New transform to project axisymmetric deflection fields along arbitrary rays

Axisymmetric tomography is used to extract quantitative information from line-of-sight measurements of gas flow and combustion fields. For instance, background oriented schlieren (BOS) measurements are typically inverted by tomographic reconstruction to estimate the density field of a high-speed or high-temperature flow. Conventional reconstruction algorithms are based on the inverse Abel transform, which assumes that rays are parallel throughout the target object. However, camera rays are not parallel, and this discrepancy can result in significant errors in many practical imaging scenarios. We present a generalization of the Abel transform for use in tomographic reconstruction of light-ray deflections through an axisymmetric target. The new transform models the exact path of camera rays instead of assuming parallel paths, thereby improving the accuracy of estimates. We demonstrate our approach with a simulated BOS scenario in which we reconstruct noisy synthetic deflection data across a range of camera positions. Results are compared to state-of-the-art Abel-based algorithms. Reconstructions computed using the new transform are consistently more stable and accurate than conventional reconstructions.

Polychromatic Hilbert diagnostics of phase and temperature disturbances, induced by candle flame in air

The work is motivated by the scientific and practical significance of the problem of non-disturbing diagnostics of phase and temperature fields induced in a gas medium by a flame of a torch (candle). The spatial conditions in which the fields are studied satisfy the model of axial symmetry of the torch associated with the vertical orientation of the candle. A method adequate to the problem to be solved has been developed, based on polychromatic Hilbert visualization of phase optical density fields, measurement of the temperature profile in selected sections of the medium under study, registration and selection of RAW images recorded by the photomatrix in RGB channels. The visualized Hilbert structures contain information on the phase optical density perturbations induced by the temperature field. The reliability of the results is confirmed by comparing the experimentally obtained hilbertograms and those reconstructed from phase structures using the Abel transform.

Digital Holographic Interferometry for the Measurement of Symmetrical Temperature Fields in Liquids

In this paper, we present a method of quantitatively measuring in real-time the dynamic temperature field change and visualization of volumetric temperature fields generated by a 2D axial-symmetric heated fluid from a pulsatile jet in a water tank through off-axis digital holographic interferometry. A Mach-Zehnder interferometer on portable platform was built for the experimental investigation. The pulsatile jet was submerged in a water tank and fed with water with higher temperature. Tomographic approach was used to reconstruct the temperature fields through the Abel Transform and the filtered back-projection. Averaged results, tomographic view, standard deviation and errors are presented. The presented results reveal digital holographic interferometry as a powerful technique to visualize temperature fields in flowing liquids and gases.

Abel transform of exponential functions for planetary and cometary atmospheres with application to observation of 46P/Wirtanen and to the OI 557.7 nm emission at Mars.

<p>Line-of-sight integration of emissions from planetary and cometary atmospheres is the Abel transform of the emission rate, under the spherical symmetry assumption. Indefinite integrals constructed from the Abel transform integral are useful for implementing remote sensing data analysis methods, such as the numerical inverse Abel transform giving the volume emission rate compatible with the observation. We obtain analytical expressions based on a suitable, non-alternating, series development to compute those indefinite integrals. We establish expressions allowing absolute accuracy control of the convergence of these series depending on the number of terms involved. We compare the analytical method with numerical computation techniques, which are found to be sufficiently accurate as well. Inverse Abel transform fitting is then tested in order to establish that the expected emission rate profiles can be retrieved from the observation of both planetary and cometary atmospheres. We show that the method is robust, especially when Tikhonov regularization is included, although it must be carefully tuned when the observation varies across many orders of magnitude. A first application is conducted over observation of comet 46P/Wirtanen, showing some variability possibly attributable to an evolution of the contamination by dust and icy grains. A second application is considered to deduce the 557.7 nm volume emission rate profile of the metastable oxygen atom in the upper atmosphere of planet Mars.</p>

Reconstruction of the spatial phase and temperature structure of a candle flame using Hilbert optics and shear interferometry methods

The study of the structure of the candle flame is discussed in the work. The optical diagnostics adapted to the study of combustion problems is based on the visualization of phase disturbances induced in the probe light field by the medium under study with using Hilbert optics and interferometry methods combined with pixel-by-pixel processing of the dynamic structure of the recorded images. The diagnostic complex is implemented on the basis of the IAB–463M device with modified blocks of optical filtration, light source, registration and information processing. The dynamic phase structure of the candle flame was visualized. The temperature was measured using thermocouples at the reference points. The phase function was restored on axisymmetric sections from the obtained hilbertograms. The temperature field of flame was reconstructed using the inverse Abel transform.