Autofocusing based on wavelength dependence of diffraction in two-wavelength digital holographic microscopy

Rapid flowing cells localization enabled by spatiotemporal manipulation of their holographic patterns

Lab-on-a-Chip microfluidic devices present an innovative and cost-effective platform in the current trend of miniaturization and simplification of imaging flow cytometry; they are excellent candidates for high-throughput single-cell analysis. In such microfluidic platforms, cell tracking becomes a fundamental tool for investigating biophysical processes, from intracellular dynamics to the characterization of cell motility and migration. However, high-throughput and long-term cell tracking puts a high demand on the consumption of computing resources. Here, we propose a novel strategy to achieve rapid 3D cell localizations along the microfluidic channel. This method is based on the spatiotemporal manipulation of recorded holographic interference fringes, and it allows fast and precise localization of cells without performing complete holographic reconstruction. Conventional holographic tracking is typically based on the phase contrast obtained by decoupling the calculation of optical axial and transverse coordinates. Computing time and resource consumption may increase because all the frames need to be calculated in the Fourier domain. In our proposed method, the 2D transverse positions are directly located by morphological calculation based on the hologram. The complex-amplitude wavefronts are directly reconstructed by spatiotemporal phase shifting to calculate the axial position by the refocusing criterion. Only spatial calculation is considered in the proposed method. We demonstrate that the computational time of transverse tracking is only one-tenth of the conventional method, while the total computational time of the proposed method decreases up to 54% with respect to the conventional approach. The proposed approach can open the route for analyzing flow cytometry in quantitative phase microscopy assays.

Spherical wave illumination scanning digital holographic profilometry

In this work, we proposed what we believe to be a novel scanning solution for the assessment of high-NA samples, referred to as spherical-wave illumination scanning digital holographic profilometry (SWS-DHP). This approach introduces a 2F optimization methodology, based on the measurement of the focal length of the object to determine the spherical component of the scanning. Furthermore, re-optimization of 2F, whether it needs to be operated depends on the measured object's NA to inspect more information. Meanwhile, utilizing phase space analysis shows SWS superiority in information transfer for high-NA samples compared to plane-wave illumination scanning. In addition, this method introduces a shape reconstruction algorithm with volumetric aberration compensation based on the propagation of the aberrated object and illumination waves to obtain high-quality measurements. Finally, the imaging merits of SWS-DHP were proved through simulations and were experimentally verified for the object of NA up to 0.87.

Fermat Principle, Ramsey Theory and Metamaterials

Reinterpretation of the Fermat principle governing the propagation of light in media within the Ramsey theory is suggested. Complete bi-colored graphs corresponding to light propagation in media are considered. The vertices of the graphs correspond to the points in real physical space in which the light sources or sensors are placed. Red links in the graphs correspond to the actual optical paths, emerging from the Fermat principle. A variety of optical events, such as refraction and reflection, may be involved in light propagation. Green links, in turn, denote the trial/virtual optical paths, which actually do not occur. The Ramsey theorem states that within the graph containing six points, inevitably, the actual or virtual optical cycle will be present. The implementation of the Ramsey theorem with regard to light propagation in metamaterials is discussed. The Fermat principle states that in metamaterials, a light ray, in going from point S to point P, must traverse an optical path length L that is stationary with respect to variations of this path. Thus, bi-colored graphs consisting of links corresponding to maxima or minima of the optical paths become possible. The graphs, comprising six vertices, will inevitably demonstrate optical cycles consisting of the mono-colored links corresponding to the maxima or minima of the optical path. The notion of the "inverse graph" is introduced and discussed. The total number of triangles in the "direct" (source) and "inverse" Ramsey optical graphs is the same. The applications of "Ramsey optics" are discussed, and an optical interpretation of the infinite Ramsey theorem is suggested.

Spectroscopic atomic sample plane localization for precise digital holography

In digital holography, the coherent scattered light fields can be reconstructed volumetrically. By refocusing the fields to the sample planes, absorption and phase-shift profiles of sparsely distributed samples can be simultaneously inferred in 3D. This holographic advantage is highly useful for spectroscopic imaging of cold atomic samples. However, unlike e.g. biological samples or solid particles, the quasi-thermal atomic gases under laser-cooling are typically featureless without sharp boundaries, invalidating a class of standard numerical refocusing methods. Here, we extend the refocusing protocol based on the Gouy phase anomaly for small phase objects to free atomic samples. With a prior knowledge on a coherent spectral phase angle relation for cold atoms that is robust against probe condition variations, an "out-of-phase" response of the atomic sample can be reliably identified, which flips the sign during the numeric back-propagation across the sample plane to serve as the refocus criterion. Experimentally, we determine the sample plane of a laser-cooled ³⁹K gas released from a microscopic dipole trap, with a δz ≈ 1 µm ≪ 2λ_p/NA² axial resolution, with a NA=0.3 holographic microscope at λ_p = 770 nm probe wavelength.

Fast autofocusing based on pixel difference with the Tanimoto coefficient between images

Focusing objects accurately over short time scales is an essential and nontrivial task for a variety of microscopy applications. In this Letter, an autofocusing algorithm using pixel difference with the Tanimoto coefficient (PDTC) is described to predict the focus. Our method can robustly distinguish differences in clarity among datasets. The generated auto-focusing curves have extremely high sensitivity. A dataset of a defocused stack acquired by an Olympus microscope demonstrates the feasibility of our technique. This work can be applied in full-color microscopic imaging systems and is also valid for single-color imaging.

Versatile optimization-based speed-up method for autofocusing in digital holographic microscopy

We propose a speed-up method for the in-focus plane detection in digital holographic microscopy that can be applied to a broad class of autofocusing algorithms that involve repetitive propagation of an object wave to various axial locations to decide the in-focus position. The classical autofocusing algorithms apply a uniform search strategy, i.e., they probe multiple, uniformly distributed axial locations, which leads to heavy computational overhead. Our method substantially reduces the computational load, without sacrificing the accuracy, by skillfully selecting the next location to investigate, which results in a decreased total number of probed propagation distances. This is achieved by applying the golden selection search with parabolic interpolation, which is the gold standard for tackling single-variable optimization problems. The proposed approach is successfully applied to three diverse autofocusing cases, providing up to 136-fold speed-up.

Improved three-dimensional localization of multiple small objects in close proximity in digital holography

Using intensity gradient- or sparsity-based focus metrics, the ability to accurately localize the three-dimensional (3D) position of a small object in a digital holographic reconstruction of a large field of view is hindered in the presence of multiple nearby objects. A more accurate alternative method for 3D localization, based on evaluation of the complex reconstructed volume, is proposed. Simulations and experimental data demonstrate a reduction in depth positional error for single objects and a notably improved axial resolution of multiple objects in close proximity.

Robust autofocusing method for multi-wavelength lensless imaging

Lensless imaging based on multi-wavelength phase retrieval becomes a promising technology widely used as it has simple acquisition, miniaturized size and low-cost setup. However, measuring the sample-to-sensor distance with high accuracy, which is the key for high-resolution reconstruction, is still a challenge. In this work, we propose a multi-wavelength criterion to realize autofocusing modulation, i.e., achieving much higher accuracy in determining the sample-to-sensor distance, compared to the conventional methods. Three beams in different spectrums are adopted to illuminate the sample, and the resulting holograms are recorded by a CCD camera. The patterns calculated by performing back propagation of the recorded holograms, with exhaustively searched sample-to-sensor distance value, are adopted to access the criterion. Image sharpness can be accessed and the optimal sample-to-sensor distance can be finely determined by targeting the valley of the curve given by the criterion. Through our novel multi-wavelength based autofocusing strategy and executing further phase retrieval process, high-resolution images can be finally retrieved. The applicability and robustness of our method is validated both in simulations and experiments. Our technique provides a useful tool for multi-wavelength lensless imaging under limited experimental conditions.

Multi-wavelength quantitative polarization and phase microscope

We introduce a snapshot multi-wavelength quantitative polarization and phase microscope (MQPPM) for measuring spectral dependent quantitative polarization and phase information. The system uniquely integrates a polarized light microscope and a snap-shot quantitative phase microscope in a single system, utilizing a novel full-Stokes camera operating in the red, green, and blue (RGB) spectrum. The linear retardance and fast axis orientation of a birefringent sample can be measured simultaneously in the visible spectra. Both theoretical analysis and experiments have been performed to demonstrate the capability of the proposed microscope. Data from liquid crystal and different biological samples are presented. We believe that MQPPM will be a useful tool in measuring quantitative polarization and phase information of live cells.

Adaptive lens-free computational coherent imaging using autofocusing quantification with speckle illumination

Multi-distance phase retrieval (MDPR) based lensfree imaging is promising for an aberration free and compact biological imaging system. In the MDPR processing, the measurement uncertainty of the sample-to-sensor distance undermines its imaging quality and imposes a heavy workload to achieve a perfect reconstruction. The optimal distance can be searched by using an image sharpness quantification function with a refocused data set, however, the scanning is sensitive to noise and aliasing artifact for MDPR. In this work, we propose an adaptive imaging scheme with the help of a diffuser inserted in the lensfree system. The optimal sample-to-sensor distance is searched by combing speckle imaging with sharpness quantification function. With this speckle-based auxiliary, intensity patterns under a coherent illumination are directly used to achieve an in-focusing image reconstruction. Experiments are given to demonstrate the stability, imaging resolution and optical sectioning for our scheme. This method provides a simple, stable and robust tool for the auto-focusing imaging.

Refractive index measurement of suspended cells using opposed-view digital holographic microscopy

Opposed-view digital holographic microscopy (OV-DHM) with autofocusing and out-of-focus background suppression was demonstrated and applied to measure the refractive index (RI) of suspended HeLa cells. In OV-DHM, a specimen is illuminated from two sides in a 4π-like configuration. The generated two opposite-view object waves, which have orthogonal polarization orientations, interfere with a common reference wave, and the generated holograms are recorded by a CMOS camera. The image plane of the sample was determined by finding the minimal variation between the two object waves. The out-of-focus background was suppressed by averaging the two object waves. Simultaneous determination of both the cell thickness and the phase retardation was avoided by using a spheroidal model for the detached cell obtained from confocal microscopy. Thus, the RI of suspended HeLa cells was measured from phase images of OV-DHM, with the thickness of the cells estimated by using a constant axial-to-lateral ratio. This measurement strategy reveals the RI with an accuracy of ∼10% of the RI difference between cells and surrounding medium.

Opposite-view digital holographic microscopy with autofocusing capability

Digital holographic microscopy (DHM) has its intrinsic ability to refocusing a sample by numerically propagating an object wave from its hologram plane to its image plane. In this paper opposite-view digital holographic microscopy (OV-DHM) is demonstrated for autofocusing, namely, digitally determining the location of the image plane, and refocusing the object wave without human intervention. In OV-DHM, a specimen is illuminated from two sides in a 4π-alike configuration, and two holograms are generated and recorded by a CCD camera along two orthogonal polarization orientations. The image plane of the sample is determined by finding the minimal variation between the two object waves, and consequently refocusing is performed by propagating the waves to the image plane. Furthermore, the field of view (FOV) of OV-DHM can be extended by combining the two object waves which have an angle in-between. The proposed technique also has the potential to reduce speckle noise and out-of-focus background.

Automatic focusing for multisectional objects in digital holography using the structure tensor

Determining the axial position of the recorded object in digital holography is a crucial step for image reconstruction. When multiple discrete sections of a three-dimensional object are overlapping each other, this issue becomes more challenging. In this Letter, an autofocusing algorithm using the structure tensor and its eigenvalues is proposed. This method can extract the focal distance of each section for a multi-sectional object irrespective of whether the sections are overlapping or not. We validate the applicability of the proposed technique with synthesized and experimental data using two types of holographic systems.

Fast autofocusing in digital holography using the magnitude differential

Typical methods of automatic estimation of focusing in digital holography calculate every single reconstructed frame to get a critical function and then ascertain the focal plane by finding the extreme value of that function. Here, we propose a digital holographic autofocusing method that computes the focused distance using the first longitudinal difference of the magnitude of the reconstructed image. We demonstrate the proposed method with both numerical simulations and optical experiments of amplitude-contrast and phase-contrast objects. The results suggest that the proposed method performs better than other existing methods, in terms of applicability and computation efficiency, with potential applications in industrial and biomedical inspections where automatic focus tracking is necessary.

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.

Digital holographic microscopy as a tool to study the thermal shape fluctuations of lipid vesicles

The bending elasticity modulus of lipid membranes is obtained by applying for the first time, to the best of our knowledge, a novel experimental technique based on digital holographic microscopy. The fluctuations of the radius with time were extracted by tracking and measuring the optical thickness at the vesicle poles. The temporal autocorrelation function of the vesicle diameter computed for each of the studied vesicles was then fitted with the theoretical expression to deduce the membrane's tension and bending constant. For the bending elasticity modulus of SOPC bilayers, the value of (0.93 ± 0.03) × 10(-12) erg was obtained. This result is in accordance with values previously obtained by means of other conventional methods for the same type of lipid membrane in the presence of sugar molecules in aqueous medium. The obtained results encourage the future development of the digital holographic microscopy as a technique suitable for the measurement of the bending elasticity of lipid membranes.

Color imaging-in-flow by digital holographic microscopy with permanent defect and aberration corrections

Color imaging-in-flow of particles is performed using red-green-blue (RGB) digital holographic microscopy (DHM), whose sources are partially coherent. RGB DHM provides intensity and quantitative phase images in the three color channels, which is valuable for observing small objects in numerous fields. In-flow investigation on a large depth of field is made possible by the refocusing capability of DHM and has many potential applications. A method is also developed to automatically correct the color balance and compensate both intensity and phase defects and aberrations, providing high-quality imaging. Experimental results show color in-flow analysis of microplankton and confirm the efficiency of the correction method.

Refocusing criterion via sparsity measurements in digital holography

Several automatic approaches have been proposed in the past to compute the refocus distance in digital holography (DH). However most of them are based on a maximization or minimization of a suitable amplitude image contrast measure, regarded as a function of the reconstruction distance parameter. Here we show that, by using the sparsity measure coefficient regarded as a refocusing criterion in the holographic reconstruction, it is possible to recover the focus plane and, at the same time, establish the degree of sparsity of digital holograms, when samples of the diffraction Fresnel propagation integral are used as a sparse signal representation. We employ a sparsity measurement coefficient known as Gini's index thus showing for the first time, to the best of our knowledge, its application in DH, as an effective refocusing criterion. Demonstration is provided for different holographic configurations (i.e., lens and lensless apparatus) and for completely different objects (i.e., a thin pure phase microscopic object as an in vitro cell, and macroscopic puppets) preparation.

Refocus criterion for both phase and amplitude objects in digital holographic microscopy

For digital holographic microscopy applications, we modify the focus criterion based on the integration of the amplitude modulus to make possible its use regardless of the phase or amplitude nature of the objects under test. When applied on holographic data, the original criterion gives, at the focus plane, a minimum or a maximum, for amplitude or phase objects. The criterion we propose here operates on high-pass filtered complex amplitudes. It is shown that the proposed criterion gives a minimum for both types of objects when the focus plane is reached. Experimental results on real samples and simulations are provided, illustrating the efficiency and the potential of the method.

Flexible focus function consisting of convex function and image enhancement filter

We propose a new focus function Λ that, like many of the existing focus functions, consists of a convex function and an image enhancement filter. Λ is rather flexible because for any convex function and image enhancement filter, it is a focus function. We proved that Λ is a focus function using a model and Jensen's inequality. Furthermore, we generated random Λs and experimentally applied them to simulated and real blurred images, finding that 98% and 99% of the random Λs, respectively, have a maximum value at the best-focused image and most of them decrease as the defocus increases. We also applied random Λs to motion-blurred images, blurred images in different-sized windows, and blurred images with different types of noise. We found that Λ can be applied to motion blur and is robust to different-sized windows and different noise types.

Holographic tracking of living cells by three-dimensional reconstructed complex wavefronts alignment

We propose here a new three-dimensional (3D) holographic tracking method capable to track, simultaneously and in a single step, all the spatial coordinates of micro-objects. The approach is based on the enhanced correlation coefficient (ECC) maximization method but applied, for the first time to the best of our knowledge, directly on the holographic reconstructed complex wave fields. The key novelty of the proposed strategy is its ability to calculate simultaneously the 3D coordinates of cells, without decoupling the contribution of amplitude and phase. The proposed strategy is tested on living cells (i.e., NIH 3T3 mouse fibroblast) flowing into a microfluidic channel and compared with classical holographic tracking approach. Theoretical description and experimental validation of the proposed strategy are reported.

High-precision topography measurement through accurate in-focus plane detection with hybrid digital holographic microscope and white light interferometer module

High-precision topography measurement of micro-objects using interferometric and holographic techniques can be realized provided that the in-focus plane of an imaging system is very accurately determined. Therefore, in this paper we propose an accurate technique for in-focus plane determination, which is based on coherent and incoherent light. The proposed method consists of two major steps. First, a calibration of the imaging system with an amplitude object is performed with a common autofocusing method using coherent illumination, which allows for accurate localization of the in-focus plane position. In the second step, the position of the detected in-focus plane with respect to the imaging system is measured with white light interferometry. The obtained distance is used to accurately adjust a sample with the precision required for the measurement. The experimental validation of the proposed method is given for measurement of high-numerical-aperture microlenses with subwavelength accuracy.

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.

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.

Autofocusing of digital holographic microscopy based on off-axis illuminations

An auto-focusing method for digital holographic microscopy has been proposed by employing two off-axis illumination beams. When specimens are illuminated by two plane waves in different directions, it is found that the farther the reconstruction plane is from the image plane, the wider the two reconstructed images are separated from each other. Thus, the image plane can be determinated by finding the minimum of the variation between the two reconstructed object waves on both the amplitude and phase distributions. The feasibility of the proposed method is demonstrated by the corresponding simulation and experiment.