Digital recording and numerical reconstruction of lensless fourier holograms in optical metrology

Fringe projector with submillimeter fringe spacing at a meter-scale field of view

State-of-the-art fringe projection systems generate fringe patterns using digital light projectors (DLP). The axial uncertainty is limited by the smallest fringe period and is directly related to the pixel count. This results in limited accuracy of current DLP systems that affect applications such as in situ measurements for laser powder bed fusion systems, where a submillimeter fringe period is needed for field-of views larger than 500m m×500m m. This work presents a scalable fringe projection technique that enables the generation of stable fringe patterns over a large field of view spanning several meters while maintaining submillimeter fringe periods. This system uses geometric phase gratings to enable variable fringe spacing and fringe orientation capabilities. The system shears a coherent beam in the Fourier plane using a pair of geometric polarization gratings. The separation between the gratings directly affects the fringe spacing, and the orientation of the gratings affects the fringe orientation. The depth of focus is only limited by the coherence of the light source, enabling high fringe periods even on tilted planes. The system is designed with a single path configuration, making the system more robust to environmental noise. With a rotating linear polarizer, we demonstrate that phase-shifting methods could be employed to acquire phase information about the object. This paper employs a single-shot Fourier transform phase estimation technique to process the intensity maps acquired using projected fringe patterns. Further, we demonstrate the capabilities of the system to produce submillimeter fringe spacing and the ability to project fringes on larger scales for measurements.

Performance optimisation of a holographic Fourier domain diffuse correlation spectroscopy instrument

We have previously demonstrated a novel interferometric multispeckle Fourier domain diffuse correlation spectroscopy system that makes use of holographic camera-based detection, and which is capable of making in vivo pulsatile flow measurements. In this work, we report on a systematic characterisation of the signal-to-noise ratio performance of our system. This includes demonstration and elimination of laser mode hopping, and correction for the instrument's modulation transfer function to ensure faithful reconstruction of measured intensity profiles. We also demonstrate a singular value decomposition approach to ensure that spatiotemporally correlated experimental noise sources do not limit optimal signal-to-noise ratio performance. Finally, we present a novel multispeckle denoising algorithm that allows our instrument to achieve a signal-to-noise ratio gain that is equal to the square root of the number of detected speckles, whilst detecting up to ∼1290 speckles in parallel. The signal-to-noise ratio gain of 36 that we report is a significant step toward mitigating the trade-off that exists between signal-to-noise ratio and imaging depth in diffuse correlation spectroscopy.

3D imaging through a highly heterogeneous double-composite random medium by common-path phase-shift digital holography

A method is proposed for 3D imaging through a highly heterogeneous double-composite random medium made of a thick mildly inhomogeneous medium followed by a thin strongly scattering layer. To realize the immunity to the heterogeneous random medium, a system of common-path phase-shift digital holography is designed in such a manner that the wavefront distortion caused by the first inhomogeneous medium is canceled out by the common-path geometry, and the influence of the random phase introduced by the second scattering layer is removed by the intensity-based recording of the digital hologram on the thin scattering layer. The validity of the method was confirmed by experiments.

Dynamic displacement measurement in digital holographic interferometry using eigenspace analysis

Non-contact measurement of displacement undergone by a deformed object is an important application problem in digital holographic interferometry. Such measurements usually demand reliable estimation of interference phase even in the presence of severe noise. This article describes a method for non-contact displacement testing by investigating a robust phase retrieval approach in digital holographic interferometry. The approach is based on eigenspace processing of the complex interference field signal in digital holographic interferometry. The performance of the proposed method for phase retrieval under severe noise conditions is illustrated using simulation results. The practical utility of the proposed method is demonstrated for dynamic deformation analysis using experimental data from digital holographic interferometry.

Recovery of the topological charge of a vortex beam propagated through a scattering layer

Coherent vortex beams have shown great potential in many applications including information transmission under non-ideal conditions, as information can be encoded in the orbital angular momentum. However, inhomogeneity of atmosphere tends to scramble the vortex structure and give rise to speckle. It is therefore of great interest to reconstruct the topological charge of a vortex beam after it propagates through a scattering medium. Here, we propose a feasible solution for this. The proposed method measures holographically the scattered field and reconstructs the spiral phase from it by taking advantage of both the deterministic nature and the ergodicity of the scattering process. Our preliminary experiments show promising results and suggest that the proposed method can have great potential in information transmission under non-ideal conditions.

An edge-lit volume holographic optical element for an objective turret in a lensless digital holographic microscope

In this paper, we propose and demonstrate the use of an edge-lit volume holographic optical element (EL-VHOE) as a reference waveguide to reduce the volume of a lensless digital holographic microscope. Additionally, a hybrid lensless Fourier transform digital holography is applied to make the EL-VHOE function as an objective turret. It used a spherical wave in the object beam of the EL-VHOE, which served as the reference beam of the microscope. Another sheared spherical wave was used to illuminate the sample. The longitudinal position of the spherical reference beam is changeable. It was shown that the tradeoff between resolution and field of view can be adjusted by changing the longitudinal position of the spherical reference beam. The corresponding experimental results matched the simulational and theoretical predictions. A resolution of approximately 3.11 μm was achieved when the object distance was 6 mm and the longitudinal distance of the spherical reference was 10 mm.

Singular value decomposition approach to coherent averaging in digital holography

We present a new approach to coherent averaging in digital holography using singular value decomposition (SVD). Digital holography enables the extraction of phase information from intensity measurements. For this reason, SVD can be used to statistically determine the orthogonal vectors that align the complex-valued measurements from multiple frames and group common modes accounting for constant phase shift terms. The SVD approach enables the separation of multiple signals, which can be applied to remove undesired artifacts such as scatter in retrieved images. The advantages of the SVD approach are demonstrated here in experiments through fog-degraded holograms with spatially incoherent and coherent scatter.

Design and development of volume phase holographic grating based digital holographic interferometer for label-free quantitative cell imaging

In this paper, a volume phase holographic optical element based digital holographic interferometer is designed and used for quantitative phase imaging of biological cells [white blood cells, red blood cells, platelets, and Staphylococcus aureus (S. aureus) bacteria cells]. The experimental results reveal that sharp images of the S. aureus bacteria cells of the order of ${\sim}{1}\;{\unicode{x00B5}{\rm m}}$∼1µm can be clearly seen. The volume phase holographic grating will remove the stray light from the system reaching toward the grating and will minimize the coherent noise (speckle noise). This will improve the sharpness in the image reconstructed from the recorded digital hologram.

Information retrieval using overlapping holograms with partial complementarity

An information retrieval technique from superimposed holograms representing 2D and 3D objects using complementary fringes is presented. By adding two different computer generated holograms with quasi-complementarity information is possible to retrieve information at a specific depth.

Full bandwidth dynamic coarse integral holographic displays with large field of view using a large resonant scanner and a galvanometer scanner

An efficient method to implement the coarse integral holographic (CIH) concept for dynamic CIH displays is to scan the information generated from a spatial light modulator (SLM) of a low space bandwidth product (SBP) but high bandwidth to form the hologram array for the integral optics. Previously, just over half of the SLMs bandwidth was utilized due to the fact that the galvanometer scanner in use could not tile all the holograms that the SLM is capable to produce, resulting in the loss of nearly half of the field of view (FOV). Here, we propose a full bandwidth dynamic CIH display using a large resonant scanner in conjunction with a hybrid raster scanner, which can utilize the full bandwidth of the spatial light modulator and double the horizontal FOV. Experimental results confirm that with the SLM and scanners as used, the FOV can reach 48° when the SLM reaches its full bandwidth. This approach can be used for future scalable and tileable CIH display systems.

High-precision rotation angle measurement method based on a lensless digital holographic microscope

To accurately measure ultrasmall rotation angles, a robust and effective method based on lensless digital holographic microscopy is proposed in this paper. The method combines holographic microscopy, solid geometry, and 3D measurement, including holographic measurement and angle measurement processes. We can calculate the 3D shape by the angular spectrum algorithm and the least-squares phase-unwrapping algorithm in the holographic process. According to the relationship between the surface shape and rotation angles, the real-time rotation angles can be calculated. To validate the feasibility and practicability of the proposed approach, numerical noise simulations and experiments were performed. The measurement precision of rotation angle can reach 0.5″ in the range of 1000″ in this paper's experiments. The holographic method has high measurement precision and good stability. In addition, the compact small volume has great potential in small-angle sensor applications.

Full-color digitized holography for large-scale holographic 3D imaging of physical and nonphysical objects

Digitized holography techniques are used to reconstruct three-dimensional (3D) images of physical objects using large-scale computer-generated holograms (CGHs). The object field is captured at three wavelengths over a wide area at high densities. Synthetic aperture techniques using single sensors are used for image capture in phase-shifting digital holography. The captured object field is incorporated into a virtual 3D scene that includes nonphysical objects, e.g., polygon-meshed CG models. The synthetic object field is optically reconstructed as a large-scale full-color CGH using red-green-blue color filters. The CGH has a wide full-parallax viewing zone and reconstructs a deep 3D scene with natural motion parallax.

Color-image reconstruction for two-wavelength digital holography using a generalized phase-shifting approach

We propose a color-image reconstruction method for two-wavelength digital holography using generalized phase-shifting digital holography (GPSDH). In this method, color interference fringes are captured by a digital camera with a Bayer array color filter, and phase shifting is simultaneously performed for all wavelengths. Color interference fringes are separated into three monochromatic interference fringes using a color-separation method that suppresses the color-filter crosstalk. The object wave is extracted from each monochromatic interference fringe using GPSDH, which prevents problems due to the phase shift wavelength dependence. Image reconstruction is performed using a shifted Fresnel transform-based method, in which the color reconstructed image is obtained by directly superposing the reconstructed images for all wavelengths. We verify the proposed method through optical experiments with a two-wavelength digital holography system. The results show that the dual-color image can be successfully reconstructed without chromatic aberration.

Ultra-short pulsed off-axis digital holography for imaging dynamic targets in highly scattering conditions

A single-shot digital holography system using an ultra-short pulsed laser is demonstrated to be very effective in suppressing the multiple-scattering noise associated with imaging dynamic targets in highly scattering environments, such as biological tissues and fuel injection systems. A planar off-axis reference wave configuration is used to generate a fixed carrier spatial frequency in the recorded holograms in order to separate coherent signal from incoherent noise in Fourier transformed holograms. The single-shot imaging system does not require averaging between multiple shots and can capture images of transient phenomena, such as the formation of diesel fuel injection sprays, and can overcome the problem of mechanical vibrations for recording holograms in industrial and laboratory environments.

Experimental characterization of the hygroscopic properties of wood during convective drying using digital holographic interferometry

In this paper, an application of digital holography for the measurement of surface deformations and the strain field to understand the shrinkage behavior of wood during convective drying is presented. Moisture absorption and desorption induce the dimensional changes and deformations in wood that leads to failure of certain components made of wood. The knowledge of the dimensional changes in wood, deformations, strain distribution and their causes are important for the best utilization of wood. For the study, lensless Fourier transform digital holographic interferometry is used to measure moisture- induced deformation, strain distribution, and the coefficient of hygroscopic shrinkage in different samples of wood. The technique is highly sensitive and enables the observation of deformation and strain distribution during the variations of moisture content in the wood. The wet wood sample was exposed to convective drying, which leads to changes in the moisture content and the associated deformations. The deformation/strain in each step of drying process is used to evaluate the coefficient of hygroscopic shrinkage in different wood samples. The experiments were repeated for differently treated woods. The experimental results show that the strain and coefficient of hygroscopic shrinkage can be minimized if the wood is dried in the presence of the proper moisture content.

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.

Study of heat dissipation process from heat sink using lensless Fourier transform digital holographic interferometry

This paper presents the results of experimental investigations about the heat dissipation process of plate fin heat sink using digital holographic interferometry. Visual inspection of reconstructed phase difference maps of the air field around the heat sink with and without electric power in the load resistor provides qualitative information about the variation of temperature and the heat dissipation process. Quantitative information about the temperature distribution is obtained from the relationship between the digitally reconstructed phase difference map of ambient air and heated air. Experimental results are presented for different current and voltage in the load resistor to investigate the heat dissipation process. The effect of fin spacing on the heat dissipation performance of the heat sink is also investigated in the case of natural heat convection. From experimental data, heat transfer parameters, such as local heat flux and convective heat transfer coefficients, are also calculated.

Measurement of natural convective heat transfer coefficient along the surface of a heated wire using digital holographic interferometry

In this paper, the local convective heat transfer coefficient (h) is measured along the surface of an electrically heated vertical wire using digital holographic interferometry (DHI). Experiments are conducted on wires of different diameters. The experimentally measured values are within the range as given in the literature. DHI is expected to provide a more accurate local convective heat transfer coefficient (h) as the value of the temperature gradient required for the calculation of "h" can be obtained more accurately than by other existing optical interferometric techniques without the use of a phase shifting technique. This is because in digital holography phase measurement accuracy is expected to be higher.

Robust phase-shift estimation method for statistical generalized phase-shifting digital holography

We propose a robust phase-shift estimation method for statistical generalized phase-shifting digital holography using a slightly off-axis optical configuration. The phase randomness condition in the Fresnel diffraction field of an object can be sufficiently established by the linear phase factor of the oblique incident reference wave. Signed phase-shift values can be estimated with a statistical approach regardless of the statistical properties of the Fresnel diffraction field of the object. We present computer simulations and optical experiments to verify the proposed method.

Phase determination method in statistical generalized phase-shifting digital holography

A simple estimation method of the relative phase shift for generalized phase-shifting digital holography based on a statistical method is proposed. This method consists of a selection procedure of an optimum cost function and a simple root-finding procedure. The value and sign of the relative phase shift are determined using the coefficient and the solution of the optimum cost function. The complex field of an object wave is obtained using the estimated relative phase shift. The proposed method lifts the typical restriction on the range of the phase shift due to the phase ambiguity problem. Computer simulations and optical experiments are performed to verify the proposed method.

Analysis and adaptation of convolution algorithms to reconstruct extended objects in digital holography

This paper discusses convolution algorithms to reconstruct off-axis digital holograms. The problem of convolution is addressed by considering the spatial spectral properties of digital holograms, especially the unusual localization property of the Fourier spectrum of the hologram, in regard to the physical object space. After deriving the sampling requirements for the transfer functions, three approaches are considered with the concept of spatial bandwidth extension: zero padding, spectrum scanning, and adjustable magnification. The theoretical discussion is completed by experimental illustrations that enable the algorithms to be objectively compared.

Lens-free imaging for biological applications

Lens-free (or lensless) imaging is emerging as a cost-effective, compact, and lightweight detection method that can serve numerous biological applications. Lens-free imaging can generate high-resolution images within a field-portable platform, which is ideal for affordable point-of-care devices aiming at resource-limited settings. In this mini-review, we first describe different modes of operation for lens-free imaging and then highlight several recent biological applications of this emerging platform technology.

Lensless phase microscopy using phase retrieval with multiple illumination wavelengths

A phase retrieval method for microscopy using multiple illumination wavelengths is proposed. A fast algorithm suitable for calculations with high numerical aperture is used for the iterative retrieval of the object wavefront. The advantages and limitations of the technique are systematically analyzed and demonstrated by both simulation and experimental results.

Digital Fresnel holography beyond the Shannon limits

This paper presents a detailed analysis of the influence of the pixel dimension in digitally-recorded holograms. The investigation is based on both theoretical and experimental viewpoints for recordings beyond the Shannon limits. After discussing the pixel paradox, the sinc amplitude modulation is experimentally demonstration. The experimental analysis is well correlated to the theoretical basics; in addition, the filling factor of the sensor can be estimated. The analysis of the phase changes of the object show that they can be obtained with a very good contrast and that they are only limited by the decorrelation noise, as when the Shannon conditions are fulfilled.

Contouring of diffused objects using lensless Fourier transform digital moiré holography

A method is proposed for contouring of diffused objects using digital holographic moiré interferometry in lensless Fourier transform configuration. Fringe projection moiré technique combined with digital double-exposure holography produces the contours in this method. Two digital holograms of a 10 mm aluminum alloy cube are recorded by tilting the illumination angle slightly between exposures, and a third one is recorded by translating the detector a little laterally with the final illumination angle unchanged. Upon numerical processing of the first two holograms, a plane parallel fringe system seems to be projected onto the object. This fringe system can be referred to as the modified grid. Processing of the second and the third hologram results in another grid, the reference grid. In effect, processing of the first and the third hologram combines the modified and the reference grids to produce the moiré contour fringes. The range of contour intervals obtained remains between 2.73 and 0.38 mm with seven different contours in between. The present method can measure details of a great variety of sizes on objects of large dimensional range. Deviations in the measured contour intervals from the theoretically calculated values are found to be within 12%-18%. This seems to be because of the deviation in the present experimental geometry from the ideal theoretical configuration, the hologram digitization, and the particular reconstruction algorithm used in the present experimental arrangement.

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.

Digital holographic interferometry for measurement of temperature in axisymmetric flames

In this paper, experimental investigations and analysis is presented to measure the temperature and temperature profile of gaseous flames using lensless Fourier transform digital holographic interferometry. The evaluations of the experimental results give the accuracy, sensitivity, spatial resolution, and range of measurements to be well within the experimental limits. Details of the experimental results and analysis are presented.

Digital holographic microscopy characterization of superdirective beam by metamaterial

Digital holographic microscopy (DHM) has been successfully applied for the first time to characterize the radiative out-of-plane emission properties of a superdirective device. Complementarily to near-field microscopy, DHM allows us to reconstruct the beam in the far-field region. The angular dispersion of the light beam radiated from a grating composed of air and anti-air metamaterial has been determined, and the proposed technique has highlighted a collimation degree higher than 0.04°, as already evaluated in a previous work. Further considerations on the retrieved phase map of the beam in the acquisition plane are presented.

Short temporal coherence digital holography with a femtosecond frequency comb laser for multi-level optical sectioning

In this paper, we demonstrate how short temporal coherence digital holography with a femtosecond frequency comb laser source may be used for multi-level optical sectioning. The object shape is obtained by digitally reconstructing and processing a sequence of holograms recorded during stepwise shifting of a mirror in the reference arm. Experimental results are presented.

Stereophotogrammetric 3D shape measurement by holographic methods using structured speckle illumination combined with interferometry

We present a unique combination of the numerical three-dimensional (3D) reconstruction of the shape of an object with interferometric deformation measurements. Two cameras record several holograms of an object that is illuminated by structured illumination. This illumination is realized by speckle patterns. To improve the image quality, an inplace speckle reduction technique is combined with the structured illumination to reduce the effect of disturbing subjective speckles which appear in the reconstructed images. Stereophotogrammetric methods are applied to extract the 3D surface information of the object out of the reconstructed images. Since the recording is done by holography and because stereophotogrammetry enables a pointwise correlation between the two views, it is possible to combine other holographic techniques with the reconstructed 3D shape. This is demonstrated by an interferometric deformation measurement of an object cooling down. The resulting interferometric fringes are mapped onto the reconstructed 3D surface. Hence, the proposed method enables automatic and dense matching of interferometric fringe-maps recorded by spatially separated holograms onto the surface of the object, which has not yet been realized by existing techniques.

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.

Digital holographic profilometry of the inner surface of a pipe using a current-induced wavelength change of a laser diode

Phase-shifting digital holography is applied to the measurement of the surface profile of the inner surface of a pipe for the detection of a hole in its wall. For surface contouring of the inner wall, a two-wavelength method involving an injection-current-induced wavelength change of a laser diode is used. To illuminate and obtain information on the inner surface, a cone-shaped mirror is set inside the pipe and moved along in a longitudinal direction. The distribution of a calculated optical path length in an experimental alignment is used to compensate for the distortion due to the misalignment of the mirror in the pipe. Using the proposed method, two pieces of metal sheet pasted on the inner wall of the pipe and a hole in the wall are detected. This shows that the three-dimensional profile of a metal plate on the inner wall of a pipe can be measured using simple image processing.

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.

Resolution analysis of a digital holography system

Although digital holography (DH) has many advantages compared to conventional holography, its resolution is limited due to CCDs or other recording devices. Three factors contribute to this limitation, namely, the pixel averaging effect within the finite detection size of one pixel, a finite CCD aperture size limitation, and the sampling effect due to a finite sampling interval. In this paper, interactions of the three factors on resolution are investigated and presented. The resolution of a DH system can be determined for given parameters of these three factors. The domains dominated by different factors are explained along with their accuracy. As a DH system is space variant, influences of object extent on resolution are also discussed. The resolution performance of in-line and off-axis systems is studied and examples of resolution determination for a practical system are provided.

Lensfree on-chip microscopy over a wide field-of-view using pixel super-resolution

We demonstrate lensfree holographic microscopy on a chip to achieve approximately 0.6 microm spatial resolution corresponding to a numerical aperture of approximately 0.5 over a large field-of-view of approximately 24 mm2. By using partially coherent illumination from a large aperture (approximately 50 microm), we acquire lower resolution lensfree in-line holograms of the objects with unit fringe magnification. For each lensfree hologram, the pixel size at the sensor chip limits the spatial resolution of the reconstructed image. To circumvent this limitation, we implement a sub-pixel shifting based super-resolution algorithm to effectively recover much higher resolution digital holograms of the objects, permitting sub-micron spatial resolution to be achieved across the entire sensor chip active area, which is also equivalent to the imaging field-of-view (24 mm2) due to unit magnification. We demonstrate the success of this pixel super-resolution approach by imaging patterned transparent substrates, blood smear samples, as well as Caenoharbditis Elegans.

Tri-arm multipinhole interferometer for wavefront measurement and diffractive imaging

We propose a tri-arm (or Y-shaped) multipinhole (MP) interferometer for wavefront measurement based on a specially designed tri-arm MP plate. We demonstrate that the complex amplitude of a wavefront sampled by the tri-arm MP plate inserted between the object and the detector plane can be extracted directly from the Fourier transform of a far-field diffraction intensity pattern without the need for any iterative algorithm. A form of coherent diffractive imaging based on a rotatable tri-arm MP plate is also demonstrated, which provides a feasible approach for lensless diffractive imaging in real time.

Undersampled digital holography

Acceptable signal recovery of the band-pass signals typically used in the off-axis digital holography systems is possible in the undersampling conditions. A typical system is considered in which the angle between two beams represents a variable parameter. For the given signal bandwidth and experimental conditions the hologram reconstruction is constrained by the sampling frequency of the array photo-detector. Reconstructions from the undersampled digital holograms are analyzed both theoretically and experimentally. It is shown how increasing the angle values beyond the Nyquist limits leads to repeatedly folding and inverting the reconstructed object image until the fading of the image. The phase point at the image fading and the non-overlapping intervals for correctly preserving the useful information are defined and evaluated. Amplitude distributions are analyzed on the example of the time-averaged holograms acquired for an oscillating membrane. Based on removing the zeroth-order reconstruction term, significant extensions of these intervals are also demonstrated.

Lensless Fourier transform digital holographic interferometer for diffusivity measurement of miscible transparent liquids

Lensless Fourier transform digital holographic technique is applied for measurement of diffusion in miscible transparent liquid solutions. The phase information at two time instances and a synthetic plane wavefront is used to determine the diffusion coefficient. The experiment was conducted to measure the diffusion coefficient of aqueous solution of NaCl in water. The measured values of diffusion coefficient deviates approximately 1.06% from the values given in literature.

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.

Large step-height measurements using multiple-wavelength holographic interferometry with tunable laser diodes

Accurate measurement of large step heights using multiple-wavelength holographic interferometry is realized using laser diodes. Due to the high-resolution wavelength tunability of such lasers, a pair of holograms with a wavelength difference of less than 0.01 nm is recorded and used to extract a phase difference having a large synthetic wavelength. Phase differences with synthetic wavelengths ranging from 2.5 to 73 mm are extracted by using pairs of holograms with wavelength differences between 0.3 and 0.01 nm. By combining the phase differences, measurements with a step height of 18 mm and an rms error of 0.04 mm could be achieved. The requirements for performing the phase unwrapping are discussed. Precise knowledge of the recording wavelengths is required to correctly perform this unwrapping.

Free-viewpoint images captured using phase-shifting synthetic aperture digital holography

Free-viewpoint images obtained from phase-shifting synthetic aperture digital holography are given for scenes that include multiple objects and a concave object. The synthetic aperture technique is used to enlarge the effective sensor size and to make it possible to widen the range of changing perspective in the numerical reconstruction. The lensless Fourier setup and its aliasing-free zone are used to avoid aliasing errors arising at the sensor edge and to overcome a common problem in digital holography, namely, a narrow field of view. A change of viewpoint is realized by a double numerical propagation and by clipping the wave field by a given pupil. The computational complexity for calculating an image in the given perspective from the base complex-valued image is estimated at a double fast Fourier transform. The experimental results illustrate the natural change of appearance in cases of both multiple objects and a concave object.

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.

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.

Wavefront sensing using speckles with fringe compensation

Wavefront sensing with numerical phase-error correction system is carried out using a random phase plate and phase retrieval using multiple intensity measurements of axially-displaced speckle patterns and the wave propagation equation. Various wavefronts with smooth curvatures incident on the developed phase plate (DPP) are examined: planar, spherical, cylindrical, and a wavefront passing through the side of a bare optical fiber. Spurious fringe pattern in the wavefront reconstructions due to a small tilt (Delta theta=0.212 degrees) in the plane illumination wave is detected and numerically corrected for. Fringe pattern of the illumination wave obtained for the setup without the phase object being investigated is used as reference fringe pattern. Fringe compensation yields wavefronts with the correct shape and numerical value based on the specifications of the setup. The numerical phase-error correction system described in this study can be extended to other types of phase errors such as those due to aberrations if optical elements are present in the setup or due to perturbations in the environment.

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.

Cortical blood flow assessment with frequency-domain laser Doppler microscopy

We report the assessment of cerebral blood flow (CBF) changes with a wide-field laser Doppler imager based on a CCD camera detection scheme, in vivo, in mice. The setup enables the acquisition of data in minimally invasive conditions. In contrast with conventional laser Doppler velocimeters and imagers, the Doppler signature of moving scatterers is measured in the frequency domain, by detuning a heterodyne optical detection. The quadratic mean of the measured frequency shift is used as an indicator of CBF. We observe a significant variability of this indicator in an experiment designed to induce blood flow changes.

Exact analysis of the effects of sampling of the scalar diffraction field

If the sampled diffraction pattern due to a planar object is used to reconstruct the object pattern by backpropagation, the obtained pattern is no longer the same as the original. The effect of such sampling on the reconstruction is analyzed. The formulation uses the plane-wave expansion, and therefore the provided solution is exact for wave propagation in media where scalar wave propagation is valid. In contrast to the sampling effects under the Fresnel approximation, the exact solution indicates that there are no modulated replicas of the original object in the reconstructed pattern. Rather, the distortion is in the form of modulated, translated, and dispersed versions of the original.

Frequency-domain wide-field laser Doppler in vivo imaging

We present a new instrument, based on a low-frame-rate (8 Hz) CCD camera used in a heterodyne optical-mixing configuration, that can create wide-field laser Doppler maps. As an illustration, we show results obtained in a mouse brain, in vivo, showing the Doppler signature of blood flow. The instrument is based on a frequency-shifting digital holography scheme.

Improvement of accuracy in digital holography by use of multiple holograms

Speckle pattern decorrelation reduces the accuracy of interferometric shape and deformation measurements. We introduce a technique for the reduction of speckle noise in digital holography. The method is not based on classical filtering techniques such as median filters. Instead it utilizes the shift theorem of the Fourier transform. For this method several holograms of the same object under test are recorded. The reconstruction leads to a set of object wave fields with different speckle patterns. A proper averaging procedure, taking into account the properties of the wrapped phases, leads to an improvement of the accuracy in the resulting phase difference. The theory of the applied method is described and our first results for technical components with an improvement of accuracy up to 1/57 of the wavelength are presented.