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Pulse retrieval

The engine can turn a FROG or d-scan trace back into a pulse, and use the retrieved pulse as the input of a run -- so a measured pulse can be propagated through a system, or a simulated measurement checked against what an instrument would let you recover.

method trace algorithm
pcgpa SHG-, PG-, SD-FROG, XFROG principal-component generalised projections (Kane 1999): project on the measured magnitudes, rebuild the outer product, one power iteration per step
epie SHG-, PG-, SD-FROG, XFROG ptychographic iterative engine adapted to FROG (Sidorenko et al. 2016): delays in random order, object and gate updated. Stochastic: it stops at a trace error of about 1e-3 and the retrieved duration scatters by about 2 % rms (rare tails to 15 % in tests over 20 seeds), so use PCGPA when the trace is clean and ePIE for noisy traces, and compare several seeds
dscan SHG d-scan (glass insertion or GDD) the measured fundamental spectrum is kept; the spectral phase (a spline through nodes points) is fitted by Levenberg-Marquardt, with a per-column calibration of the SHG detection eliminated

| multiFrog (doubleFrog) | several FROG traces sharing unknown pulses | all traces together (below) |

All use exactly the forward models of the engine's frog, xfrog and dscan instruments.

Trace kinds

kind gate notes
shg-frog E(t) E(t - tau) symmetric in the delay; the direction of time (sign of the chirp) is ambiguous
pg-frog `E(t) E(t - tau)
sd-frog E(t)^2 E*(t - tau) self-diffraction; no ambiguity; PCGPA takes E from the right singular vector (the probe is E*)
xfrog E(t) R(t - tau), R known sum-frequency (SFG) cross-correlation FROG; the reference fixes the time origin and the direction; PCGPA is the least-squares step `E = O R* / sum

The kind is never guessed silently. It comes from (1) the kind argument, (2) a "kind" key in a JSON / dict trace, (3) the instrument that made the trace (frogType; TraceData.FromInstrument, and summary.json next to a result.npz). If none is available the retrieval assumes shg-frog only when the trace is symmetric in the delay (as every SHG trace is) and says so in its notes; an asymmetric trace stops with an error asking for the kind. Naming shg-frog for an asymmetric trace adds a warning note. An XFROG trace needs its reference (reference_time_s, reference_field_re, reference_field_im, reference_omega_rad_s): the xfrog instrument's arrays carry it.

Command line

ultrafast retrieve pcgpa trace.npz -o retrieved            # FROG: delay_s, omega_rad_s (or wavelength_m), trace
ultrafast retrieve dscan dscan.npz --fundamental spectrum.csv --material FusedSilica -o retrieved

The trace file is an NPZ or JSON with the row axis (delay_s, insertion_m or gdd_s2), the column axis (omega_rad_s or wavelength_m, signal frequencies) and trace (2-D, rows x columns). A results folder's result.npz works directly (the instrument's arrays are found by suffix). The output folder gets:

  • retrieved_spectrum.csv -- wavelength (nm), intensity, phase: use it as a run-spec pulse ("pulse": {"shape": "spectrum", "spectrum": {"csv": "retrieved/retrieved_spectrum.csv"}, "energyJ": ...});
  • retrieval.json (error, iterations, FWHM, notes, and a ready-to-paste pulse object);
  • retrieval.npz (field, spectrum, measured and retrieved traces, error history).

Python

res = uf.run(system, spec_with_frog)          # or a measured trace
out = uf.retrieve("pcgpa", {"delay_s": res["frog_delay_s"], "omega_rad_s": res["frog_omega_rad_s"], "trace": res["frog_trace"]})
out["error"], out["fwhmS"]
spec2 = b.run_spec(out["pulse"])              # the retrieved pulse as an input

Multi-trace retrieval

Traces that share unknown pulses are retrieved together (Kida et al., Opt. Express 22, 3004 (2014), "double FROG"): the SHG-FROG of a reference pulse, the SHG-FROG of a test pulse, and the XFROG trace of the test pulse gated by the reference. Each SHG trace alone leaves the time direction of its pulse open; the XFROG trace ties them, and the two SHG traces remove the common twin.

out = uf.retrieve_multi([
    {"trace": ref_shg,  "kind": "shg-frog", "pulse": "ref"},
    {"trace": test_shg, "kind": "shg-frog", "pulse": "test"},
    {"trace": xfrog,    "kind": "xfrog",    "pulse": "test", "gate": "ref"},   # gate: the unknown pulse that gates it
], maxIterations=600)
out["pulses"]["test"]["pulse"], out["traceErrors"]

Every pulse has its own carrier (fixed by an SHG / PG / SD trace; otherwise give carriersRadS in the options). All pulses live on one grid (points, dtS); in every sweep each trace projects onto its measured magnitudes and updates its pulses (SHG / PG / SD: the PCGPA step; XFROG: least squares for the test pulse with the gate fixed, then for the gate with the test pulse fixed). The JSON command is {"command": "retrieve", "method": "multiFrog", "traces": [...], "options": {...}}; C#: MultiTraceRetrieval.Run(terms, options). An XFROG term without gate uses the reference stored in its trace as a known gate. Tested on six random starts for both pulses (MultiTraceRetrievalTests).

Wavefront from two intensities: Gerchberg-Saxton

A beam's phase from its near-field and far-field intensities (Gerchberg & Saxton, Optik 35, 237 (1972)):

ultrafast retrieve gerchbergSaxton pair.npz -o phase

pair.npz holds near, far (intensities, [x][y], even numbers of pixels), x_m, y_m. The far image must be centred and on the conjugate grid of the near field: far pixel = λ f / (N dx). Plain error reduction stalls in local minima, so the method starts from a flat phase and from restarts (12) seeded smooth random phases, and continues the best for iterations (500) (options, Python: uf.retrieve("gerchbergSaxton", "pair.npz", output="phase", restarts=12)). phase/phase.npz (x_m, y_m, amplitude, phase_rad) is ready for initialProfile kind measured or a mask of kind file. The piston is undetermined, and a symmetric near field cannot tell φ(x, y) from −φ(−x, −y): check the far-field error (farFieldError) and use an asymmetric near field where you can. Checked on a known phase (far-field error < 1 %, rms phase error < 0.1 rad, FieldToolsTests).

C#

var trace = TraceData.FromInstrument(result, "frog");          // or TraceData.Load("trace.npz", "shg-frog")
var r = Retrievals.Run("epie", trace, new JsonObject().Set("maxIterations", 200));
var pulse = r.ToPulseJson(energyJ: 1e-6);

Options: points (FROG grid, default the next power of two ≥ the delay count, ≤ 512), maxIterations, tolerance, seed; ePIE stepSize; d-scan nodes (16), points (2048).

What to expect

  • The FROG error G is the rms difference of the normalised traces on the retrieval grid; below ~5·10⁻³ on clean data.
  • SHG-FROG cannot tell E(t) from E*(-t): the sign of the spectral phase (the direction of the chirp) is ambiguous. PG-FROG and d-scan are not.
  • d-scan needs the fundamental spectrum (the measured spectrum, or FundamentalOmega / FundamentalIntensity in code).

Your own algorithm

Implement UltrafastEngine.Retrieval.IRetrieval and register it (Retrievals.Register, or a plugin's ctx.RegisterRetrieval(...)); it is then available by name in the CLI, the C API and Python.

Tests: FrogKindsTests (PG / SD / XFROG trace tilt against the analytic slopes, retrieval of a chirped pulse with the sign, kind inference), MultiTraceRetrievalTests, RetrievalTests (PCGPA and ePIE on a chirped pulse: error, duration, |GDD|; d-scan: GDD with its sign, duration, and the retrieved field reused as a run input).