Paul Urbach

Measuring the size of the proton

The size of an atom’s nucleus is roughly five orders of magnitude smaller than the size of the atom. Consequently, the nuclear corrections to atomic energy levels are very tiny. However, these corrections have become important in recent highprecision measurements of transitions in the hydrogen atom, which are being performed to test quantum electrodynamics (QED) and to determine related fundamental constants. Today, the interpretation of this data is only limited by the uncertainties in the size of the nucleus, which in the case of hydrogen is a single proton. The charge radius rp of the proton is a physical parameter that characterizes important aspects of the effective size of the proton. Its value is used together with the Rydberg constant in the calculations of bound-state QED involving hydrogen atoms as well as muonic hydrogen atoms that have a muon orbiting the nucleus rather than the electron. (Muons are like electrons but 200 times heavier.) A recent spectroscopic study of muonic hydrogen resulted in a new measurement of the proton root mean square (rms) charge radius.1 The reported value, rp D 0:84184.67/fm, differs by 5 standard deviations from (and is a factor of 10 more precise than) previous determinations. These earlier values come from three very different methods that are based mostly on electronic hydrogen data. Specifically, a compilation of physical constants (CODATA) gives rp D 0:8768.69/fm,2 the Lamb shift of electronic hydrogen results in rp D 0:883.14/fm,3, 4 and electron scattering from hydrogen yields rp D 0:895.18/fm.5 It is noteworthy that QED considerations show6 that the electron scattering experiments and the atomic hydrogen spectroscopy determine the same Figure 1. Block diagram of the layout of the first approach to a dedicated nonlinear laser source.

Iterative learning control of a membrane deformable mirror for optimal wavefront correction

We present an iterative learning control (ILC) algorithm for controlling the shape of a membrane deformable mirror (DM). We furthermore give a physical interpretation of the design parameters of the ILC algorithm. On the basis of this insight, we derive a simple tuning procedure for the ILC algorithm that, in practice, guarantees stable and fast convergence of the membrane to the desired shape. In order to demonstrate the performance of the algorithm, we have built an experimental setup that consists of a commercial membrane DM, a wavefront sensor, and a real-time controller. The experimental results show that, by using the ILC algorithm, we are able to achieve a relatively small error between the real and desired shape of the DM while at the same time we are able to control the saturation of the actuators. Moreover, we show that the ILC algorithm outperforms other control algorithms available in the literature.

A Lanczos model-order reduction technique to efficiently simulate electromagnetic wave propagation in dispersive media

In this paper we present a Krylov subspace model-order reduction technique for time- and frequency-domain electromagnetic wave fields in linear dispersive media. Starting point is a self-consistent first-order form of Maxwells equations and the constitutive relation. This form is discretized on a standard staggered Yee grid, while the extension to infinity is modeled via a recently developed global complex scaling method. By applying this scaling method, the time- or frequency-domain electromagnetic wave field can be computed via a so-called stability-corrected wave function. Since this function cannot be computed directly due to the large order of the discretized Maxwell system matrix, Krylov subspace reduced-order models are constructed that approximate this wave function. We show that the system matrix exhibits a particular physics-based symmetry relation that allows us to efficiently construct the time- and frequency-domain reduced-order models via a Lanczos-type reduction algorithm. The frequency-domain models allow for frequency sweeps meaning that a single model provides field approximations for all frequencies of interest and dominant field modes can easily be determined as well. Numerical experiments for two- and three-dimensional configurations illustrate the performance of the proposed reduction method.

Using saddle points for challenging optical design tasks

The present research is part of an effort to develop tools that make the lens design process more systematic. In typical optical design tasks, the presence of many local minima in the optical merit function landscape makes design non-trivial. With the method of Saddle Point Construction (SPC) which was developed recently ([F. Bociort and M. van Turnhout, Opt. Engineering 48, 063001 (2009)]) new local minima are obtained efficiently from known ones by adding and removing lenses in a systematic way. To illustrate how SPC and special properties of the lens design landscape can be used, we will present the step-by-step design of a wide-angle pinhole lens and the automatic design of a 9-lens system which, after further development with traditional techniques, is capable of good performance. We also give an example that shows how to visualize the saddle point that can be constructed at any surface of any design of an imaging system that is a local minimum.

Theoretical analysis for best defocus measurement plane for robust phase retrieval

We study the phase retrieval (PR) technique using through-focus intensity measurements and explain the dependence of PR on the defocus distance. An optimal measurement plane in the out-of-focus region is identified where the intensity distribution on the optical axis drops to the first minimum after focus. Experimental results confirm the theoretical predictions and are in good agreement with an independent phase measurement.

Tunable binary Fresnel lens based on stretchable PDMS/CNT composite

This paper presents a tunable micro Fresnel lens made by a polydimethylsiloxane/carbon nanotubes (PDMS/CNTs) configuration that can change its focal length by simply stretching the substrate. We believe this is the first time that this configuration has been realized and demonstrated. The Fresnel lens is formed by embedding vertically aligned CNTs bundles in a 2mm thick PDMS layer. It utilizes the transparency and flexibility of the PDMS and the excellent optical absorption properties of CNTs. The lens is fabricated using a straightforward process, which requires only one lithography step. Preliminary results show that this Fresnel lens has good optical properties, and focal length change can be realized by simply stretching the polymer substrate.

Simulating multiple diffraction in imaging systems using a path integration method.

We present a method for simulating multiple diffraction in imaging systems based on the Huygens-Fresnel principle. The method accounts for the effects of both aberrations and diffraction and is entirely performed using Monte Carlo ray tracing. We compare the results of this method to those of reference simulations for field propagation through optical systems and for the calculation of point spread functions. The method can accurately model a wide variety of optical systems beyond the exit pupil approximation.

Depth resolved quantitative profiling of stratum corneum lipids and water content using short-wave infrared spectroscopy

We show the feasibility of short wave infrared spectroscopy combined with tape stripping as a simple and noninvasive method for the analysis of lipids and the degree of hydration as a function of depth in the stratum corneum. The spectroscopic method utilizes differential detection with three wavelengths 1720, 1750, and 1770 nm, corresponding to the lipid vibrational bands that lay “in between” the prominent water absorption bands. The results are compared with other biophysical devices such as Corneometer and Sebumeter.

High sensitivity optical method for objective assessment of the gloss of human skin

We report a low-cost optical method with high sensitivity for the quantitative assessment of the gloss of human skin in the low gloss regime relevant for physiological skin gloss conditions. Using Monte Carlo simulations, experiments on gloss calibration standards and in-vivo skin gloss experiments using an optical prototype, we demonstrate the improved sensitivity of the proposed method in the low gloss regime compared to professional industrial and skin gloss measurement devices.

Ray-based method for simulating cascaded diffraction in high-numerical-aperture systems

The electric field at the output of an optical system is in general affected by both aberrations and diffraction. Many simulation techniques treat the two phenomena separately, using a geometrical propagator to calculate the effects of aberrations and a wave-optical propagator to simulate the effects of diffraction. We present a ray-based simulation method that accounts for the effects of both aberrations and diffraction within a single framework. The method is based on the Huygens-Fresnel principle, is entirely performed using Monte Carlo ray tracing, and, in contrast to our previously published work, is able to calculate the full electromagnetic field. The method can simulate the effects of multiple diffraction in systems with a high numerical aperture.