## Optoacoustic imaging:## Thermoelastic expansion## Steven L. Jacques, Guenther Paltauf |

The pressure generated in an object by thermoelastic expansion due to a very short laser pulse is described:

where | M | = Bulk Modulus [Pa/strain], strain is dimensionless |

= ρc_{s}^{2}, ρ = density [kg/m^{3}], c_{s} = sound velocity [m/s] | ||

β | = Thermal expansivity [strain/degreeC], strain is dimensionless | |

rho | = Density [kg/m^{3}] | |

C_{p} | = Specific heat [(J/(kg degC)] | |

Γ | = Grueneisen coefficient [dimensionless] | |

μ_{a} | = Absorption coefficient [m^{-1}] | |

H | = Radiant exposure [J/m^{2}] | |

W | = Energy depostion [J/m^{3}] |

The energy deposition W = μ_{a}H [J/m^{3}].

The temperature rise ΔT = (energy deposition)/(rho C_{p}) [degree C].

The strain ε = βΔT [dimensionless].

The stress or pressure = Mε [J/m^{3}] = [kg/(m s^{2}] = [Pa].

The Grueneisen coefficient Γ = Mβ/(ρ C_{p}) [dimensionless].

The units of pressure (P) are (force)/(area). The units of energy deposition (W) are (energy)/(volume) = (force x distance)/(area x distance) in which the distance term cancels to equal (force)/(area). Hence the units of pressure and energy deposition are identical. The conversion factor for pressure is 1 J/m^{3} = 1 Pa = 10^{-5} [bar].