Monochromatic Phase Research Articles

Tracing the phase of focused broadband laser pulses

Precise knowledge of the behaviour of the phase of light in a focused beam is fundamental to understanding and controlling laser-driven processes. More than a hundred years ago an axial phase anomaly for focused monochromatic light beams was discovered and is now commonly known as the Gouy phase. Recent theoretical work has brought into question the validity of applying this monochromatic phase formulation to the broadband pulses becoming ubiquitous today. Based on electron back-scattering at sharp nanometre-scale metal tips, a method is available to measure light fields with sub-wavelength spatial resolution and sub-optical cycle time resolution. Here we report such a direct, three-dimensional measurement of the spatial dependence of the optical phase of a focused, 4-fs, near-infrared laser pulse. The observed optical phase deviates substantially from the monochromatic Gouy phase - exhibiting a much more complex spatial dependence, both along the propagation axis and in the radial direction. In our measurements, these significant deviations are the rule and not the exception for focused, broadband laser pulses. Therefore, we expect wide ramifications for all broadband laser-matter interactions, such as in high-harmonic and attosecond pulse generation, femtochemistry, ophthalmological optical coherence tomography and light-wave electronics.

Potential relativistic dispersion in material medium

Lorentz space-time transformation has been applied to the phase factor of a plane electromagnetic wave in linear material medium. The derivation shows in the limiting case for v=c, the phase velocity converges to its monochromatic value implying no such dispersion effect can exist in free space. However in linear material medium, wave speed may exceed the monochromatic phase velocity by a factor purely due to the relativistic consideration of the phase factor invariant under Lorentz transformation. The equation suggests such speed dispersion factor will be higher in the denser medium to its monochromatic material phase velocity. A critical cut-off number for the refractive index may exist to excite such mode in the material. The results can be interesting particularly for materials with high refractive index as well as for anisotropic space-time metric formulations in Transformation Optics.

SU‐E‐I‐144: Radiation Dose Reduction in Monochromatic Phase Contrast X‐Ray Mammography Using Equally Sloped Tomography

Purpose: In mammography, while maintaining the image quality, it is necessary to keep the delivered dose as low as possible since breast is a highly radiosensitive organ. Monochromatic phase contrast X‐ray mammography has shown its potential at higher sensitivity and lower impact in terms of dose delivery compared to absorption based diagnostic X‐ray mammography. An exact Fourier‐based iterative technique termed Equally Sloped Tomography(EST) has been newly developed and implemented on it. Using this technique, we conducted a series of comparative experiments to explore the further more radiation dose reduction in phase contrast mammography through reduction of projection numbers. Methods: Experiment took place at the biomedical beamline at ESRF(ID17). Full Human breasts samples were fixed in 4% formalin solution. Planar imaging and Computed Tomography(CT) modalities were combined to PCI techniques at 60KeV and using a 2kx2k taper optics CCD detector(45 micron pixel). The number of projections scanned was 2000 and digitally removed to 512 for reconstructions. Comparison reconstructions were produced by Filtered‐Back Projection(FBP) with a standard uncropped‐ramp filter. To optimize the result, Non‐local‐means regularization was applied for post‐processing in both cases. Results: Compared to the FBP reconstruction using 2000 projections, EST using 512 projections has comparable SNRs and CNRs, no obvious contrast degradation is observed between tumor and normal glandular tissue. In addition, the collagen exhibit similar visibility. Conclusions: Our results indicate that in the phase contrast mammography, EST technique can reduce the dose up to 50%∼75% by reducing number of projections, while images have comparable quality as the full dose FBP reconstruction. Furthermore, it makes the acquisition time 2∼4 times faster, which is important in in‐vivo imaging. The main reason for this is that EST is an exact Fourier‐based iterative algorithm that can incorporate different physical and mathematical constraints. It is always guided towards a lowest‐possible noisy state while keeping strictly consistent with measurements.Research sponsored by UC Discovery / TomoSoft Technologies Grant #ITL07‐10166.

Improved optical profiling using the spectral phase in spectrally resolved white-light interferometry

In spectrally resolved white-light interferometry (SRWLI), the white-light interferogram is decomposed into its monochromatic constituent. The phase of the monochromatic constituents can be determined using a phase-shifting technique over a range of wavelengths. These phase values have fringe order ambiguity. However, the variation of the phase with respect to the wavenumber is linear and its slope gives the absolute value of the optical-path difference. Since the path difference is related to the height of the test object at a point, a line profile can be determined without ambiguity. The slope value, though less precise helps us determine the fringe order. The fringe order combined with the monochromatic phase value gives the absolute profile, which has the precision of phase-shifting interferometry. The presence of noise in the phase may lead to the misidentification of fringe order, which in turn gives unnecessary jumps in the precise profile. The experimental details of measurement on standard samples with SRWLI are discussed in this paper.

Time reversal versus phase conjugation in a multiple scattering environment

We present experimental results on the reversibility of ultrasound in a multiple scattering medium. An ultrasonic pulsed wave is transmitted from a point source to a 128-element receiving array through 2D samples with various thickness. The samples consist of random collections of parallel steel rods immersed in water. The scattered waves are recorded, time reversed and sent back into the medium. The time-reversed waves are converging back to their source and the quality of spatial and temporal focusing on the source is related to the second-order moments of the scattered wave (correlation) in time and in space. Experimental results show that it is possible to obtain a robust estimation of the correlations on a single realisation of disorder, taking advantage of the wide frequency bandwidth. The spatial resolution of the system is only limited by the correlation length of the scattered field, and no longer by diffraction. Moreover, successful time-reversal focusing using a single element instead of an array is possible, whereas a one-channel monochromatic phase conjugation fails. The efficiency of broad-band time reversal compared to monochromatic phase conjugation lies in the number of `information grains' in the frequency bandwidth.

Chaos and time-reversed acoustics

The objective of this paper is to show that time-reversal invariance can be exploited in acoustics to accurately control wave propagation through random propagating media as well as through chaotic reverberant cavities. To illustrate these concepts, several experiments are presented. They show that chaotic dynamics reduces the number of transducers needed to insure an accurate time-reversal experiment. Multi-pathing in random media and in chaotic cavities enhances resolution in time-reversal acoustics by making the effective size of time reversal mirrors much larger than its physical size. Comparisons with phase conjugated experiments will show that this effect is typical of broadband time-reversed acoustics and is not observed in monochromatic phase conjugation. Self averaging properties of time reversal experiments conducted in chaotic scattering environments will be emphasized.

Monochromatic phase curves and albedos for the lunar disk

Photoelectric observations of the entire lunar disk made in 1964-1965 over phase angles from 6 to 12 deg in nine narrow bands from 0.35 to 1.0 microns and in UBV are reviewed. Phase curves are presented as a function of wavelength. The results confirm a reddening with increasing phase angle found by previous investigators for particular areas.