30:T972,function createFFTUtils(fftInstance) { function fft2d(interleaved, nx, ny) { const rows = []; for (let i = 0; i < nx; i++) { rows.push(interleaved.slice(2 * i * ny, 2 * (i + 1) * ny)); } const out = fftInstance.fft2d(rows); const result = new Float32Array(2 * nx * ny); for (let i = 0; i < nx; i++) result.set(out[i], 2 * i * ny); return result; } function ifft2d(interleaved, nx, ny) { const n = nx * ny; const conj = new Float32Array(2 * n); for (let i = 0; i < n; i++) { conj[2 * i] = interleaved[2 * i]; conj[2 * i + 1] = -interleaved[2 * i + 1]; } const result = fft2d(conj, nx, ny); for (let i = 0; i < n; i++) { result[2 * i] = result[2 * i] / n; result[2 * i + 1] = -result[2 * i + 1] / n; } return result; } // applies phase ramp in-place to a Fourier-space array function applyPhaseRamp(spectrum, nx, ny, dx, dy) { const kx = fftfreq(nx, 1); const ky = fftfreq(ny, 1); const rampX = new Float32Array(2 * nx); const rampY = new Float32Array(2 * ny); for (let i = 0; i < nx; i++) { const phase = -2 * Math.PI * kx[i] * dx; rampX[2 * i] = Math.cos(phase); rampX[2 * i + 1] = Math.sin(phase); } for (let j = 0; j < ny; j++) { const phase = -2 * Math.PI * ky[j] * dy; rampY[2 * j] = Math.cos(phase); rampY[2 * j + 1] = Math.sin(phase); } for (let i = 0; i < nx; i++) { const xre = rampX[2 * i], xim = rampX[2 * i + 1]; for (let j = 0; j < ny; j++) { const yre = rampY[2 * j], yim = rampY[2 * j + 1]; const cre = xre * yre - xim * yim; const cim = xre * yim + xim * yre; const idx = 2 * (i * ny + j); const re = spectrum[idx], im = spectrum[idx + 1]; spectrum[idx] = re * cre - im * cim; spectrum[idx + 1] = re * cim + im * cre; } } return spectrum; } // fourierShift: input/output space controlled by { inputFS, outputFS } function fourierShift( interleaved, nx, ny, dx, dy, { inputFS = false, outputFS = false } = {} ) { const spectrum = inputFS ? new Float32Array(interleaved) : fft2d(interleaved, nx, ny); applyPhaseRamp(spectrum, nx, ny, dx, dy); return outputFS ? spectrum : ifft2d(spectrum, nx, ny); } return { fft2d, ifft2d, applyPhaseRamp, fourierShift }; }31:T6a6,function aberrationSurface(alpha, phi, wavelength, aberrationCoefs = {}) { const n = alpha.length; const chi = new Float32Array(n); const prefactor = (2 * Math.PI) / wavelength; const get = (name) => aberrationCoefs[name] ?? 0.0; const has = (...keys) => keys.some((k) => k in aberrationCoefs); for (let i = 0; i < n; i++) { const a = alpha[i]; const p = phi[i]; const a2 = a * a; const a3 = a * a2; const a4 = a2 * a2; const a5 = a2 * a3; const a6 = a3 * a3; let c = 0; if (has("C10", "C12", "phi12")) c += 0.5 * a2 * (get("C10") + get("C12") * Math.cos(2 * (p - get("phi12")))); if (has("C21", "phi21", "C23", "phi23")) c += (1 / 3) * a3 * (get("C21") * Math.cos(p - get("phi21")) + get("C23") * Math.cos(3 * (p - get("phi23")))); if (has("C30", "C32", "phi32", "C34", "phi34")) c += (1 / 4) * a4 * (get("C30") + get("C32") * Math.cos(2 * (p - get("phi32"))) + get("C34") * Math.cos(4 * (p - get("phi34")))); if (has("C41", "phi41", "C43", "phi43", "C45", "phi45")) c += (1 / 5) * a5 * (get("C41") * Math.cos(p - get("phi41")) + get("C43") * Math.cos(3 * (p - get("phi43"))) + get("C45") * Math.cos(5 * (p - get("phi45")))); if (has("C50", "C52", "phi52", "C54", "phi54", "C56", "phi56")) c += (1 / 6) * a6 * (get("C50") + get("C52") * Math.cos(2 * (p - get("phi52"))) + get("C54") * Math.cos(4 * (p - get("phi54"))) + get("C56") * Math.cos(6 * (p - get("phi56")))); chi[i] = c * prefactor; } return chi; }32:T5d4,function drawScalebar(ctx, plotWidth, plotHeight, width, scalebar) { const { sampling = 1, units = "px", length = null, color = "white", loc = "lower right" } = scalebar; const pad = 10; const barHeight = 3; const fontSize = 11; const { lengthUnits, lengthPx: lengthPxRaw } = length !== null ? { lengthUnits: length, lengthPx: length / sampling } : estimateScalebarLength(width, sampling); // scale bar length in display pixels const lengthDisplay = (lengthPxRaw / width) * plotWidth; const label = lengthUnits % 1 === 0 ? `${lengthUnits.toFixed(0)} ${units}` : `${lengthUnits.toFixed(2)} ${units}`; ctx.font = `${fontSize}px sans-serif`; const textW = ctx.measureText(label).width; const blockW = Math.max(lengthDisplay, textW); const isBottom = !loc.includes("upper"); const isRight = !loc.includes("left"); const x = isRight ? plotWidth - pad - blockW : pad; const y = isBottom ? plotHeight - pad - barHeight - fontSize - 2 : pad + fontSize + 2; const barX = x + (blockW - lengthDisplay) / 2; // bar ctx.fillStyle = color; ctx.fillRect(barX, y + fontSize + 2, lengthDisplay, barHeight); // label — above bar if upper, below if lower ctx.fillStyle = color; ctx.textAlign = "center"; ctx.textBaseline = isBottom ? "bottom" : "top"; ctx.fillText(label, barX + lengthDisplay / 2, isBottom ? y + fontSize : y); ctx.textAlign = "left"; ctx.textBaseline = "alphabetic"; }33:T12e5,function show2d({ data, width, height, complex = false, chromaBoost = 1, plotWidth = 512, plotHeight = 512, label = "", colormap = null, showTooltip = false, onHover = null, scalebar = null // e.g. { sampling: 0.1, units: "Å", loc: "lower right" } }) { // --- compute RGBA --- const n = width * height; const rgba = new Uint8ClampedArray(4 * n); if (complex) { const { amplitude, angle } = complexToAmplitudeAngle(data, { normalize: true }); for (let i = 0; i < n; i++) { const L = amplitude[i] * 0.75; const C = chromaBoost * 0.15 * amplitude[i]; const h = (angle[i] * 180) / Math.PI + 180; const [r, g, b] = oklch_to_sRGB(L, C, h); rgba[4 * i] = Math.round(Math.max(0, Math.min(1, r)) * 255); rgba[4 * i + 1] = Math.round(Math.max(0, Math.min(1, g)) * 255); rgba[4 * i + 2] = Math.round(Math.max(0, Math.min(1, b)) * 255); rgba[4 * i + 3] = 255; } } else { let minV = Infinity, maxV = -Infinity; for (let i = 0; i < n; i++) { if (data[i] < minV) minV = data[i]; if (data[i] > maxV) maxV = data[i]; } const range = maxV - minV || 1; const cm = colormap ?? ((v) => [v, v, v]); for (let i = 0; i < n; i++) { const v = (data[i] - minV) / range; const [r, g, b] = cm(v); rgba[4 * i] = Math.round(Math.max(0, Math.min(1, r)) * 255); rgba[4 * i + 1] = Math.round(Math.max(0, Math.min(1, g)) * 255); rgba[4 * i + 2] = Math.round(Math.max(0, Math.min(1, b)) * 255); rgba[4 * i + 3] = 255; } } // --- build canvas --- const offscreen = new OffscreenCanvas(width, height); offscreen .getContext("2d") .putImageData(new ImageData(rgba, width, height), 0, 0); const canvas = DOM.canvas(plotWidth, plotHeight); const ctx = canvas.getContext("2d"); ctx.imageSmoothingEnabled = false; ctx.drawImage(offscreen, 0, 0, plotWidth, plotHeight); // --- border --- ctx.strokeStyle = "white"; ctx.lineWidth = 1; ctx.strokeRect(0, 0, plotWidth, plotHeight); // --- label (top left) --- if (label) { ctx.fillStyle = "white"; ctx.font = "13px sans-serif"; ctx.fillText(label, 10, 20); } // after drawing the border and label in ctx: if (showTooltip || onHover) { ctx.fillStyle = "rgba(255,255,255,0.75)"; ctx.font = "11px sans-serif"; ctx.fillText("click to toggle hover", 10, plotHeight - 10); } // --- scalebar --- if (scalebar) drawScalebar(ctx, plotWidth, plotHeight, width, scalebar); canvas.style.cursor = showTooltip || onHover ? "crosshair" : "default"; canvas.style.display = "block"; const container = Object.assign(document.createElement("div"), { style: "position: relative; display: inline-block;" }); container.append(canvas); // --- hover --- if (showTooltip || onHover) { let hoverEnabled = true; // click to toggle canvas.addEventListener("click", () => { hoverEnabled = !hoverEnabled; canvas.style.cursor = hoverEnabled ? "crosshair" : "default"; if (!hoverEnabled) tooltip.style.display = "none"; }); const tooltip = Object.assign(document.createElement("div"), { style: ` position: absolute; pointer-events: none; background: rgba(0,0,0,0.7); color: white; font: 12px monospace; padding: 3px 7px; border-radius: 4px; display: none; white-space: nowrap; ` }); container.append(tooltip); canvas.addEventListener("pointermove", (event) => { if (!hoverEnabled) return; const rect = canvas.getBoundingClientRect(); const fx = (event.clientX - rect.left) / rect.width; const fy = (event.clientY - rect.top) / rect.height; if (fx < 0 || fx > 1 || fy < 0 || fy > 1) return; const ix = Math.floor(fx * width); const iy = Math.floor(fy * height); const idx = iy * width + ix; const value = complex ? { re: data[2 * idx], im: data[2 * idx + 1], amp: Math.sqrt(data[2 * idx] ** 2 + data[2 * idx + 1] ** 2) } : data[idx]; if (showTooltip) { const valStr = complex ? `amp: ${value.amp.toExponential(3)}` : `val: ${value.toExponential(3)}`; tooltip.textContent = `[${ix}, ${iy}] ${valStr}`; tooltip.style.display = "block"; const tx = event.clientX - rect.left; const ty = event.clientY - rect.top; tooltip.style.left = tx > plotWidth * 0.75 ? `${tx - tooltip.offsetWidth - 8}px` : `${tx + 12}px`; tooltip.style.top = `${ty - 28}px`; } if (onHover) onHover({ x: fx, y: fy, ix, iy, value }); }); canvas.addEventListener("pointerleave", () => { tooltip.style.display = "none"; }); } return container; }34:[] 2e:{"title":"Utilities for Electron Microscopy Numerical Computing","cells":[{"id":0,"value":"# Utilities for Electron Microscopy Numerical Computing","pinned":false,"hidden":false,"mode":"md"},{"id":12,"value":"## FFT utilities","pinned":false,"hidden":false,"mode":"md"},{"id":5,"value":"function fftfreq(n, d) {\n // returns Float32Array of fft frequencies, equiv to np.fft.fftfreq\n const f = new Float32Array(n);\n const val = 1.0 / (n * d);\n const half = Math.floor(n / 2);\n for (let i = 0; i <= half; i++) f[i] = i * val;\n for (let i = half + 1; i < n; i++) f[i] = (i - n) * val;\n return f;\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":38,"value":"function fftshift2d(data, nx, ny) {\n const hn = Math.floor(nx / 2);\n const hn2 = Math.floor(ny / 2);\n const out = new Float32Array(data.length);\n for (let i = 0; i < nx; i++) {\n const si = (i + hn) % nx;\n const srcRight = 2 * (i * ny + hn2);\n const dstLeft = 2 * (si * ny);\n out.set(data.subarray(srcRight, srcRight + 2 * hn2), dstLeft);\n const srcLeft = 2 * (i * ny);\n const dstRight = 2 * (si * ny + hn2);\n out.set(data.subarray(srcLeft, srcLeft + 2 * hn2), dstRight);\n }\n return out;\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":16,"value":"$30","pinned":false,"hidden":false,"mode":"ojs"},{"id":43,"value":"## STEM probe utilities","pinned":false,"hidden":false,"mode":"md"},{"id":52,"value":"function electronWavelength(energy) {\n const m = 9.109383e-31;\n const e = 1.602177e-19;\n const c = 299792458;\n const h = 6.62607e-34;\n return (\n (h /\n Math.sqrt(2 * m * e * energy) /\n Math.sqrt(1 + (e * energy) / (2 * m * c * c))) *\n 1e10\n );\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":45,"value":"function spatialFrequencies(gpts, sampling) {\n const kx = fftfreq(gpts[0], sampling[0]);\n const ky = fftfreq(gpts[1], sampling[1]);\n const nx = gpts[0],\n ny = gpts[1];\n const kxa = new Float32Array(nx * ny);\n const kya = new Float32Array(nx * ny);\n for (let i = 0; i < nx; i++) {\n for (let j = 0; j < ny; j++) {\n kxa[i * ny + j] = kx[i];\n kya[i * ny + j] = ky[j];\n }\n }\n return { kxa, kya };\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":48,"value":"function polarCoordinates(kxa, kya) {\n const n = kxa.length;\n const k = new Float32Array(n);\n const phi = new Float32Array(n);\n for (let i = 0; i < n; i++) {\n k[i] = Math.sqrt(kxa[i] ** 2 + kya[i] ** 2);\n phi[i] = Math.atan2(kya[i], kxa[i]);\n }\n return { k, phi };\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":50,"value":"function scatteringAngles(k, phi, wavelength) {\n const alpha = new Float32Array(k.length);\n for (let i = 0; i < k.length; i++) alpha[i] = k[i] * wavelength;\n return { alpha, phi };\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":58,"value":"$31","pinned":false,"hidden":false,"mode":"ojs"},{"id":60,"value":"function softApertureFunction(alpha, phi, semiangle_cutoff, angularSampling) {\n const semirad = semiangle_cutoff * 1e-3;\n const n = alpha.length;\n const aperture = new Float32Array(n);\n for (let i = 0; i < n; i++) {\n const denom = Math.sqrt(\n (Math.cos(phi[i]) * angularSampling[0] * 1e-3) ** 2 +\n (Math.sin(phi[i]) * angularSampling[1] * 1e-3) ** 2\n );\n aperture[i] = Math.min(1, Math.max(0, (semirad - alpha[i]) / denom + 0.5));\n }\n return aperture;\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":62,"value":"function hardApertureFunction(alpha, semiangle_cutoff) {\n const semirad = semiangle_cutoff * 1e-3;\n const aperture = new Float32Array(alpha.length);\n for (let i = 0; i < alpha.length; i++)\n aperture[i] = alpha[i] < semirad ? 1 : 0;\n return aperture;\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":64,"value":"function apertureFunction(\n alpha,\n phi,\n semiangle_cutoff,\n angularSampling,\n { soft = true } = {}\n) {\n if (!soft) {\n const semirad = semiangle_cutoff * 1e-3;\n const aperture = new Float32Array(alpha.length);\n for (let i = 0; i < alpha.length; i++)\n aperture[i] = alpha[i] < semirad ? 1 : 0;\n return aperture;\n }\n const semirad = semiangle_cutoff * 1e-3;\n const n = alpha.length;\n const aperture = new Float32Array(n);\n for (let i = 0; i < n; i++) {\n const denom = Math.sqrt(\n (Math.cos(phi[i]) * angularSampling[0] * 1e-3) ** 2 +\n (Math.sin(phi[i]) * angularSampling[1] * 1e-3) ** 2\n );\n aperture[i] = Math.min(1, Math.max(0, (semirad - alpha[i]) / denom + 0.5));\n }\n return aperture;\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":70,"value":"function probeFourierSpace(\n alpha,\n phi,\n wavelength,\n semiangleCutoff,\n angularSampling,\n aberrationCoefs = {},\n { soft = true } = {}\n) {\n const aperture = apertureFunction(\n alpha,\n phi,\n semiangleCutoff,\n angularSampling,\n { soft }\n );\n const chi = aberrationSurface(alpha, phi, wavelength, aberrationCoefs);\n const n = alpha.length;\n const interleaved = new Float32Array(2 * n);\n for (let i = 0; i < n; i++) {\n interleaved[2 * i] = aperture[i] * Math.cos(chi[i]);\n interleaved[2 * i + 1] = -aperture[i] * Math.sin(chi[i]);\n }\n return interleaved;\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":75,"value":"## Plotting utilities","pinned":false,"hidden":false,"mode":"md"},{"id":77,"value":"function oklch_to_sRGB(L, C, h_deg) {\n // Oklch -> Oklab\n const h = (h_deg * Math.PI) / 180;\n const a = C * Math.cos(h);\n const b = C * Math.sin(h);\n\n // Oklab -> linear sRGB (single matrix multiplication)\n const l_ = L + 0.3963377774 * a + 0.2158037573 * b;\n const m_ = L - 0.1055613458 * a - 0.0638541728 * b;\n const s_ = L - 0.0894841775 * a - 1.291485548 * b;\n\n const l = l_ ** 3;\n const m = m_ ** 3;\n const s = s_ ** 3;\n\n const r = 4.0767416621 * l - 3.3077115913 * m + 0.2309699292 * s;\n const g = -1.2684380046 * l + 2.6097574011 * m - 0.3413193965 * s;\n const bv = -0.0041960863 * l - 0.7034186147 * m + 1.707614701 * s;\n\n // gamma encode\n const gamma = (v) =>\n v <= 0.0031308\n ? 12.92 * v\n : 1.055 * Math.pow(Math.max(0, v), 1 / 2.4) - 0.055;\n\n return [gamma(r), gamma(g), gamma(bv)];\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":93,"value":"function complexToIntensity(interleaved, { normalize = true } = {}) {\n const n = interleaved.length / 2;\n const intensity = new Float32Array(n);\n let maxI = 0;\n\n for (let i = 0; i < n; i++) {\n intensity[i] = interleaved[2 * i] ** 2 + interleaved[2 * i + 1] ** 2;\n if (normalize && intensity[i] > maxI) maxI = intensity[i];\n }\n if (normalize && maxI > 0) for (let i = 0; i < n; i++) intensity[i] /= maxI;\n return intensity;\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":96,"value":"function complexToAmplitudeAngle(interleaved, { normalize = true } = {}) {\n const n = interleaved.length / 2;\n const amplitude = new Float32Array(n);\n const angle = new Float32Array(n);\n let maxA = 0;\n for (let i = 0; i < n; i++) {\n const re = interleaved[2 * i],\n im = interleaved[2 * i + 1];\n amplitude[i] = Math.sqrt(re ** 2 + im ** 2);\n angle[i] = Math.atan2(im, re);\n if (amplitude[i] > maxA) maxA = amplitude[i];\n }\n if (normalize && maxA > 0) for (let i = 0; i < n; i++) amplitude[i] /= maxA;\n return { amplitude, angle };\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":109,"value":"function estimateScalebarLength(totalPixels, sampling) {\n const d = (totalPixels * sampling) / 2;\n const exp = Math.floor(Math.log10(d));\n const base = d / 10 ** exp;\n const spacing = base < 2.1 ? 0.5 : base < 4.6 ? 1.0 : 2.0;\n const lengthUnits = spacing * 10 ** exp;\n return { lengthUnits, lengthPx: lengthUnits / sampling };\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":111,"value":"$32","pinned":false,"hidden":false,"mode":"ojs"},{"id":79,"value":"$33","pinned":false,"hidden":false,"mode":"ojs"},{"id":87,"value":"function hstack({ gap = 8, minWidth = 300, maxWidth = 500 }, ...plots) {\n const div = htl.html`

`;\n\n plots.forEach((p) => div.appendChild(p));\n\n return div;\n}","pinned":false,"hidden":false,"mode":"ojs"}],"files":"$W34","stdlib":"1","titling":"auto"}