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

Lensless single-shot dual-wavelength digital holography for industrial metrology

We demonstrate lensless single-shot dual-wavelength digital holography for high-speed 3D imaging in industrial inspection. Single-shot measurement is realized by combining off-axis digital holography and spatial frequency multiplexing of the two wavelengths on the detector. The system has 9.1 µm lateral resolution and a 50 µm unambiguous depth range. We determine the theoretical accuracy of off-axis dual-wavelength phase reconstruction for the case of shot-noise-limited detection. Experimental results show good agreement with the proposed model. The system is applied to industrial metrology of calibrated test samples and chip manufacturing.

Intensity correlation holography for remote phase sensing and 3D imaging

Holography is an established technique for measuring the wavefront of optical signals through interferometric combination with a reference wave. Conventionally the integration time of a hologram is limited by the interferometer coherence time, thus making it challenging to prepare holograms of remote objects, especially using weak illumination. Here, we circumvent this limitation by using intensity correlation interferometry. Although the exposure time of individual holograms must be shorter than the interferometer coherence time, we show that any number of randomly phase-shifted holograms can be combined into a single intensity-correlation hologram. In a proof-of-principle experiment, we use this technique to perform phase imaging and 3D reconstruction of an object at a ∼3 m distance using weak illumination and without active phase stabilization.

Low-intensity illumination for lensless digital holographic microscopy with minimized sample interaction

Exposure to laser light alters cell culture examination via optical microscopic imaging techniques based on label-free coherent digital holography. To mitigate this detrimental feature, researchers tend to use a broader spectrum and lower intensity of illumination, which can decrease the quality of holographic imaging due to lower resolution and higher noise. We study the lensless digital holographic microscopy (LDHM) ability to operate in the low photon budget (LPB) regime to enable imaging of unimpaired live cells with minimized sample interaction. Low-cost off-the-shelf components are used, promoting the usability of such a straightforward approach. We show that recording data in the LPB regime (down to 7 µW of illumination power) does not limit the contrast or resolution of the hologram phase and amplitude reconstruction compared to regular illumination. The LPB generates hardware camera shot noise, however, to be effectively minimized via numerical denoising. The ability to obtain high-quality, high-resolution optical complex field reconstruction was confirmed using the USAF 1951 amplitude sample, phase resolution test target, and finally, live glial restricted progenitor cells (as a challenging strongly absorbing and scattering biomedical sample). The proposed approach based on severely limiting the photon budget in lensless holographic microscopy method can open new avenues in high-throughout (optimal resolution, large field-of-view, and high signal-to-noise-ratio single-hologram reconstruction) cell culture imaging with minimized sample interaction.

Effects of measurement noise on the construction of a transmission matrix

The effects of time-varying measurement noise on transmission matrix acquisition processes are considered for the first time, to our knowledge. Dominant noise sources are discussed, and the noise properties of a typical interferometer system used for characterizing a multimode fiber transmission matrix are quantified. It is demonstrated that an appropriate choice of measurement basis allows a more accurate transmission matrix to be more quickly obtained in the presence of measurement noise. Finally, it is shown that characterizing the noise figure of the experimental system allows the inverse transmission matrix to be constructed with an ideal amount of regularization, which can in turn be used for optimal image acquisition.

Digital holographic microscopy implementation for capillary filling measurements in nanoporous materials

We report the implementation of lensless off-axis digital holographic microscopy as a non-destructive optical analyzer for nano-scale structures. The measurement capacity of the system was validated by analyzing the topography of a metallic grid with ≈150nm thick opaque features. In addition, an experimental configuration of self-reference was included to study the dynamics of the capillary filling phenomena in nanostructured porous silicon. The fluid front position as a function of time was extracted from the holograms, and the typical square root of time kinematics was recovered. The results shown are in agreement with previous works on capillary imbibition in similar structures and confirm a first step towards unifying holographic methods with fluid dynamics theory to develop a spatially resolved capillary tomography system for nanoporous materials characterization.

Linearity and Optimum-Sampling in Photon-Counting Digital Holographic Microscopy

In the image plane configurations frequently used in digital holographic microscopy (DHM) systems, interference patterns are captured by a photo-sensitive array detector located at the image plane of an input object. The object information in these patterns is localized and thus extremely sensitive to phase errors caused by nonlinear hologram recordings (grating profiles are either square or saturated sinusoidal) or inadequate sampling regarding the information coverage (undersampled around the Nyquist frequency or arbitrarily oversampled). Here, we propose a solution for both hologram recording problems through implementing a photon-counting detector (PCD) mounted on a motorized XY translation stage. In such a way, inherently linear (because of a wide dynamic range of PCD) and optimum sampled (due to adjustable steps) digital holograms in the image plane configuration are recorded. Optimum sampling is estimated based on numerical analysis. The validity of the proposed approach is confirmed experimentally.

Accurate and practical feature extraction from noisy holograms

Quantitative phase imaging using holographic microscopy is a powerful and non-invasive imaging method, ideal for studying cells and quantifying their features such as size, thickness, and dry mass. However, biological materials scatter little light, and the resulting low signal-to-noise ratio in holograms complicates any downstream feature extraction and hence applications. More specifically, unwrapping phase maps from noisy holograms often fails or requires extensive computational resources. We present a strategy for overcoming the noise limitation: rather than a traditional phase-unwrapping method, we extract the continuous phase values from holograms by using a phase-generation technique based on conditional generative adversarial networks employing a Pix2Pix architecture. We demonstrate that a network trained on random surfaces can accurately generate phase maps for test objects such as dumbbells, spheres, and biconcave discoids. Furthermore, we show that even a rapidly trained network can generate faithful phase maps when trained on related objects. We are able to accurately extract both morphological and quantitative features from the noisy phase maps of human leukemia (HL-60) cells, where traditional phase unwrapping algorithms fail. We conclude that deep learning can decouple noise from signal, expanding potential applications to real-world systems that may be noisy.

Holo-UNet: hologram-to-hologram neural network restoration for high fidelity low light quantitative phase imaging of live cells

Intensity shot noise in digital holograms distorts the quality of the phase images after phase retrieval, limiting the usefulness of quantitative phase microscopy (QPM) systems in long term live cell imaging. In this paper, we devise a hologram-to-hologram neural network, Holo-UNet, that restores high quality digital holograms under high shot noise conditions (sub-mW/cm² intensities) at high acquisition rates (sub-milliseconds). In comparison to current phase recovery methods, Holo-UNet denoises the recorded hologram, and so prevents shot noise from propagating through the phase retrieval step that in turn adversely affects phase and intensity images. Holo-UNet was tested on 2 independent QPM systems without any adjustment to the hardware setting. In both cases, Holo-UNet outperformed existing phase recovery and block-matching techniques by ∼ 1.8 folds in phase fidelity as measured by SSIM. Holo-UNet is immediately applicable to a wide range of other high-speed interferometric phase imaging techniques. The network paves the way towards the expansion of high-speed low light QPM biological imaging with minimal dependence on hardware constraints.

Simultaneous two-color imaging in digital holographic microscopy

We demonstrate the use of two-color digital holographic microscopy (DHM) for imaging microbiological subjects. The use of two wavelengths significantly reduces artifacts present in the reconstructed data, allowing us to image weakly-scattering objects in close proximity to strongly-scattering objects. We demonstrate this by reconstructing the shape of the flagellum of a unicellular eukaryotic parasite Leishmania mexicana in close proximity to a more strongly-scattering cell body. Our approach also yields a reduction of approximately one third in the axial position uncertainty when tracking the motion of swimming cells at low magnification, which we demonstrate with a sample of Escherichia coli bacteria mixed with polystyrene beads. The two-wavelength system that we describe introduces minimal additional complexity into the optical system, and provides significant benefits.

In situ nanoscale observations of gypsum dissolution by digital holographic microscopy

Recent topography measurements of gypsum dissolution have not reported the absolute dissolution rates, but instead focus on the rates of formation and growth of etch pits. In this study, the in situ absolute retreat rates of gypsum (010) cleavage surfaces at etch pits, at cleavage steps, and at apparently defect-free portions of the surface are measured in flowing water by reflection digital holographic microscopy. Observations made on randomly sampled fields of view on seven different cleavage surfaces reveal a range of local dissolution rates, the local rate being determined by the topographical features at which material is removed. Four characteristic types of topographical activity are observed: 1) smooth regions, free of etch pits or other noticeable defects, where dissolution rates are relatively low; 2) shallow, wide etch pits bounded by faceted walls which grow gradually at rates somewhat greater than in smooth regions; 3) narrow, deep etch pits which form and grow throughout the observation period at rates that exceed those at the shallow etch pits; and 4) relatively few, submicrometer cleavage steps which move in a wave-like manner and yield local dissolution fluxes that are about five times greater than at etch pits. Molar dissolution rates at all topographical features except submicrometer steps can be aggregated into a continuous, mildly bimodal distribution with a mean of 3.0 µmolm-2 s-1 and a standard deviation of 0.7 µmolm-2 s-1.

Common-path digital holographic microscopy for near-field phase imaging based on surface plasmon resonance

We develop a common-path digital holographic microscopy based on prism-coupling surface plasmon resonance (SPR) for near-field phase imaging. A single beam splitter with specific configuration is introduced in an SPR imaging system to realize off-axis holographic recording. By measuring the phase shift difference of the reflected light at SPR exploiting the proposed holographic microscopy with high temporal stability, near-field characteristic measurement can be realized. With its simplicity, vibration isolation, and inherent capability of phase curvature compensation, the recommended system shows advanced performance in monitoring tiny refractive index variations and imaging biological tissues.

Phase Uncertainty in Digital Holographic Microscopy Measurements in the Presence of Solution Flow Conditions

Digital holographic microscopy (DHM) is a surface topography measurement technique with reported sub-nanometer vertical resolution. Although it has been made commercially available recently, few studies have evaluated the uncertainty or noise in the phase measurement by the DHM. As current research is using the DHM to monitor surface topography changes of dissolving materials under flowing water conditions, it is necessary to evaluate the effect of water and flow rate on the uncertainty in the measurement. Uncertainty in this study was concerned with the temporal standard deviation per pixel of the reconstructed phase. Considering the effects of solution flow rate, magnification, objective lens type (air or immersion), and experimental configuration, measurements under static conditions in air and in water with an immersion lens yielded the smallest amount of uncertainty (mean of ≤ 0.5 nm up to 40× magnification). Increasing the water flow rate resulted in an increase in mean uncertainty to ≤ 0.6 nm up to 40× with an immersion lens. Observations of a sample through a glass window at 20× magnification in flowing water also yielded increasing uncertainty, with mean values of ≤ 0.5 nm, ≤ 0.8 nm, and ≤ 1.1 nm for flow rates of 0 mL min^-1, 15 mL min^-1, and 33 mL min^-1. Different hologram acquisition rates (12.5 s^-1 and 25 s^-1) did not significantly impact the uncertainty in the phase. Collecting holograms in single-wavelength versus dual-wavelength modes did impact the uncertainty, with the mean uncertainty at 10× magnification for the same wavelength being ≤ 0.5 nm from the single-wavelength mode compared to ≤ 1.5 nm from the dual-wavelength mode. When the quantified uncertainty was applied to simulated dissolution data, lower limits of measured dissolution rates were found below which the measured data may not be distinguishable from the uncertainty in the measurement. The limiting surface-normal dissolution velocity is -10^-11.7 m s^-1 for experiments with an immersion lens in flowing water conditions and -10^-11.7 m s^-1, -10^-11.4 m s^-1, and -10^-11.0 m s^-1 for static (0 mL min^-1), slow (≤ 15 mL min^-1), and fast (≤ 109 mL min^-1) flowing water conditions in experiments with a glass window, respectively. The data presented by this study will allow for better experimental design and methodology for future dissolution or precipitation studies using DHM and will provide confidence in the data produced in postprocessing.

Versatile spectral modulation of a broadband source for digital holographic microscopy

We demonstrate the potential of spatial light modulators for the spectral control of a broadband source in digital holographic microscopy. Used in a 'pulse-shaping' geometry, the spatial light modulator provides a versatile control over the bandwidth and wavelength of the light source. The control of these properties enables adaptation to various experimental conditions. As a first application, we show that the source bandwidth can be adapted to the off-axis geometry to provide quantitative phase imaging over the whole field of view. As a second application, we generate sequences of appropriate wavelengths for a hierarchical optical phase unwrapping algorithm, which enables the measurement of the topography of high-aspect ratio structures without phase ambiguity. Examples are given with step heights up to 50 µm.

Cell nuclei have lower refractive index and mass density than cytoplasm

Common perception regards the nucleus as a densely packed object with higher refractive index (RI) and mass density than the surrounding cytoplasm. Here, the volume of isolated nuclei is systematically varied by electrostatic and osmotic conditions as well as drug treatments that modify chromatin conformation. The refractive index and dry mass of isolated nuclei is derived from quantitative phase measurements using digital holographic microscopy (DHM). Surprisingly, the cell nucleus is found to have a lower RI and mass density than the cytoplasm in four different cell lines and throughout the cell cycle. This result has important implications for conceptualizing light tissue interactions as well as biological processes in cells.

Pushing phase and amplitude sensitivity limits in interferometric microscopy

Sensitivity of the amplitude and phase measurements in interferometric microscopy is influenced by factors such as instrument design and environmental interferences. Through development of a theoretical framework followed by experimental validation, we show photon shot noise is often the limiting factor in interferometric microscopy measurements. Thereafter, we demonstrate how a state-of-the-art camera with million-level electrons full well capacity can significantly reduce shot noise contribution resulting in a stability of optical path length down to a few picometers even in a near-common-path interferometer.

Dynamical measurement of refractive index distribution using digital holographic interferometry based on total internal reflection

We present a method for dynamically measuring the refractive index distribution in a large range based on the combination of digital holographic interferometry and total internal reflection. A series of holograms, carrying the index information of mixed liquids adhered on a total reflection prism surface, are recorded with CCD during the diffusion process. Phase shift differences of the reflected light are reconstructed exploiting the principle of double-exposure holographic interferometry. According to the relationship between the reflection phase shift difference and the liquid index, two dimensional index distributions can be directly figured out, assuming that the index of air near the prism surface is constant. The proposed method can also be applied to measure the index of solid media and monitor the index variation during some chemical reaction processes.

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.

Optimum phase shift for quantitative phase microscopy in volume measurement

Volume measurement of a phase object is one of the most distinctive capabilities of quantitative phase microscopy (QPM). However, the accuracy of a measured volume is limited by the different noises of a measurement system and the finite bandpass filter used in the phase extraction algorithm. In this paper, we analyze the inherent errors in volume measurement with QPM and propose the optimum condition that can minimize these errors. We find that phase information of a sample in the frequency domain nonlinearly oscillates as a function of the phase shift corresponding to the sample and its medium, and that the phase information of a sample inside the bandpass filter can be maximized by a proper phase shift. Through numerical simulations and actual experiments, we demonstrate that the error in phase volume measurement can be effectively reduced by the enhancement of the phase signal inside the bandpass region using an optimum amount of phase, which can be controlled by changing either the medium index or the wavelength of illumination.

Review of quantitative phase-digital holographic microscopy: promising novel imaging technique to resolve neuronal network activity and identify cellular biomarkers of psychiatric disorders

Quantitative phase microscopy (QPM) has recently emerged as a new powerful quantitative imaging technique well suited to noninvasively explore a transparent specimen with a nanometric axial sensitivity. In this review, we expose the recent developments of quantitative phase-digital holographic microscopy (QP-DHM). Quantitative phase-digital holographic microscopy (QP-DHM) represents an important and efficient quantitative phase method to explore cell structure and dynamics. In a second part, the most relevant QPM applications in the field of cell biology are summarized. A particular emphasis is placed on the original biological information, which can be derived from the quantitative phase signal. In a third part, recent applications obtained, with QP-DHM in the field of cellular neuroscience, namely the possibility to optically resolve neuronal network activity and spine dynamics, are presented. Furthermore, potential applications of QPM related to psychiatry through the identification of new and original cell biomarkers that, when combined with a range of other biomarkers, could significantly contribute to the determination of high risk developmental trajectories for psychiatric disorders, are discussed.

Exploring neural cell dynamics with digital holographic microscopy

In this review, we summarize how the new concept of digital optics applied to the field of holographic microscopy has allowed the development of a reliable and flexible digital holographic quantitative phase microscopy (DH-QPM) technique at the nanoscale particularly suitable for cell imaging. Particular emphasis is placed on the original biological information provided by the quantitative phase signal. We present the most relevant DH-QPM applications in the field of cell biology, including automated cell counts, recognition, classification, three-dimensional tracking, discrimination between physiological and pathophysiological states, and the study of cell membrane fluctuations at the nanoscale. In the last part, original results show how DH-QPM can address two important issues in the field of neurobiology, namely, multiple-site optical recording of neuronal activity and noninvasive visualization of dendritic spine dynamics resulting from a full digital holographic microscopy tomographic approach.

Noise and signal scaling factors in digital holography in weak illumination: relationship with shot noise

We have performed off-axis heterodyne holography with very weak illumination by recording holograms of the object with and without object illumination in the same acquisition run. We have experimentally studied how the reconstructed image signal (with illumination) and noise background (without) scale with the holographic acquisition and reconstruction parameters that are the number of frames and the number of pixels of the reconstruction spatial filter. The first parameter is related to the frequency bandwidth of detection in time, the second one to the bandwidth in space. The signal to background ratio varies roughly like the inverse of the bandwidth in time and space. We have also compared the noise background with the theoretical shot-noise background calculated by Monte Carlo simulation. The experimental and Monte Carlo noise background agree very well with each other.

Real-time monitoring of the solution concentration variation during the crystallization process of protein-lysozyme by using digital holographic interferometry

We report a real-time measurement method of the solution concentration variation during the growth of protein-lysozyme crystals based on digital holographic interferometry. A series of holograms containing the information of the solution concentration variation in the whole crystallization process is recorded by CCD. Based on the principle of double-exposure holographic interferometry and the relationship between the phase difference of the reconstructed object wave and the solution concentration, the solution concentration variation with time for arbitrary point in the solution can be obtained, and then the two-dimensional concentration distribution of the solution during crystallization process can also be figured out under the precondition which the refractive index is constant through the light propagation direction. The experimental results turns out that it is feasible to in situ, full-field and real-time monitor the crystal growth process by using this method.

Temperature measurement of axisymmetric flame under the influence of magnetic field using lensless Fourier transform digital holography

In this paper the effect of uniform magnetic field B on the temperature and temperature profile of the diffusion flame is investigated using lensless Fourier transform digital holographic interferometry. The evaluation of temperature profile reveals that the width of flame as well as the maximum value of temperature inside the flame is increased.

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.

Enhanced robustness digital holographic microscopy for demanding environment of space biology

We describe an optimized digital holographic microscopy system (DHM) suitable for high-resolution visualization of living cells under conditions of altered macroscopic mechanical forces such as those that arise from changes in gravitational force. Experiments were performed on both a ground-based microgravity simulation platform known as the random positioning machine (RPM) as well as during a parabolic flight campaign (PFC). Under these conditions the DHM system proved to be robust and reliable. In addition, the stability of the system during disturbances in gravitational force was further enhanced by implementing post-processing algorithms that best exploit the intrinsic advantages of DHM for hologram autofocusing and subsequent image registration. Preliminary results obtained in the form of series of phase images point towards sensible changes of cytoarchitecture under states of altered gravity.

Beyond the lateral resolution limit by phase imaging

We present a theory to extend the classical Abbe resolution limit by introducing a spatially varying phase into the illumination beam of a phase imaging system. It allows measuring lateral and axial distance differences between point sources to a higher accuracy than intensity imaging alone. Various proposals for experimental realization are debated. Concretely, the phase of point scatterers' interference is experimentally visualized by high numerical aperture (NA = 0.93) digital holographic microscopy combined with angular scanning. Proof-of-principle measurements are presented by using sub-wavelength nanometric holes on an opaque metallic film. In this manner, Rayleighs classical two-point resolution condition can be rebuilt. With different illumination phases, enhanced bandpass information content is demonstrated, and its spatial resolution is theoretically shown to be potentially signal-to-noise ratio limited.

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.

Quantization noise and its reduction in lensless Fourier digital holography

Digital holography is an imaging technique that enables recovery of topographic 3D information about an object under investigation. In digital holography, an interference pattern is recorded on a digital camera. Therefore, quantization of the recorded hologram is an integral part of the imaging process. We study the influence of quantization error in the recorded holograms on the fidelity of both the intensity and phase of the reconstructed image. We limit our analysis to the case of lensless Fourier off-axis digital holograms. We derive a theoretical model to predict the effect of quantization noise and we validate this model using experimental results. Based on this, we also show how the resultant noise in the reconstructed image, as well as the speckle that is inherent in digital holography, can be conveniently suppressed by standard speckle reduction techniques. We show that high-quality images can be obtained from binary holograms when speckle reduction is performed.

Temperature measurement in laminar free convective flow using digital holography

A method for measurement of temperature in laminar free convection flow of water is presented using digital holographic interferometry. The method is relatively simple and fast because the method uses lensless Fourier transform digital holography, for which the reconstruction algorithm is simple and fast, and also the method does not require use of any extra experimental efforts as in phase shifting. The quantitative unwrapped phase difference is calculated experimentally from two digital holograms recorded in two different states of water--one in the quiescent state, the other in the laminar free convection. Unknown temperature in laminar free convection is measured quantitatively using a known value of temperature in the quiescent state from the unwrapped phase difference, where the equation by Tilton and Taylor describing the variation of refractive index of water with temperature is used to connect the phase with temperature. Experiments are also performed to visualize the turbulent free convection flow.