Additional Notes

• Zernike.metrics(ΔW::Wavefront) exists;

• Zernike.format_strings(Z::AbstractPolynomial) will return both the Unicode and LaTeX string representations directly;

• Zernike.print_strings(j_max::Int) will print the Unicode string representations of the polynomials up to j_max;

• The zplot function can be invoked independently using Polynomial and Wavefront function types, quantized wavefront errors, and Observables of each; the plot will update each time the Observable changes (see the docstring for more info);

• If you resize the plot window, right clicking on the figure will resize / trim the plot automatically so that it fits within the window without extra space;

• Polynomial and Wavefront types can be indexed (zero-based) to return a specific coefficient; their full vector of coefficients can be conveniently accessed using single-argument getindex (e.g. z[], w[]);

• Callable types can be called with complex arguments as a convenient method to evaluate them in Cartesian coordinates;

• The Zernike polynomials are currently only valid up to degree ~812 at which point the maximum coefficient approaches the maximum for double-precision floating-point numbers (~1e308);

  • because 64-bit floats are used for an expanded range by default the coefficients are exactly accurate up to order ~47, limited by the 53-bit (~1e16) precision of the significand after which results are only approximate; if more accuracy is desired arbitrary precision or plain Ints can be specified by passing the appropriate type (Int, BigInt, BigFloat) as the third argument to Zernike.radial_coefficients;

• If you're interested in precompiling the package into a system image in order to speed up load times please see the precompile directory (at the moment PrecompileTools or the like is not used);

• If you're interested in only the full vector of Zernike expansion coefficients obtained through the least squares fit and want to avoid computing extra values and plotting the results you can call:

Zernike.wavefront_coefficients(ρ, θ, OPD, n_max)

which will return the weights and the corresponding residual error.

Similarly you can do this for the radial polynomial coefficients and the NA transformed wavefront error expansion coefficients by importing the functions radial_coefficients and transform_coefficients, respectively.