Hi,
Fitting an Airy function to the fringes you have identified can be a good approach to accurately model and remove the fringes from your image. An Airy function is a special case of the more general Bessel function, which describes the diffraction pattern of a circular aperture.
To fit an Airy function to your data, you could use a nonlinear least squares fitting algorithm. This involves defining an objective function that measures the difference between the Airy function and your data, and then minimizing this objective function to find the parameters of the Airy function that best fit your data.
The parameters of the Airy function include the radius of the circular aperture, which you have already identified, and the amplitude and width of the function. You could start by estimating these parameters from your data, for example by using the height and width of the fringes you have identified.
Once you have an estimate of the parameters, you can use a fitting algorithm such as the Levenberg-Marquardt algorithm to minimize the objective function and find the best-fit parameters. There are many libraries available in various programming languages that can perform nonlinear least squares fitting, such as SciPy in Python.
After fitting the Airy function to your data, you can subtract it from your original image to remove the fringes. Alternatively, you could use the fitted function to interpolate the fringes and remove them from your image.
Keep in mind that fitting an Airy function can be sensitive to noise and other sources of error in your data. It may be helpful to first preprocess your data to remove noise or correct for other sources of distortion before fitting the Airy function.
