GitHub

Overview

VectorPSFs.jl provides a comprehensive toolkit for computing fully vectorial point spread functions (PSFs) under various conditions, including the presence or absence of aberrations induced by plane-parallel plates. The package features specialized optimizations for modeling the PSFs of NV centers and supports quantitative aberration analysis by computing Strehl ratios and identifying plate thicknesses that preserve near-diffraction-limited performance ($\mathrm{Strehl} > 0.8$).

Features

  • PSF Computations: The PSF(...) function handles scenarios involving normal or tilted incidence, immersion objectives, and spectral weighting. Users can specify (x, y, z) coordinates in micrometers, a chosen objective, and optionally a plane-parallel plate with a tilt angle.

  • Aberrations: Refractive-index mismatched transparent materials situated in the path of converging rays introduce aberrations. This package enables the computation of aberrated PSFs using a fully vectorial approach.

  • Plane-Parallel Plate Materials: Create PlaneParallelPlate objects for various materials, including diamond, fused silica, BK7 (borosilicate crown), magnesium fluoride, sapphire, or custom transparent plates whose refractive indices are given by Sellmeier equation.

  • Aberration Quantification: Compute Strehl ratios across defocus ranges or tilt scenarios, and automate the search for plate thicknesses that ensure near-diffraction-limited performance ((\mathrm{Strehl} \geq 0.8)).

  • Microscope Objective Conditioning: Define Objective structures to capture parameters such as focal length, numerical aperture, refractive index, and immersion medium (e.g., air, oil).

  • NV-Center Integration: Includes a specialized workflow for NV photoluminescence, utilizing spline-interpolated spectral data to compute polychromatic PSFs at different wavelengths.

Basic Steps

  1. Define Microscope Objectives: Create Objective objects by specifying numerical aperture, immersion medium, and focal length.

  2. Construct Plane-Parallel Plates: Build PlaneParallelPlate instances (e.g., diamond, fused silica, BK7) using either built-in materials or custom Sellmeier models.

  3. Compute PSFs: Use PSF(...) to compute PSFs by specifying (x, y, z) in micrometers along with the relevant optical parameters (e.g., objective, plate). For compile-time dispatch, utilize the PSFParams parametric struct.

For installation and setup instructions, see Installation. To explore practical code examples, refer to Examples.

Installation

To install VectorPSFs.jl, open the Julia package manager (Pkg REPL mode) and run:

] add https://github.com/IvanLuznetsoff/VectorPSFs.jl

The package requires:

  • HCubature.jl for multi-dimensional integration,
  • StaticArrays.jl for efficient small-array handling,
  • SmoothingSplines.jl for NV-spectrum fitting,
  • Optim.jl for Strehl ratio optimizations,
  • plus standard libraries like LinearAlgebra, Statistics, etc.

Once installed, you can using VectorPSFs in your Julia session:

using VectorPSFs

Check your environment’s compatibility with Julia ≥ 1.6 (recommended 1.10 or above).

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)

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 weighted summation 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.

Here’s the proofread version of your citation text:

Citation

This package was developed as part of academic research. If you use it in your research, we would appreciate if you could cite our work (arXiv:2402.14422).