Examples

PSF Calculation

The function PSF(x, y, z, ...) computes the on-axis or off-axis field intensity, integrating vectorially over the back pupil. You can choose among multiple overloads:

• No plate, direct calculation (simple, air):

  PSF(x, y, z, λ, NA; rtol=1e-3, atol=1e-4)

• No plate, with Objective:

  PSF(x, y, z, λ, obj::Objective; rtol=1e-3, atol=1e-4)

• Normal-incidence plate, with Objective:

  PSF(x, y, z, λ, obj::Objective, plate::PlaneParallelPlate; ...)

• Tilted-incidence plate, with Objective:

  PSF(x, y, z, λ, obj::Objective, plate::PlaneParallelPlate, α; ...)

Here, (x, y, z) are in micrometers (µm). λ is the wavelength in µm, NA is numerical aperture, α is tilt angle in radians.

Example (normal incidence, no aberration):

using VectorPsfs

obj = MPlanApo50x()         # e.g. 50x objective
λ   = 0.632                 # 632 nm = 0.632 µm

To obtain a PSF map on a plane:

xs = range(-1,1,201)
ys = range(-1,1,201)
psf_map_xy = [PSF(x, y, 0.0, λ, obj) for x in xs, y in ys]

Strehl Ratio

The Strehl ratio is a measure of aberration severity, defined by the ratio of maximum intensity of the aberrated PSF to that of an unaberrated (diffraction-limited) PSF. Functions:

Strehl(t::Float64, λ::Float64, obj::Objective; ...)
Strehl(t::Float64, λ::Float64, α::Float64, obj::Objective; ...)

These calls do an internal defocus optimization. If S > 0.8, we often call it “diffraction-limited.”

Example:

using VectorPsfs, Optim

obj = MPlanApo100x()
λ   = 0.7         # 700 nm
s = Strehl(50.0, λ, obj, Diamond; zrange=[0.0, 5.0])  # Diamond thickness=50 µm
println("Strehl ratio = ", s)

NV-Center Weighted PSF

We also offer a polychromatic approach for NV emission:

PSF(x, y, z, obj::Objective, nv::NVCenter; ...)

where NVCenter is a struct storing smoothed spectral weights. This integrates over multiple wavelengths.

Example:

using VectorPsfs

nv = NVCenter(NVspectrum.wavelength)  # smoothing-based weighting
obj = MPlanApo100x()
plate_diamond = Diamond(100.0)
val_NV = PSF(0.0, 0.0, 3.0, obj, nv, plate_diamond)
println("NV-weighted PSF intensity = ", val_NV)

Additional Topics

• PlaneParallelPlate: Constructors like Diamond(t), FusedSilica(t), BorosilicateCrown(t), etc., each define a wavelength-dependent refractive index using Sellmeier equations.
• Objective: Typical usage: MPlanApo50x(), MPlanApo100x(), etc., or define your own Objective(f, NA, n).
• ParametricPSF: A more advanced method is to use parametric structs (e.g., PSFParams{Mode}) for compile-time dispatch of different incidence modes (no plate, normal, tilted).

For more details, consult the source code in psf_core.jl, plane_parallel_plates.jl, objectives.jl, etc. ```