AIDT 온디바이스 STEM X선 광자 상관 분광(XPCS) 결맞는 스펙클 동역학 서보 엔진

using System;
using System.Runtime.CompilerServices;

namespace ZeliDesk.Stem.Xpcs
{
    public readonly ref struct XpcsSpeckleState
    {
        public readonly double ScatteringQInvNm;     // 산란 파수 q (1/nm)
        public readonly double RelaxationTimeTauMs;  // 완화 시상수 tau (ms)
        public readonly double DiffusionCoefficient; // 유효 확산 계수 D (10^-12 m^2/s)
        public readonly double SpeckleContrastBeta;  // 스펙클 결맞음 콘트라스트 beta
        public readonly double HydrodynamicRadiusNm; // 스토크스-아인슈타인 반경 RH (nm)
        public readonly double AutocorrelationG2;    // 현재 지연 시간 g2 값

        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public XpcsSpeckleState(double q, double tau, double diff, double beta, double rh, double g2)
        {
            ScatteringQInvNm = q;
            RelaxationTimeTauMs = tau;
            DiffusionCoefficient = diff;
            SpeckleContrastBeta = beta;
            HydrodynamicRadiusNm = rh;
            AutocorrelationG2 = g2;
        }
    }

    public ref struct XpcsCorrelatorEngine
    {
        private const double Kb = 1.380649e-23;      // J/K
        private const double SolventViscosityPaS = 1.002e-3; // 20도 물 점도 (Pa*s)

        private double _temperatureK;                // 시료 온도 (K)
        private double _speckleContrast;             // 광학 결맞음 계수 beta

        public XpcsCorrelatorEngine(double tempK = 293.15, double initBeta = 0.25)
        {
            _temperatureK = tempK;
            _speckleContrast = initBeta;
        }

        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public XpcsSpeckleState StepServo(double qInvNm, double measuredG2At10Ms, double dtSec)
        {
            double safeQ = Math.Max(qInvNm, 0.005);

            // 1. Siegert 관계식으로부터 1차 상관값 역산
            // g2 = 1 + beta * exp(-2 * t / tau)
            double excessG2 = Math.Clamp(measuredG2At10Ms - 1.0, 0.001, _speckleContrast);
            double fieldCorrSquared = excessG2 / _speckleContrast;
            double fieldCorr = Math.Sqrt(Math.Clamp(fieldCorrSquared, 0.0001, 1.0));

            // 2. 완화 시상수 tau (ms) 계산 (t = 10 ms 기준)
            double decayRateGamma = -Math.Log(fieldCorr) / 10.0; // 1/ms
            double tauMs = (decayRateGamma > 1e-5) ? (1.0 / decayRateGamma) : 1000.0;
            tauMs = Math.Clamp(tauMs, 0.1, 5000.0);

            // 3. 확산 계수 D = 1 / (tau * q^2) 계산 (m^2/s)
            // q in 1/nm -> 1e9 1/m, tau in ms -> 1e-3 s
            double qMeters = safeQ * 1e9;
            double tauSec = tauMs * 1e-3;
            double diffM2PerS = 1.0 / (tauSec * qMeters * qMeters);

            // 4. 스토크스-아인슈타인 유체역학적 반경 R_H (nm)
            // RH = Kb * T / (6 * pi * eta * D)
            double rhMeters = (Kb * _temperatureK) / (6.0 * Math.PI * SolventViscosityPaS * Math.Max(diffM2PerS, 1e-16));
            double rhNm = Math.Clamp(rhMeters * 1e9, 0.5, 500.0);

            return new XpcsSpeckleState(
                q: safeQ,
                tau: tauMs,
                diff: diffM2PerS * 1e12,
                beta: _speckleContrast,
                rh: rhNm,
                g2: measuredG2At10Ms
            );
        }
    }
}