### Abstract

When studying the regularities of variations of laser beam parameters, a problem arises to measure the intensity J(ρ, t) in the beam cross section. One of the possible methods of intensity measurement is its reconstruction from the temperature field T(ρ, t) on the target surface. The theory of solving of the inverse heat transfer problem and results of numerical experiment for uniform target irradiated by nonuniform laser beam was reported. In the case of a thin thermally insulated target the following relationship was obtained. (1 - R)I(ρ, t) = k L/a^{2}[∂/∂t T(ρ, t) - a^{2} Δ_{⊥} T(ρ, t)]. where R is the reflection coefficient; a^{2} and k are the thermal diffusivity and conductivity, respectively; L is the target thickness; Δ_{⊥} = ∂/∂x^{2} + ∂/∂y^{2} is the transverse Laplacian operator. Deriving algorithms for this equation, the authors use the difference procedure. For decreasing of the effect of random errors filtration of initial data is performed. A simple and effective filter that ensures satisfactory accuracy is the convolution of initial data with a stabilizing function sinc(x) = sin(α_{max} x)/π x, α_{max} ≈ 2 cm^{-1}.

Original language | English |
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Title of host publication | Conference on Lasers and Electro-Optics Europe - Technical Digest |

Editors | Anon |

Pages | 249 |

Number of pages | 1 |

Publication status | Published - 1996 |

Externally published | Yes |

Event | Proceedings of the 1996 Conference on Lasers and Electro-Optics Europe, CLEO/Europe - Hamburg, Ger Duration: 8 Sep 1996 → 13 Sep 1996 |

### Conference

Conference | Proceedings of the 1996 Conference on Lasers and Electro-Optics Europe, CLEO/Europe |
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City | Hamburg, Ger |

Period | 8.9.96 → 13.9.96 |

### Fingerprint

### ASJC Scopus subject areas

- Control and Systems Engineering
- Electrical and Electronic Engineering

### Cite this

*Conference on Lasers and Electro-Optics Europe - Technical Digest*(pp. 249)

**Retrieving of laser beam intensity distribution from the temperature along surface of heated thin target.** / Aksenov, V.; Isaev, Yu; Zakharova, E.; Reino, V.; Tsvik, R.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Conference on Lasers and Electro-Optics Europe - Technical Digest.*pp. 249, Proceedings of the 1996 Conference on Lasers and Electro-Optics Europe, CLEO/Europe, Hamburg, Ger, 8.9.96.

}

TY - GEN

T1 - Retrieving of laser beam intensity distribution from the temperature along surface of heated thin target

AU - Aksenov, V.

AU - Isaev, Yu

AU - Zakharova, E.

AU - Reino, V.

AU - Tsvik, R.

PY - 1996

Y1 - 1996

N2 - When studying the regularities of variations of laser beam parameters, a problem arises to measure the intensity J(ρ, t) in the beam cross section. One of the possible methods of intensity measurement is its reconstruction from the temperature field T(ρ, t) on the target surface. The theory of solving of the inverse heat transfer problem and results of numerical experiment for uniform target irradiated by nonuniform laser beam was reported. In the case of a thin thermally insulated target the following relationship was obtained. (1 - R)I(ρ, t) = k L/a2[∂/∂t T(ρ, t) - a2 Δ⊥ T(ρ, t)]. where R is the reflection coefficient; a2 and k are the thermal diffusivity and conductivity, respectively; L is the target thickness; Δ⊥ = ∂/∂x2 + ∂/∂y2 is the transverse Laplacian operator. Deriving algorithms for this equation, the authors use the difference procedure. For decreasing of the effect of random errors filtration of initial data is performed. A simple and effective filter that ensures satisfactory accuracy is the convolution of initial data with a stabilizing function sinc(x) = sin(αmax x)/π x, αmax ≈ 2 cm-1.

AB - When studying the regularities of variations of laser beam parameters, a problem arises to measure the intensity J(ρ, t) in the beam cross section. One of the possible methods of intensity measurement is its reconstruction from the temperature field T(ρ, t) on the target surface. The theory of solving of the inverse heat transfer problem and results of numerical experiment for uniform target irradiated by nonuniform laser beam was reported. In the case of a thin thermally insulated target the following relationship was obtained. (1 - R)I(ρ, t) = k L/a2[∂/∂t T(ρ, t) - a2 Δ⊥ T(ρ, t)]. where R is the reflection coefficient; a2 and k are the thermal diffusivity and conductivity, respectively; L is the target thickness; Δ⊥ = ∂/∂x2 + ∂/∂y2 is the transverse Laplacian operator. Deriving algorithms for this equation, the authors use the difference procedure. For decreasing of the effect of random errors filtration of initial data is performed. A simple and effective filter that ensures satisfactory accuracy is the convolution of initial data with a stabilizing function sinc(x) = sin(αmax x)/π x, αmax ≈ 2 cm-1.

UR - http://www.scopus.com/inward/record.url?scp=0029747739&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0029747739&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:0029747739

SP - 249

BT - Conference on Lasers and Electro-Optics Europe - Technical Digest

A2 - Anon, null

ER -