원자현미경(AFM) 캔틸레버 태핑 모드 & 1,000Hz 0-Alloc C# 레너드-존스 원자간력 진폭 변조 피드백 엔진

using System;
using System.Runtime.CompilerServices;

namespace ZeliDesk.Education.StemPhysics.AtomicForceMicroscopy
{
    public readonly record struct AfmCantileverConfig(
        float ResonanceFreqKhz,     // 공진 주파수 f0 (kHz, 예: 300.0 kHz)
        float SpringConstantNPerM,  // 탄성 계수 kc (N/m, 예: 40.0 N/m)
        float QualityFactorQ,       // Q 팩터 (예: 450.0)
        float FreeAmplitudeNm,      // 자유 진폭 A0 (nm, 예: 20.0 nm)
        float AmplitudeSetpointRatio// 셋포인트 비 (예: 0.75 -> A = 15nm 유지)
    );

    public ref struct AfmScanTelemetry
    {
        public float TipSampleDistanceNm;
        public float InteratomicForceNanoNewton;
        public float CurrentAmplitudeNm;
        public float FrequencyShiftHz;
        public float PhaseShiftDeg;
        public float ZPiezoCorrectionNm;
        public float TopographyZNm;
    }

    public static class AfmCantileverEngineCore
    {
        private const float SigmaNm = 0.34f; // LJ 평형 반경 (nm)
        private const float EpsilonJ = 1.65e-21f; // LJ 퍼텐셜 깊이 (J)

        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public static void StepControlLoop(
            in AfmCantileverConfig config,
            float sampleSurfaceHeightNm,
            ref float inOutZPiezoPositionNm,
            ref AfmScanTelemetry telemetry)
        {
            // 1. 팁-샘플 유효 거리 d = Z_piezo - Z_surface (0-Alloc)
            float d = MathF.Max(0.2f, inOutZPiezoPositionNm - sampleSurfaceHeightNm);
            telemetry.TipSampleDistanceNm = d;

            // 2. 레너드-존스 원자간력 계산 (nN)
            float ratio = SigmaNm / d;
            float ratio6 = ratio * ratio * ratio * ratio * ratio * ratio;
            float ratio12 = ratio6 * ratio6;
            
            // F_ts = (24*eps/sigma) * [2*(sigma/d)^13 - (sigma/d)^7]
            float forceN = (24.0f * EpsilonJ / (SigmaNm * 1e-9f)) * (2.0f * ratio12 * ratio - ratio6 * ratio);
            float forceNn = forceN * 1e9f;
            telemetry.InteratomicForceNanoNewton = forceNn;

            // 3. 힘 구배 dF/dz 및 공진 주파수 편차 Delta f0 (Hz)
            float forceGrad = -(forceNn * 1e-9f) / (MathF.Max(0.1f, d) * 1e-9f);
            float f0Hz = config.ResonanceFreqKhz * 1000.0f;
            float deltaF = -(f0Hz / (2.0f * config.SpringConstantNPerM)) * forceGrad;
            telemetry.FrequencyShiftHz = deltaF;

            // 4. 태핑 진폭 감쇠 A 모델링
            // 표면과의 간헐적 반발로 인한 진폭 감소: A ~ A0 / sqrt(1 + (2*Q*deltaF/f0)^2)
            float x = (2.0f * config.QualityFactorQ * deltaF) / f0Hz;
            float currentAmp = config.FreeAmplitudeNm / MathF.Sqrt(1.0f + x * x);
            if (d < config.FreeAmplitudeNm)
            {
                currentAmp = MathF.Min(currentAmp, d * 0.98f);
            }
            telemetry.CurrentAmplitudeNm = currentAmp;

            // 위상 지연 각도 (deg)
            telemetry.PhaseShiftDeg = 90.0f + MathF.Atan(x) * (180.0f / MathF.PI);

            // 5. Z축 나노 압전 스테이지 PID 피드백 (0-Alloc)
            float targetAmp = config.FreeAmplitudeNm * config.AmplitudeSetpointRatio;
            float ampError = targetAmp - currentAmp; // 오차가 양수면(너무 눌렸으면) Z 상승
            
            float kP = 0.45f;
            float zStep = ampError * kP;
            inOutZPiezoPositionNm += zStep;
            telemetry.ZPiezoCorrectionNm = zStep;

            // 지형 높이 산출 (Z_piezo 위치가 샘플 형상을 정밀 추적)
            telemetry.TopographyZNm = inOutZPiezoPositionNm;
        }
    }
}