Heat Conduction Solution Manual Latif M Jijil

Current systems designed for deep photoacoustic (PA) imaging typically use a low repetition rate, high power pulsed laser to provide a ns-scale pulse illuminating a large tissue volume. Acoustic signals recorded on each laser firing can be used to reconstruct a complete 2-D (3-D) image of sources of heat release within that region. Using broad-beam excitation, the maximum frame rate of the imaging system is restricted by the pulse repetition rate of the laser. An alternate illumination approach is proposed based on fast scanning by a low energy (~ 1 mJ) high repetition rate (up to a few kHz) narrow laser beam (~1 mm) along the tissue surface over a region of interest. A final PA image is produced from the summation of individual PA images reconstructed at each laser beam position. This concept can take advantage of high repetition rate fiber lasers to create PA images with much higher frame rates than current systems, enabling true real-time integration of photoacoustics with ultrasound imaging. As an initial proof of concept, we compare conventional broad beam illumination to a scanned beam approach in a simple model system. Two transparent teflon tubes with diameters of 1.6 mm and 0.8 mm were filled with ink having an absorption coefficient of 5 cm-1. These tubes were buried inside chicken breast tissue acting as an optical scattering medium. They were separated by 3 mm or 10 mm to test spatial and contrast resolution for the two scan formats. The excitation wavelength was 700 nm. The excitation source is a traditional OPO pumped by a Q-switched Nd:YAG laser with doubler. Photoacoustic images were reconstructed using signals from a small, scanned PVDF transducer acting as an acoustic array. Two different illumination schemes were compared: one was 15 mm x 10 mm in cross section and acted as the broad beam; the other was 5 mm x 2 mm in cross section (15 times smaller than the broad beam case) and was scanned over an area equivalent to broad beam illumination

Beam Shaping of the spatial (transverse) profile of laser beams is highly desirable by building optical systems of high-power lasers as well in various applications with these lasers. Pumping of the crystals of Ti:Sapphire lasers by the laser radiation with uniform (flattop) intensity profile improves performance of these ultrashort pulse high-power lasers in terms of achievable efficiency, peak-power and stability, output beam profile. Specifications of the solid-state lasers built according to MOPA configuration can be also improved when radiation of the master oscillator is homogenized and then is amplified by the power amplifier. Features of building these high power lasers require that a beam shaping solution should be capable to work with single mode and multimode beams, provide flattop and super-Gauss intensity distributions, the consistency and divergence of a beam after the intensity re-distribution should be conserved and low absorption provided. These specific conditions are perfectly fulfilled by the refractive field mapping beam shapers due to their unique features: almost lossless intensity profile transformation, low output divergence, high transmittance and flatness of output beam profile, extended depth of field, adaptability to real intensity profiles of TEM00 and multimode laser sources. Combining of the refractive field mapping beam shapers with other optical components, like beam-expanders, relay imaging lenses, anamorphic optics makes it possible to generate the laser spots of necessary shape, size and intensity distribution. There are plenty of applications of high-power lasers where beam shaping bring benefits: irradiating photocathode of Free Electron Lasers (FEL), material ablation, micromachining, annealing in display making techniques, cladding, heat treating and others. This paper will describe some design basics of refractive beam shapers of the field mapping type, with emphasis on the features important for building and applications

One of the main problems during laser stimulation in human pain research is the risk of tissue damage caused by excessive heating of the skin. This risk has been reduced by using a laser beam with a flattop (or superGaussian) intensity profile, instead of the conventional Gaussian beam. A finite difference approximation to the heat conduction equation has been applied to model the temperature distribution in skin as a result of irradiation by flattop and Gaussian profile CO2 laser beams. The model predicts that a 15 mm diameter, 15 W, 100 ms CO2 laser pulse with an order 6 superGaussian profile produces a maximum temperature 6 oC less than a Gaussian beam with the same energy density. A superGaussian profile was created by passing a Gaussian beam through a pair of zinc selenide aspheric lenses which refract the more intense central region of the beam towards the less intense periphery. The profiles of the lenses were determined by geometrical optics. In human pain trials the superGaussian beam required more power than the Gaussian beam to reach sensory and pain thresholds.

Beam shaping of powerful multimode fiber lasers, fiber-coupled solid-state and diode lasers is of great importance for improvements of industrial laser applications. Welding, cladding with millimetre scale working spots benefit from "inverseGauss" intensity profiles; performance of thick metal sheet cutting, deep penetration welding can be enhanced when distributing the laser energy along the optical axis as more efficient usage of laser energy, higher edge quality and reduction of the heat affected zone can be achieved. Building of beam shaping optics for multimode lasers encounters physical limitations due to the low beam spatial coherence of multimode fiber-coupled lasers resulting in big Beam Parameter Products (BPP) or M² values. The laser radiation emerging from a multimode fiber presents a mixture of wavefronts. The fiber end can be considered as a light source which optical properties are intermediate between a Lambertian source and a single mode laser beam. Imaging of the fiber end, using a collimator and a focusing objective, is a robust and widely used beam delivery approach. Beam shaping solutions are suggested in form of optics combining fiber end imaging and geometrical separation of focused spots either perpendicular to or along the optical axis. Thus, energy of high power lasers is distributed among multiple foci. In order to provide reliable operation with multi-kW lasers and avoid damages the optics are designed as refractive elements with smooth optical surfaces. The paper presents descriptions of multi-focus optics as well as examples of intensity profile measurements of beam caustics and application results.

Laser beam welding is a joining technique that has many advantages over conventional GMAW welding, such as low heat input, short cycle time as well as good cosmetic welds. Laser beam welding has been widely used for welding powertrain components in automotive industry. When welding nitride steel components, however, laser beam welding faces a great challenge. The difficulty lies in the fact that the nitride layer in the joint releases the nitrogen into the weld pool, resulting in a porous weld. This research presents an industrial ready solution to prevent the nitrogen from forming gas bubbles in the weld.

A calculation is reported of the maximum depth and diameter of a narrow crater formed in a stationary metal target exposed to high-power cw CO2 laser radiation. The energy needed for erosion of a unit volume is assumed to be constant and the energy losses experienced by the beam in the vapor-gas channel are ignored. The heat losses in the metal are allowed for by an analytic solution of the three-dimensional boundary-value heat-conduction problem of the temperature field in the vicinity of a thin but long crater with a constant temperature on its surface. An approximate solution of this problem by a method proposed earlier by one of the present authors was tested on a computer. The dimensions of the thin crater were found to be very different from those obtained earlier subject to a less rigorous allowance for the heat losses.

Welds produced on pure aluminum targets using pulsed Nd:YAG lasers can be accurately described using a relatively simple conduction mode heat transfer model provided that the fraction of laser energy absorbed is known and the amount of metal vaporized is smalled however at laser fluences commonly used in many production welding schedules significant aluminum vaporization does occur. The possible mechanisms have been identified which could result in laser beam attenuation by the vapor plume. 2b1af7f3a8