34 research outputs found
Thermodynamic Limits of Spatial Resolution in Active Thermography
Thermal waves are caused by pure diffusion: their amplitude is decreased by
more than a factor of 500 within a propagation distance of one wavelength. The
diffusion equation, which describes the temperature as a function of space and
time, is linear. For every linear equation the superposition principle is
valid, which is known as Huygens principle for optical or mechanical wave
fields. This limits the spatial resolution, like the Abbe diffraction limit in
optics. The resolution is the minimal size of a structure which can be detected
at a certain depth. If an embedded structure at a certain depth in a sample is
suddenly heated, e.g. by eddy current or absorbed light, an image of the
structure can be reconstructed from the measured temperature at the sample
surface. To get the resolution the image reconstruction can be considered as
the time reversal of the thermal wave. This inverse problem is ill-conditioned
and therefore regularization methods have to be used taking additional
assumptions like smoothness of the solutions into account. In the present work
for the first time methods of non-equilibrium statistical physics are used to
solve this inverse problem without the need of such additional assumptions and
without the necessity to choose a regularization parameter. For reconstructing
such an embedded structure by thermal waves the resolution turns out to be
proportional to the depth and inversely proportional to the natural logarithm
of the signal-to-noise ratio. This result could be derived from the diffusion
equation by using a delta-source at a certain depth and setting the entropy
production caused by thermal diffusion equal to the information loss. No
specific model about the stochastic process of the fluctuations and about the
distribution densities around the mean values was necessary to get this result.Comment: Submission to International Journal of Thermophysics. Keywords:
Diffusion; Entropy production; Information loss; Kullback-Leibler divergence;
Chernoff-Stein Lemma; Stochastic thermodynamics. arXiv admin note: text
overlap with arXiv:1502.0021
Heat diffusion blurs photothermal images with increasing depth
In this tutorial, we aim to directly recreate some of our "aha" moments when
exploring the impact of heat diffusion on the spatial resolution limit of
photothermal imaging. Our objective is also to communicate how this physical
limit can nevertheless be overcome and include some concrete technological
applications. Describing diffusion as a random walk, one insight is that such a
stochastic process involves not only a Gaussian spread of the mean values in
space, with the variance proportional to the diffusion time, but also temporal
and spatial fluctuations around these mean values. All these fluctuations
strongly influence the image reconstruction immediately after the short heating
pulse. The Gaussian spread of the mean values in space increases the entropy,
while the fluctuations lead to a loss of information that blurs the
reconstruction of the initial temperature distribution and can be described
mathematically by a spatial convolution with a Gaussian thermal
point-spread-function (PSF). The information loss turns out to be equal to the
mean entropy increase and limits the spatial resolution proportional to the
depth of the imaged subsurface structures. This principal resolution limit can
only be overcome by including additional information such as sparsity or
positivity. Prior information can be also included by using a deep neural
network with a finite degrees of freedom and trained on a specific class of
image examples for image reconstruction
Breaking the Resolution limit in Photoacoustic Imaging using Positivity and Sparsity
In this tutorial, we aim to directly recreate some of our "aha" moments when
exploring the impact of heat diffusion on the spatial resolution limit of
photothermal imaging. Our objective is also to communicate how this physical
limit can nevertheless be overcome and include some concrete technological
applications. Describing diffusion as a random walk, one insight is that such a
stochastic process involves not only a Gaussian spread of the mean values in
space, with the variance proportional to the diffusion time, but also temporal
and spatial fluctuations around these mean values. All these fluctuations
strongly influence the image reconstruction immediately after the short heating
pulse. The Gaussian spread of the mean values in space increases the entropy,
while the fluctuations lead to a loss of information that blurs the
reconstruction of the initial temperature distribution and can be described
mathematically by a spatial convolution with a Gaussian thermal
point-spread-function (PSF). The information loss turns out to be equal to the
mean entropy increase and limits the spatial resolution proportional to the
depth of the imaged subsurface structures. This principal resolution limit can
only be overcome by including additional information such as sparsity or
positivity. Prior information can be also included by using a deep neural
network with a finite degrees of freedom and trained on a specific class of
image examples for image reconstructio