Hologram reconstruction by use of optical wavelet transform

Direct measurement of particle size and 3D velocity of a gas-solid pipe flow with digital holographic particle tracking velocimetry

The 3D measurement of the particles in a gas-solid pipe flow is of great interest, but remains challenging due to curved pipe walls in various engineering applications. Because of the astigmatism induced by the pipe, concentric ellipse fringes in the hologram of spherical particles are observed in the experiments. With a theoretical analysis of the particle holography by an ABCD matrix, the in-focus particle image can be reconstructed by the modified convolution method and fractional Fourier transform. Thereafter, the particle size, 3D position, and velocity are simultaneously measured by digital holographic particle tracking velocimetry (DHPTV). The successful application of DHPTV to the particle size and 3D velocity measurement in a glass pipe's flow can facilitate its 3D diagnostics.

Asymmetric wavelet reconstruction of particle hologram with an elliptical Gaussian beam illumination

We propose an asymmetric wavelet method to reconstruct a particle from a hologram illuminated by an elliptical, astigmatic Gaussian beam. The particle can be reconstructed by a convolution of the asymmetric wavelet and hologram. The reconstructed images have the same size and resolution as the recorded hologram; therefore, the reconstructed 3D field is convenient for automatic particle locating and sizing. The asymmetric wavelet method is validated by both simulated holograms of spherical particles and experimental holograms of opaque, nonspherical coal particles.

Modified convolution method to reconstruct particle hologram with an elliptical Gaussian beam illumination

Application of the modified convolution method to reconstruct digital inline holography of particle illuminated by an elliptical Gaussian beam is investigated. Based on the analysis on the formation of particle hologram using the Collins formula, the convolution method is modified to compensate the astigmatism by adding two scaling factors. Both simulated and experimental holograms of transparent droplets and opaque particles are used to test the algorithm, and the reconstructed images are compared with that using FRFT reconstruction. Results show that the modified convolution method can accurately reconstruct the particle image. This method has an advantage that the reconstructed images in different depth positions have the same size and resolution with the hologram. This work shows that digital inline holography has great potential in particle diagnostics in curvature containers.

Extended wavelet transformation to digital holographic reconstruction: application to the elliptical, astigmatic Gaussian beams

Wavelet analysis provides an efficient tool in numerous signal processing problems and has been implemented in optical processing techniques, such as in-line holography. This paper proposes an improvement of this tool for the case of an elliptical, astigmatic Gaussian (AEG) beam. We show that this mathematical operator allows reconstructing an image of a spherical particle without compression of the reconstructed image, which increases the accuracy of the 3D location of particles and of their size measurement. To validate the performance of this operator we have studied the diffraction pattern produced by a particle illuminated by an AEG beam. This study used mutual intensity propagation, and the particle is defined as a chirped Gaussian sum. The proposed technique was applied and the experimental results are presented.

Phase reconstruction of digital holography with the peak of the two-dimensional Gabor wavelet transform

We describe a numerical reconstruction technique for digital holography by means of the two-dimensional Gabor wavelet transform (2D-GWT). Applying the 2D-GWT to digital holography, the object wave can be reconstructed by calculating the wavelet coefficients of the hologram at the peak of the 2D-GWT automatically. At the same time the effect of the zero-order diffraction image and the twin image are eliminated without spatial filtering. Comparing the numerical reconstruction of a holographic image by the analysis of the one-dimensional Gabor wavelet transform (1D-GWT) with the 2D-GWT, we show that the 2D-GWT method is superior to the 1D-GWT method, especially when the fringes of the hologram are not just along the y direction. The theory and the results of a simulation and experiments are shown.

Visualization of fast-moving cells in vivo using digital holographic video microscopy

Digital in-line holography offers some significant advantages over conventional optical holography and microscopy to image biological specimens. By combining holography with digital video microscopy, an in-line holographic video microscope is developed and is capable of recording spatial 3D holographic images of biological specimens, while preserving the time dimension. The system enables high-speed video recording of fast cell movement, such as the rapid movement of blood cells in the blood stream in vivo. This capability is demonstrated with observations of fast 3-D movement of live cells in suspension cultures in response to a gentle shake to the Petri dish. The experimental and numerical procedures are incorporated with a fast reconstruction algorithm for reconstruction of holographic video frames at various planes (z axis) from the hologram and along the time axis. The current system enables both lateral and longitudinal resolutions down to a few micrometers. Postreconstruction processing of background subtraction is utilized to eliminate noise caused by scattered light, thereby enabling visualization of, for example, blood streams of live Xenopos tadpoles. The combination of digital holography and microscopy offers unique advantages for imaging of fast moving cells and other biological particles in three dimensions in vivo with high spatial and temporal resolution.

Applications of fractional transforms to object reconstruction from in-line holograms

We propose a method for the digital reconstruction of an object whose diffraction pattern has been recorded on a hologram. The fractional Fourier transform is used for the object reconstruction. To determine the position of the object, the fractional order is scanned. The fractional cosine and fractional Hartley transforms are also employed for object reconstruction. These two transforms are real valued and allow the reconstruction to be done with lower computing complexity. Simulations and experimental results are presented.

Application of the two-dimensional fractional-order Fourier transformation to particle field digital holography

We demonstrate that the fractional-order Fourier transformation is a suitable method to analyze the diffraction patterns of particle field holograms. This method permits reconstruction of in-line digital holograms beyond the Fraunhofer condition (d2/lambdaz approximately/= 10). We show that the diameter of spherical particles is measured with good accuracy. Simulation and experimental results are presented.