wavefront(ρ, θ, OPD, n_max)

Estimates wavefront error by expressing optical aberrations as a linear combination of weighted Zernike polynomials using a linear least squares method. The accuracy of this type of wavefront reconstruction represented as an expanded series depends upon a sufficiently sampled phase field and a suitable choice of the fitting order n_max.

ρ, θ, and OPD must be floating-point vectors of equal length; at each specific index the values are elements of an ordered triple over the exit pupil.

• ρ: normalized radial exit pupil position variable {0 ≤ ρ ≤ 1};
• θ: angular exit pupil variable in radians (mod 2π), defined positive counter-clockwise from the horizontal x-axis;
• OPD: measured optical path difference in waves;
• n_max: maximum radial degree to fit to.

Note that specifying n_max will fit using the full range of Zernike polynomials from j = 0 to j_max corresponding to the last polynomial with degree n_max. If instead you only want to fit to a subset of Zernike polynomials you can specify a vector of (m, n) tuples in place of n_max using the method:

wavefront(ρ, θ, OPD, orders::Vector{Tuple{Int, Int}})

If your phase data is in the form of a floating-point matrix instead you can call the method:

wavefront(OPD, fit_to; options...)

This assumes the wavefront error was uniformly measured using polar coordinates; the matrix is expected to be a polar grid of regularly spaced periodic samples with the first element referring to the value at the origin and the end points including the boundary of the pupil (i.e. ρ, θ = 0.0:step:1.0, 0.0:step:2π). The first axis of the matrix (the rows) must correspond to the angular variable θ while the second axis (the columns) must correspond to the radial variable ρ.

If instead your data is not equally spaced you can call:

wavefront(ρ::Vector, θ::Vector, OPD::Matrix, fit_to; options...)

under the aforementioned dimensional ordering assumption.

fit_to can be either n_max::Int or orders::Vector{Tuple{Int, Int}}.

It is also possible to input normalized Cartesian coordinates using the method with 3 positional arguments and passing fit_to as a keyword argument:<br> wavefront(x, y, OPD; fit_to, options...).

The function returns seven values contained within a WavefrontOutput type, with fields:

1. recap: vector of named tuples containing the Zernike polynomial indices and the corresponding expansion coefficients rounded according to precision;
2. v: full vector of Zernike wavefront error expansion coefficients;
3. metrics: named 3-tuple with the peak-to-valley error, RMS wavefront error, and Strehl ratio;
4. W: the WavefrontError function ΔW(ρ, θ);
5. fig: the plotted Makie figure;
6. axis: the plot axis;
7. plot: the surface plot object.