Focus detection criterion for refocusing in multi-wavelength digital holography

Refocus criterion from image-plane speckle correlation in digital holographic interferometry

In digital holography and holographic interferometry, refocusing to the correct image plane can be challenging and may be obtained by various metrics. This paper proposes a digital refocus approach utilizing the linear relationship between in-plane speckle motion and defocus as a response to an induced phase gradient. The theory based on cross-correlations between pairs of intensity images reconstructed at different distances from the recording plane is discussed. Two simple metrics, based on the cross-correlation properties of the reconstructed speckle images, are proposed and evaluated utilizing both simulations and experiments. Experiments exhibit similar trends in which the estimate of the correct reconstruction distance differs by a small amount between the two metrics. The difference is found less than 1% in the estimate of the true reconstruction distance. The results show that either metric is able to yield a sufficient reconstruction distance for the reconstruction of the image plane.

Digital holographic microscopy of spiropyran-based dynamic materials

Spiropyran (SP)-based dynamic materials undergo structural changes in response to external stimuli. In this paper, we show that digital holographic microscopy (DHM) is an effective candidate for characterisation of SPs (embedded in polymer matrices) and for monitoring of their dynamical changes. The polymer matrices are polylactic acid (PLA) and poly(methyl methacrylate) (PMMA) films, which are decorated with SPs and immobilised on graphene quantum dots (GQDs). GQDs are modified by benzylamines prior to the loading of SP species because of the enhancement of hydrophobic characteristics. UV irradiation is used as the external stimulus and the dynamical changes of the samples before and after UV irradiation are measured. DHM is arranged on a novel self-referencing setup, which substantially reduces the sensitivity of DHM to environmental vibrations. Morphometric information for characterisation of the samples is obtained by analysis of the recorded digital holograms. The experimental results demonstrate the potential of the presented technique to serve as an alternative technique for surface measurement methodologies such as atomic force microscope and stylus profiler for surface characterisation of similar materials.

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.

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.

Object plane detection and phase retrieval from single-shot holograms using multi-wavelength in-line holography

Phase retrieval and the twin-image problem in digital in-line holographic microscopy can be resolved by iterative reconstruction routines. However, recovering the phase properties of an object in a hologram requires an object plane to be chosen correctly for reconstruction. In this work, we present a novel multi-wavelength iterative algorithm to determine the object plane using single-shot holograms recorded at multiple wavelengths in an in-line holographic microscope. Using micro-sized objects, we verify the object positioning capabilities of the method for various shapes and derive the phase information using synthetic and experimental data. Experimentally, we built a compact digital in-line holographic microscopy setup around a standard optical microscope with a regular RGB-CCD camera and acquired holograms of micro-spheres, E. coli, and red blood cells, which are illuminated using three lasers operating at 491 nm, 532 nm, and 633 nm, respectively. We demonstrate that our method provides accurate object plane detection and phase retrieval under noisy conditions, e.g., using low-contrast holograms with an inhomogeneous background. This method allows for automatic positioning and phase retrieval suitable for holographic particle velocimetry, and object tracking in biophysical or colloidal research.

Quality assessment of refocus criteria for particle imaging in digital off-axis holography

This paper proposes a quality assessment of focusing criteria for imaging in digital off-axis holography. In the literature, several refocus criteria have been proposed in the past to get the best refocus distance in digital holography. As a general rule, the best focusing plane is determined by the reconstruction distance for which the criterion function presents a maximum or a minimum. To evaluate the robustness of these criteria, 13 criteria are compared with application on both amplitude and phase objects from off-axis holographic data. Simulation and experimental results lead to define a general rule and to exhibit the most robust criteria for accurate and rapid refocusing in digital holography.

Refocus criterion based on maximization of the coherence factor in digital three-wavelength holographic interferometry

This Letter presents an alternative approach for image refocusing in digital Fresnel holography. In the literature, a large majority of reported focus detection criteria is based on amplitude contrast or phase contrast. We propose a focus detection criterion based on the speckle phase coherence factor. This factor reaches its maximum value at the best focus distance. At any reconstruction distance, estimation of the coherence factor is based on robust noise estimation from anisotropic diffusion. We propose a theoretical relation to estimate the coherence factor from the measured standard deviation. Experimental results for the case of three-color holographic imaging and interferometry are provided. Experimental results show the suitability of the proposed approach for image plane refocusing.

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.

Microtomography imaging of an isolated plant fiber: a digital holographic approach

This paper describes a method for optical projection tomography for the 3D in situ characterization of micrometric plant fibers. The proposed approach is based on digital holographic microscopy, the holographic capability being convenient to compensate for the runout of the fiber during rotations. The setup requires a telecentric alignment to prevent from the changes in the optical magnification, and calibration results show the very good experimental adjustment. Amplitude images are obtained from the set of recorded and digitally processed holograms. Refocusing of blurred images and correction of both runout and jitter are carried out to get appropriate amplitude images. The 3D data related to the plant fiber are computed from the set of images using a dedicated numerical processing. Experimental results exhibit the internal and external shapes of the plant fiber. These experimental results constitute the first attempt to obtain 3D data of flax fiber, about 12  μm×17  μm in apparent diameter, with a full-field optical tomography approach using light in the visible range.

Influence of defocus on quantitative analysis of microscopic objects and individual cells with digital holography

Digital holography offers a unique method for studying microscopic objects using quantitative measurements of the optical phase delays of transmitted light. The optical phase may be integrated across the object to produce an optical volume measurement, a parameter related to dry mass by a simple scaling factor. While digital holography is useful for comparing the properties of microscopic objects, especially cells, we show here that quantitative comparisons of optical phase can be influenced by the focal plane of the measurement. Although holographic images can be refocused digitally using Fresnel propagation, ambiguity can result if this aspect is not carefully controlled. We demonstrate that microscopic objects can be accurately profiled by employing a digital refocusing method to analyze phase profiles of polystyrene microspheres and red blood cells.

Fast and robust automatic calibration for single-shot dual-wavelength digital holography based on speckle displacements

The objective of this paper is to describe a fast and robust automatic single-shot dual-wavelength holographic calibration method that can be used for online shape measurement applications. We present a model of the correction in two terms for each lobe, one to compensate the systematic errors caused by off-axis angles and the other for the curvature of the reference waves, respectively. Each hologram is calibrated independently without a need for an iterative procedure or information of the experimental set-up. The calibration parameters are extracted directly from speckle displacements between different reconstruction planes. The parameters can be defined as any fraction of a pixel to avoid the effect of quantization. Using the speckle displacements, problems associated with phase wrapping is avoided. The procedure is shown to give a shape accuracy of 34 μm using a synthetic wavelength of 1.1 mm for a measurement on a cylindrical test object with a trace over a field of view of 18  mm×18  mm.

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.

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.

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.

High-precision three-dimensional shape reconstruction via digital refocusing in multi-wavelength digital holography

Three-dimensional (3D) shape reconstructions and metrology measurements are often limited by depth-of-field constraints. Current focus-detection-based techniques are insufficient to profile out-of-focus 3D objects with high axial accuracy. Extended-focus imaging (EFI) techniques can improve the range and precision of such measurements. By incorporating digital refocusing with multiwavelength interferometry, a holographic imaging solution is presented in this paper to accurately measure 3D objects over a large depth range. Accuracy and repeatability of the proposed EFI technique are validated by digital simulations and refocusing experiments. A reconstruction example demonstrates the feasibility of high-precision 3D measurements of objects deeper than the system's classical depth of field.