Generation of high amplitude compressions and rarefactions in a photoacoustically excited droplet.

Photoacoustic excitation of a fluid sphere generates an outgoing ultrasonic wave whose time profile permits determination of the density, sound speed, and diameter of the sphere. Experiments with pulsed laser beams have confirmed the major predictions of existing theory. With regard to acoustic waves generated within spheres, although mathematical expressions for their properties are known, virtually no exploration of the waveforms in theory or experiment has taken place. Here, two cases for photoacoustic excitation of a droplet are discussed: first, absorption of radiation in a region of fluid external to the droplet, and, second, absorption of radiation by the droplet itself. Large amplitude transients, compressions in the former and rarefactions in the latter, are generated as the waves approach the center of the sphere. The high amplitudes of the waves suggest shock wave formation.

Heterodyned photoacoustic effect generated by irradiation of single particles by two laser beams modulated at different frequencies.

When a modulated light beam is absorbed by an incompressible particle, the photoacoustic effect can take place through heat diffusion into the surrounding fluid followed by thermal expansion and the generation of sound. When two laser beams modulated at different frequencies irradiate a particle in aqueous solution, the effect of one laser is to modulate the thermal expansion coefficient of the solution in the proximity of the particle at its modulation frequency. Heat diffusion into the same region of fluid from absorption of radiation from the second laser takes place in fluid where the thermal expansion coefficient is modulated so that the photoacoustic effect is produced at the sum and difference frequencies of the two lasers. Here, a theory for the photoacoustic effect at the heterodyne frequency for a single particle and the corresponding experiments with carbon particles of different sizes are reported.

Differential Infrared Pyrometry for Determination of Microkelvin Temperature Variations.

Precise measurement of temperature is important in studies of chemical and biological systems as reaction kinetics are almost universally sensitive to temperature. However, the use of conventional temperature probes can introduce an exogenous temperature disturbance resulting in measurement artifacts. Infrared pyrometry is a noninvasive technique for temperature measurement, however, the challenge for current infrared pyrometry is low sensitivity to small temperature variations, which in many cases precludes determination of key diagnostic information. Here, we report a sensitive differential infrared pyrometer based on spatial modulation using a resonant oscillating mirror, which enables a sensitivity to temperature variations on the microkelvin scale. The instrument is employed to monitor minuscule heat evolution in an acid-base reaction and the decomposition of H2O2 by bovine liver catalase. The instrument holds great promise for monitoring the dynamics of heat evolution in a range of chemical and biological systems in a completely noninvasive manner.

Photothermal determination of the angular dependence of emissivity.

A method for directional emissivity determination by measurement of absorption through a photothermal effect is described. The experimental results found for Au, Al, and graphite show good agreement with the theoretical prediction of the electromagnetic theory. It is shown as well that complex refractive indices can be determined by fitting angular absorption data with theory.

Emissivity determination using the photoacoustic effect.

We show that emissivities in the near infrared can be determined relative to a reference surface employing the photoacoustic effect. The photoacoustic cell is equipped with two windows and a pair of synchronously moving chopping wheels so that the cell alternately views the test and the reference surface. The acoustic signals produced in the cell are detected with a microphone and that output is fed to a lock-in amplifier. The temperature of the test surface is varied to produce a null in the lock-in amplifier, which permits determination of a relative emissivity. Results of measurements for several plastic and metal surfaces are reported.

Photoacoustic trace detection of gases at the parts-per-quadrillion level with a moving optical grating.

The amplitude of the photoacoustic effect for an optical source moving at the sound speed in a one-dimensional geometry increases linearly in time without bound in the linear acoustic regime. Here, use of this principle is described for trace detection of gases, using two frequency-shifted beams from a CO2 laser directed at an angle to each other to give optical fringes that move at the sound speed in a cavity with a longitudinal resonance. The photoacoustic signal is detected with a high-[Formula: see text], piezoelectric crystal with a resonance on the order of [Formula: see text] kHz. The photoacoustic cell has a design analogous to a hemispherical laser resonator and can be adjusted to have a longitudinal resonance to match that of the detector crystal. The grating frequency, the length of the resonator, and the crystal must all have matched frequencies; thus, three resonances are used to advantage to produce sensitivity that extends to the parts-per-quadrillion level.

Photoacoustic effect generated by moving optical sources: Motion in three dimensions.

Although the photoacoustic effect is commonly produced through use of pulsed or amplitude-modulated radiation, it can also be generated by a steady source moving in space. Here, the properties of the photoacoustic effect generated by moving sources in three dimensions are investigated. The mathematics for the moving photoacoustic point source are shown to be closely related to that for derivation of the Lienard-Wiéchert potential for a moving point charge. The cases of rectilinear motion with the speeds lower than, equal to, and greater than the sound speed, as well as a point source oscillating in space are reported. Of note is that a bounded amplification effect is found for a Gaussian source moving at the sound speed, which is in contrast to the unbounded amplification seen in a one-dimensional geometry.

Optical pyrometer based on the gas phase photoacoustic effect.

A photoacoustic cell containing an infrared active gas and equipped with a pair of infrared transmitting windows that alternately views two bodies at different temperatures through a pair of chopping wheels acts as a differential detector of the radiation emitted by the two bodies. A theory for the photoacoustic signal shows that the device acts to monitor the difference in the incidances between the two bodies integrated over the absorptions of the gas in the cell. Experiments are reported showing that the response of the pyrometer depends on the relative temperatures of heated bodies, the absorption coefficient of the gas in the cell, and the modulation frequency of the chopping wheels. The instrument is shown to be a sensitive detector of a null in the integrated incidance of the two bodies.

Photoacoustic transients generated by laser irradiation of thin films.

Irradiation of an optically thin layer immersed in a transparent fluid with pulsed laser radiation can generate photoacoustic waves through two mechanisms. The first of these is the conventional optical heating of the layer followed by thermal expansion, in which the mechanical motion of the expansion launches a pair of oppositely directed sound waves. A second, recently reported mechanism, is operative when heat is conducted to the transparent medium raising its temperature, while at the same time reducing the temperature in the absorbing body. The latter mechanism has been shown to result in compressive transients at the leading edges of the photoacoustic waveforms. Here the photoacoustic effect produced by irradiating thin metal films which undergo negligible thermal expansion under optical irradiation, but which generate sound solely by the heat transfer mechanism is investigated. Solution to the wave equation for the photoacoustic effect from the heat transfer mechanism is given and compared with the results of experiments using nanosecond laser pulses to irradiate thin metal films.

Theory of self-oscillation and mode locking in a longitudinal photoacoustic resonator.

The wave equation for pressure that governs generation of the photoacoustic effect possesses a forcing term proportional to the time derivative of the energy delivered to the gas per unit volume and time. A positive pressure fluctuation, with its accompanying density increase, thus increases the optical absorption and provides a positive feedback mechanism for sound generation. A theory for self-oscillation in a one-dimensional resonator is given. Expressions for the photoacoustic pressure are derived for the cases of highly and weakly absorbing gases that indicate mode-locked sound generation. Experiments with CO2 lasers are reported where evidence of the self-generation effect was sought.

Mathieu function solutions for photoacoustic waves in sinusoidal one-dimensional structures.

The photoacoustic effect for a one-dimensional structure, the sound speed of which varies sinusoidally in space, is shown to be governed by an inhomogeneous Mathieu equation with the forcing term dependent on the spatial and temporal properties of the exciting optical radiation. New orthogonality relations, traveling wave Mathieu functions, and solutions to the inhomogeneous Mathieu equation are found, which are used to determine the character of photoacoustic waves in infinite and finite length phononic structures. Floquet solutions to the Mathieu equation give the positions of the band gaps, the damping of the acoustic waves within the band gaps, and the dispersion relation for photoacoustic waves. The solutions to the Mathieu equation give the photoacoustic response of the structure, show the space equivalent of subharmonic generation and acoustic confinement when waves are excited within band gaps.

X-ray spatial harmonic imaging of phase objects.

Refractive index gradients in materials or at material interfaces lead to x-ray diffraction. Interference of this radiation with adjacent x-ray waves causes phase contrast that can be used for imaging purposes if an x-ray source with sufficient spatial coherence is used. The imaging modality presented here uses hard x radiation diffracted at interfaces, but requires only little spatial coherence. We report experiments showing, first, that image contrast is not diminished by motional blurring, and second, that contrast can be increased by orders of magnitude relative to in-line x-ray phase-contrast imaging. These properties substantially broaden the applicability of phase-sensitive imaging to moving samples and very weak density gradients.

Effects of exothermic chemical reaction on the photoacoustic effect from particulate suspensions.

Irradiation of chemically reactive particulate suspensions by high power, pulsed laser radiation initiates reactions at the sites of the particles so that besides the absorbed optical energy, chemical energy is liberated. In addition to the release of chemical energy, chemical reaction can result in gas production both of which result in enhancement in the amplitude of the photoacoustic effect. Here we report photoacoustic and transient grating experiments with colloidal C in mixtures of H(2)O(2) with H(2)O. The inclusion of H(2)O(2) in an aqueous C suspension changes the normally endothermic reaction of C with H(2)O into the highly exothermic reaction of C with H(2)O(2) leading to both an enhanced photoacoustic effect and an increase in light emission from the suspension. As well, laser-initiated exothermic reactions in suspensions of C with CH(3)NO(2) and particulate Hg(CNO)(2) in H(2)O are shown to result in greatly enhanced photoacoustic signal amplitudes.

Comparison of ultrasonic distillation to sparging of liquid mixtures.

The application of intense ultrasound to a liquid-gas interface results in the formation of an ultrasonic fountain and generates both mist and vapor from the liquid. Here, the composition of the vapor and aerosol above an ultrasonic fountain is determined as a function of irradiation time and compared with the results of sparging for five different solutions. The experimental apparatus for determining the efficiency of separation consists of a glass vessel containing a piezoelectric transducer driven at either 1.65 or 2.40 MHz. Dry nitrogen is passed over the ultrasonic fountain to remove the vapor and aerosol. The composition of the liquid solutions are recorded as a function of irradiation time using gas chromatography, refractive index measurement, nuclear magnetic resonance, or spectrophotometry. Data are presented for ethanol-water and ethyl acetate-ethanol solutions, cobalt chloride in water, colloidal silica, and colloidal gold. The experiments show that ultrasonic distillation produces separations that are somewhat less complete than what is obtained using sparging.

X-ray phase contrast imaging: Transmission functions separable in cylindrical coordinates.

A Fresnel-Kirchhoff integral can be used to calculate x-ray phase contrast images when the transmission function is known. Here expressions for image intensity are derived for objects with axial symmetry for an x-ray source with non-vanishing dimensions. An expression for the image intensity is given for an x-ray source whose intensity distribution is described by a Gaussian function, from which an expression for the limiting case of a point source of radiation is found. The expressions for image intensity are evaluated for cases where the magnification is substantially greater than one, as would be employed in biological imaging. Experiments using a microfocus x-ray tube and charge coupled device camera are reported to determine the capability of the method for imaging small spherical objects, such as gold particles, which might find application as contrast agents in biomedical imaging.

Laser generation of gas bubbles: Photoacoustic and photothermal effects recorded in transient grating experiments.

Absorption of high power laser radiation by colloidal suspensions or solutions containing photoreactive chemicals can result in bubble production. Here, transient grating experiments are reported where picosecond and nanosecond lasers are used to initiate photoinduced processes that lead to bubble formation. Irradiation of colloidal Pt suspensions is found to produce water vapor bubbles that condense back to liquid on a nanosecond time scale. Laser irradiation of Pt suspensions supersaturated with CO(2) liberates dissolved gas to produce bubbles at the sites of the colloidal particles. Laser induced chemical reactions that produce bubbles are found in suspensions of particulate C in water, and in the sensitized decarboxylation of oxalic acid. Theory based on linear acoustics as well as the Rayleigh-Plesset equation is given for description of the bubble motion.

Low density contrast agents for x-ray phase contrast imaging: the use of ambient air for x-ray angiography of excised murine liver tissue.

We report a new preparative method for providing contrast through reduction in electron density that is uniquely suited for propagation-based differential x-ray phase contrast imaging. The method, which results in an air or fluid filled vasculature, makes possible visualization of the smallest microvessels, roughly down to 15 microm, in an excised murine liver, while preserving the tissue for subsequent histological workup. We show the utility of spatial frequency filtering for increasing the visibility of minute features characteristic of phase contrast imaging, and the capability of tomographic reconstruction to reveal microvessel structure and three-dimensional visualization of the sample. The effect of water evaporation from livers during x-ray imaging on the visibility of blood vessels is delineated. The deformed vascular tree in a cancerous murine liver is imaged.

X-ray phase-contrast imaging: transmission functions separable in Cartesian coordinates.

In-line, x-ray phase-contrast imaging is responsive to both phase changes and absorption as the x radiation traverses a body. Expressions are derived for phase-contrast imaging of objects having transmission functions separable in Cartesian coordinates. Starting from the Fresnel-Kirchhoff integral formula for image formation, an expression is found for the phase-contrast image produced by an x-ray source with nonvanishing dimensions. This expression is evaluated in limiting cases where the source-to-object distance is large, where the source acts as a point source, and where the weak phase approximation is valid. The integral expression for the image is evaluated for objects with simple geometrical shapes, showing the influence of the source dimensions on the visibility of phase-contrast features. The expressions derived here are evaluated for cases where the magnification is substantially greater than one as would be employed in biological imaging. Experiments are reported using the in-line phase-contrast imaging method with a microfocus x-ray source and a CCD camera.

Transient gratings generated by particulate suspensions: the uniformly irradiated sphere and the point source.

Expressions for the time dependence of the state variables in a transient grating experiment carried out on suspensions of particles can be determined by integration over space of the solutions for the temperature and photoacoustic pressure for a single particle. The method relies on independent computation of the thermal and acoustic modes of wave motion which are combined to give the temperature, pressure, and density in the grating as a function of time. Calculations are given for the uniformly irradiated droplet and the point source, the latter including the effects of a temperature-dependent thermal expansion coefficient. Transient grating experiments are reported in colloidal Pt that show features described in the calculation.

Mathematical analysis of thermal diffusion shock waves.

Thermal diffusion, also known as the Ludwig-Soret effect, refers to the separation of mixtures in a temperature gradient. For a binary mixture the time dependence of the change in concentration of each species is governed by a nonlinear partial differential equation in space and time. Here, an exact solution of the Ludwig-Soret equation without mass diffusion for a sinusoidal temperature field is given. The solution shows that counterpropagating shock waves are produced which slow and eventually come to a halt. Expressions are found for the shock time for two limiting values of the starting density fraction. The effects of diffusion on the development of the concentration profile in time and space are found by numerical integration of the nonlinear differential equation.