Shock-wave imaging by density recovery from intensity measurements

Abstract

A method for quantitative estimation of density variation in high-speed flow, which uses light as an interrogating tool, is described. The wavefront distortion of the interrogating beam induced by the compressible flow field is estimated quantitatively, in which the density gradient of the flow field is seen as refractive-index gradient by the probing beam. The distorted wavefront is measured quantitatively by using the cross-sectional intensities of the distorted wavefront along the optical axis. Iterative algorithms are developed using both deterministic (Gauss-Newton) and stochastic (ensemble Kalman filter) update strategies to recover unknown parameters such as the phase of the wavefront or the refractive index distribution in the flow directly from the measured intensities. With phase recovered in the first step, a ray tomography algorithm is used to obtain the refractive index and density distributions in the flow from the phase. Experiments are conducted to quantitatively visualize the shock-wave-induced flow field in a shock-tunnel facility. The reconstructed density cross sections, obtained using different reconstruction methods, are presented and compared with those obtained by solving the Navier-Stokes equation using computational fluid dynamic routines. It is observed that the iterative algorithms always outperform those depending on solution of the transport-of-intensity equation. In particular, when using the iterative algorithms, the stochastic search scheme outperforms the Gauss-Newton method.

Pebrine diagnosis using quantitative phase imaging and machine learning

“…Such drifted spores are removed from further processing, because they are also a source of phase reconstruction error. The remaining subimages are interpolated by a scale of two (128 × 128 pixels) to smoothen the sharp edged‐boundaries at spore walls, another source of phase reconstruction error 42 . Cropping the FOVs reduces the computation cost, which is proportional to the number of pixels to be processed.…”

Time-resolved quantitative visualization of complex flow field emitted from an open ended shock tube using a wavefront measuring camera

“…The process of recovering field parameter (density in this case) from projections belong to the broad class of inverse problems in which tomographic reconstruction algorithms centered around series expansion and transform based schemes [39] are used. Here, the unwrapped phase ( , ) xy  The used ST has circular symmetry at the exit and therefore the axis-symmetric assumption is made while performing tomographic reconstruction from the recorded projections.…”

“…The process of recovering field parameter (density in this case) from projections belong to the broad class of inverse problems in which tomographic reconstruction algorithms centered around series expansion and transform based schemes [39] are used. Here, the unwrapped phase ( , ) xy  obtained through Eq.…”

Low-light phase imaging using in-line digital holography and the transport of intensity equation

“…The advantage of the TIE is that it is computationally efficient and experimentally cost-effective because it requires the acquisition of the intensity across only two transverse planes separated along the axis of propagation [26][27][28]. The TIE has been applicable in various fields due to its simple experimental setup and computational efficiency, such as wavefront sensing [29,30], phase unwrapping [31,32], microscopy [33][34][35][36], optical metrology [37], and optical information processing [38][39][40]. Zuo et al [32] described the applicability of the TIE to unwrap phase discontinuities.…”