Fluorescence BPM Simulation

Differentiable beam propagation method (BPM) for fluorescence microscopy simulation in heterogeneous biological tissue.

Physics

Split-step propagation:

E(z+dz) = F⁻¹[F[E(z)·exp(ik₀·Δn·dz)]·H(dz)]

Fresnel propagator:

H(k_x,k_y) = exp(2πi·dz·√((n/λ)² - k_x² - k_y²))

Incoherent fluorescence (Monte Carlo):

I_total = Σ |F⁻¹[P(k)·F[√(F(r))·exp(iφ_random)]]|²

Installation

conda env create -f environment.yaml
conda activate fluorescence-bpm
pip install -e .

Usage

Quick start (default parameters):

from fluorescence_bpm import run_simulation

run_simulation(
    refractive_index_path='./data/KidneyL_30.tif',
    fluorescence_path='./data/Fluo_2_30.tif',
    n_iterations=1000
)

Custom parameters:

run_simulation(
    refractive_index_path='./data/KidneyL_30.tif',
    fluorescence_path='./data/Fluo_2_30.tif',
    nm=1.33,        # Medium refractive index
    na=0.5,         # Numerical aperture
    dx=0.1154,      # Pixel size [μm]
    lbda=0.5320,    # Wavelength [μm]
    dz=1.0,         # Axial step [μm]
    z_min=-15.0,    # Volume start [μm]
    z_max=15.0,     # Volume end [μm]
    device='cuda:0',
    n_iterations=1000
)

Using Config object:

from fluorescence_bpm import FluorescenceBPM, Config
import torch

config = Config(nm=1.33, na=0.5, dx=0.1154)
model = FluorescenceBPM(config)

phi = torch.rand((512, 512), device='cuda:0') * 2 * torch.pi
I = model(field_number=0, phi=phi)

Dataset engine (config driven)

For generating ground-truth datasets — a volume filled with spherical cells of differing brightness, imaged and delivered on a chosen voxel grid — one YAML describes the whole experiment and the engine writes one log folder:

python simulate.py -c config/base/reference_optics.yaml -o log/my_run
python analyze_run.py log/my_run                  # measure against ground truth

Parameterized sweeps are one spec file each:

python run_sweep.py -s config/sweeps/MC_sweep.yaml     # Monte-Carlo draws
python run_sweep.py -s config/sweeps/RI_sweep.yaml     # cell refractive index
python run_sweep.py -s config/sweeps/PSF_sweep.yaml    # numerical aperture

The YAML covers the volume and phantom (cells, spheroid or a bead grid), the refractive-index landscape of the medium and inside the cells, the optics (NA, wavelength, Zernike pupil aberration), the emission Monte Carlo, and the detector (binning to the delivered voxel, Poisson and read noise).

• RUNNING.md — how to run the sweeps and change the sample or the imaging
• archive/note/note.pdf — the forward model in one page, then the three sweeps measured against it
• ACQUISITION.md — the reference acquisition the defaults follow
• DATASET.md — dataset conventions and measured properties

Two constraints the engine enforces or documents, both learned the hard way:

• volume.dx must satisfy dx < lbda/(2*NA), else the pupil mask is larger than the sampled k-space, passes everything, and the simulation has no optical sectioning — the configuration is rejected with the maximum usable NA.
• Image plane k is focused on sample plane k. The core returns the focal stack indexed from the exit face inward, so an unflipped stack is mirrored in z against the sample; test_registration.py pins this.

Runs are byte-for-byte repeatable at a fixed seed (test_determinism.py).

Data Format

Place TIFF files in ./data/:

• KidneyL_30.tif: Refractive index volume (Δn values)
• Fluo_2_30.tif: Fluorophore concentration volume

TIFF format: [z, y, x] → code transposes to [x, y, z]

Output

• fluorescence_final.tif: Final accumulated intensity
• fluo_iter_XXXX.tif: Intermediate checkpoints (every 100 iterations)

Theory

Propagation equation

Helmholtz equation with varying n(r):

∇²E + k₀²n²(r)E = 0

BPM approximation (paraxial):

∂E/∂z = i/(2k₀n₀)[∇_⊥²E + k₀²(n²-n₀²)E]

Split-step method

1. Phase accumulation: E' = E·exp(ik₀·Δn·dz)
2. Diffraction: E(z+dz) = F⁻¹[F[E']·H(dz)]
3. Pupil filtering: E_det = F⁻¹[P·F[E]] where P = pupil function

Fluorescence modeling

Incoherent sum over random phase realizations:

I(r) = ⟨|E_emission(r,φ)|²⟩_φ

Citation

Based on optical diffraction tomography and beam propagation methods for thick biological samples.

License

Janelia Open-Source License