FPM

Fourier Ptychographic Microscopy

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Standard reconstruction benchmark — forward model perfectly known, no calibration needed. Score = 0.5 × clip((PSNR−15)/30, 0, 1) + 0.5 × SSIM

# Method Score PSNR (dB) SSIM Source
🥇 PtychoDV 0.781 33.8 0.935 ✓ Certified Shamshad et al., IEEE TCI 2019
🥈 Fourier PtychoNet 0.743 32.3 0.910 ✓ Certified Jiang et al., BOE 2018
🥉 Gradient Descent FPM 0.645 28.5 0.840 ✓ Certified Tian & Waller, Optica 2015
4 Alternating Projections 0.527 25.0 0.720 ✓ Certified Zheng et al., Nat. Photonics 2013

Dataset: PWM Benchmark (4 algorithms)

Blind Reconstruction Challenge — forward model has unknown mismatch, must calibrate from data. Score = 0.4 × PSNR_norm + 0.4 × SSIM + 0.2 × (1 − ‖y − Ĥx̂‖/‖y‖)

# Method Overall Score Public
PSNR / SSIM
 Dev
PSNR / SSIM
 Hidden
PSNR / SSIM
 Trust Source
🥇 PtychoDV + gradient 0.679
0.766
31.38 dB / 0.936
0.653
26.11 dB / 0.835
0.618
24.68 dB / 0.792
✓ Certified Shamshad et al., IEEE TCI 2019
🥈 Gradient Descent FPM + gradient 0.656
0.666
25.51 dB / 0.818
0.660
26.31 dB / 0.841
0.643
25.08 dB / 0.805
✓ Certified Tian & Waller, Optica 2015
🥉 Fourier PtychoNet + gradient 0.592
0.741
29.65 dB / 0.911
0.580
22.74 dB / 0.721
0.455
18.84 dB / 0.542
✓ Certified Jiang et al., BOE 2018
4 Alternating Projections + gradient 0.566
0.620
23.29 dB / 0.742
0.568
22.16 dB / 0.697
0.511
19.91 dB / 0.594
✓ Certified Zheng et al., Nat. Photonics 2013

Complete score requires all 3 tiers (Public + Dev + Hidden).

Join the competition →
Scoring: 0.4 × PSNR_norm + 0.4 × SSIM + 0.2 × (1 − ‖y − Ĥx̂‖/‖y‖) PSNR 40% · SSIM 40% · Consistency 20%
Public 5 scenes

Full-access development tier with all data visible.

What you get & how to use

What you get: Measurements (y), ideal forward operator (H), spec ranges, ground truth (x_true), and true mismatch spec.

How to use: Load HDF5 → compare reconstruction vs x_true → check consistency → iterate.

What to submit: Reconstructed signals (x_hat) and corrected spec as HDF5.

Public Leaderboard
# Method Score PSNR SSIM
1 PtychoDV + gradient 0.766 31.38 0.936
2 Fourier PtychoNet + gradient 0.741 29.65 0.911
3 Gradient Descent FPM + gradient 0.666 25.51 0.818
4 Alternating Projections + gradient 0.620 23.29 0.742
Spec Ranges (3 parameters)
Parameter Min Max Unit
led_position -0.1 0.2 mm
na_error 0.095 0.11
defocus -2.0 4.0 μm
View Details →
Dev 5 scenes

Blind evaluation tier — no ground truth available.

What you get & how to use

What you get: Measurements (y), ideal forward operator (H), and spec ranges only.

How to use: Apply your pipeline from the Public tier. Use consistency as self-check.

What to submit: Reconstructed signals and corrected spec. Scored server-side.

Dev Leaderboard
# Method Score PSNR SSIM
1 Gradient Descent FPM + gradient 0.660 26.31 0.841
2 PtychoDV + gradient 0.653 26.11 0.835
3 Fourier PtychoNet + gradient 0.580 22.74 0.721
4 Alternating Projections + gradient 0.568 22.16 0.697
Spec Ranges (3 parameters)
Parameter Min Max Unit
led_position -0.12 0.18 mm
na_error 0.094 0.109
defocus -2.4 3.6 μm
Submit Reconstruction View Details →
Hidden 5 scenes

Fully blind server-side evaluation — no data download.

What you get & how to use

What you get: No data downloadable. Algorithm runs server-side on hidden measurements.

How to use: Package algorithm as Docker container / Python script. Submit via link.

What to submit: Containerized algorithm accepting y + H, outputting x_hat + corrected spec.

Hidden Leaderboard
# Method Score PSNR SSIM
1 Gradient Descent FPM + gradient 0.643 25.08 0.805
2 PtychoDV + gradient 0.618 24.68 0.792
3 Alternating Projections + gradient 0.511 19.91 0.594
4 Fourier PtychoNet + gradient 0.455 18.84 0.542
Spec Ranges (3 parameters)
Parameter Min Max Unit
led_position -0.07 0.23 mm
na_error 0.0965 0.1115
defocus -1.4 4.6 μm
Submit Algorithm View Details →

Blind Reconstruction Challenge

Challenge

Given measurements with unknown mismatch and spec ranges (not exact params), reconstruct the original signal. A method must be evaluated on all three tiers for a complete score. Scored on a composite metric: 0.4 × PSNR_norm + 0.4 × SSIM + 0.2 × (1 − ‖y − Ĥx̂‖/‖y‖).

Input

Measurements y, ideal forward model H, spec ranges

Output

Reconstructed signal x̂

About the Imaging Modality

Fourier ptychographic microscopy (FPM) achieves a high space-bandwidth product by illuminating the sample from multiple angles using an LED array, capturing a set of low-resolution images, and computationally stitching them in Fourier space to synthesize a high-NA image with both amplitude and phase. Each LED angle shifts the sample's spatial frequency spectrum in Fourier space, and overlapping spectral regions provide redundancy for phase retrieval. The synthetic NA equals the objective NA plus the illumination NA. Reconstruction uses iterative phase retrieval algorithms (sequential or gradient-based).

Principle

Fourier Ptychographic Microscopy synthetically increases the NA of a low-magnification objective by illuminating the sample from multiple angles (LED array) and computationally stitching together the resulting images in Fourier space. Each LED angle shifts the sample spectrum so different spatial-frequency bands enter the objective pupil, allowing recovery of both amplitude and phase at high resolution over a large field of view.

How to Build the System

Replace the microscope condenser with a programmable LED matrix (e.g., 32×32 RGB LED array, ~4 mm pitch, placed ~80 mm above the sample). Use a low-magnification objective (4-10×, 0.1-0.3 NA) for large FOV. Acquire one image per LED (typically 100-300 images for the full matrix). Precise knowledge of LED positions is required for Fourier-space stitching.

Common Reconstruction Algorithms

  • Alternating projection (Gerchberg-Saxton style in Fourier space)
  • Embedded pupil function recovery (joint sample + aberration estimation)
  • Wirtinger gradient descent with total-variation regularization
  • Neural network-accelerated FPM (learned initialization + refinement)
  • Multiplexed FPM (multiple LEDs simultaneously for faster acquisition)

Common Mistakes

  • Inaccurate LED position calibration causing ghosting and resolution loss
  • Insufficient overlap between Fourier-space patches (need ≥60 % overlap)
  • Ignoring pupil aberrations of the low-NA objective
  • LED intensity non-uniformity not corrected across the array
  • Vibration or sample drift between sequential LED acquisitions

How to Avoid Mistakes

  • Calibrate LED positions using a self-calibration algorithm or known test target
  • Ensure adequate angular spacing to maintain >60% Fourier overlap between adjacent LEDs
  • Use embedded pupil recovery to jointly estimate and correct aberrations
  • Normalize LED intensities with a blank-sample calibration acquisition
  • Stabilize the setup mechanically; use fast cameras to minimize inter-frame drift

Forward-Model Mismatch Cases

  • The widefield fallback produces a single (64,64) image, but FPM acquires 25+ images from different LED illumination angles — output shape (25,16,16) captures distinct spatial-frequency bands for each angle
  • FPM is fundamentally nonlinear (intensity = |F^-1{P * F{O * exp(i*k_led*r)}}|^2) — the widefield linear blur cannot model the coherent pupil filtering and phase recovery that enables synthetic aperture

How to Correct the Mismatch

  • Use the FPM operator that generates one low-resolution intensity image per LED angle, each capturing a different region of the sample's Fourier spectrum shifted by the illumination wavevector
  • Reconstruct using alternating projection (Gerchberg-Saxton in Fourier space) or embedded pupil recovery, which require the correct coherent forward model with known LED positions

Experimental Setup — Signal Chain

Experimental setup diagram for Fourier Ptychographic Microscopy

Experimental Setup

Instrument: Custom FPM setup / 4f relay with LED array
Objective: Plan 4x / 0.13 NA (low-power, large FOV)
Synthetic Na: 0.5
Led Array: 15x15 (225 LEDs) programmable matrix
Num Images: 225
Pixel Size Um: 1.56
Wavelength Nm: 530
Illumination Na Max: 0.36
Detector: Thorlabs CS895MU monochrome CMOS
Reconstruction: sequential phase retrieval / DPC

Key References

  • Zheng et al., 'Wide-field, high-resolution Fourier ptychographic microscopy', Nature Photonics 7, 739-745 (2013)
  • Tian & Waller, 'Quantitative differential phase contrast imaging in an LED array microscope', Optics Express 23, 11394-11403 (2015)

Canonical Datasets

  • Zheng lab FPM datasets (UCONN)
  • Waller lab FPM benchmark data (Berkeley)

Spec DAG — Forward Model Pipeline

S(LED array) → C(PSF_NA) → Σ_θ → D(g, η₁)

S LED Array Illumination (LED)
C Low-NA PSF (PSF_NA)
Σ Angular Sum (θ)
D Camera (g, η₁)

Mismatch Parameters

Symbol Parameter Description Nominal Perturbed
Δr_LED led_position LED position error (mm) 0 0.1
ΔNA na_error Numerical aperture error 0.1 0.105
Δz defocus Defocus error (μm) 0 2.0

Credits System

40%
Platform Profit Pool
Revenue allocated to benchmark rewards
30%
Winner Share
Top algorithm receives from pool
$100
Min Withdrawal
Minimum payout threshold
Spec Primitives Reference (11 primitives)
P Propagation

Free-space or medium propagation kernel (Fresnel, Rayleigh-Sommerfeld).

M Mask / Modulation

Spatial or spatio-temporal amplitude modulation (coded aperture, SLM pattern).

Π Projection

Geometric projection operator (Radon transform, fan-beam, cone-beam).

F Fourier Sampling

Sampling in the Fourier / k-space domain (MRI, ptychography).

C Convolution

Shift-invariant convolution with a point-spread function (PSF).

Σ Summation / Integration

Summation along a physical dimension (spectral, temporal, angular).

D Detector

Sensor readout with gain g and noise model η (Gaussian, Poisson, mixed).

S Structured Illumination

Patterned illumination (block, Hadamard, random) applied to the scene.

W Wavelength Dispersion

Spectral dispersion element (prism, grating) with shift α and aperture a.

R Rotation / Motion

Sample or gantry rotation (CT, electron tomography).

Λ Wavelength Selection

Spectral filter or monochromator selecting a wavelength band.