Numerical Reconstruction Process Research Articles

Quantitative phase reconstruction method based on an infrared-like single wave conversion in dual-wavelength phase-shift digital holography

Dual-wavelength digital holography has recently become a promising tool for achieving higher axial measurement ranges in microscopy. However, digital filtering, such as Fourier transform, or a separate hologram acquisition process is essential for retrieving the quantitative phase information of each respective wavelength. In this paper, a quantitative phase reconstruction method based on an infrared-like single wave conversion in dual-wavelength phase-shift digital holography, which does not require any of the processes mentioned above, has been proposed. Based on the proposed method, the quantitative phase information on the axial measurement specimen was simply obtained by only a phase-shift of a quarter of an infrared-like single wave which has the same magnitude of the synthetic wavelength. This approach simplifies not only the hologram acquisition process but also the numerical reconstruction process. The newly proposed theory is verified and evaluated using simulations and experimental validation.

Object wave field extraction in off-axis holography by clipping its frequency components.

Suitable extraction of an object's wave field in an off-axis digital holographic array is the core for any numerical reconstruction process. In this manuscript, we propose an algorithm that reduces the number of pixels needed for an object's wave field trimming, reducing notably its processing time without significant changes in the quality of the reconstructed image. Our method generates an extraction window containing a complete object's wave field. The energy that the generated extraction window must contain is analyzed, defined, and used as a reference value. Our proposal reduces significantly the number of operations and execution time for holographic reconstruction.

Simultaneous reconstruction of space-dependent heat transfer coefficients and initial temperature

Many complex physical phenomena and engineering systems, e.g., in heat exchanges, reflux condensers, combustion chambers, nuclear vessels, etc., due to the high temperatures/high pressures hostile environment involved, possess certain properties which are inaccessible to measure and therefore their influence/determination using inverse analysis is very important and desirable. In this spirit, the purpose of this paper is to mathematically formulate and analyse a new inverse problem in which given measurements of temperature at two different instants, it is required to obtain the space-dependent heat transfer coefficients (HTCs) and the initial temperature. This simultaneous identification is challenging since it is both nonlinear and ill-posed. The uniqueness of solution is established based on the max–min principle for parabolic equations and the contraction mapping principle for the existence and uniqueness of a fixed point. The novel inverse mathematical model that is proposed offers appropriate scientific guidance to the polymer/heat transfer processing industry as to which data to measure/provide in order to be able to reliably determine the desirable HTCs along with the initial temperature, which is in general unknown. Furthermore, for the reconstruction, the surface HTC is determined separately, whilst the variational formulation is introduced for the simultaneous determination of the domain HTC and the initial temperature. The Fréchet gradient of the minimizing objective functional is derived. The numerical reconstruction process is based on the conjugate gradient method (CGM) regularized by the discrepancy principle. Accurate and stable numerical solutions are obtained even in the presence of noise in the input temperature data. Since noisy data are invented, the study models realistic practical situations in which temperature measurements recorded using sensors or thermocouples are inherently contaminated with random noise.

A direct approach for instantaneous 3D density field reconstruction from background-oriented schlieren (BOS) measurements

We present a new numerical method for reconstruction of instantaneous density volume from 3D background-oriented schlieren (3DBOS) measurements, with a validation on a dedicated flexible experimental BOS bench. In contrast to previous works, we use a direct formulation where density is estimated from measured deviation fields without the intermediate step of density gradient reconstruction. Regularization techniques are implemented to deal with the ill-posed problem encountered. The resulting high-dimensional optimization is conducted by conjugate gradient techniques. A parallel algorithm, implemented on graphics processing unit, helps to speed up the calculation. The resulting software is validated on synthetic BOS images of a 3D density field issued from a numerical simulation. Then, we describe a dedicated 3DBOS experimental facility which has been built to study various BOS settings and to assess the performance of the proposed numerical reconstruction process. Results on various datasets illustrate the potential of the method for flow characterization and measurement in real-world conditions.

English

This paper investigates the application of Fresnel based numerical algorithms for the reconstruction of Gabor in-line holograms. A simple in-line digital holographic system was used to record blood cell. The Fresnel transformation (FS) method was used for reconstruction of the hologram. High contrast blood cell images were used to demonstrate numerical reconstruction process by Matlab. Sine, cosin, and amplitude holograms were reconstructed. This method provides new insights into the dynamics of the red blood cells and will be further used to investigate the effect of physiological and pharmacological effectors on RBCs. The spontaneous cell membrane fluctuations (CMF) of the red blood cell (RBC) was investigated, by calculating both thickness and refraction index of the cell blood.   Key words: Digital holography, blood cell, refractive index.

Numerical correction of splicing dislocation between sub-holograms in synthetic aperture digital holography using convolution approach

We propose a new correction method for the splicing dislocation of sub-holograms in synthetic aperture digital holography. By adjusting the splicing distances between sub-holograms during the numerical reconstruction process using the convolution approach, the influence of non-paraxial aberration for the quality of the synthetic reconstructed image is avoided and synthetic reconstructed images corresponding to different splicing distances are obtained. Then, the accurate splicing distance between sub-holograms is determined by evaluating the quality of the corresponding synthetic reconstructed images. Accurate correction for the splicing dislocation of sub-holograms is achieved and high-quality reconstructed images without nonparaxial aberration are obtained.

Continuous-wave terahertz digital holography by use of a pyroelectric array camera

Terahertz (THz) digital holography is realized based on a 2.52 THz far-IR gas laser and a commercial 124 × 124 pyroelectric array camera. Off-axis THz holograms are obtained by recording interference patterns between light passing through the sample and the reference wave. A numerical reconstruction process is performed to obtain the field distribution at the object surface. Different targets were imaged to test the system's imaging capability. Compared with THz focal plane images, the image quality of the reconstructed images are improved a lot. The results show that the system's imaging resolution can reach at least 0.4 mm. The system also has the potential for real-time imaging application. This study confirms that digital holography is a promising technique for real-time, high-resolution THz imaging, which has extensive application prospects.

One-exposure phase-shifting digital holography based on the self-imaging effect

A diffractive optical element with self-imaging capabilities is used to make a phase-shifting digital holography optical system simpler and cheaper. Sequential phase-shifting requires multiple exposures, and parallel phase-shifting demands a more complicated optical system. As opposed to typical phase-shifting methods, using the self-imaging diffractive optical element requires only one exposure on a low-cost CMOS matrix, and due to the small number of needed elements, the optical system is very compact. Instead of the approximation and interpolation methods, the properties of the self-imaging effect are utilized in the recording process and in the numerical reconstruction process.

Correct self-assembling of spatial frequencies in super-resolution synthetic aperture digital holography

Synthetic aperture enlargement is obtained, in lensless digital holography, by introducing a diffraction grating between the object and the CCD camera with the aim of getting super-resolution. We demonstrate here that the spatial frequencies are naturally self-assembled in the reconstructed image plane when the NA is increased synthetically at its maximum extent of three times. By this approach it possible to avoid the use of the grating transmission formula in the numerical reconstruction process, thus reducing significantly the noise in the final super-resolved image. Demonstrations are reported in 1D and 2D with an optical target and a biological sample, respectively.

Improved-resolution digital holography using the generalized sampling theorem for locally band-limited fields

We describe the recording conditions that, together with the appropriate numerical reconstruction process, permit high-lateral-resolution reconstruction of in-line digital holograms. By high resolution, we mean a resolution that is beyond the Nyquist frequency, which is achieved by common methods. The proposed method is based on a previously reported generalized sampling theory that presents the conditions to precisely reconstruct fields that in certain cases may be sampled with a sampling rate lower than the Nyquist rate. We examine the hologram-recording process in the Wigner space. On the basis of this analysis, we demonstrate a simple high-resolution numerical reconstruction method.

Experimental demonstration of the longitudinal image shift in digital holography

In digital holography, it is necessary to know the distance of the object from the recording charge-coupled device camera to obtain a correct numerical reconstruction process. The presence of a plane parallel plate along the path of the object beam, such as a beamsplitter cube, often used in interferometers, affects the actual reconstruction distance. This effect, to our knowledge, has never been discussed in the literature despite the fact that it adds a contribution that cannot be ignored in the reconstruction process. We evaluate the effect for a spherical object wavefront as well as in the case of an extended object.

Hybrid holographic microscopy: visualization of three-dimensional object information by use of viewing angles

One of the attractive features of hybrid holographic microscopy, in which the hologram of a microscopic object recorded by an image sensor is numerically reconstructed with a computer, is that the three-dimensional (3-D) information of a recorded object is obtained. The 3-D information has often been extracted by means of changing the reconstruction distance in the numerical reconstruction process, but here we describe an alternative technique that allows for variable viewing angles. That is, the perspective from which the object is viewed can be varied. The approximation used enables use of the fast-Fourier-transform algorithm for numerical reconstruction even in the high-resolution case in which the Fresnel approximation is no longer valid. The resolution of the proposed technique is also discussed.

Acoustic Tomography for Three Dimensional Temperature and CO2-Concentration Measurements of Environmental Fields.

Noncontact and nondestructive measurements for determining temperature and CO2-concentration distributions in environmental fields are under investigation by acoustic tomography. A new method to reconstruct the three-dimensional temperature and CO2-concentration distributions from the projected ultrasonic phase differences is proposed in this paper. A set of programs to evaluate the projected data is made and a numerical reconstruction process is also offered. An experimental system consisting of several pairs of ultrasonic sensors is established to apply our new method to axisymmetric temperature and CO2-concentration fields. The temperature profiles reconstructed by the present acoustical tomography agree well with the results of the thermocouple measurements. As a result, the procedure proposed in this paper is verified to be reasonable.

Numerical reconstruction of apodized acoustical holograms

Apodization is a process that was first used to improve the resolving power of imaging systems involving diffraction patterns. It originally signified a reduction in the energy in the side lobes, but it can also be used in a broader sense, as will be done here, to include either a reduction or an enlargement of the side lobes in an acoustical hologram. Since apodization can produce desired characteristics in a reconstructed image of an acoustical hologram, it adds flexibility to the numerical reconstruction process. This flexibility may help to solve one of the most formidable problems facing numerical holography—the large demands for computer memory and computer processing time. It is the objective of the study to show that this is so. Apodization cannot usually produce an overall improvement in the quality of a reconstructed image of an acoustical hologram: although one aspect of the image is improved, another is degraded. However, apodization can be helpful since it can improve the characteristic of interest, even at the expense of other aspects. In this paper, an example is given in which apodization is applied by a computer during the numerical reconstruction of an acoustical hologram. Numerical holography was chosen because the type of apodization described here is readily applied and, as far as could be determined, has not yet been used in numerical holography, although it has been applied with great effectiveness to the shading of sonar arrays. In order to understand the application, a rectangular object formed by illuminating a slot is taken as the first object to be viewed by means of holography. A mathematical description of the resulting hologram is determined by means of the Huygens-Fresnel diffraction formula. Examination of the expression reveals a pattern to which apodization can be applied. The acoustic pattern consists of a large main lobe with monotonically decreasing minor lobes (side lobes) on either side. This paper describes and evaluates a method of apodization in which all side lobes are held at a specified level and the main lobe assumes the minimum width possible for the side lobe level. After demonstrating the method with the rectangle, a triangle is used as the second object, this time expressing it as a summation of rectangles. When this object also worked well, it raised the possibility that any two- or three-dimensional object could be used after expressing it as a summation of rectangular prisms. This proved to be the case for the two-dimensional object chosen, the head of a horse.