Improvement of accuracy in digital holography by use of multiple holograms

Towards Reduced CNNs for De-Noising Phase Images Corrupted with Speckle Noise

Digital holography is a very efficient technique for 3D imaging and the characterization of changes at the surfaces of objects. However, during the process of holographic interferometry, the reconstructed phase images suffer from speckle noise. In this paper, de-noising is addressed with phase images corrupted with speckle noise. To do so, DnCNN residual networks with different depths were built and trained with various holographic noisy phase data. The possibility of using a network pre-trained on natural images with Gaussian noise is also investigated. All models are evaluated in terms of phase error with HOLODEEP benchmark data and with three unseen images corresponding to different experimental conditions. The best results are obtained using a network with only four convolutional blocks and trained with a wide range of noisy phase patterns.

Theoretical analysis of surface-shape-induced decorrelation noise in multi-wavelength digital holography

This paper presents analytical modelling for describing the speckle noise decorrelation in phase data from two- or multiple-wavelength digital holography. A novel expression for the modulus of the coherence factor is proposed for the case of two-wavelength speckle decorrelation from imaging roughness and surface shape through an optical system. The expression permits us to estimate the speckle decorrelation phase noise in surface shape measurements. The theoretical analysis is supported by realistic simulations including both the surface roughness and shape. The results demonstrate the very good agreement between the modulus of the coherence factor estimated with the simulation and the one calculated with theory.

Enhancing laser speckle reduction by decreasing the pitch of a chiral nematic liquid crystal diffuser

The artefact known as speckle can plague numerous imaging applications where the narrow linewidth of laser light is required, which includes laser projection and medical imaging. Here, we report on the use of thin-film chiral nematic liquid crystal (LC) devices that can be used to mitigate the influence of speckle when subjected to an applied electric field. Results are presented which show that the speckle contrast (a quantitative measure of the presence of speckle) can be significantly reduced by decreasing the pitch of the chiral nematic LC from 2700 to 244 nm. Further reduction in the speckle contrast can be observed by operating the diffuser technology at a temperature close to the chiral nematic to isotropic transition. At such temperatures, we observe a simultaneous improvement in the transmission of light through the device and a decrease in the electric field amplitude required for the minimum speckle contrast value. We conclude by presenting a laser projected image of the 1951 USAF target with and without the LC device to demonstrate the visual improvement as a result of the speckle reduction.

Physical pupil manipulation for speckle reduction in digital holographic microscopy

The reduction of speckle noise by physically changing the pupil of the imaging system, as first envisioned in optical holography, is experimentally applied to a digital holographic microscope (DHM). The imaging pupil of a DHM, operating in image plane telecentric-afocal architecture, is changed in a controlled way between successive recordings, allowing the shooting of multiple partially-decorrelated holograms. Averaging the numerically reconstructed holograms yields amplitude and/or phase images with reduced speckle noise. Experimental results of biological specimens and a phase-only resolution test show the feasibility to recover micron-sized features in images with reduced speckle noise.

Simulation of digital holographic recording and reconstruction using a generalized matrix method

In recent years, research efforts in the field of digital holography have expanded significantly, due to the ability to obtain high-resolution intensity and phase images. The information contained in these images have become of great interest to the machine learning community, with applications spanning a wide portfolio of research areas, including bioengineering. In this work, we seek to demonstrate a high-fidelity simulation of holographic recording. By accurately and numerically simulating the propagation of a coherent light source through a series of optical elements and the object itself, we accurately predict the optical interference of the object and reference wave at the recording plane, including diffraction effects, aberrations, and speckle. We show that the optical transformation that predicts the complex field at the recording plane can be generalized for arbitrary holographic recording configurations using a matrix method. In addition, we provide a detailed description of digital phase reconstruction and aberration compensation for a variety of off-axis holographic configurations. Reconstruction errors are presented for the various holographic recording geometries and complex field objects. While the primary objective of this work is not to evaluate phase reconstruction approaches, the reconstruction of simulated holograms provides validation of the generalized simulation method. The long-term goal of this work is that the generalized holographic simulation motivates the use of phase reconstruction of the simulated holograms to populate databases for training machine-learning algorithms aimed at classifying relevant objects recorded through a variety of holographic setups.

Speckle Noise Reduction in Digital Holography Using a DMD and Multi-Hologram Resampling

Speckle noise is a well-documented problem on coherent imaging techniques like Digital Holography. A method to reduce the speckle noise level is presented, based on introducing a Digital Micromirror Device to phase modulate the illumination over the object. Multiple holograms with varying illuminations are recorded and the reconstructed intensities are averaged to obtain a final improved image. A simple numerical resampling scheme is proposed to further improve noise reduction. The obtained results demonstrate the effectiveness of the hybrid approach.

Hybrid method for speckle noise reduction in digital holography

In digital holography, the inherited speckle noise degrades imaging quality due to the coherent laser source. To overcome this problem, a hybrid method for speckle noise reduction is presented by combining a novel angular diversity approach with the block-matching and 3D filtering (BM3D) algorithm. A serial of holograms is first captured by the proposed recording approach, and then the image with high signal-to-noise ratio is obtained by averaging multiple reconstructed intensity images. Finally, the residual noise in the averaged image is further eliminated by the BM3D filtering algorithm. The speckle noise is significantly suppressed, and a nearly speckle-free image can be obtained. Experimental results demonstrate the effectiveness of the proposed method.

Comparative study of multi-look processing for phase map de-noising in digital Fresnel holographic interferometry

This paper presents a comparative study of multi-look approaches for de-noising phase maps from digital holographic interferometry. A database of 160 simulated phase fringe patterns with eight different phase fringe patterns with fringe diversity was computed. For each fringe pattern, 20 realistic noise realizations are generated in order to simulate a multi-look process with 20 inputs. A set of 22 de-noising algorithms was selected and processed for each simulation. Three approaches for multi-look processing are evaluated. Quantitative appraisal is obtained using two metrics. The results show good agreement for algorithm rankings obtained with both metrics. One singular and highly practical result of the study is that a multi-look approach with average looks before noise processing performs better than averaging computed with all de-noised looks. The results also demonstrate that the two-dimensional windowed Fourier transform filtering exhibits the best performance in all cases and that the block-matching 3D (BM3D) algorithm is second in the ranking.

Strategies for reducing speckle noise in digital holography

Digital holography (DH) has emerged as one of the most effective coherent imaging technologies. The technological developments of digital sensors and optical elements have made DH the primary approach in several research fields, from quantitative phase imaging to optical metrology and 3D display technologies, to name a few. Like many other digital imaging techniques, DH must cope with the issue of speckle artifacts, due to the coherent nature of the required light sources. Despite the complexity of the recently proposed de-speckling methods, many have not yet attained the required level of effectiveness. That is, a universal denoising strategy for completely suppressing holographic noise has not yet been established. Thus the removal of speckle noise from holographic images represents a bottleneck for the entire optics and photonics scientific community. This review article provides a broad discussion about the noise issue in DH, with the aim of covering the best-performing noise reduction approaches that have been proposed so far. Quantitative comparisons among these approaches will be presented.

Reduction of speckle noise in holographic images using spatial jittering in numerical reconstructions

This Letter presents an easy, fast, and efficient single-shot method to reduce speckle noise in digital Fresnel holography. In this method, several images from a single hologram are reconstructed by introducing spatial displacements in the Fresnel kernel. Spatial jitters produce images with different speckle positions. Averaging the set of numerically produced images leads to a strong reduction of speckle noise in both amplitude and phase difference images. The experimental results show the suitability of the proposed approach and confirm its applicability to digital holographic interferometry.

Spatially multiplexed interferometric microscopy with partially coherent illumination

We have recently reported on a simple, low cost, and highly stable way to convert a standard microscope into a holographic one [Opt. Express 22, 14929 (2014)]. The method, named spatially multiplexed interferometric microscopy (SMIM), proposes an off-axis holographic architecture implemented onto a regular (nonholographic) microscope with minimum modifications: the use of coherent illumination and a properly placed and selected one-dimensional diffraction grating. In this contribution, we report on the implementation of partially (temporally reduced) coherent illumination in SMIM as a way to improve quantitative phase imaging. The use of low coherence sources forces the application of phase shifting algorithm instead of off-axis holographic recording to recover the sample’s phase information but improves phase reconstruction due to coherence noise reduction. In addition, a less restrictive field of view limitation (1/2) is implemented in comparison with our previously reported scheme (1/3). The proposed modification is experimentally validated in a regular Olympus BX-60 upright microscope considering a wide range of samples (resolution test, microbeads, swine sperm cells, red blood cells, and prostate cancer cells).

Phase retrieval deblurring for imaging of dense object within a low scattering soft biological tissue

Tissues are characterized by a strong scattering of visible optical radiation, which prevents one from achieving deep-tissue imaging. We propose a computational imaging technique for the inference of specific macroscopic, spatial phase distribution features of the scattering media. The spatial phase distribution is reconstructed from several defocused intensity images. We empirically demonstrate the method by reconstructing the location of two fibula chicken bones, embedded within chicken breast tissue. The suggested technique is safe, using visible laser illumination, and noninvasive. It is also cost-effective since a simple optical system is used and the images are acquired using a conventional camera, and it does not require interferometric detection as well as direct access to the object in absence of the layer.

Quasi noise-free digital holography

One of the main drawbacks of Digital Holography (DH) is the coherent nature of the light source, which severely corrupts the quality of holographic reconstructions. Although numerous techniques to reduce noise in DH have provided good results, holographic noise suppression remains a challenging task. We propose a novel framework that combines the concepts of encoding multiple uncorrelated digital holograms, block grouping and collaborative filtering to achieve quasi noise-free DH reconstructions. The optimized joint action of these different image-denoising methods permits the removal of up to 98% of the noise while preserving the image contrast. The resulting quality of the hologram reconstructions is comparable to the quality achievable with non-coherent techniques and far beyond the current state of art in DH. Experimental validation is provided for both single-wavelength and multi-wavelength DH, and a comparison with the most used holographic denoising methods is performed.

Quantitative appraisal for noise reduction in digital holographic phase imaging

This paper discusses on a quantitative comparison of the performances of different advanced algorithms for phase data de-noising. In order to quantify the performances, several criteria are proposed: the gain in the signal-to-noise ratio, the Q index, the standard deviation of the phase error, and the signal to distortion ratio. The proposed methodology to investigate de-noising algorithms is based on the use of a realistic simulation of noise-corrupted phase data. A database including 25 fringe patterns divided into 5 patterns and 5 different signal-to-noise ratios was generated to evaluate the selected de-noising algorithms. A total of 34 algorithms divided into different families were evaluated. Quantitative appraisal leads to ranking within the considered criteria. A fairly good correlation between the signal-to-noise ratio gain and the quality index has been observed. There exists an anti-correlation between the phase error and the quality index which indicates that the phase errors are mainly structural distortions in the fringe pattern. Experimental results are thoroughly discussed in the paper.

Single-shot speckle reduction in numerical reconstruction of digitally recorded holograms

A single-shot method to reduce the speckle noise in the numerical reconstructions of electronically recorded holograms is presented. A recorded hologram with the dimensions N×M is split into S=T×T sub-holograms. The uncorrelated superposition of the individually reconstructed sub-holograms leads to an image with the speckle noise reduced proportionally to the 1/S law. The experimental results are presented to support the proposed methodology.

Improving holographic reconstruction by automatic Butterworth filtering for microelectromechanical systems characterization

Digital holographic microscopy is an important interferometric tool in optical metrology allowing the investigation of engineered surfaces with microscale lateral resolution and nanoscale axial precision. In particular, microelectromechanical systems (MEMS) surface analysis, conducted by holographic characterization, requires high accuracy for functional testing. The main issues related to MEMS inspection are the superficial roughness and the complex geometry resulting from the several fabrication steps. Here, an automatic procedure, particularly suited in the case of high-roughness surfaces, is presented to selectively filter the spectrum, providing very low-noise reconstructed images. The numerical procedure is based on Butterworth filtering, and the obtained results demonstrate a significant increase in the images' quality and in the accuracy of the measurements, making our technique highly applicable for quantitative phase imaging in MEMS analysis. Furthermore, our method is fully tunable to the spectrum under investigation and automatic. This makes it highly suitable for real-time applications. Several experimental tests show the suitability of the proposed approach.

Speckle reduction in holographic projection by random pixel separation with time multiplexing

A speckle-reduction method with random locations of sparse object points is proposed for image quality improvement based on a time-multiplexing approach in holographic reconstruction. The object points of a reconstructed image are divided into groups of sparse object points. Pixel separation of the periodic location, in general, is used for the sparse object points. However, an unwanted periodic fringe pattern is caused, and it dominantly degrades the reconstructed image quality. The proposed random pixel separation enables the reconstructed image quality to improve more effectively. The numerical simulation and the optical experiment are presented to confirm the performance of the proposed method.

Encoding multiple holograms for speckle-noise reduction in optical display

In digital holography (DH) a mixture of speckle and incoherent additive noise, which appears in numerical as well as in optical reconstruction, typically degrades the information of the object wavefront. Several methods have been proposed in order to suppress the noise contributions during recording or even during the reconstruction steps. Many of them are based on the incoherent combination of multiple holographic reconstructions achieving remarkable improvement, but only in the numerical reconstruction i.e. visualization on a pc monitor. So far, it has not been shown the direct synthesis of a digital hologram which provides the denoised optical reconstruction. Here, we propose a new effective method for encoding in a single complex wavefront the contribution of multiple incoherent reconstructions, thus allowing to obtain a single synthetic digital hologram that show significant speckle-reduction when optically projected by a Spatial Light Modulator (SLM).

Imaging adherent cells in the microfluidic channel hidden by flowing RBCs as occluding objects by a holographic method

Imaging through turbid media is a challenging topic. A liquid is considered turbid when dispersed particles provoke strong light scattering, thus destroying the image formation by any standard optical system. Generally, colloidal solutions belong to the class of turbid media since dispersed particles have dimensions ranging between 0.2 μm and 2 μm. However, in microfluidics, another relevant issue has to be considered in the case of flowing liquid made of a multitude of occluding objects, e.g. red blood cells (RBCs) flowing in veins. In such a case instead of severe scattering processes unpredictable phase delays occur resulting in a wavefront distortion, thus disturbing or even hindering the image formation of objects behind such obstructing layer. In fact RBCs can be considered to be thin transparent phase objects. Here we show that sharp amplitude imaging and phase-contrast mapping of cells hidden behind biological occluding objects, namely RBCs, is possible in harsh noise conditions and with a large field-of view by Multi-Look Digital Holography microscopy (ML-DH). Noteworthy, we demonstrate that ML-DH benefits from the presence of the RBCs, providing enhancement in terms of numerical resolution and noise suppression thus obtaining images whose quality is higher than the quality achievable in the case of a liquid without occlusive objects.

Accelerated numerical processing of electronically recorded holograms with reduced speckle noise

The numerical reconstruction of digitally recorded holograms suffers from speckle noise. An accelerated method that uses general-purpose computing in graphics processing units to reduce that noise is shown. The proposed methodology utilizes parallelized algorithms to record, reconstruct, and superimpose multiple uncorrelated holograms of a static scene. For the best tradeoff between reduction of the speckle noise and processing time, the method records, reconstructs, and superimposes six holograms of 1024 × 1024 pixels in 68 ms; for this case, the methodology reduces the speckle noise by 58% compared with that exhibited by a single hologram. The fully parallelized method running on a commodity graphics processing unit is one order of magnitude faster than the same technique implemented on a regular CPU using its multithreading capabilities. Experimental results are shown to validate the proposal.

Dual-channel low-coherence interferometry and its application to quantitative phase imaging of fingerprints

We introduce an off-axis, wide-field, low-coherence and dual-channel interferometric imaging system, which is based on a simple-to-align, common-path interferometer. The system requires no optical-path-difference matching between the interferometric arms in order to obtain interference with low-coherence light source, and is capable of achieving two channels of off-axis interference with high spatial frequency. The two 180°-phase-shifted interferograms are acquired simultaneously using a single digital camera, and processed into a single, noise-reduced and DC-suppressed interferogram. We demonstrate using the proposed system for phase imaging of fingerprint templates. Due to the fact that conventional phase unwrapping algorithms cannot handle the complex and deep surface topography imposed by fingerprint templates, we experimentally implemented two-wavelength phase unwrapping using a supercontinuum laser coupled to acousto-optical tunable filter, together functioning as a low-coherence tunable light source. From the unwrapped phase map, we produced high quality depth profiles of fingerprint templates.

Clear coherent imaging in turbid microfluidics by multiple holographic acquisitions

Recently it has been demonstrated that digital holography is a powerful means allowing imaging of both amplitude and phase objects in turbid flowing media. However, in quasi-static turbid microfluidics, multiple scattering contributions through the colloids superimpose coherently to the recording device, resulting in speckle noise and hindering a clear vision of the objects. In this Letter we exploit the Brownian motion of the colloidal particles to get multiple uncorrelated holograms, and we combine them to reduce the speckle contrast. In this way we get a multi-look gain without losing image resolution.

High topographical accuracy by optical shot noise reduction in digital holographic microscopy

In this work, we present a new method to reduce the shot noise in phase imaging of digital holograms. A spatial averaging process of phase images reconstructed at different reconstruction distances is performed, with the reconstruction distance range being specified by the numerical focus depth of the optical system. An improved phase image is attained with a 50% shot noise reduction. We use the integral of the angular spectrum as a reconstruction method to obtain a single-object complex amplitude that is needed to perform our proposal. We also show the corresponding simulations and experimental results. The topography of a homemade TiO2 stepwise of 100 nm high was measured and compared with the atomic force microscope results.

Estimation of wavelength difference using scale adjustment in two-wavelength digital holographic interferometry

We propose a method for an estimation of wavelength difference using scale adjustment in two-wavelength digital holographic interferometry. To estimate wavelength difference, two holograms recorded with different wavelengths are reconstructed on the basis of the Fresnel diffraction integral, and pixel sizes in the reconstruction plane, which depend on the wavelength in recording hologram, are analyzed. In the analysis, a zero-padding method and an intensity correlation function are used to adjust pixel sizes in the reconstruction plane and then obtain a wavelength difference given by a difference between the pixel sizes. Theoretical predictions and experimental results are shown to indicate the usefulness of the proposed method in this paper.

Experimental and theoretical investigation of the pixel saturation effect in digital holography

This paper presents an experimental investigation and an analytical modeling of the nonlinear pixel saturation effect in digital off-axis holography. The theoretical analysis is based on a semiempirical modeling and supported by the experimental analysis. Taking into account the nonlinearity of the phenomenon, an exponential law for the high-order harmonic amplitude is proposed and validated by the experimental results. The conclusion of this analysis is that the saturation effect can be described by the use of a linear operator that involves autoconvolution of the initial object wave, even though the saturation phenomenon is nonlinear.

Magnified reconstruction of digitally recorded holograms by Fresnel-Bluestein transform

A method for numerical reconstruction of digitally recorded holograms with variable magnification is presented. The proposed strategy allows for smaller, equal, or larger magnification than that achieved with Fresnel transform by introducing the Bluestein substitution into the Fresnel kernel. The magnification is obtained independent of distance, wavelength, and number of pixels, which enables the method to be applied in color digital holography and metrological applications. The approach is supported by experimental and simulation results in digital holography of objects of comparable dimensions with the recording device and in the reconstruction of holograms from digital in-line holographic microscopy.

Optimal noise suppression in Fresnel incoherent correlation holography (FINCH) configured for maximum imaging resolution

An optimal setup in the sense of imaging resolution for the Fresnel incoherent correlation holography (FINCH) system is proposed and analyzed. Experimental results of the proposed setup in reflection mode suffer from low signal-to-noise ratio (SNR) due to a granular noise. SNR improvement is achieved by two methods that rely on increasing the initial amount of phase-shifted recorded holograms. In the first method, we average over several independent complex-valued digital holograms obtained by recording different sets of three digital phase-shifted holograms. In the second method, the least-squares solution for solving a system of an overdetermined set of linear equations is approximated by utilizing the Moore-Penrose pseudoinverse. These methods improve the resolution of the reconstructed image due to their ability to reveal fine and weak details of the observed object.

High resolution digital holographic synthetic aperture applied to deformation measurement and extended depth of field method

This paper discusses the potential of the synthetic-aperture method in digital holography to increase the resolution, to perform high accuracy deformation measurement, and to obtain a three-dimensional topology map. The synthetic aperture method is realized by moving the camera with a motorized x-y stage. In this way a greater sensor area can be obtained resulting in a larger numerical aperture (NA). A larger NA enables a more detailed reconstruction combined with a smaller depth of field. The depth of field can be increased by applying the extended depth of field method, which yields an in-focus reconstruction of all longitudinal object regions. Moreover, a topology map of the object can be obtained.

General theoretical formulation of image formation in digital Fresnel holography

We present a detailed analysis of image formation in digital Fresnel holography. The mathematical modeling is developed on the basis of Fourier optics, making possible the understanding of the different influences of each of the physical effects invoked in digital holography. Particularly, it is demonstrated that spatial resolution in the reconstructed plane can be written as a convolution product of functions that describe these influences. The analysis leads to a thorough investigation of the effect of the width of the sensor, the surface of pixels, the numerical focusing, and the aberrations of the reference wave, as well as to an explicit formulation of the Shannon theorem for digital holography. Experimental illustrations confirm the proposed theoretical analysis.

Influence of shot noise on phase measurement accuracy in digital holographic microscopy

Digital Holographic Microscopy (DHM) is a single shot interferometric technique, which provides quantitative phase images with subwavelength axial accuracy. A short hologram acquisition time (down to microseconds), allows DHM to offer a reduced sensitivity to vibrations, and real time observation is achievable thanks to present performances of personal computers and charge coupled devices (CCDs). Fast dynamic imaging at low-light level involves few photons, requiring proper camera settings (integration time and gain of the CCD; power of the light source) to minimize the influence of shot noise on the hologram when the highest phase accuracy is aimed. With simulated and experimental data, a systematic analysis of the fundamental shot noise influence on phase accuracy in DHM is presented.

Determination of large-scale out-of-plane displacements in digital Fourier holography

A novel approach for the determination of large-scale out-of-plane displacements from digital Fourier holograms is presented. The proposed method is invariant to lateral object shifts. It is based on the determination of the scaling of the reconstructed image that occurs when the recording distance is changed. For a precise determination of the scaling factor, we utilize the Mellin transform. After the discussion of mathematical and computational issues, experimental results are presented to verify the theoretical considerations. The results show that displacements of at least up to 8.4% from the initial recording distance can be detected with this approach. The displacements could be determined with a deviation of typically less than 1.0% from the set values.

Aperture synthesis in phase retrieval using a volume-speckle field

The resolution of the reconstructed wave by a phase-retrieval method using a volume-speckle field depends on the aperture defined by the size of the CCD array. The use of a larger aperture is introduced by measuring the speckle field at two different positions in the transverse plane and stitching the measurements together. Improvements in the quality of reconstructions are demonstrated experimentally and by computer simulations. Undesirable effects of camera tilt on the quality of reconstructions from synthetic aperture intensity measurements are experimentally observed and corrected.