Fish embryo multimodal imaging by laser Doppler digital holography

A laser Doppler imaging scheme combined to an upright microscope is proposed. Quantitative Doppler imaging in both velocity norm and direction, as well as amplitude contrast of either zebrafish flesh or vasculature is demonstrated.Comment: Signal Recovery and Synthesis, Jul 2014, Seattle, United States. (Optical Society of America), OSA Technical Digest (online) 2014, paper JTu4A.7., Imaging and Applied Optics 2014, http://www.opticsinfobase.org/abstract.cfm?URI=SRS-2014-JTu4A.

Localizing Volatilities

We propose two main applications of Gy\"{o}ngy (1986)'s construction of inhomogeneous Markovian stochastic differential equations that mimick the one-dimensional marginals of continuous It\^{o} processes. Firstly, we prove Dupire (1994) and Derman and Kani (1994)'s result. We then present Bessel-based stochastic volatility models in which this relation is used to compute analytical formulas for the local volatility. Secondly, we use these mimicking techniques to extend the well-known local volatility results to a stochastic interest rates framework

Singular value demodulation of phase-shifted holograms

We report on phase-shifted holographic interferogram demodulation by singular value decomposition. Numerical processing of optically-acquired interferograms over several modulation periods was performed in two steps : 1- rendering of off-axis complex-valued holograms by Fresnel transformation of the interferograms; 2- eigenvalue spectrum assessment of the lag-covariance matrix of hologram pixels. Experimental results in low-light recording conditions were compared with demodulation by Fourier analysis, in the presence of random phase drifts.Comment: 4 pages, 3 figure

Spatiotemporal heterodyne detection

We describe a scheme into which a camera is turned into an efficient tunable frequency filter of a few Hertz bandwidth in an off-axis, heterodyne optical mixing configuration, enabling to perform parallel, high-resolution coherent spectral imaging. This approach is made possible through the combination of a spatial and temporal modulation of the signal to reject noise contributions. Experimental data obtained with dynamically scattered light by a suspension of particles in brownian motion is interpreted

Short-time Fourier transform laser Doppler holography

We report a demonstration of laser Doppler holography at a sustained acquisition rate of 250 Hz on a 1 Megapixel complementary metal-oxide-semiconductor (CMOS) sensor array and image display at 10 Hz frame rate. The holograms are optically acquired in off-axis configuration, with a frequency-shifted reference beam. Wide-field imaging of optical fluctuations in a 250 Hz frequency band is achieved by turning time-domain samplings to the dual domain via short-time temporal Fourier transformation. The measurement band can be positioned freely within the low radio-frequency spectrum by tuning the frequency of the reference beam in real-time. Video-rate image rendering is achieved by streamline image processing with commodity computer graphics hardware. This experimental scheme is validated by a non-contact vibrometry experiment

Shot Noise in Digital Holography

We discuss on noise in heterodyne holography in an off-axis configuration. We show that, for a weak signal, the noise is dominated by the shot noise on the reference beam. This noise corresponds to an equivalent noise on the signal beam of one photoelectron per pixel, for the whole sequence of images used to build the digital hologram

Options on Hedge Funds under the High Water Mark Rule

The rapidly growing hedge fund industry has provided individual and institutional investors with new investment vehicles and styles of management. It has also brought forward a new form of performance contract: hedge fund managers receive incentive fees which are typically a fraction of the fund net asset value (NAV) above its starting level - a rule known as high water mark. Options on hedge funds are becoming increasingly popular, in particular because they allow investors with limited capital to get exposure to this new asset class. The goal of the paper is to propose a valuation of plain-vanilla options on hedge funds which accounts for the high water market rule. Mathematically, this valuation leads to an interesting use of local times of Brownian motion. Option prices are numerically computed by inversion of their Laplace transforms

Phase-resolved heterodyne holographic vibrometry with a strobe local oscillator

We report a demonstration of phase-resolved vibrometry, in which out-of-plane sinusoidal motion is assessed by heterodyne holography. In heterodyne holography, the beam in the reference channel is an optical local oscillator (LO). It is frequency-shifted with respect to the illumination beam to enable frequency conversion within the sensor bandwidth. The proposed scheme introduces a strobe LO, where the reference beam is frequency-shifted and modulated in amplitude, to alleviate the issue of phase retrieval. The strobe LO is both tuned around the first optical modulation side band at the vibration frequency, and modulated in amplitude to freeze selected mechanical vibration states sequentially. The phase map of the vibration can then be derived from the demodulation of successive vibration states