Underwater digital holography for studies of marine plankton

Conventional and digital holographies are proving to be increasingly important for studies of marine zooplankton and other underwater biological applications. This paper reports on the use of a subsea digital holographic camera (eHoloCam) for the analysis and identification of marine organisms and other subsea particles. Unlike recording on a photographic film, a digital hologram (e-hologram) is recorded on an electronic sensor and reconstructed numerically in a computer by simulating the propagation of the optical field in space. By comparison with other imaging techniques, an e-hologram has several advantages such as three-dimensional spatial reconstruction, non-intrusive and non-destructive interrogation of the recording sampling volume and the ability to record holographic videos. The basis of much work in optics lies in Maxwell's electromagnetic theory and holography is no exception: we report here on two of the numerical reconstruction algorithms we have used to reconstruct holograms obtained using eHoloCam and how their starting point lies in Maxwell's equations. Derivation of the angular spectrum algorithm for plane waves is provided as an exact method for the in-line numerical reconstruction of digital holograms. The Fresnel numerical reconstruction algorithm is derived from the angular spectrum method. In-line holograms are numerically processed before and after reconstruction to remove periodic noise from captured images and to increase image contrast. The ability of the Fresnel integration reconstruction algorithm to extend the reconstructed volume beyond the recording sensor dimensions is also shown with a 50% extension of the reconstruction area. Finally, we present some images obtained from recent deployments of eHoloCam in the North Sea and Faeroes Channel.     

Effects of quantization in phase-shifting digital holography

We discuss quantization effects of hologram recording on the quality of reconstructed images in phase-shifting digital holography. We vary bit depths of phase-shifted holograms in both numerical simulation and experiments and then derived the complex amplitude, which is subjected to Fresnel transformation for the image reconstruction. The influence of bit-depth limitation in quantization has been demonstrated in a numerical simulation for spot-array patterns with linearly varying intensities and a continuous intensity object. The objects are provided with uniform and random phase modulation. In experiments, digital holograms are originally recorded at 8 bits and the bit depths are changed to deliver holograms at bit depths of 1 to 8 bits for the image reconstruction. The quality of the reconstructed images has been evaluated for the different quantization levels.     

Multi-plane imaging for arbitrary reconstruction positions in digital holography

A novel method for multi-plane imaging in digital holography is proposed: holograms of objects located at various places are recorded and then reconstructed simultaneously through one-step Fresnel diffraction using the quadratic distorted phase factor (QDPF). The theory of one-step Fresnel diffraction with the QDPF is deduced and experimental results support the theoretical investigation.     

Fourier-domain digital holographic optical coherence imaging of living tissue

Digital holographic optical coherence imaging is a full-frame coherence-gated imaging approach that uses a CCD camera to record and reconstruct digital holograms from living tissue. Recording digital holograms at the optical Fourier plane has advantages for diffuse targets compared with Fresnel off-axis digital holography. A digital hologram captured at the Fourier plane requires only a 2D fast Fourier transform for numerical reconstruction. We have applied this technique for the depth-resolved imaging of rat osteogenic tumor multicellular spheroids and acquired cross-section images of the anterior segment and the retinal region of a mouse eye. A penetration depth of 1.4 mm for the tumor spheroids was achieved.     

Three-dimensional remote sensing by optical scanning holography

A technique is presented by which holograms can be recorded when an object or scene is scanned with an optically heterodyned Fresnel zone pattern. The experimental setup, based on optical scanning holography, is described and experimental results are presented. We apply the scanning holography technique to three-dimensional reflective objects for the first time to our knowledge and address the unique requirements for such a system. We discuss holographic recording and numerical image reconstruction using a system point-spread function (PSF) approach. We demonstrate numerical image reconstruction of experimentally recorded holograms by two techniques: deconvolution with a simulated PSF and an experimentally acquired PSF.     

Digital holography of particle fields: reconstruction by use of complex amplitude

Digital holography appears to be a strong contender as the next-generation technology for holographic diagnostics of particle fields and holographic particle image velocimetry for flow field measurement. With the digital holographic approach, holograms are directly recorded by a digital camera and reconstructed numerically. This not only eliminates wet chemical processing and mechanical scanning, but also enables the use of complex amplitude information inaccessible by optical reconstruction, thereby allowing flexible reconstruction algorithms to achieve optimization of specific information. However, owing to the inherently low pixel resolution of solid-state imaging sensors, digital holography gives poor depth resolution for images, a problem that severely impairs the usefulness of digital holography especially in densely populated particle fields. This paper describes a technique that significantly improves particle axial-location accuracy by exploring the reconstructed complex amplitude information, compared with other numerical reconstruction schemes that merely mimic traditional optical reconstruction. This novel method allows accurate extraction of particle locations from forward-scattering particle holograms even at high particle loadings.     

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.     

Three-dimensional Displacement Analysis by Windowed Phase-shifting Digital Holographic Interferometry

Abstract:  Phase-shifting digital holography is a new method for measuring the displacement distribution on the surface of an object. The authors previously proposed a windowed phase-shifting digital holographic interferometry (windowed PSDHI). This method provides accurate displacement distributions by decreasing the effect of speckle patterns. In this study, the method is extended to analyse three-dimensional displacement components in a microscope. Three object laser beams in the optical system are used. Four phase-shifted holograms are recorded for each object laser beam. The complex amplitude of each reconstructed light at the object is calculated by the Fresnel diffraction integral of the complex amplitude of the hologram. The reconstructed distance is obtained at the point with the maximum of the standard deviation of the intensities of the object reconstructed with changing the reconstruction distance. The three phase-difference values between before and after deformation provide the three-dimensional displacement components. Theoretical treatment and experimental results of three-dimensional displacement measurement using this method are shown.     

Optimally tuned spatial light modulators for digital holography

Digital holography and comparative digital holography are applications that require computer-addressable modulators for the optical reconstruction of digital holograms. The quality of the reconstructed holograms depends on the modulator's properties. Therefore a characterization of the modulators is required. We show the result of a modulator characterization and the modulator's influence on the quality of the reconstructed hologram. We then compare qualitatively and quantitatively the optical reconstruction of phase and amplitude holograms by considering their level of detail and their diffraction efficiency.     

Time-alternating method based on single-sideband holography with half-zone-plate processing for the enlargement of viewing zones

The single-sideband method of holography, as is well known, cuts off beams that come from conjugate images for holograms produced in the Fraunhofer region and from objects with no phase components. The single-sideband method with half-zone-plate processing is also effective in the Fresnel region for beams from an object that has phase components. However, this method restricts the viewing zone to a narrow range. We propose a method to improve this restriction by time-alternating switching of hologram patterns and a spatial filter set on the focal plane of a reconstruction lens.     

Infrared holography using a microbolometer array

We describe a series of experiments to demonstrate holography at far-infrared wavelengths using an uncooled microbolometer array. Simple interference patterns and Fresnel zone holograms are recorded with a 10 W cw CO(2) laser illumination in a Mach-Zehnder interferometer setup. A sparse-sampling method is used to sample the hologram at a rate dependent on the bandwidth of the object wavefront rather than the carrier frequency. The samples are then used to reconstruct the complex object wavefront in the hologram plane, which is Fresnel backpropagated for image reconstruction. Uncooled microbolometer arrays are most commonly used in passive mode to image the thermal-blackbody radiation. Their technology has matured to include the wavelength range of far-infrared to submillimeter radiation. The use of microbolometers with active illumination for holography, as described in this paper, suggests their interesting future applications.     

Size measurement of bubbles in a cavitation tunnel by digital in-line holography

Digital in-line holography (DIH) with a divergent beam is used to measure size and concentration of cavitation bubbles (6-100 μm) in hydrodynamic facilities. A sampling probe is directly inserted in the cavitation tunnel, and the holograms of the bubbles are recorded through a transparent test section specially designed for DIH measurements. The recording beam coming from a fiber-coupled laser diode illuminates the sample volume, and holograms are recorded by a CMOS camera. From each hologram, the sampling volume can be reconstructed slice by slice by applying a wavelet-based reconstruction method. Because of the geometry of the recording beam, a magnification ratio must be introduced for recovering the 3D location and size of each bubble. The method used for processing holograms recorded in such a configuration is presented. Then, statistical results obtained from 5000 holograms recorded under different pressures in the cavitation tunnel are compared and discussed.     

High-fidelity numerical realization of multiple-step Fresnel propagation for the reconstruction of digital holograms

A cascaded Fresnel algorithm for the flexible reconstruction of digital holograms is proposed. Since the fast-Fourier-transform-based numerical realization of the Fresnel integral shows a dependency of its pixel resolution and its computation window size on the propagation distance different from that of the corresponding physical system, the computation window can be smaller than the actual physical diffraction field in the intermediate plane. Consequently, distortions in the final reconstruction may occur. A method is proposed to eliminate such distortion. The validity of this method is shown by both numerical simulations and experimental results.     

Complex-wave retrieval from a single off-axis hologram

We present a new digital two-step reconstruction method for off-axis holograms recorded on a CCD camera. First, we retrieve the complex object wave in the acquisition plane from the hologram's samples. In a second step, if required, we propagate the wave front by using a digital Fresnel transform to achieve proper focus. This algorithm is sufficiently general to be applied to sophisticated optical setups that include a microscope objective. We characterize and evaluate the algorithm by using simulated data sets and demonstrate its applicability to real-world experimental conditions by reconstructing optically acquired holograms.     

Study of the Mechanical Behaviour of a Clarinet Reed Under Forced and Auto-oscillations With Digital Fresnel Holography

Abstract:  This paper presents methods for vibration analysis using digital Fresnel holography. Methods are based on time averaging for forced oscillations and pulsed recording devoted to auto-oscillations. The two methods are applied to a clarinet reed. In the forced oscillation regime, the reed is excited by an acoustic wave with controlled frequency and amplitude such that the reconstructed holograms exhibit resolvable Bessel fringes. In the case of the auto-oscillation regime, the reed is placed in an artificial mouth. Deformation of the clarinet reed can be extracted with the recording of 3150 pulsed digital holograms. Experimental results show the vibration behaviour of the clarinet reed under forced and auto-oscillation regimes, exhibiting the modal structures and high amplitude shocks.     

Digital recording and reconstruction of holograms in hologram interferometry and shearography

The fundamentals of digital recording and mathematical reconstruction of Fresnel holograms are described. The object is recorded in two different states, and the holograms are stored electronically with a charge-coupled-device detector. In the process of reconstruction the digitally sampled holograms are applied to the different coherent optical methods as hologram interferometry and shearography. If the holograms are superimposed and reconstructed jointly, a holographic interferogram results. If a shearing is introduced in the reconstruction process, a shearogram results. This means that the evaluation technique, e.g., hologram interferometry or shearography, can be influenced by numerical methods.     

Inverse-problem approach for particle digital holography: accurate location based on local optimization

We propose a microparticle localization scheme in digital holography. Most conventional digital holography methods are based on Fresnel transform and present several problems such as twin-image noise, border effects, and other effects. To avoid these difficulties, we propose an inverse-problem approach, which yields the optimal particle set that best models the observed hologram image. We resolve this global optimization problem by conventional particle detection followed by a local refinement for each particle. Results for both simulated and real digital holograms show strong improvement in the localization of the particles, particularly along the depth dimension. In our simulations, the position precision is > or =1 microm rms. Our results also show that the localization precision does not deteriorate for particles near the edge of the field of view.     

Some opportunities for vibration analysis with time averaging in digital Fresnel holography

Features offered by the combination of time averaging and digital Fresnel holography are investigated. In particular, we introduce the concept of the zero-crossing phase of Bessel fringes, which allows a highly contrasted determination of the dark fringes in the hologram. We discuss some particularities of the digital reconstruction and show how time-averaged digital holography can be used to study vibration drifts. Experiment results are presented in the case of a loudspeaker under a sinusoidal excitation; digital and analogical holography are also compared.     

Direct extraction of the mean particle size from a digital hologram

Digital holography, which consists of both acquiring the hologram image in a digital camera and numerically reconstructing the information, offers new and faster ways to make the most of a hologram. We describe a new method to determine the rough size of particles in an in-line hologram. This method relies on a property that is specific to interference patterns in Fresnel holograms: Self-correlation of a hologram provides access to size information. The proposed method is both simple and fast and gives results with acceptable precision. It suppresses all the problems related to the numerical depth of focus when large depth volumes are analyzed.