Radial functions

calc_radial_symm!([::Type{TA},] sz::NTuple,  fct; scale = one(real(T)), myrr2sep = rr2_sep(size(arr); scale=scale, offset=size(arr).÷2 .+1)) where {N,T}

evaluates the radial function fct over the entire array. The function needs to accept the radius as argument. The calculation is done fast by only evaluating on the first quadrant and replicating the results by copy operations using copy_corners!().

Arguments

• TA: The array type for the newly created array.
• sz: The size of the newly created array.
• fct: The function of the radius, to be evaluate on the array coordinates.
• scale: the vetorized scaling of the pixels (only used, if myrr2sep is not supplied by the user)
• myrr2sep: The separable xx^2 and yy^2 etc. information as obtained by rr2_sep().

calc_radial_symm!(arr::TA, fct; scale = one(real(T)), myrr2sep = rr2_sep(size(arr); scale=scale, offset=size(arr).÷2 .+1)) where {N,T}

evaluates the radial function fct over the entire array. The function needs to accept the radius as argument. The calculation is done fast by only evaluating on the first quadrant and replicating the results by copy operations using copy_corners!().

Arguments

• arr: The array into which to evaluate the radial function
• fct: The function of the radius, to be evaluate on the array coordinates.
• scale: the vetorized scaling of the pixels (only used, if myrr2sep is not supplied by the user)
• myrr2sep: The separable xx^2 and yy^2 etc. information as obtained by rr2_sep().

propagator_col([]::Type{TA},] sz::NTuple{N, Int}; Δz=one(eltype(TA)), k_max=0.5f0, scale=0.5f0 ./ (max.(sz ./ 2, 1))) where{TA, N}

generates a propagator for propagating optical fields via exp(i kz Δz) with kz=sqrt(k0^2-kx^2-ky^2). The k-space radius is stated by k_max relative to the Nyquist frequency, as long as the scale remains to be 1 ./ (2 max.(sz ./ 2, 1))).

#Arguments

• TA: type of the array to generate. E.g. Array{Float64} or CuArray{Float32}.
• sz: size of the array to generate. If a 3rd dimension is present, a stack a propagators is returned, one for each multiple of Δz.
• Δz: distance in Z to propagate per slice.
• k_max: maximum propagation radius in k-space. I.e. limit of the k-sphere. This is not the aperture limit!
• scale: specifies how to interpret k-space positions. Should remain to be 1 ./ (2 max.(sz ./ 2, 1))).

propagator_col!(arr::AbstractArray{T,N}; Δz=one(eltype(TA)), k_max=0.5f0, scale=0.5f0 ./ (max.(sz ./ 2, 1))) where{TA, N}

generates a propagator for propagating optical fields via exp(i kz Δz) with kz=sqrt(k0^2-kx^2-ky^2). The k-space radius is stated by k_max relative to the Nyquist frequency, as long as the scale remains to be 1 ./ (2 max.(sz ./ 2, 1))).

#Arguments

• arr: the array to fill with propagators. If a 3rd dimension is present, a stack a propagators is returned, one for each multiple of Δz.
• Δz: distance in Z to propagate per slice.
• k_max: maximum propagation radius in k-space. I.e. limit of the k-sphere. This is not the aperture limit!
• scale: specifies how to interpret k-space positions. Should remain to be 1 ./ (2 max.(sz ./ 2, 1))).

phase_kz_col([::Type{TA},] sz::NTuple{N, Int};k_max=0.5f0, scale=0.5f0 ./ (max.(sz ./ 2, 1))) where{TA, N}

Calculates a propagation phase (without the 2pi factor!) for a given z-position, which can be defined via a 3rd entry in the offset supplied to the function. By default, Nyquist sampling it is assumed such that the lateral kxy corresponds to the XY border in frequency space at the edge of the Ewald circle. However, via the xy scale entries the kmax can be set appropriately. The propagation equation should Δz .* sqrt.(1-kxyrel^2) as the propagation phase. The Z-propagation distance (Δz) has to be specified in units of the wavelength in the medium (λ = n*λ₀). Note that since the phase is normalized to 1 instead of 2pi, you need to use this phase in the following sense: `cispi.(2.*phasekz(...))`.

#Arguments

• TA: Array type of the result array. For cuda calculations use CuArray{Float32}.
• sz: Size (2D) of the result array.
• k_max: maximum propagation radius in k-space. I.e. limit of the k-sphere. This is not the aperture limit!
• scale: specifies how to interpret k-space positions. Should remain to be 1 ./ (2 max.(sz ./ 2, 1))).

phase_kz_col!(arr::AbstractArray{T,N}; k_max=0.5f0, scale=0.5f0 ./ (max.(sz ./ 2, 1))) where{TA, N}

Calculates a propagation phase (without the 2pi factor!) for a given z-position, which can be defined via a 3rd entry in the offset supplied to the function. By default, Nyquist sampling it is assumed such that the lateral kxy corresponds to the XY border in frequency space at the edge of the Ewald circle. However, via the xy scale entries the kmax can be set appropriately. The propagation equation uses Δz .* sqrt.(1-kxyrel^2) as the propagation phase. The Z-propagation distance (Δz) has to be specified in units of the wavelength in the medium (λ = n*λ₀). Note that since the phase is normalized to 1 instead of 2pi, you need to use this phase in the following sense: `cispi.(2.*phasekz(...))`.

#Arguments

• arr: the array to fill with propagators. If a 3rd dimension is present, a stack a propagators is returned, one for each multiple of Δz.
• k_max: maximum propagation radius in k-space. I.e. limit of the k-sphere. This is not the aperture limit!
• scale: specifies how to interpret k-space positions. Should remain to be 1 ./ (2 max.(sz ./ 2, 1))).