Measuring the elasticity distribution inside the human body is of great interest because elastic abnormalities can serve as indicators of several diseases. We present a method for mapping elasticity inside soft tissues by imaging surface acoustic waves (SAWs) with digital holographic interferometry. With this method, we show that SAWs are consistent with Rayleigh waves, with velocities proportional to the square root of the elastic modulus greater than 2-40 kPa in homogeneous tissue phantoms. In two-layer phantoms, the SAW velocity transitions approximately from that of the lower layer to that of the upper layer as frequency is increased in agreement with the theoretical relationship between SAW dispersion and the depth-dependent stiffness profile. We also observed deformation in the propagation direction of SAWs above a stiff inclusion placed 8 mm below the surface. These findings demonstrate the potential for quantitative digital holography-based elastography of soft tissues as a noninvasive method for disease detection.
KEYWORDS: Modulation, Absorption, Oxygen, Spectroscopy, Vertical cavity surface emitting lasers, Optical amplifiers, Atmospheric optics, Signal detection, Data acquisition, Signal to noise ratio
Wavelength modulation spectroscopy (WMS) with simultaneous detection at high harmonics (up to and
including N = 11) is reported for the first time. A Vertical Cavity Surface Emitting Laser (VCSEL) is used to probe
atmospheric oxygen using a multi-pass optical cell. The laser frequency is modulated at a low modulation index while
synchronous detection is performed simultaneously at all harmonics up to the 11th. These higher harmonic signals allow
for better resolution of congested spectra. Experimental results are used to detect and resolve absorption features in the
A-band region of oxygen. The high harmonic signals are used to distinguish between stronger rotational-vibrational
absorption lines in oxygen and weaker absorption lines formed by low-density isotopic oxygen. This detection method
also allows for the resolution of overlap between these weaker isotopic spectra. Higher harmonic signals resolve
additional structure, which does not appear at direct absorption measurements, or even in lower harmonic signals (N <
3). Since harmonic signal power decreases rapidly with detection order (N), the technique employed clearly shows that
the commonly used signal-to-noise power ratio, while important, is not the only criterion for a good measurement. We
examine the effects of optical pathlength saturation for these weak isotopic lines by measuring the effect of an optically
thick path (at fixed density) on the signal.
We present a novel approach to quantifying and optimizing the amount of information available in radiation
patterns. The technique presented and the results obtained are applicable on a broad scale, including those
in infrared, nanophotonics and other non-intrusive sensing techniques. We investigate the amount of
information lost due to limitations of the detector system. The method, which is based on information
principles developed by Shannon, expands on the many conventional approaches to optimizing performance
of sensors. The fundamental question of how many bits of information can be extracted by any sensor is
addressed. We focus on answering this question for the measurement of the radiation pattern from an
antenna array. The effects of a finite detector size, on the structure of the radiation pattern, are presented,
and we quantify the relationship between loss of structure and loss of information. The work presented may
be extended to a wide range of applications, including remote sensing. While the information content of
antenna array radiation patterns is based on the spatial distribution of photons, the method presented is
general and may be applied to a variety of distributions, such as lineshape functions, important in
spectroscopy, where the information is contained in the frequency distribution of photons.
KEYWORDS: Modulation, Signal to noise ratio, Signal detection, Absorption, Spectroscopy, Interference (communication), Information theory, Sensors, Molecules, Amplifiers
Shannon's information theory is applied to Wavelength Modulation Spectroscopy (WMS) providing quantitative figures
of merit such as the measurement precision and a prediction of the optimal detection harmonic order to be used. The
amount of information, in bits, that can be extracted in any WMS measurement is calculated. The theory is applied to
experimental results we have obtained in WMS experiments in congested spectra with overlapping lines that have highly
disparate absorption cross-sections. A key result is that the complexity of signal structure can play a much more
important role than the conventional signal to noise ratio. We show that there are some parts (where it exhibits turning
points and zero crossings) of the structurally-rich WMS signal that play a larger role in conveying information about the
measurement than other parts of the signal. Practical applications follow immediately. We also show that, for a particular
noise limitation of the apparatus, there is a finite amount of information that can be transmitted (to the detection
equipment) by the probe laser as it samples the probed species. The apparatus is analogous to a Shannon's information
channel. Application of the theory developed to our experimental absorption measurements in the Oxygen A-band shows
why high detection harmonic orders (up to the 7th or 8th) yield the highest resolution. This is in contrast to statements in
the literature, based on conventional signal to noise ratio considerations, that the best results are to be expected with
second harmonic detection.
Wavelength Modulation Spectroscopy (WMS) has been extensively used as a tool for sensitive detection through precise
measurements of the absorption lineshape function of gaseous species. In this paper pathlength saturation in wavelength
modulation spectroscopy is studied. New effects are found when one takes advantage of demodulation at higher
harmonics of the modulation frequency. We show here that modulation spectroscopy is a much more sensitive probe of
these effects. In particular, when synchronous detection is performed at higher harmonics of the modulation frequency,
even very small pathlength saturation effects become clearly visible. The method discussed allows one to probe
lineshape profiles by observing how the signal profile varies with absorption pathlength. In particular, the signal around
line center displays effects of saturation that are characteristic of the lineshape. This method is powerful because,
ultimately, all the information about any measurement is contained in the lineshape profile. Since different lineshape
profiles exhibit different saturation behavior, higher harmonic detection provides a new method to perform sensitive
detection. We have shown effects of saturation on the central lobes of harmonic signals. We also show that there are
definite relationships between the variation of the individual side lobes as well as their relative magnitudes that yield
further information about the lineshape function.
Absorption and emission spectroscopy measurements have been extensively and effectively utilized in the probing and monitoring of gases. As in any real experimental situation, the measurement of absorption or emission profiles results in a loss of information due to practical limitations, such as a finite precision of the detector. Also, it is now accepted that there is a relationship between information loss and thermodynamics. Hence, the question "How much information, in bits, is lost when making a practical spectroscopic measurement and how much heat is generated in the process?" arises. Shannon's information theoretical concepts are used to quantify the information lost due to the finite precision in wavelength measurement, of a detector used in a spectroscopic measurement. The heat generated in such a detector is also studied. The relationship between the heat generated and information lost as a result of the finite precision of a practical detector is investigated.
Wavelength Modulation Spectroscopy (WMS) utilizes low frequency modulation of the probe, followed by synchronous detection at the modulation frequency or at one of the harmonics. WMS provides a particularly useful tool for resolving highly disparate overlapping lines, because the high-order derivative-like structure of higher harmonics results in an enhancement of features, not possible with conventional ("direct") absorption spectroscopy. An important question, not yet systematically addressed in the literature is, "Given that in any measurement seeking to resolve overlapping spectra there is always a minimum harmonic detection order, how does one determine this order?" To address this issue, a Rayleigh-like criterion is defined and used to determine when two lines are barely resolved. Shannon's information theoretical principles are then used to calculate the information obtained when overlapping spectra are barely resolved at a particular harmonic. The results obtained allow one to predict the minimal harmonic detection order that should be used to resolve overlapping lines.
An information theoretic approach to maximizing the efficacy of optical sensing devices is presented. The principles used and the results obtained are applicable on a wide range of scales, including those in nano photonics sensing and detection. A key factor which is investigated is the aspect of extraction of the maximum amount of information in any given environment. The method used, which is based on information principles developed by Shannon, augments the many conventional approaches to optimizing performance of sensors. The fundamental issue of how many bits of information can be extracted by a sensor is addressed. The radiation pattern from a radiating or receiving sensor-array provides a spatial probability density function, which carries all the information about the system. Various such arrays are treated and the significance of the structure of the radiation pattern is examined. The technique is extended to the well-known concept of the lineshape profile of radiative atomic and molecular transitions, which is a probability density function in the frequency domain. Extensions of this work have applications in nanotechnology.
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