Most of the signal processing that we will study in this course involves local operations on a signal, namely transforming the signal by applying linear combinations of values in the neighborhood of each sample point. You are familiar with such operations from Calculus, namely, taking derivatives and you are also familiar with this from optics namely blurring a signal. We will be looking at sampled signals only. Let's start with a few basic examples. Local difference Suppose we have a 1D image and we take the local difference of intensities, DI(x) = 1 2 (I(x + 1) − I(x − 1)) which give a discrete approximation to a partial derivative. (We compute this for each x in the image.) What is the effect of such a transformation? One key idea is that such a derivative would be useful for marking positions where the intensity changes. Such a change is called an edge. It is important to detect edges in images because they often mark locations at which object properties change. These can include changes in illumination along a surface due to a shadow boundary, or a material (pigment) change, or a change in depth as when one object ends and another begins. The computational problem of finding intensity edges in images is called edge detection. We could look for positions at which DI(x) has a large negative or positive value. Large positive values indicate an edge that goes from low to high intensity, and large negative values indicate an edge that goes from high to low intensity. Example Suppose the image consists of a single (slightly sloped) edge:

http://ieeexplore.ieee.org/iel5/5/31307/01456462.pdf

Linear systems

Optical Waveguide Theory

In order to enable optical systems to operate with a high degree of compactness and reliability it is necessary to combine large number of optical functions in small monolithic structures. A development, somewhat reminiscent of that that took place in Integrated Electronics, is now beginning to take place in optics. The initial challenge in this emerging field, known appropriately as "Integrated Optics", is to demonstrate the possibility of performing basic optical functions such as light generation, coupling, modulation, and guiding in Integrated Optical configurations. The talk will review the main theoretical and experimental developments to date in Integrated Optics. Specific topics to be discussed include: Material considerations, guiding mechanisms, modulation, coupling and mode losses. The fabrication and applications of periodic thin film structures will be discussed.

Integrated optics

Elastic optical scattering, the dominant light-interaction process in biological tissues, prevents tissues from being transparent. Although scattering may appear stochastic, it is in fact deterministic in nature. We show that, despite experimental imperfections, optical phase conjugation (λ = 532 nm) can force a transmitted light field to retrace its trajectory through a biological target and recover the original light field. For a 0.69-mm-thick chicken breast tissue section, we can enhance point-source light return by a factor of ~5 x 10^3 and achieve a light transmission enhancement factor of 3.8 within a collection angle of 29°. Additionally, we find that the reconstruction's quality, measured by the width of the reconstructed point source, is independent of tissue thickness (up to a thickness of 0.69 mm). This phenomenon may be used to enhance light transmission through tissue, enable measurement of small tissue movements, and form the basis of new tissue imaging techniques.

/pdf/optical-phase-conjugation-for-turbidity-suppression-in-2hh8y7kynz.pdf

Optical phase conjugation for turbidity suppression in biological samples.

A Treatise on the Analytical Dynamics of Particles and Rigid Bodies: THE GENERAL THEORY OF ORBITS

In this work we formulate the main properties of the gyrator operation which produces a rotation in the twisting (position - spatial frequency) phase planes. This transform can be easily performed in paraxial optics that underlines its possible application for image processing, holography, beam characterization, mode conversion and quantum information.As an example, it is demonstrated the application of gyrator transform for the generation of a variety of stable modes.

/pdf/gyrator-transform-properties-and-applications-2cq0lnalv4.pdf

Gyrator transform: properties and applications.

The gyrator transform (GT) promises to be a useful tool in image processing, holography, beam characterization, mode transformation, and quantum information. We introduce what we believe to be the first flexible optical experimental setup that performs the GT for a wide range of transformation parameters. The feasibility of the proposed scheme is demonstrated on the gyrator transformation of Hermite-Gaussian modes. For certain parameters the output mode corresponds to the Laguerre-Gaussian one.

/pdf/experimental-implementation-of-the-gyrator-transform-2cws1kru23.pdf

Experimental implementation of the gyrator transform

Permanent holographic storage has been demonstrated in a photopolymerizable organically modified silica glass. The glass was prepared by dispersing a titanocene photoinitiator and a high refractive index acrylic monomer in a porous silica matrix. This glass exhibits unprecedented sensitivity and refractive index change upon a moderate exposure to green light and can be fabricated in thickness up to several millimeters. A photopolymerizable storage medium of such a thickness with good holographic properties is needed for practical holographic storage devices. Lack of such medium has been considered the main obstacle in development of write-once holographic memories. In our glass, we have stored permanent volume holograms of diffraction efficiency approaching 100% and refractive index modulation up to 4.5×10−3, making this photopolymerizable material suitable for use in holographic data storage.

/pdf/a-photopolymerizable-glass-with-diffraction-efficiency-near-11s2q5a8sm.pdf

A photopolymerizable glass with diffraction efficiency near 100% for holographic storage

Applications of gyrator transform for image processing

We report a stationary Fourier-transform spectrometer chip implemented in silicon microphotonic waveguides. The device comprises an array of 32 Mach-Zehnder interferometers (MZIs) with linearly increasing optical path delays between the MZI arms across the array. The optical delays are achieved by using Si-wire waveguides arranged in tightly coiled spirals with a compact device footprint of 12 mm(2). Spectral retrieval is demonstrated in a single measurement of the stationary spatial interferogram formed at the output waveguides of the array, with a wavelength resolution of 40 pm within a free spectral range of 0.75 nm. The phase and amplitude errors arising from fabrication imperfections are compensated using a transformation matrix spectral retrieval algorithm.

/pdf/high-resolution-fourier-transform-spectrometer-chip-with-3wtll38m88.pdf

Maria L. Calvo

Papers

Gyrator transform: properties and applications.

Experimental implementation of the gyrator transform

A photopolymerizable glass with diffraction efficiency near 100% for holographic storage

Applications of gyrator transform for image processing

High-resolution Fourier-transform spectrometer chip with microphotonic silicon spiral waveguides