A practical inverse-problem approach to digital holographic reconstruction.

In this paper, we propose a new technique for high-quality reconstruction from single digital holographic acquisitions. The unknown complex object field is found as the solution of a nonlinear inverse problem that consists in the minimization of an energy functional. The latter includes total-variation (TV) regularization terms that constrain the spatial amplitude and phase distributions of the reconstructed data. The algorithm that we derive tolerates downsampling, which allows to acquire substantially fewer measurements for reconstruction compared to the state of the art. We demonstrate the effectiveness of our method through several experiments on simulated and real off-axis holograms.

Full field vertical scanning in short coherence digital holographic microscope.

In Digital holography Microscopes (DHM) implemented in the so-called "off axis" configuration, the object and reference wave fronts are not co-planar but form an angle of a few degrees. This results into two main drawbacks. First, the contrast of the interference is not uniform spatially when the light source has low coherence. The interference contrast is optimal along a line, but decreases when moving away from it, resulting in a lower image quality. Second, the non-coplanarity between the coherence plane of both wavefronts impacts the coherence vertical scanning measurement mode: when the optical path difference between the signal and the reference beam is changed, the region of maximum interference contrast shifts laterally in the plane of the objective. This results in more complex calculations to extract the topography of the sample and requires scanning over a much larger vertical range, leading to a longer measurement time. We have previously shown that by placing a volume diffractive optical element (VDOE) in the reference arm, the wavefront can be made coplanar with the object wavefront and the image plane of the microscope objective, resulting in a uniform and optimal interferogram. In this paper, we demonstrate a vertical scanning speed improvement by an order of magnitude. Noise in the phase and intensity images caused by scattering and non-uniform diffraction in the VDOE is analyzed quantitatively. Five VDOEs were fabricated with an identical procedure. We observe that VDOEs introduce a small intensity non-uniformity in the reference beam which results in a 20% noise increase in the extracted phase image as compared to the noise in extracted phase image when the VDOE is removed. However, the VDOE has no impact on the temporal noise measured from extracted phase images.

Optical reconstruction of transparent objects with phase-only SLMs.

Three approaches for visualization of transparent micro-objects from holographic data using phase-only SLMs are described. The objects are silicon micro-lenses captured in the near infrared by means of digital holographic microscopy and a simulated weakly refracting 3D object with size in the micrometer range. In the first method, profilometric/tomographic data are retrieved from captured holograms and converted into a 3D point cloud which allows for computer generation of multi-view phase holograms using Rayleigh-Sommerfeld formulation. In the second method, the microlens is computationally placed in front of a textured object to simulate the image of the textured data as seen through the lens. In the third method, direct optical reconstruction of the micrometer object through a digital lens by modifying the phase with the Gerchberg-Saxton algorithm is achieved.

Determination of transmembrane water fluxes in neurons elicited by glutamate ionotropic receptors and by the cotransporters KCC2 and NKCC1: a digital holographic microscopy study.

Digital holographic microscopy (DHM) is a noninvasive optical imaging technique that provides quantitative phase images of living cells. In a recent study, we showed that the quantitative monitoring of the phase signal by DHM was a simple label-free method to study the effects of glutamate on neuronal optical responses (Pavillon et al., 2010). Here, we refine these observations and show that glutamate produces the following three distinct optical responses in mouse primary cortical neurons in culture, predominantly mediated by NMDA receptors: biphasic, reversible decrease (RD) and irreversible decrease (ID) responses. The shape and amplitude of the optical signal were not associated with a particular cellular phenotype but reflected the physiopathological status of neurons linked to the degree of NMDA activity. Thus, the biphasic, RD, and ID responses indicated, respectively, a low-level, a high-level, and an "excitotoxic" level of NMDA activation. Moreover, furosemide and bumetanide, two inhibitors of sodium-coupled and/or potassium-coupled chloride movement strongly modified the phase shift, suggesting an involvement of two neuronal cotransporters, NKCC1 (Na-K-Cl) and KCC2 (K-Cl) in the genesis of the optical signal. This observation is of particular interest since it shows that DHM is the first imaging technique able to monitor dynamically and in situ the activity of these cotransporters during physiological and/or pathological neuronal conditions.

Accelerated autofocusing of off-axis holograms using critical sampling.

In this Letter we propose a fast off-axis hologram autofocusing (AF) approach that is based on the redundant data elimination by the critical resampling of the contained complex field. Implementation of the proposed methodology enables the real-time AF with up to 12× speed-up factors in comparison to the classical approach. The method is further extended for single-shot physical autofocus of the fluorescence imaging channel of multimodal imaging instruments capable of off-axis hologram acquisition.

Local demodulation of holograms using the Riesz transform with application to microscopy.

We propose a Riesz transform approach to the demodulation of digital holograms. The Riesz transform is a higher-dimensional extension of the Hilbert transform and is steerable to a desired orientation. Accurate demodulation of the hologram requires a reliable methodology by which quadrature-phase functions (or simply, quadratures) can be constructed. The Riesz transform, by itself, does not yield quadratures. However, one can start with the Riesz transform and construct the so-called vortex operator by employing the notion of quasi-eigenfunctions, and this approach results in accurate quadratures. The key advantage of using the vortex operator is that it effectively handles nonplanar fringes (interference patterns) and has the ability to compensate for the local orientation. Therefore, this method results in aberration-free holographic imaging even in the case when the wavefronts are not planar. We calibrate the method by estimating the orientation from a reference hologram, measured with an empty field of view. Demodulation results on synthesized planar as well as nonplanar fringe patterns show that the accuracy of demodulation is high. We also perform validation on real experimental measurements of Caenorhabditis elegans acquired with a digital holographic microscope.

Reconstruction in interferometric synthetic aperture microscopy: comparison with optical coherence tomography and digital holographic microscopy.

It is shown that the spatial frequencies recorded in interferometric synthetic aperture microscopy do not correspond to exact backscattering [as they do in unistatic synthetic aperture radar (SAR)] and that the reconstruction process based on SAR is therefore based on an approximation. The spatial frequency response is developed based on the three-dimensional coherent transfer function approach and compared with that in optical coherence tomography and digital holographic microscopy.

Monte Carlo simulation of the field back-scattered from rough surfaces.

A novel approach for the simulation of the field back-scattered from a rough surface is presented. It takes into account polarization and multiple scattering events on the surface, as well as diffraction effects. The validity and usefulness of this simulation is demonstrated in the case of surface topology measurement.

Nonlinear Reconstruction of Images from Patterns Generated by Deterministic or Random Optical Masks-Concepts and Review of Research.

Indirect-imaging methods involve at least two steps, namely optical recording and computational reconstruction. The optical-recording process uses an optical modulator that transforms the light from the object into a typical intensity distribution. This distribution is numerically processed to reconstruct the object's image corresponding to different spatial and spectral dimensions. There have been numerous optical-modulation functions and reconstruction methods developed in the past few years for different applications. In most cases, a compatible pair of the optical-modulation function and reconstruction method gives optimal performance. A new reconstruction method, termed nonlinear reconstruction (NLR), was developed in 2017 to reconstruct the object image in the case of optical-scattering modulators. Over the years, it has been revealed that the NLR can reconstruct an object's image modulated by an axicons, bifocal lenses and even exotic spiral diffractive elements, which generate deterministic optical fields. Apparently, NLR seems to be a universal reconstruction method for indirect imaging. In this review, the performance of NLR isinvestigated for many deterministic and stochastic optical fields. Simulation and experimental results for different cases are presented and discussed.

Dual wavelength full field imaging in low coherence digital holographic microscopy.

A diffractive optical element (DOE) is presented to simultaneously manipulate the coherence plane tilt of a beam containing a plurality of discrete wavelengths. The DOE is inserted into the reference arm of an off-axis dual wavelength low coherence digital holographic microscope (DHM) to provide a coherence plane tilt so that interference with the object beam generates fringes over the full detector area. The DOE maintains the propagation direction of the reference beam and thus it can be inserted in-line in existing DHM set-ups. We demonstrate full field imaging in a reflection commercial DHM with two wavelengths, 685 nm and 794 nm, resulting in an unambiguous range of 2.494 micrometers.

Quantitative phase restoration by direct inversion using the optical transfer function.

Quantitative phase recovery of phase objects is achieved by a direct inversion using the defocused weak object transfer function. The presented method is noniterative and is based on partially coherent principles. It also takes into account the optical properties of the system and gives the phase of the object directly. The proposed method is especially suitable for application to weak phase objects, such as live and unstained biological samples but, surprisingly, has also been shown to work with comparatively strong phase objects.

Exact complex-wave reconstruction in digital holography.

We address the problem of exact complex-wave reconstruction in digital holography. We show that, by confining the object-wave modulation to one quadrant of the frequency domain, and by maintaining a reference-wave intensity higher than that of the object, one can achieve exact complex-wave reconstruction in the absence of noise. A feature of the proposed technique is that the zero-order artifact, which is commonly encountered in hologram reconstruction, can be completely suppressed in the absence of noise. The technique is noniterative and nonlinear. We also establish a connection between the reconstruction technique and homomorphic signal processing, which enables an interpretation of the technique from the perspective of deconvolution. Another key contribution of this paper is a direct link between the reconstruction technique and the two-dimensional Hilbert transform formalism proposed by Hahn. We show that this connection leads to explicit Hilbert transform relations between the magnitude and phase of the complex wave encoded in the hologram. We also provide results on simulated as well as experimental data to validate the accuracy of the reconstruction technique.

Roadmap on Digital Holography-Based Quantitative Phase Imaging.

Quantitative Phase Imaging (QPI) provides unique means for the imaging of biological or technical microstructures, merging beneficial features identified with microscopy, interferometry, holography, and numerical computations. This roadmap article reviews several digital holography-based QPI approaches developed by prominent research groups. It also briefly discusses the present and future perspectives of 2D and 3D QPI research based on digital holographic microscopy, holographic tomography, and their applications.

Iterative method for zero-order suppression in off-axis digital holography.

We propose a method to suppress the so-called zero-order term in a hologram, based on an iterative principle. During the hologram acquisition process, the encoded information includes the intensities of the two beams creating the interference pattern, which do not contain information about the recorded complex wavefront, and that can disrupt the reconstructed signal. The proposed method selectively suppresses the zero-order term by employing the information obtained during wavefront reconstruction in an iterative procedure, thus enabling its suppression without any a priori knowledge about the object. The method is analyzed analytically and its convergence is studied. Then, its performance is shown experimentally. Its robustness is assessed by applying the procedure on various types of holograms, such as topographic images of microscopic specimens or speckle holograms.

Real time, nanometric 3D-tracking of nanoparticles made possible by second harmonic generation digital holographic microscopy.

In the past decade, quantitative phase imaging gave a new dimension to optical microscopy, and the recent extension of digital holography techniques to nonlinear microscopy appears very promising, for the phase of nonlinear signal provides additional information, inaccessible to incoherent imaging schemes. In this work, we show that the position of second harmonic generation (SHG) emitters can be determined from their respective phase, at the nanometer scale, with single-shot off-axis digital holography, making possible real-time nanometric 3D-tracking of SHG emitters such as nanoparticles.

Physical interpretation of the phase function related parameter γ studied with a fractal distribution of spherical scatterers.

The optical properties within limited volumes of diffusive media can be probed by carrying spatially-resolved measurements of diffused light at short source-detector separation (typically one scattering mean free path). At such distance, analytical models only relying on the absorption and reduced scattering coefficients fail at correctly predicting reflectance and it was demonstrated that adding a third optical coefficient γ improves the description of light propagation conditions near the source. In an attempt to relate the γ coefficient to physical properties of turbid media, this paper uses a fractal distribution law for modeling scatterers' sizes distributions and investigates numerically and experimentally how γ is related to the fractal power α. The results indicate that within the range of γ typically encountered in biological samples, this coefficient is approximately linearly correlated with α.

Microscopy image resolution improvement by deconvolution of complex fields.

Based on truncated inverse filtering, a theory for deconvolution of complex fields is studied. The validity of the theory is verified by comparing with experimental data from digital holographic microscopy (DHM) using a high-NA system (NA=0.95). Comparison with standard intensity deconvolution reveals that only complex deconvolution deals correctly with coherent cross-talk. With improved image resolution, complex deconvolution is demonstrated to exceed the Rayleigh limit. Gain in resolution arises by accessing the objects complex field - containing the information encoded in the phase - and deconvolving it with the reconstructed complex transfer function (CTF). Synthetic (based on Debye theory modeled with experimental parameters of MO) and experimental amplitude point spread functions (APSF) are used for the CTF reconstruction and compared. Thus, the optical system used for microscopy is characterized quantitatively by its APSF. The role of noise is discussed in the context of complex field deconvolution. As further results, we demonstrate that complex deconvolution does not require any additional optics in the DHM setup while extending the limit of resolution with coherent illumination by a factor of at least 1.64.

Digital holographic reflectometry.

Digital holographic microscopy (DHM) is an interferometric technique that allows real-time imaging of the entire complex optical wavefront (amplitude and phase) reflected by or transmitted through a sample. To our knowledge, only the quantitative phase is exploited to measure topography, assuming homogeneous material sample and a single reflection on the surface of the sample. In this paper, dual-wavelength DHM measurements are interpreted using a model of reflected wave propagation through a three-interfaces specimen (2 layers deposited on a semi-infinite layer), to measure simultaneously topography, layer thicknesses and refractive indices of micro-structures. We demonstrate this DHM reflectometry technique by comparing DHM and profilometer measurement of home-made SiO(2)/Si targets and Secondary Ion Mass Spectrometry (SIMS) sputter craters on specimen including different multiple layers.

Label-free second-harmonic phase imaging of biological specimen by digital holographic microscopy.

We have previously developed a new way for nonscanning second-harmonic generation (SHG) microscopy [Opt. Lett. 34, 2450 (2009)]. Based on digital holography, this technique captures, in single-shot hologram acquisition, both the amplitude and the phase of a coherent SHG radiation, which makes possible second harmonic phase microscopy. In this work, we present holographic SHG phase microscopy of a label-free biological tissue and discuss its added value to SHG microscopy.

Extended depth-of-focus by digital holographic microscopy.

A recurrent problem in microscopy is the finite depth-of-focus linked to the NA of microscope objectives. Digital holographic microscopy (DHM) has the unique feature of being able to numerically change the focus from a single hologram without the need of moving the sample. Extended depth of focus of amplitude images has been demonstrated, but it has marginal interest for the metrological application of DHM that needs the topography. In this Letter, we demonstrate that DHM is able to provide not only extended depth-of-focus amplitude images but extended focused complex data from which the topography is computed. For this purpose, reflection and transmission measurements on micro-optics (microlens and retroreflector) performed by using standard reconstruction or the extended focused complex data are compared. These experiments demonstrate that DHM measures, from a single hologram acquisition, the accurate sample topography on a numerically increased depth-of-focus.