● XPS Denoising Software

Your spectra are noisier than they need to be.

Fourier-AI replaces manual smoothing guesswork with an automated, provably superior algorithm — giving you cleaner data in seconds, with full scientific transparency into every cutoff decision.

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cuval_1_scan.csv — GH Filter
CuVal 1 scan — Raw (black), GH-filtered (green), Residuals (red)
ag4s_1_scan.csv — GH Filter
Ag4s 1 scan — Raw (black), GH-filtered (green), Residuals (red)
17,000+
Citations (lead scientist)
500+
Peer-reviewed publications
2
Provisional patents filed
J. Vac. Sci.
Published methodology, 2025
Nat. Acad.
Sciences — team member
The Problem

Conventional smoothing leaks noise and damages your signal

Conventional smoothing methods — including the Savitzky-Golay and boxcar filters many labs actually use — have two problems: they leave high-frequency noise in your data, and they distort the signal information you actually care about. Any filter can remove noise by cutting the frequency low enough. The hard part is removing noise while preserving the information.

🤖

Noisy spectra break AI models

Neural networks trained on noisy XPS data can interpret the noise as signal. High-quality pre-denoised training data is much preferred for reliable AI.

Pre-denoising is table stakes for AI
⏱

Instrument time is expensive

More scans mean more time — and time on XPS instruments costs your lab real money. Noise from lower S/N spectra can often be reliably removed with the right denoising algorithm.

Every scan saved = cost recovered
☢️

Beam damage limits scan counts

Beam-sensitive samples may not be able to generate high-quality (low noise) spectra before they are damaged. Denoised spectra are often closer to the true spectra than the original noisy spectra!

Denoise fewer scans to same quality
The Solution

Built on peer-reviewed science. Patent-pending.

Fourier-AI applies a Gauss-Hermite transfer function in reciprocal space — where the physics actually lives — with fully automated software-predicted cutoff placement.

📊
Patent pending

Binary Residual Map™

A novel heatmap-like visualization tool showing the color-coded residuals across a wide range of cutoff values simultaneously. See the full picture in one plot – no competitor offers this.

🎯
Patent pending

Automated Software-Predicted Cutoff

Fourier-transformed spectra generally have a region dominated by signal and a region dominated by noise. Our algorithm automatically identifies and places the cutoff between them – no Fourier expertise required. Expert users can override and reset at any time.

〰️
Provably superior

Gauss-Hermite Filter

Flat and nearly unity at low frequencies — signal preserved, not just tolerated. Approaches zero at high frequencies — noise removed. Smooth monotonic transition that avoids signal distortion. Solves both problems conventional filters fail: noise leakage and information damage.

Process

From raw spectra to publication-ready in four steps

No Fourier expertise required. The software handles the math — you get the results.

1

Import your data

Upload CSV, TSV, VAMAS (.vms), or multi-spectrum files via drag-and-drop.

2

Fourier transform

The software computes a full sweep of Fourier cutoffs across the entire coefficient space — all at once.

3

Automated cutoff placed

The cutoff between signal-dominated and noise-dominated Fourier coefficients is placed automatically. The Binary Residual Map™ gives you full diagnostic transparency into that decision.

4

Export denoised spectra

Download publication-ready denoised data as CSV. Adjust cutoff via slider if desired — reset to software-predicted at any time.

Binary Residual Map™
Binary Residual Map — actual tool output
Neutral(+) Residuals(-) ResidualsSoftware-predicted cutoff

See every relevant cutoff at once

The Binary Residual Map™ simultaneously plots the colored signs of the residuals for every relevant Fourier cutoff. Long runs of one color mean the residuals are structured – a sign of a poor fit. The software-predicted cutoff is generally where the colors begin to mix randomly.

No competing tool visualizes denoising decisions this way. It's both a diagnostic and a teaching tool — your team can see exactly why the algorithm chose what it chose.

⚑ Provisional patent filed
Comparison

Why conventional smooths fall short

The conventional filters in common use work in direct space. They leave high-frequency noise in data and are also hard to optimize in real space, which means more noise gets left in data. In the conventional approach, one is blind to what is going on in reciprocal space, which can also lead to data distortion.

CapabilityLow-order Savitzky-Golay filtersBoxcar SmoothFourier-AI
Transfer function monotonically approaches zero at high frequencies (noise effectively removed)✗ Transfer functions oscillate in reciprocal space✗ Sinc-like response – the transfer function bounces, leaving noise✓ Gauss-Hermite monotonically drops to zero
Nearly flat response at low frequencies (signal preserved)~ Partial~ Partial✓ Flat at low frequencies
Automated software-predicted cutoff placement✗ Manual selection required✗ Manual selection required✓ Algorithm-determined, patent pending
Full-sweep diagnostic visualization of transfer function cutoffs✗ None✗ None✓ Binary Residual Map™
Preserves signal information while removing noise (no distortion)✗ Damages signal — oscillating transfer function distorts information✗ Sinc response causes ringing artifacts in signal✓ Monotonic rolloff — information preserved, noise removed
Works in reciprocal space (physics-native)✗✗✓
Peer-reviewed methodology~ Legacy literature~ Legacy literature✓ J. Vac. Sci. Technol. A, 2025
The AI Era

Clean data isn't optional anymore

  • →Neural networks trained on noisy XPS spectra learn the noise as signal — models underperform on unseen clean or even noisy data
  • →Pre-denoising XPS spectra before feeding them into ML pipelines is emerging as a requirement, not a nice-to-have
  • →High-throughput XPS imaging produces inherently noisy fast-acquisition data — denoising can be a path to usable signal
  • →Fourier-AI produces spectra measurably closer to the "true" spectra
From the white paper

“Denoised XPS spectra are demonstrably closer to the true spectra than their raw counterparts.”

J. Vac. Sci. Technol. A, 2025, 43, 033401. The methodology behind Fourier-AI is not a claim — it is a peer-reviewed finding. Also available at: ssrn.com/abstract=6614772

The Team

Built by scientists with something to prove

Fourier-AI was founded by researchers with decades of combined publishing, institutional credibility, and domain expertise.

ML

Matthew R. Linford

Chief Executive Officer

BYU professor and XPS authority. Co-inventor of the automated cutoff algorithm.

17,000+ citations500+ publicationsh-index 57
MJ

Michael P. Jones

Co-founder · Technology

BYU CS professor and former VP at multiple software companies. Leads the software architecture and AI integration for the platform.

BYU CS facultyAI expertiseSaaS veteran
DA

David E. Aspnes

Scientific Advisor

Applied physicist and noise removal specialist. Emeritus NC State professor and member of the National Academy of Sciences.

Nat. Acad. SciencesNC StateNoise theory
Access

Start with the right tier for your lab

We're working directly with early adopters to shape the product. Preferred customers receive prioritized support, feature input, and early access to new modules.

Individual

Academic Researcher

  • ✓Full denoising tool access
  • ✓CSV / TSV / VAMAS import
  • ✓Binary Residual Map™
  • ✓Export denoised spectra
⭐ Preferred Customer

Lab or Institution

  • ✓Everything in Academic
  • ✓Prioritized feature input
  • ✓Direct line to the dev team
  • ✓Early access to new modules
  • ✓D-parameter tool (coming soon)
Enterprise

Government / Defense

  • ✓Everything in Preferred
  • ✓Custom deployment options
  • ✓White-paper deliverables
  • ✓Dedicated research support
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