Solving ptychography with a convex relaxation

Ptychography is a powerful computational imaging technique that transforms a collection of low-resolution images into a high-resolution sample reconstruction. Unfortunately, algorithms that are currently used to solve this reconstruction problem lack stability, robustness, and theoretical guarantees. Recently, convex optimization algorithms have improved the accuracy and reliability of several related reconstruction efforts. This paper proposes a convex formulation of the ptychography problem. This formulation has no local minima, it can be solved using a wide range of algorithms, it can incorporate appropriate noise models, and it can include multiple a priori constraints. The paper considers a specific algorithm, based on low-rank factorization, whose runtime and memory usage are near-linear in the size of the output image. Experiments demonstrate that this approach offers a 25% lower background variance on average than alternating projections, the current standard algorithm for ptychographic reconstruction.Comment: 8 pages, 8 figure

Qubit-Initialisation and Readout with Finite Coherent Amplitudes in Cavity QED

We consider a unitary transfer of an arbitrary state of a two-level atomic qubit in a cavity to the finite amplitude coherent state cavity field. Such transfer can be used to either provide an effective readout measurement on the atom by a subsequent measurement on the light field or as a method for initializing a fixed atomic state - a so-called "attractor state", studied previously for the case of an infinitely strong cavity field. We show that with a suitable adjustment of the coherent amplitude and evolution time the qubit transfers all its information to the field, attaining a selected state of high purity irrespectively of the initial state.Comment: 6 pages, 4 figure

Analysis and modeling of an ultrasound-modulated guide star to increase the depth of focusing in a turbid medium

The effects of strong scattering in tissue limit the depth to which light may be focused. However, it has been shown that scattering may be reduced utilizing adaptive optics with a focused ultrasound (US) beam guidestar. The optical signal traveling through the US beam waist is frequency shifted and may be isolated with demodulation. This paper utilizes a multiphysics simulation to model the optical and US interactions in both synthetic tissue and random scattering media. The results illustrate that optical energy may be focused within a turbid medium utilizing a US guidestar. The results also suggest that optical energy travels preferentially along optical channels within a turbid medium

Diffusion model for ultrasound-modulated light

Researchers use ultrasound (US) to modulate diffusive light in a highly scattering medium like tissue. This paper analyzes the US–optical interaction in the scattering medium and derives an expression for the US-modulated optical radiance. The diffusion approximation to the radiative transport equation is employed to develop a Green’s function for US-modulated light. The predicted modulated fluence and flux are verified using finite-difference time-domain simulations. The Green’s function is then utilized to illustrate the modulated reflectance as the US–optical interaction increases in depth. The intent of this paper is to focus on high US frequencies necessary for high-resolution imaging because they are of interest for applications such as phase conjugation

A model for ultrasound modulated light in a turbid medium

The ability to focus light in most tissue degrades quickly with depth due to high optical scattering. Researchers have investigated using both ultrasound (US) and light synergistically to overcome this difficulty. Ultrasound has been utilized to modulated light within tissue to create a diffusive wave at that is modulated at the US frequency. Recently, there has been interest in the modulated sidebands which reside at optical frequency plus or minus the US frequency. This paper will discuss a model for US-light interactions in a scattering medium. We will use this model to relate the radiance in the probe beam to the radiance in the diffusive wave. We will then employ the P-1 approximation to the radiative transport equation to find the fluence and flux of the modulated wave. We will use these parameters to write a diffusion equation for the modulated wave that can be described in terms of the incoming optical power, and the US intensity and geometry

High-resolution geophysical surveying at the Springfield Fault, New Zealand

To trace the active Springfield Fault (South Island, New Zealand) and map its character at shallow depths on a terrace where it exhibits no surface expression, we recorded 3-D georadar data across an approximately rectangular 110 x 40 m survey area. In addition, we carried out multi-electrode geoelectric measurements along a 198 m long profile that crossed the georadar survey area. Although the georadar depth penetration was limited to only ~5 m, the processed images revealed the presence of a prominent reflecting horizon disrupted by three main discontinuities. Semi-continuous subhorizontal reflection patterns were interpreted to represent sedimentary units within the fluvial deposits, whereas three detected discontinuities were interpreted as fault traces with small near-vertical offsets (~0.4 m). This interpretation was supported by vertical and lateral changes visible on the final inverted resistivity model indicating lithological boundaries and fault branches

12^{12}C/13^{13}C ratio in planetary nebulae from the IUE archives

We investigated the abundance ratio of $^{12}$C/$^{13}$C in planetary nebulae by examining emission lines arising from \ion{C}{3} 2s2p ^3P_{2,1,0} \to 2s^2 ^1S_0. Spectra were retrieved from the International Ultraviolet Explorer archives, and multiple spectra of the same object were coadded to achieve improved signal-to-noise. The $^{13}$C hyperfine structure line at 1909.6 \AA was detected in NGC 2440. The $^{12}$C/$^{13}$C ratio was found to be $\sim4.4\pm$1.2. In all other objects, we provide an upper limit for the flux of the 1910 \AA line. For 23 of these sources, a lower limit for the $^{12}$C/$^{13}$C ratio was established. The impact on our current understanding of stellar evolution is discussed. The resulting high signal-to-noise \ion{C}{3} spectrum helps constrain the atomic physics of the line formation process. Some objects have the measured 1907/1909 flux ratio outside the low-electron density theoretical limit for $^{12}$C. A mixture of $^{13}$C with $^{12}$C helps to close the gap somewhat. Nevertheless, some observed 1907/1909 flux ratios still appear too high to conform to the presently predicted limits. It is shown that this limit, as well as the 1910/1909 flux ratio, are predominantly influenced by using the standard partitioning among the collision strengths for the multiplet $^1S_0$--$^3P_J$ according to the statistical weights. A detailed calculation for the fine structure collision strengths between these individual levels would be valuable.Comment: ApJ accepted: 19 pages, 3 Figures, 2 Table

A model for ultrasound modulated light in a turbid medium

The ability to focus light in most tissue degrades quickly with depth due to high optical scattering. Researchers have investigated using both ultrasound (US) and light synergistically to overcome this difficulty. Ultrasound has been utilized to modulated light within tissue to create a diffusive wave at that is modulated at the US frequency. Recently, there has been interest in the modulated sidebands which reside at optical frequency plus or minus the US frequency. This paper will discuss a model for US-light interactions in a scattering medium. We will use this model to relate the radiance in the probe beam to the radiance in the diffusive wave. We will then employ the P-1 approximation to the radiative transport equation to find the fluence and flux of the modulated wave. We will use these parameters to write a diffusion equation for the modulated wave that can be described in terms of the incoming optical power, and the US intensity and geometry