Edge Enhancement of Phase Objects with Hilbert Transforms in Optical Tomography (original) (raw)

Hilbert transform and optical tomography for anisotropic edge enhancement of phase objects

Journal of Physics: Conference Series, 2011

In phase object tomography a slice reconstruction is related to distribution of refractive index. Typically, this is obtained by applying the filtered back-projection algorithm to the set of projections (sinogram) obtained experimentally, which are sequentially obtained by calculating the phase of the wave emerging from the slice of the object at different angles. In this paper, based on optical implementation of the Hilbert-transform in a 4f Fourier operator, the Hilbert transform of the projections leaving of the object are obtained numerically. When these projection data are captured for a set of viewing angles an unconventional sinogram is eventually obtained, we have called it as an Hilbert-sinogram. The reconstruction obtained by applying the filtered back-projection algorithm is proportional to the Hilbert transform of the distribution of refractive index of the slice and the obtained image shows a typical isotropic edge enhancement. In this manuscript, the theoretical analysis and the numerical implementation of the Hilberttransform, mathematical model of the edge enhancement reconstructed are extensively detailed.

Isotropic edge-enhancement by the Hilbert-transform in optical tomography of phase objects

Optics Express, 2011

In optical tomography, isotropic edge-enhancement of phaseobject slices under the refractionless limit approximation can be reconstructed using spatial filtering techniques. The optical Hilberttransform of the transmittance function leaving the object at projection angles 00 (0 ,360 )   , is one of these techniques with some advantages. The corresponding irradiance of the so modified transmittance is considered as projection data, and is proved that they share two properties with the Radon transform: its symmetry property and its zeroth-moment conservation. Accordingly, a modified sinogram able to reconstruct edge-enhanced phase slices is obtained. In this paper, the theoretical model is amply discussed and illustrated both with numerical and experimental results.

Directional edge enhancement in optical tomography of thin phase objects

Optics Express, 2011

In this paper, we make a proposal to obtain the Hilbert-transform for each entry of the projection data leaving the slice of a thin phase object. These modified projections are stacked in such a way that they form a modified sinogram called Hilbert-sinogram. We prove that the inverse Radon-transform of this sinogram is the directional Hilbert-transform of the slice function, and the reconstructed image is the directional edge enhancement of the distribution function on the slice. The Hilbert-transform is implemented by a 4f optical Fourier-transform correlator and a spatial filter consisting of a phase step of π radians. One important feature of this proposal is to perform a turn of 180° in the spatial filter at a certain value of the projection angle within the range   0 , 360  . The desired direction of enhancement can be chosen by the proper selection of such turning angle. We present both the mathematical modeling and numerical results.

Anisotropic edge-enhanced of a phase object slice by spatial filtering and optical tomography

2009

It has been shown that edge-enhanced images by using optical spatial filtering system of double Fourier-transform can be successfully obtained by implemented the optical Hilbert-transform . This implementation can be obtained by placing a phase step filter of ¿ radians at the frequency plane. Under this background, in this paper, we show how the edge-enhanced of a phase object slice using optical tomography and optical spatial filtering could be obtained. This procedure is principally based by obtaining sequentially the Hilbert-transform of each projection and by applying the filtered back-projection algorithm to obtain the image reconstruction. In this paper, both theoretical analysis and numerical simulations are shown.

Optical Fourier techniques for medical image processing and phase contrast imaging

Optics Communications, 2008

This paper briefly reviews the basics of optical Fourier techniques (OFT) and applications for medical image processing as well as phase contrast imaging of live biological specimens. Enhancement of microcalcifications in a mammogram for early diagnosis of breast cancer is the main focus. Various spatial filtering techniques such as conventional 4f filtering using a spatial mask, photoinduced polarization rotation in photosensitive materials, Fourier holography, and nonlinear transmission characteristics of optical materials are discussed for processing mammograms. We also reviewed how the intensity dependent refractive index can be exploited as a phase filter for phase contrast imaging with a coherent source. This novel approach represents a significant advance in phase contrast microscopy.

Image restoration method based on Hilbert transform for full-field optical coherence tomography

Applied Optics, 2008

A full-field optical coherence tomography (FF-OCT) system utilizing a simple but novel image restoration method suitable for a high-speed system is demonstrated. An en-face image is retrieved from only two phase-shifted interference fringe images through using the mathematical Hilbert transform. With a thermal light source, a high-resolution FF-OCT system having axial and transverse resolutions of 1 and 2.2 m, respectively, was implemented. The feasibility of the proposed scheme is confirmed by presenting the obtained en-face images of biological samples such as a piece of garlic and a gold beetle. The proposed method is robust to the error in the amount of the phase shift and does not leave residual fringes. The use of just two interference images and the strong immunity to phase errors provide great advantages in the imaging speed and the system design flexibility of a high-speed high-resolution FF-OCT system.

Image processing with the radial Hilbert transform: theory and experiments

Optics Letters, 2000

The Hilbert transform is useful for image processing because it can select which edges of an input image are enhanced and to what degree the edge enhancement occurs. However, the transform operation is one dimensional and is not applicable for arbitrarily shaped two-dimensional objects. We introduce a radially symmetric Hilbert transform that permits two-dimensional edge enhancement. We implement onedimensional, two-dimensional, and radial Hilbert transforms with a programmable phase-only liquid-crystal spatial light modulator. Experimental results are presented. 

Optical implementation of the fractional Hilbert transform for two-dimensional objects

The classical Hilbert transform can be implemented optically as a spatial-filtering process, whereby half the Fourier spectrum is -phase shifted. Recently the Hilbert transform was generalized. The generalized version, called the fractional Hilbert transform, is quite easy to implement optically if the input is one dimensional. Here we show how to implement the fractional Hilbert transform for two-dimensional inputs. Hence the new transform is now suitable for image processing.

Optical phase-space-time-frequency tomography

Optics Express, 2011

We present a new approach for constructing optical phase-space-time-frequency tomography (OPSTFT) of an optical wave field. This tomography can be measured by using a novel fourwindow optical imaging system based on two local oscillator fields balanced heterodyne detection. The OPSTFT is a Wigner distribution function of two independent Fourier Transform pairs, i.e., phase-space and time-frequency. From its theoretical and experimental aspects, it can provide information of position, momentum, time and frequency of a spatial light field with precision beyond the uncertainty principle. Besides the distributions of x − p and t − ω, the OPSTFT can provide four other distributions such as x − t, p − t, x − ω and p − ω. We will simulate the OPSTFT for a light field obscured by a wire and a single-line absorption filter. We believe that the four-window system can provide spatial and temporal properties of a wave field for quantum image processing and biophotonics.

Three-Dimensional Measurements Using Hilbert Phase Microscopy

New Physics: Sae Mulli, 2017

In this study, we used Hilbert phase microscopy to obtain quantitative, high spatial resolution phase images of sample objects with a large depth of field (DOF) based on interferometric methods. The Hilbert microscope is suitable for investigating fast-occurring phenomena because it requires only one image. The pitch of the interference pattern can be controlled by changing the angle between the two interference beams, and the DOF can be controlled by varying the overlapping width of the beam. The Hilbert transform was used to retrieve the phase of the sample in computer simulations, as well as in experiments, that measure the phase by using the fringe method.