The HEVC intra main coding profile is used for the compression of the different representations in both planes, either for experimental holograms or computer generated holograms.The HEVC intra compression in the object plane outperforms encoding in the hologram plane. Furthermore, encoding computer generated holograms in the object plane has a larger benefit than the same encoding over the experimental holograms. This difference was expected, since experimental holograms are affected by a larger negative influence of speckle noise, resulting in a loss of compression efficiency.This work emphasizes the possibility of holographic coding on the object plane, instead of the common encoding in the hologram plane approach. Moreover, this possibility allows direct visualization of the Object Plane Amplitude in a regular 2D display without any transformation methods. The complementary phase information can easily be used to render 3D features such as depth map, multi-view or even holographic interference patterns for further 3D visualization depending on the display technology.

Numerical dark field illumination applied to experimental digital lensless holographic microscopy for reconstructions with enhanced contrast.

The implementation of a numerical dark field illumination to obtain reconstructions with enhanced contrast in digital lensless holographic (DLHM) microscopy is presented. In this proposal, an opaque circular stop is numerically inserted in the light path between the sample and hologram plane. The contrast of the reconstructed holograms is increased at least 46% in comparison with that obtained by the regular reconstruction methods. This proposal has been validated using experimental holograms of a paramecium in water and a section of the head of a Drosophila melanogaster fly recorded in DLHM.

Regularized reconstruction of absorbing and phase objects from a single in-line hologram, application to fluid mechanics and micro-biology.

Reconstruction of phase objects is a central problem in digital holography, whose various applications include microscopy, biomedical imaging, and fluid mechanics. Starting from a single in-line hologram, there is no direct way to recover the phase of the diffracted wave in the hologram plane. The reconstruction of absorbing and phase objects therefore requires the inversion of the non-linear hologram formation model. We propose a regularized reconstruction method that includes several physically-grounded constraints such as bounds on transmittance values, maximum/minimum phase, spatial smoothness or the absence of any object in parts of the field of view. To solve the non-convex and non-smooth optimization problem induced by our modeling, a variable splitting strategy is applied and the closed-form solution of the sub-problem (the so-called proximal operator) is derived. The resulting algorithm is efficient and is shown to lead to quantitative phase estimation on reconstructions of accurate simulations of in-line holograms based on the Mie theory. As our approach is adaptable to several in-line digital holography configurations, we present and discuss the promising results of reconstructions from experimental in-line holograms obtained in two different applications: the tracking of an evaporating droplet (size ∼ 100μm) and the microscopic imaging of bacteria (size ∼ 1μm).

Pixel super-resolution in digital holography by regularized reconstruction

In-line digital holography (DH) and lensless microscopy are 3D imaging techniques used to reconstruct the volume of micro-objects in many fields. However, their performances are limited by the pixel size of the sensor. Recently, various pixel super-resolution algorithms for digital holography have been proposed. A hologram with improved resolution was produced from a stack of laterally shifted holograms, resulting in better resolved reconstruction than a single low-resolution hologram. Algorithms for super-resolved reconstructions based on inverse problems approaches have already been shown to improve the 3D reconstruction of opaque spheres. Maximum a posteriori (MAP) approaches have also been shown capable of reconstructing the object field more accurately and more efficiently and to extend the usual field-of-view. Here we propose an inverse problem formulation for DH pixel super-resolution and an algorithm that alternates registration and reconstruction steps. The method is described in detail and used to reconstruct synthetic and experimental holograms of sparse 2D objects. We show that our approach improves both the shift estimation and reconstruction quality. Moreover, the reconstructed field-of-view can be expanded by up to a factor 3, thus making it possible to multiply the analyzed area 9 fold.

Comparative analysis of autofocus functions in digital in-line phase-shifting holography.

Numerical reconstruction of digital holograms relies on a precise knowledge of the original object position. However, there are a number of relevant applications where this parameter is not known in advance and an efficient autofocusing method is required. This paper addresses the problem of finding optimal focusing methods for use in reconstruction of digital holograms of macroscopic amplitude and phase objects, using digital in-line phase-shifting holography in transmission mode. Fifteen autofocus measures, including spatial-, spectral-, and sparsity-based methods, were evaluated for both synthetic and experimental holograms. The Fresnel transform and the angular spectrum reconstruction methods were compared. Evaluation criteria included unimodality, accuracy, resolution, and computational cost. Autofocusing under angular spectrum propagation tends to perform better with respect to accuracy and unimodality criteria. Phase objects are, generally, more difficult to focus than amplitude objects. The normalized variance, the standard correlation, and the Tenenbaum gradient are the most reliable spatial-based metrics, combining computational efficiency with good accuracy and resolution. A good trade-off between focus performance and computational cost was found for the Fresnelet sparsity method.

Fast numerical autofocus of multispectral complex fields in digital holographic microscopy with a criterion based on the phase in the Fourier domain.

The knowledge of the complex amplitude of optical fields, that is, both quantitative phase and intensity, enables numeric reconstruction along the optical axis. Nonetheless, a criterion is required for autofocusing. This Letter presents a robust and rapid refocusing criterion suitable for color interferometric digital holographic microscopy, and, more generally, for applications where complex amplitude is known for at least two different wavelengths. This criterion uses the phase in the Fourier domain, which is compared among wavelengths. It is applicable whatever the nature of the observed object: opaque, refractive, or both mixed. The method is validated with simulated and experimental holograms.

3D boundary line measurement of irregular particle with digital holography

The morphology of an irregular particle plays a key role in its interactions with the surroundings, and the 3D characterization of an irregular particle is of essential importance. Digital inline holography in Gabor configuration is applied to measure the 2D shadow texture and 3D position, as well as the 3D boundary line of irregular particles. The depth position of the 3D boundary line can be determined with a criterion of the local deviation of the directional gradient over a small tilted rectangle, which covers the interrogated boundary section. The method is firstly verified by rigorous simulated particle holograms and then by accurate experimental fiber hologram. The 3D boundary line of an irregular coal particle is also measured. Results show that the 3D boundary line of an irregular particle can be accurately retrieved from the reconstructed volumetric optical particle field. This capability of 3D boundary line measurement enables the application of digital inline holography to the 3D diagnostic of the morphology and dynamics of irregular objects, including 3D rotation.

Physical compensation of phase curvature in digital holographic microscopy by use of programmable liquid lens.

Quantitative phase measurements obtained with digital holographic microscopes are strongly dependent on the optical arrangement of the imaging system. The nontelecentric operation provides phase measurements affected by a parabolic phase factor and requires numerical postprocessing, which does not always remove all the perturbation. Accurate phase measurements are achieved by using the imaging system in telecentric mode. Unfortunately, this condition is not accomplished when a commercial microscope is used as the imaging system. In this paper, we present an approach for obtaining accurate phase measurements in nontelecentric imaging systems without the need for numerical postprocessing. The method uses an electrically tunable liquid lens to illuminate the sample so that the perturbing parabolic wavefront is cancelled out. Experimental holograms of a Fresnel lens and a section of the thorax of a Drosophila melanogaster fly are captured to verify the proposed method.

Comparative analysis of the modified enclosed energy metric for self-focusing holograms from digital lensless holographic microscopy.

A comparative analysis of the performance of the modified enclosed energy (MEE) method for self-focusing holograms recorded with digital lensless holographic microscopy is presented. Notwithstanding the MEE analysis previously published, no extended analysis of its performance has been reported. We have tested the MEE in terms of the minimum axial distance allowed between the set of reconstructed holograms to search for the focal plane and the elapsed time to obtain the focused image. These parameters have been compared with those for some of the already reported methods in the literature. The MEE achieves better results in terms of self-focusing quality but at a higher computational cost. Despite its longer processing time, the method remains within a time frame to be technologically attractive. Modeled and experimental holograms have been utilized in this work to perform the comparative study.

Reconstruction of purely absorbing, absorbing and phase-shifting, and strong phase-shifting objects from their single-shot in-line holograms

We address the problem of reconstructing phase-shifting objects from their single shot in-line holograms. We show that a phase-shifting object cannot be reliably recovered from its in-line hologram by non-iterative reconstruction routines, and that an iterative reconstruction should be applied. We demonstrate examples of simulated in-line holograms of objects with the following properties: purely absorbing, both absorbing and phase shifting, and strong phase-shifting. We investigate the effects of noise and interference contrast in holograms on the reconstruction results and discuss details of an optimal iterative procedure to quantitatively recover the correct absorbing and phase-shifting properties of the object. We also review previously published reconstructions of experimental holograms and summarize the optimal parameters for retrieval of phase-shifting objects from their in-line holograms.

Direct particle depth displacement measurement in DHPTV using spatial correlation of focus metric curves

A method to accurately measure the particle depth displacement between a hologram pair is presented. A simple theoretical model formulates that the focus metric curves of a particle in a hologram pair are strongly spatially correlated, and that the particle's depth displacement is essentially encoded in the shift between the focus metric curves. The particle depth displacement can be directly evaluated from the cross correlation of the focus metric curves, rather than prior locating the particle's depth positions. Both simulation and experimental hologram pairs with depth displacement ranging from 10μm to 1000μm are tested, and results show that the depth displacement can be accurately obtained with the proposed method. This method has great potential in accurate 3D velocity computation in DHPTV.

Characterization of atomization and breakup of acoustically levitated drops with digital holography

A digital holographic particle tracking velocimetry system is applied to quantitatively study the drop atomization induced by capillary waves, and the breakup caused by increased sound pressure levels. A wavelet-based algorithm is used for particle detection and autofocusing with a wide size range of 20μm-2mm. To eliminate the influence of large particles on small particles, a two-step detection method is adopted. Large drops are first characterized and simulated by a diffraction-based model. Then the contributions of the drops are subtracted from the original hologram followed by the detection of small droplets. Finally, the velocity and size distribution of the secondary droplets are obtained from the experimental holograms. The results demonstrate the validity of the digital in-line holographic technique for the atomization and breakup study of acoustically levitated drops.

In-line particle holography with an astigmatic beam: setup self-calibration using an "inverse problems" approach.

The use of digital in-line holography for the characterization of confined flows in cylindrical geometry confinements (e.g., cylindrical pipe or cylindrical capillaries) is discussed. Due to cylindrical geometry of the walls, the illuminating laser wave can be strongly astigmatic, which renders the use of classical reconstruction techniques impossible. Contrary to plane wave holography setup, the diffraction pattern of the particles strongly depends on the axial distance of the latter to the entry face of the confinement structure. To address this reconstruction issue, we propose to use an "inverse problems" approach. This approach amounts to finding the best match (least squares solution) between a diffraction pattern model and the captured hologram. For this purpose, a direct imaging model for astigmatic holograms, based on the use of transfer matrices, is presented and validated by comparing experimental and simulated holograms. The accuracy of the "inverse problems" reconstruction is then used to calibrate the experimental setup adjustable parameters. Finally, the approach is tested through experimental astigmatic hologram reconstruction, thus paving the way to its use in pipe flow studies.

Refinement of particle detection by the hybrid method in digital in-line holography.

Digital in-line holography provides simultaneous particle size and three-dimensional position measurements. In general, the measurement accuracy varies locally, and tends to decrease where particles are closely spaced, due to noise resulting from diffraction by adjacent particles. Aggravating the situation is the identification of transversely adjoining particles as a single particle, which introduces significant errors in both size and position measurements. Here, we develop a refinement procedure that distinguishes such erroneous particles from accurately detected ones and further separates individual particles. Effectiveness of the refinement is characterized using simulations, experimental holograms of calibration fields, and a few practical applications to liquid breakup. Significant improvements in the accuracy of the measured particle sizes, positions, and displacements confirm the usefulness of the proposed method.

Automatic method for focusing biological specimens in digital lensless holographic microscopy.

A self-focusing method applicable to digital lensless holographic microscopy is presented. The method searches for the global minimum of the area enclosing a given amount of energy in a region surrounding the object of interest. The proposed modified enclosed energy method has been tested on self-focusing experimental holograms of a paramecium specimen and a section of the head of a drosophila melanogaster fly. The presented self-focusing technique also has been contrasted with some of the already reported methods to seek the best focus image.

Refocusing based on amplitude analysis in color digital holographic microscopy

A refocusing criterion adapted to red-green-blue (RGB) digital holographic microscopy is established. It is applicable for both amplitude and phase objects. This color criterion is based on a monochromatic criterion, using the integrated modulus amplitude. Simulated RGB holograms show the value of having color information, even for colorless samples; in addition, the position of the focus plane along the optical axis is determined more accurately. Simulations take into account both the numerical apertures of lenses and noise during the holographic process. We also implement an algorithm exponentially reducing the computation time required for detecting the focus plane. The method is validated on experimental holograms.