Markus E. Testorf

Instrumentation and design of a frequency-domain diffuse optical tomography imager for breast cancer detection.

The instrument development and design of a prototype frequency-domain optical imaging device for breast cancer detection is described in detail. This device employs radio-frequency intensity modulated near-infrared light to image quantitatively both the scattering and absorption coefficients of tissue. The functioning components of the system include a laser diode and a photomultiplier tube, which are multiplexed automatically through 32 large core fiber optic bundles using high precision linear translation stages. Image reconstruction is based on a finite element solution of the diffusion equation. This tool for solving the forward problem of photon migration is coupled to an iterative optical property estimation algorithm, which uses a Levenberg-Marquardt routine with total variation minimization. The result of this development is an automated frequency-domain optical imager for computed tomography which produces quantitatively accurate images of the test phantoms used to date. This paper is a description and characterization of an automated frequency-domain computed tomography scanner, which is more quantitative than earlier systems used in diaphanography because of the combination of intensity modulated signal detection and iterative image reconstruction.

Hippocampal interictal epileptiform activity disrupts cognition in humans

Objective: We investigated whether interictal epileptiform discharges (IED) in the human hippocampus are related to impairment of specific memory processes, and which characteristics of hippocampal IED are most associated with memory dysfunction. Methods: Ten patients had depth electrodes implanted into their hippocampi for preoperative seizure localization. EEG was recorded during 2,070 total trials of a short-term memory task, with memory processing categorized into encoding, maintenance, and retrieval. The influence of hippocampal IED on these processes was analyzed and adjusted to account for individual differences between patients. Results: Hippocampal IED occurring in the memory retrieval period decreased the likelihood of a correct response when they were contralateral to the seizure focus (p < 0.05) or bilateral (p < 0.001). Bilateral IED during the memory maintenance period had a similar effect (p < 0.01), particularly with spike-wave complexes of longer duration (p < 0.01). IED during encoding had no effect, and reaction time was also unaffected by IED. Conclusions: Hippocampal IED in humans may disrupt memory maintenance and retrieval, but not encoding. The particular effects of bilateral IED and those contralateral to the seizure focus may relate to neural compensation in the more functional hemisphere. This study provides biological validity to animal models in the study of IED-related transient cognitive impairment. Moreover, it strengthens the argument that IED may contribute to cognitive impairment in epilepsy depending upon when and where they occur.

Talbot effect for oblique angle of light propagation

The Talbot effect is investigated for oblique angles of illumination. From the transfer function of free space assuming small diffraction angles we calculate the self-imaging condition for periodic diffractive elements. Additionally, aberrations are considered, which are of third order in spatial frequency. These aberrations originate from the asymmetric off-axis configuration and cause distortions of the self-images. We include experimental verifications of our considerations and suggest applications of the off-axis Talbot effect to planar optics.

Holography in phase space

Holography is reformulated by using the framework of phase-space optics. The Leith-Upatnieks off-axis reference hologram is compared with precursors, namely, single-sideband holography. The phase-space representation of complex amplitudes focuses on similarities between different holographic recording schemes and is particularly useful for investigating the degree of freedom and the space-bandwidth product of optical signals and systems. This allows one to include computer-generated holography and recent developments in digital holography in the discussion.

Application of three-dimensional micro-optical components formed by lithography, electroforming, and plastic molding

Micro-optics is usually associated with planar waveguides or integrated optical circuits. In this case the propagation of light is restricted to one or two dimensions, and the three-dimensional nature of light propagation is disregarded. We present a method of fabricating three-dimensional micro-optical components by the so-called LIGA process, a lithography, electroforming, and plastic molding process in which poly(methyl methacrylate) is structured by high-energy synchrotron radiation. We demonstrate an experimental system of image formation that uses microprisms and microlenses for a threedimensional microintegration of optical components.

Phase-space interpretation of deterministic phase retrieval.

Deterministic phase retrieval is reinterpreted in terms of phase-space optics. A novel derivation of the transport-of-intensity equation is presented based on the Wigner distribution function and the ambiguity function. The phase retrieval problem is formulated as estimating the local first-order moment of the Wigner function from intensity information. A comparison with phase-space tomography suggests a generalization of deterministic phase retrieval that provides larger flexibility for signal recovery. In addition, one particular numerical implementation of generalized deterministic phase retrieval is presented. Simulated intensity data are used to validate the method.

Astigmatic gradient-index elements for laser-diode collimation and beam shaping

For the conversion of light from edge-emitting laser diodes into symmetric laser beams two main tasks have to be performed: collimation and beam shaping. Generally these two jobs are performed separately. Because of the inherently different divergence angles of the emitted light, collimation with astigmatic lenses generally results in a beam with an elliptically shaped amplitude distribution. This asymmetry has to be compensated for by an anamorphic imaging step to obtain the desired spherical beam profile. It can be advantageous to combine both jobs in one element. We demonstrate the design, the fabrication, and the application of refractive gradient-index elements, which allow one to perform both jobs with a single element. Our astigmatic lenses were fabricated by silver-sodium ion exchange in glass.

Sampling of time- and frequency-domain signals in Monte Carlo simulations of photon migration

We compare two fundamentally different ways to evaluate the time dependence in Monte Carlo simulations of photon migration: estimating the pulse response in time versus evaluating the transfer function at discrete points in the frequency domain. We show that these two methods differ in accuracy owing to quantization and sampling errors, whereas the statistical error is essentially the same for both methods. From our analysis we also derive alternative methods to sample the time-domain pulse response with reduced quantization and sampling error. Simulation results are included to illustrate our theoretical analysis.

Index-distributed planar microlenses for three-dimensional micro-optics fabricated by silver-sodium ion exchange in BGG35 substrates

Fabrication of planar microlens arrays by silver-sodium ion exchange is possible by using a new glass type, optimized for this technology. Because of its nonlinear diffusion response it is well suited to the fabrication of microlens arrays. We show that the diffusion coefficient can be described theoretically by an exponential concentration dependence. The parameters of the planar microlenses are measured interferometrically and by imaging experiments. Because of the specific index distribution, new evaluation techniques for the determination of lens parameters from interferometric measurements have been applied. We also present a simple model that relates the achievable lens parameters to the diffusion conditions.

Implementation of Fourier array illuminators using pixelated SLM: efficiency limitations

We investigate the performance of diffractive optical elements implemented with pixelated spatial light modulators. A fill factor of the active area less than 100% affects the maximum diffraction efficiency which can be achieved. We investigate the relation between the maximum diffraction efficiency, the fill factor and the desired diffraction pattern. Numerical results for particular cases are included for illustration.