eesti teaduste
akadeemia kirjastus
Estonian Journal of Engineering

Correlation between hardening depth and thermal parameters based on photothermal measurements; 423–435

Full article in PDF format

Dennis Kruse, Helmut Prekel, Gert Goch, Heinz G. Walther


In steel hardening processes, laser treatments and wear or machining of ceramics, the microstructural variations of the material are combined with variations of the thermal properties and therefore become detectable by non-destructive photothermal methods. This paper presents the theoretical basis of a parameter profile reconstruction, based on photothermally measured data. It compares numerical approach using the finite difference method with analytical solution, derived directly from the thermal diffusion equation. Both models are applied to photothermal measurements, leading to depth profiles of steel hardness, which are compared with data, destructively obtained from the same samples using Vickers indentation techniques.


  1. Mandelis, A. (ed.). Nondestructive Evaluation. Progress in Photothermal and Photoacoustic Science and Technology, Vol. 2. Prentice Hall, Englewood Cliff, NJ, 1994.

  2. Kruse, D., Prekel, H. and Goch, G. Automated photothermal detection of burning and hardening depth. In Proc. 9th International Conference on Infrared Sensors & Systems. Nürnberg, 2006, 341–346.

  3. Goch, G., Schmitz, B. and Reick, M. Photothermal sensing techniques for measuring material properties and near-surface defects. Ann. CIRP, 1994, 42, 623–626.

  4. Goch, G., Geerkens, J., Reick, M. and Schmitz, B. Analysis of surface layer variations by photothermal means. J. Physique IV, 1994, 319–322.

  5. Fivez, J. and Thoen, J. Thermal waves in materials with linearly inhomogeneous thermal conductivity. J. Appl. Phys., 1994, 75, 7696–7699.

  6. Friedrich, K., Seidel, U., Walther, H. G., Karpen, W. and Busse, G. Proposal for photothermal characterization of boundaries between layer and substrate. Res. Nondestr. Eval., 1993, 5, 31–39.

  7. Ritter, R., Reick, M., Schmitz, B. and Goch, G. Nondestructive and contactless evaluation of surface coatings and adhesion defects by photothermal radiometry. Proc. SPIE, 1996, 2782, 662–673.

  8. Seidel, U., Lan, T. T. N., Walther, H. G., Schmitz, B., Geerkens, J. and Goch, G. Quantitative characterization of material inhomogeneities by thermal waves. Opt. Eng., 1997, 36, 376–390.

  9. Lan, T. T. N., Seidel, U. and Walther, H. G. Theory of microstructure depth profiling by photo­thermal measurements. J. Appl. Phys., 1995, 77, 4739–4741.

10. Lan, T. T. N. and Walther, H. G. Photothermal depth profiling using only phase data. J. Appl. Phys., 1996, 80, 5289–5291.

11. Reigl, M. Methoden zur Quantifizierung photothermischer Signale. PhD Thesis, Universität Ulm, 1997.

12. Lan, T. T. N., Seidel, U., Walther, H. G., Goch, G. and Schmitz, B. Experimental results of photothermal microstructural depth profiling. J. Appl. Phys., 1995, 78, 4108–4111.

Back to Issue