Differentiable beam propagation method (BPM) for fluorescence microscopy simulation in heterogeneous biological tissue.
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
conda env create -f environment.yaml
conda activate fluorescence-bpm
pip install -e .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)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]
fluorescence_final.tif: Final accumulated intensityfluo_iter_XXXX.tif: Intermediate checkpoints (every 100 iterations)
Helmholtz equation with varying n(r):
∇²E + k₀²n²(r)E = 0
BPM approximation (paraxial):
∂E/∂z = i/(2k₀n₀)[∇_⊥²E + k₀²(n²-n₀²)E]
- Phase accumulation:
E' = E·exp(ik₀·Δn·dz) - Diffraction:
E(z+dz) = F⁻¹[F[E']·H(dz)] - Pupil filtering:
E_det = F⁻¹[P·F[E]]where P = pupil function
Incoherent sum over random phase realizations:
I(r) = ⟨|E_emission(r,φ)|²⟩_φ
Based on optical diffraction tomography and beam propagation methods for thick biological samples.
Janelia Open-Source License