Photoacoustic Imaging Calculator

Initial pressure, diffuse light penetration, acoustic resolution and the skin exposure limit for photoacoustic microscopy and tomography.

Model: Textbook approximation

Laser

Wavelength (nm)

Wavelength sets only the skin-exposure factor C_A; enter μ_a and μ_s′ for your wavelength.

Pulse width (ns)Fluence on the skin (mJ/cm²)Repetition rate (Hz)

Tissue

Target absorption μ_a (cm⁻¹)Background absorption μ_a (cm⁻¹)Background reduced scattering μ_s′ (cm⁻¹)Grüneisen parameter ΓTarget depth (mm)

Ultrasound detection

Speed of sound (m/s)Centre frequency f₀ (MHz)Bandwidth Δf (% of f₀)Acoustic NAAcoustic attenuation (dB cm⁻¹ MHz⁻¹)

Results

Initial pressure at the surface p₀20.0 kPa

Background μ_eff1.741 cm⁻¹

Optical penetration depth 1/μ_eff5.74 mm

Transport mean free path0.990 mm

Fluence at the target14.12 mJ/cm²

Initial pressure at the target14.12 kPa

Acoustic loss to the surface at f₀0.50 dB

Axial resolution271.0 µm

Lateral resolution437.4 µm

Stress confinement time (axial resolution)176 ns vs 5 ns pulse

Skin limit, one pulse (ICNIRP)25.18 mJ/cm² (79 %)

Average irradiance vs ≥ 10 s limit200 / 252 mW/cm²

p₀ = Γ μ_a F, valid when the pulse is shorter than the stress relaxation time d_c/v_s (Xu & Wang, Rev. Sci. Instrum. 77, 041101, 2006). Wang & Hu (2012) give about 800 Pa per mK of heating; over ρC ≈ 4.2 MJ m⁻³ K⁻¹ that is Γ ≈ 0.19.

F(z) = F₀ exp(−μ_eff z), μ_eff = √(3μ_a(μ_a + μ_s′)) in the background. Below a broad beam the fluence is k·F₀·e^(−μ_eff z) with a build-up factor k = 3 + 5.1R_d − 2e^(−9.7R_d) ≈ 2.8–6 for a diffuse reflectance R_d = 0.1–0.6 at a tissue/air surface (Jacques 1998, eq. 12, for depths beyond about 1/μ_eff); this page sets k = 1, so the fluence and p₀ at depth are underestimated by that factor.

R_A = 0.88 v/Δf and R_L = 0.71 v/(NA f₀) for acoustic-resolution PAM and partial-view tomography; detection is one-way, so there is no pulse-echo factor 2 (Wang & Hu, Science 335, 1458, 2012).

Skin limits: ICNIRP 2013 Table 7 at the pulse width, and 2.0 C_A kW/m² for 10 s or more, for a beam wider than the 3.5 mm averaging aperture. The repetitive-pulse rules are not applied.

Initial Pressure vs Target Depth

Resolution vs Centre Frequency

Model and references

Textbook approximation. A standard approximation from the literature (for example paraxial, plane-wave or Gaussian-beam), valid within the range the page states. About the tiers

p₀ = Γμ_aF under stress confinement; fluence k·F₀·exp(−μ_eff z) from diffusion theory with the build-up factor k (≈ 2.8–6, Jacques 1998) set to 1, so p₀ at depth is low; one-way acoustic resolution of acoustic-resolution PAM and partial-view tomography. Skin limits are ICNIRP 2013 single-pulse and ≥ 10 s values, without the repetitive-pulse rules.

Xu M., Wang L. V. (2006). Photoacoustic imaging in biomedicine. Rev. Sci. Instrum. 77, 041101. Thermal and stress confinement and the initial pressure p₀ = Γμ_aF. doi:10.1063/1.2195024
Jacques S. L. (1998). Light distributions from point, line and plane sources for photochemical reactions and fluorescence in turbid biological tissues. Photochem. Photobiol. 67, 23–32. Eqs. 11–13: build-up factor k(R_d). doi:10.1111/j.1751-1097.1998.tb05161.x
Wang L. V., Hu S. (2012). Photoacoustic tomography: in vivo imaging from organelles to organs. Science 335, 1458–1462. Axial resolution 0.88 v_s/Δf, lateral 0.71 v_s/(NA f₀), about 800 Pa per mK. doi:10.1126/science.1216210
ICNIRP (2013). Guidelines on limits of exposure to laser radiation of wavelengths between 180 nm and 1,000 µm. Health Phys. 105, 271–295. Table 7, skin limits. doi:10.1097/HP.0b013e3182983fd4

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