Unbiased iterative reconstruction of polarization and space-charge profiles from thermal-wave experiments

Abstract

The thermal-wave technique or laser-intensity modulation method is an important tool for the non-destructive probing of space-charge and polarization profiles in electrets. Analysing the experimental data requires solving a Fredholm integral equation which is known to be an ill-conditioned problem. This paper presents an iterative approach that is capable of reconstructing inherently unsmooth distributions. The deviations from the true profiles are slightly smaller than those obtained with Tikhonov regularization, while the computational burden is not a limiting factor on modern personal computers. The optimum number of iterations is estimated using the randomized generalized cross-validation technique. Results are shown for a number of model distributions, as well as for experimental data from a layered polyvinylidene fluoride film sandwich.

Kramers-Kronig relations in laser intensity modulation method

“…Issues concerning LIMM data analysis and the reconstruction of the space charge and polarization profiles with various, ingenious methods were discussed earlier. [7][8][9][10] In this paper, we discuss the Kramers-Kronig relations in LIMM, present an analysis, and apply the transformation to estimate imaginary current data from the real and the converse, for simulated and experimental data, respectively.…”

“…The integral in Eq. ͑1͒ is evaluated over the sample thickness s. For a free standing film, T͑ , z͒ is 10,11 T͑,z͒ = A͑␤͒ −1 cosh͓␤͑s − z͔͒csch͑␤s͒. ͑2͒…”

Thermal-Pulse Tomography of Space-charge and Polarization Distributions in Electret Polymers

“…2 (a Fredholm integral equation of the first kind) is known to be an illposed problem. Several techniques have been developed in order to extract physically meaningful solutions g(z) from the experimental data, such as Tikhonov regularization [19] (sometimes combined with polynomial approximations [20,21]), a scale-transformation method [22], iterative approaches [23], and Monte Carlo techniques [24]. In the present study, regularization in combination with the L-curve method [25] was used for thinner samples (d < 25 µm) [16], whereas the simpler scale-transformation approach was used when the near-surface polarization in thicker samples was of interest [26].…”

Nondestructive testing of ferroelectrics by thermal wave methods

“…Other approaches of pyroelectric coefficient depth profile reconstruction are based on the LAGRANGE interpolation formula [21], on the LANDWEBER iteration [22,23], or simply on the principle of parsinomy (choosing the smoothest profile based on physical intuition) [7]. Eqs.…”