Stabilized nonlinear regression for interferogram analysis
Abstract:
A simple but accurate regression method for reducing the conventional single-frame interferograms that primarily arise in flow and heat-transfer measurements is proposed and tested. Phase extraction from the nonlinear interferogram intensity model becomes an ill-posed nonuniqueness problem. Unlike previous regression techniques, the method is based on iterative independent estimation of the individual terms appearing in the model to resolve this problem. Testing demonstrates stable convergence under a wide range of fringe numbers and noise levels. In comparison with the Fourier transform method the regression method provides enhanced accuracy, especially for cases involving few fringes, opaque boundaries, and phase discontinuities. It also allows direct gradient calculation. These features are very attractive for flow measurements despite its slow processing time.
Related Concept Videos
Calibration Curves: Linear Least Squares
For data that follow a straight line, the standard method for fitting is the linear...
Reconstruction of Signal using Interpolation
Linear Approximation in Time Domain
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length, the...
Linear Approximation in Frequency Domain
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear.
BIBO stability of continuous and discrete -time systems
To determine the BIBO stability, the convolution integral is utilized when a bounded continuous-time input is applied to a Linear Time-Invariant (LTI) system.
Residuals and Least-Squares Property
If the observed data point lies above the line, the residual is positive, and the line underestimates the actual data value for y. If the observed data point lies below the line, the residual is negative, and the line overestimates the actual data value for y.
The process of fitting the best-fit...


