ZScope

Publication-Grade Electrochemical Impedance Spectroscopy Platform

       

Story · Capabilities · Workflow · Benchmarks · Applications · Installation · Citation

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🔬 The Story Behind ZScope

ZScope was not designed in the abstract. The idea for ZScope was born in the laboratory during my own experimental work.

During an electrochemical study, I needed to capture a baseline EIS spectrum at the start of a reaction — then measure six more spectra at different oxidation states as the reaction progressed. Each spectrum represented a distinct state of the system, and together they told the story of a mechanism evolving in time.

The analysis became a frustration. Working through seven spectra with existing tools was slow, disjointed, and offered no intuitive sense of how parameters evolved across the series. There was no way to interactively explore the relationship between circuit components and spectrum shape — to build the physical intuition that makes EIS meaningful.

I kept thinking: what if I could draw a circuit, move a slider, and watch the simulated Nyquist plot respond in real time — overlaid on my experimental data? Not as a fitter, but as a lens for understanding. A way to arrive at a physically motivated starting point before handing off to a numerical optimizer.

That idea became the first version of ZScope.

As the tool took shape, it grew. The fitting engine followed — built with the same insistence on reliability and physical transparency. Then Bayesian uncertainty quantification, because a parameter without an honest uncertainty estimate has limited scientific value. Then data validation, custom components, automatic circuit suggestion, and structured reporting.

ZScope is the tool I needed during that experiment. It is free, and I hope it gives other researchers something better than what was available to me.

Distribution: ZScope is released as a ready-to-install application for Windows. Source code is not publicly distributed. Full scientific documentation, validation benchmarks, and an in-app help manual are provided so you can trust what happens inside.

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⚡ Key Capabilities

🖥️ Real-Time Interactive Simulation The feature that started it all. Draw an equivalent circuit on the visual canvas, set your parameters, and the Nyquist, Bode, and Phase plots update instantly — with your experimental data overlaid. Adjusting R_ct, CPE exponent, or Warburg coefficient by hand and watching the spectrum respond builds the kind of physical intuition no black-box fitter can provide. Drag-and-drop canvas with grid snapping Presets: Randles, Randles+Warburg, CPE variants, inductive loops, battery (FLW), Gerischer Save your own circuits to a personal library Circuit notation input/output (Rs-[Rct/Cdl]-W)	📥 Flexible Data Import Import EIS data without fighting file formats. ZScope auto-detects column assignments, cross-validates Re/Im vs Mag/Phase representations, and handles sign convention differences between instruments. Auto-detection and consistency cross-check of column pairs Sign convention toggle for different potentiostats Row-level filtering: exclude drift, artefacts, or outliers while keeping them visible Frequency sub-band restriction for fitting
✅ Kramers–Kronig Validation Before fitting any parameters, confirm your data is worth fitting. ZScope implements the linear KK test with quantitative residual mapping. Residual Status Action < 0.5% ✅ Valid Proceed 0.5–2% ⚠️ Minor drift Narrow frequency range > 2% ❌ Violation Repeat measurement One keystroke (Ctrl+K), < 2 second result.	🎯 Advanced Fitting Engine A three-stage hybrid optimizer designed to find the true global minimum, not just the nearest local one: LHS — Latin Hypercube Sampling for space-filling parameter coverage DE — Differential Evolution for multimodal landscapes TRF — Trust-Region Reflective for gradient-precise local refinement $$\chi^2 = \sum_{k} \frac{(Z'_k - \hat{Z}'_k)^2 + (Z''_k - \hat{Z}''_k)^2}{|Z_k|^2}$$ Modulus weighting · Soft-L1 robust loss · AIC/BIC model selection · Warm-start for series measurements (60–80% speed gain)
📊 Bayesian MCMC Uncertainty A single point estimate is not enough. ZScope uses the emcee affine-invariant ensemble sampler to map the full posterior distribution P(θ | Z_exp): 95% credible intervals — probability-direct, not frequentist approximations Marginal and joint posterior distributions Parameter correlation and covariance analysis Convergence diagnostics: R̂ (Gelman–Rubin) + autocorrelation time Predictive uncertainty bands from 300 posterior draws	🔧 Extensible Element Library Element Physical Meaning R, C, L Resistance, capacitance, inductance CPE Surface roughness / inhomogeneity W (Warburg) Semi-infinite diffusion FLW / FSW Finite diffusion (permeable/blocking) Gerischer Diffusion + chemical reaction Transmission line Porous electrode models Custom Any Z(ω) or Y(ω) expression Custom elements are defined through a GUI designer, exported as .json, and behave identically to built-ins in all fitting and simulation contexts — no coding required.

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🗺️ Recommended Workflow

  Load Data  ──▶  KK Validate  ──▶  Build Circuit  ──▶  Fit  ──▶  MCMC  ──▶  Export
      │                │                  │               │          │           │
  auto-detect      < 2 seconds       real-time sim    DE+LHS+TRF  posterior  txt/csv/
  column format    residual map      overlay data     warm-start   credible   json/PDF

1. Import — ZScope detects column format, cross-validates consistency, and lets you filter rows before any calculation
2. Validate (Ctrl+K) — Confirm linearity and stationarity; investigate flagged frequency regions
3. Build your circuit — Draw on canvas, choose a preset, or request an algorithmic suggestion based on spectral fingerprinting
4. Fit — Configure weighting, loss function, restarts, and frequency band; run the optimizer
5. Quantify uncertainty — Run Bayesian MCMC for full posteriors, credible intervals, and convergence diagnostics
6. Export — Publication-ready figures (PNG/SVG/PDF), parameter tables, and structured reports

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📈 Validation & Benchmarks

Validated on synthetic data with known ground-truth parameters. Four circuits × three noise levels = 12 test cases. All 12 converged successfully.

Circuit	Noise	Accuracy
Randles	0%	Relative error < 10⁻¹² % — machine precision
Randles + Warburg	2%	RMSE 1.68–1.74% · max individual error 1.22%
CPE Randles	5%	Recovery within noise level · Q–α correlation correctly identified
Two-Time-Constants	5%	Recovery within noise level

The Q–α correlation in the CPE case is not a software deficiency — it reflects a genuine physical interdependence in CPE parameterization. ZScope correctly detects and reports it.

All benchmark data, comparison tables, and analysis scripts are in benchmarks/ for independent verification.

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🔭 Scientific Applications

Domain	Typical Use
Battery Science	SEI/CEI characterization · charge-transfer kinetics · Li-ion diffusion · state-of-health monitoring
Photovoltaics	Recombination dynamics · ion migration · hysteresis · capacitance spectroscopy
Corrosion Science	Polarization resistance · coating integrity · inhibitor screening · lifetime prediction
Fuel Cells & Electrolyzers	Ohmic · kinetic · mass-transport deconvolution in PEM, AEM, and solid-oxide systems
Supercapacitors	Double-layer behaviour · faradaic contributions · porous electrode transmission-line analysis
Bioelectrochemistry	Redox probe kinetics · biosensor interfacial impedance · biomolecular binding
Mechanistic Studies	Multi-state or time-series EIS — the exact scenario ZScope was designed for

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🆚 Why ZScope?

Capability	Commercial Tools	Academic Scripts	ZScope
Real-time interactive simulation	Rarely	✗	✅ Instantaneous
Bayesian MCMC posteriors	Rarely	Manual	✅ Full emcee engine
Kramers–Kronig validation	Limited	Manual	✅ Integrated + residual maps
Global optimization (DE+LHS)	✗ local only	Variable	✅ Three-stage hybrid
Algorithmic circuit suggestion	Uncommon	✗	✅ Spectral fingerprinting
Custom elements (no coding)	Restricted	Script-level	✅ GUI designer
Sequential warm-start fitting	Rarely	Manual	✅ Automatic
Structured export (txt/csv/json/PDF)	Partial	Manual	✅ Full
Cost	💰 Annual license	Free	✅ Free

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💾 Installation

Windows — Standalone Installer

⬇ Download Latest Release

No Python. No package manager. No dependencies. Download, run the installer, open ZScope.

macOS and Linux support are planned. If you work on those platforms, please open an issue — user demand shapes the roadmap.

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📖 Citation

If ZScope contributes to published research, please cite it so others can find it:

@software{zscope2026,
  author  = {Mohammadi, Tecush},
  title   = {ZScope: Publication-Grade Electrochemical Impedance Spectroscopy Analysis Platform},
  year    = {2026},
  url     = {https://github.com/Tecush/ZScope}
}

DOI:

📬 Contact

Developer: Tecush Mohammadi Email: tecush@gmail.com GitHub: @Tecush Issues & feature requests: GitHub Issues

Questions about scientific methods, specific use cases, or validation data are welcome by email.

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Built from a real experiment, for real researchers. Because good science deserves better tools.