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

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.

Shape Measurement Method of Two-Dimensional Micro-Structures beyond the Diffraction Limit Based on Speckle Interferometry

A technique based on speckle interferometry for observing microstructures beyond the diffraction limit by detecting the spatial phase distribution of scattered light from microstructures has previously been reported. In this study, the development of this technique using a two-dimensional method is discussed. In order to observe general two-dimensional images, development of new technology in several stages is required. A two-dimensional filtering technique to reduce the noise component and a two-dimensional integration path to detect the three-dimensional shape of the surface are described in detail. As a first step toward observing complex two-dimensional structures in the future, it is investigated that directional two-dimensional information such as fibrous materials and micro-linear structures can be visually captured and treated as meaningful two-dimensional structures. As a result, it is shown that it is possible to observe fine two-dimensional letters with a line width of 100 nm, which is beyond the diffraction limit of the objective lens, demonstrating the effectiveness of the observation technique for microstructures by phase detection.

Noise and bias in off-axis digital holography for measurements in acoustic waveguides

This paper discusses noise and bias in the method of holographic interferometry applied to the study of acoustics phenomena. The influence of noise on the measurement of acoustic pressure is described by an analytical approach. Relationships to quantify the minimum measurable fluid density and acoustic pressure are given by taking into account the experimental parameters of the setup. These parameters are related to the spatial bandwidths, number of electrons in pixels, readout noise, and quantization noise. Experimental results show that theoretical relations are relatively close to experimental data and that the lower pressure measurement limit is on the order of 15 Pa for the acoustics pressure. The case of waveguides excited by an internal or external acoustic source is investigated. Specifically, for the case of studies in thermoacoustics, this paper demonstrates that the parasitic coupling of vibrations can be compensated. The proposed method is based on the determination of the amplitude and phase of the parasitic oscillation, requiring a few assumptions related to the physics of the underlying phenomenon. Successful compensation is obtained and yields experimental data in agreement with the theoretical predictions.

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.

Selection of the tagged photons by off axis heterodyne holography in ultrasound-modulated optical tomography

Ultrasound-modulated optical tomography (UOT) is a technique that images optical contrast deep inside scattering media. Heterodyne holography is a promising tool that is able to detect UOT-tagged photons with high efficiency. In this work, we describe theoretically the detection of the tagged photon in heterodyne holography-based UOT, show how to filter the untagged photon, and discuss the effect of shot noise. The discussion also considers speckle decorrelation. We show that optimal detection sensitivity can be reached, if the frame exposure time of the camera used to perform the holographic detection is on the order of the decorrelation time.

Blood flow imaging in zebrafish by laser doppler digital holography

Microvessel blood flow imaging techniques are widely used in biomedical research and clinical diagnostics where many diseases have a vascular etiology or involvement. For testing purposes, zebrafish embryo provides an ideal animal model to achieve high-resolution imaging of superficial and deeply localized vessels. Moreover, the study of the formation of a closed circulatory system in vertebrates is a topic of recent interest in biophysics. However, most of the existing techniques are invasive due to the use of a contrast agent for imaging purposes. Recent developments in Digital Holography and Laser Doppler Holography techniques can be considered to alleviate this issue. Laser Doppler holography and transmission microscopy can be coupled to analyze blood flow in fish embryos by adapting a laser Doppler holographic setup to a standard bio-microscope: the two beams of the holographic interferometer (illumination of the object and reference), whose frequency offset is controlled, were addressed to the microscope by optical fibers. Multimodal acquisition and analysis of the data is made by acting on the frequency offset of the two beams, and on the location of the Fourier space filtered zone. In this work, we show that it is possible to select the signal of moving scatterers, and to image Red Blood Cells (RBCs) and blood vessels. Individual RBCs are imaged, and movies showing the RBC motion are obtained. Microsc. Res. Tech. 81:153-161, 2018. © 2016 Wiley Periodicals, Inc.

Co-design of an in-line holographic microscope with enhanced axial resolution: selective filtering digital holography

Common-path digital in-line holography is considered as a valuable 3D diagnostic technique for a wide range of applications. This configuration is cost effective and relatively immune to variation in the experimental environment. Nevertheless, due to its common-path geometry, the signal-to-noise ratio of the acquired hologram is weak as most of the detector (i.e., CCD/CMOS sensor) dynamics are occupied by the reference field signal, whose energy is orders of magnitude higher than the field scattered by the imaged object. As it is intrinsically impossible to modify the ratio of energy of reference to the object field, we propose a co-design approach (optics/data processing) to tackle this issue. The reference to the object field ratio is adjusted by adding a 4-f device to a conventional in-line holographic setup, making it possible to reduce the weight of the reference field while keeping the object field almost constant. Theoretical analysis of the Crámer-Rao lower bounds of the corresponding imaging model illustrates the advantages of this approach. These lower bounds can be asymptotically reached using a parametric inverse problem reconstruction. This implementation results in a 60% gain in axial localization accuracy (for 100 μm diameter spherical objects) compared to a classical in-line holography setup.

Quality assessment of combined quantization-shot-noise-induced decorrelation noise in high-speed digital holographic metrology

this paper discusses on the influence of decorrelation noise induced by quantization and shot-noise when recording digital holograms at very high frame rate. A criterion based on the coherence factor of the hologram phase difference is proposed. The main parameters of interest are the ratio between the reference and the object waves and the sensor dynamics, depending on the photo-electron capacity of pixels. The study is based on a full numerical simulation of the holographic process, which provides useful rules. This leads to define the optimal conditions for recording at very-high frame rate with minimization of the decorrelation noise. Experimental results obtained with frame rate at 50kHz confirm the proposed approach.

Singular-value demodulation of phase-shifted holograms

We report on phase-shifted holographic interferogram demodulation by singular-value decomposition. Numerical processing of optically acquired interferograms over several modulation periods was performed in two steps: (1) rendering of off-axis complex-valued holograms by Fresnel transformation of the interferograms; and (2) eigenvalue spectrum assessment of the lag-covariance matrix of hologram pixels. Experimental results in low-light recording conditions were compared with demodulation by Fourier analysis, in the presence of random phase drifts.

Vibration of low amplitude imaged in amplitude and phase by sideband versus carrier correlation digital holography

Sideband holography can be used to get field images (E0 and E1) of a vibrating object for both the carrier (E0) and the sideband (E1) frequency with respect to vibration. Here we propose to record E0 and E1 sequentially and to image the product E1E0* or the correlation 〈E1E0*〉. We show that these quantities are insensitive to the phase related to the object roughness and directly reflect the phase of the mechanical motion. The signal to noise can be improved by averaging E1E0* over a neighbor pixel, yielding 〈E1E0*〉. Experimental validation is made with a vibrating cube of wood and a clarinet reed. At 2 kHz, vibrations of amplitude down to 0.01 nm are detected.

Digital holography at light levels below noise using a photon-counting approach

Recording of digital holograms of a weak signal [0.44 counts per second (cps)] hidden below the detector's noise (21 cps) is investigated by employing the high dynamic range of a photon-counting detector. Recording conditions are discussed in terms of the most important holographic measures, namely, the fringe visibility (or contrast) and signal-to-noise ratio (SNR), and in relation to the main holographic parameters. Theoretically evaluated curves are tested by recording holograms for a wide range of the parameter values. We found that (i) the optimum set of holographic parameters can be determined for a harsh signal conditions, (ii) increasing the visibility does not necessarily improve the more important SNR, and (iii) in cases of nearly constant visibility, the SNR clearly reveals differences in the quality of holographic recordings.

Laser Doppler holographic microscopy in transmission: application to fish embryo imaging

We have extended Laser Doppler holographic microscopy to transmission geometry. The technique is validated with living fish embryos imaged by a modified upright bio-microcope. By varying the frequency of the holographic reference beam, and the combination of frames used to calculate the hologram, multimodal imaging has been performed. Doppler images of the blood vessels for different Doppler shifts, images where the flow direction is coded in RGB colors or movies showing blood cells individual motion have been obtained as well. The ability to select the Fourier space zone that is used to calculate the signal, makes the method quantitative.