{ "cells": [ { "cell_type": "markdown", "id": "1902f216", "metadata": {}, "source": [ "# `harmonic_ud_grade` vs `ud_grade`: A Focused Comparison\n", "\n", "When working with HEALPix maps, it is often necessary to change the\n", "resolution — for example, to downgrade a high-resolution observation\n", "map to a lower Nside for comparison with a model, or to reduce\n", "computational cost for large-scale analyses.\n", "\n", "healpy provides two functions for this:\n", "\n", "- **`ud_grade`**: operates purely in **pixel space** by averaging\n", " groups of sub-pixels. It is fast, but because it does not apply any\n", " anti-aliasing filter, high-multipole power from the input grid\n", " \"folds\" back into the output — a phenomenon known as\n", " [aliasing](https://en.wikipedia.org/wiki/Aliasing).\n", "\n", "- **`harmonic_ud_grade`**: operates in **spherical-harmonic space**.\n", " It decomposes the input map into $a_{\\ell m}$ coefficients, applies\n", " the pixel-window correction following the prescription in\n", " [Planck 2015 XVI Eq. 1](https://arxiv.org/abs/1502.01587), and\n", " optionally scales the beam. Because the harmonic transform\n", " naturally band-limits the output, aliasing is eliminated.\n", "\n", "## How `harmonic_ud_grade` works\n", "\n", "The function implements the following per-$\\ell$ transfer\n", "([Planck 2015 XVI Eq. 1](https://arxiv.org/abs/1502.01587)):\n", "\n", "$$\n", "a^{\\rm out}_{\\ell m}\n", "= \\frac{p^{\\rm out}_\\ell}{p^{\\rm in}_\\ell}\n", " \\cdot \\frac{b^{\\rm out}_\\ell}{b^{\\rm in}_\\ell}\n", " \\cdot a^{\\rm in}_{\\ell m}\n", "$$\n", "\n", "where $p_\\ell$ is the HEALPix pixel-window function and $b_\\ell$ is\n", "a Gaussian beam transfer function. The algorithm proceeds in three\n", "steps:\n", "\n", "1. **Analysis:** The input map is decomposed into $a_{\\ell m}$ via\n", " `map2alm` (using pixel weights by default for high accuracy).\n", "2. **Transfer:** Each $a_{\\ell m}$ is multiplied by the ratio of\n", " output/input pixel windows and beams. Modes above\n", " $\\ell_{\\max}^{\\rm out}$ are discarded (band-limiting).\n", "3. **Synthesis:** The modified $a_{\\ell m}$ are synthesised into a\n", " map at `nside_out` via `alm2map`.\n", "\n", "### Function signature and arguments\n", "\n", "```python\n", "hp.harmonic_ud_grade(\n", " map_in, # Input map(s), RING ordering\n", " nside_out, # Target Nside\n", " lmax=None, # Max multipole (default: min(3*nside_out - 1, 3*nside_in - 1))\n", " mmax=None, # Max m (default: lmax)\n", " iter=None, # map2alm iterations (see below)\n", " pol=True, # Treat 3-component input as TQU/TEB\n", " pixwin=True, # Deconvolve/apply pixel windows\n", " fwhm_in, # Input beam FWHM [radians] (required when smoothing)\n", " fwhm_out=None, # Output beam FWHM [radians] (see below)\n", " use_weights=False, # Use ring weights in map2alm\n", " datapath=None, # Path to pixel-weight files\n", " use_pixel_weights=True, # Use full pixel weights (recommended)\n", " dtype=None, # Cast output to this dtype\n", ")\n", "```\n", "\n", "**Key defaults and their rationale:**\n", "\n", "| Argument | Default | Rationale |\n", "|----------|---------|-----------|\n", "| `lmax` | `min(...)` | Standard HEALPix bandlimit, capped by the input resolution. See explanation below. |\n", "| `iter` | `None` (auto) | Uses 0 iterations when pixel weights are active and `lmax <= 1.5*nside_in` (the regime where pixel weights alone are sufficient); otherwise 3 iterations. |\n", "| `pixwin` | `True` | Deconvolves the input pixel window $p^{\\rm in}_\\ell$ and applies the output pixel window $p^{\\rm out}_\\ell$, ensuring the output map has the correct effective resolution. |\n", "| `fwhm_in` | required* | FWHM of the input beam in radians. **Must** be set to the actual beam FWHM when working with beam-convolved data, otherwise the output will be incorrectly deconvolved. Pass ``0`` or ``fwhm_out=0`` if the input map has no beam. |\n", "| `fwhm_out` | `None` (auto) | Auto-computed as ``PLANCK_K * nside2resol(nside_out)`` where ``PLANCK_K = 160.0 / (degrees(nside2resol(64)) * 60)`` (≈ 2.91). This matches the exact FWHM-to-pixel ratio used consistently across all Planck resolutions. Pass `0` to disable output smoothing. |\n", "| `use_pixel_weights` | `True` | Uses full per-pixel weights for high-accuracy spherical harmonic transforms. If the weight files are not available, an error is raised (pass `False` to fall back to unweighted transforms). |\n", "\n", "*`lmax` default:* `3·nside_out – 1` is the standard HEALPix bandlimit, but\n", "it is capped to `3·nside_in – 1` when *upgrading* resolution. This prevents\n", "the transform from requesting multipoles the input map cannot meaningfully\n", "provide.\n", "\n", "*`fwhm_in` required:* Because ``fwhm_out`` defaults to a Planck-scaled\n", "smoothing beam, ``fwhm_in`` is required so the beam transfer ratio is\n", "always explicit. If the input map has no beam, pass ``fwhm_in=0``\n", "(the equivalent of ``fwhm_out=0`` disables this requirement).\n", "\n", "## Notebook overview\n", "\n", "This notebook compares the two methods through four tests:\n", "1. **Aliasing stress test** — a single high-$\\ell$ mode that should\n", " vanish after downgrading.\n", "2. **Power-spectrum recovery** — a broadband synthetic signal where\n", " spectral fidelity matters.\n", "3. **Noise aliasing** — a realistic scenario with \"blue\" noise that\n", " grows at high $\\ell$, mimicking beam-deconvolved instrumental\n", " noise.\n", "4. **Point sources** — a case where `ud_grade` is the better choice\n", " due to Gibbs ringing in the harmonic approach." ] }, { "cell_type": "code", "execution_count": 1, "id": "202dbb07", "metadata": { "execution": { "iopub.execute_input": "2026-05-06T04:12:34.435148Z", "iopub.status.busy": "2026-05-06T04:12:34.434760Z", "iopub.status.idle": "2026-05-06T04:12:35.865218Z", "shell.execute_reply": "2026-05-06T04:12:35.859936Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "healpy 1.19.1.dev35+ga8141afaa.d20260505\n", "Planck FWHM/pixel ratio: 2.9108\n" ] } ], "source": [ "import time\n", "import numpy as np\n", "import healpy as hp\n", "import matplotlib.pyplot as plt\n", "\n", "plt.rcParams.update({\"figure.dpi\": 120, \"font.size\": 11})\n", "\n", "# Planck 2013 XXIII Table 1: exact FWHM-to-pixel ratio\n", "PLANCK_K = 160.0 / (np.degrees(hp.nside2resol(64)) * 60)\n", "print(f\"healpy {hp.__version__}\")\n", "print(f\"Planck FWHM/pixel ratio: {PLANCK_K:.4f}\")" ] }, { "cell_type": "markdown", "id": "48bdf21a", "metadata": {}, "source": [ "## 1. Aliasing Stress Test: A Single High-$\\ell$ Mode\n", "\n", "The simplest way to reveal aliasing is to construct a pathological\n", "input: a map at `nside_in = 128` that contains power at **exactly\n", "one** spherical-harmonic multipole, $\\ell = 120$.\n", "\n", "The target resolution is `nside_out = 32`, whose maximum resolvable\n", "multipole is $\\ell_{\\max} = 3 \\times 32 - 1 = 95$. Since\n", "$\\ell = 120 > \\ell_{\\max}$, a correct downgrade must produce an\n", "output whose angular power spectrum is identically zero.\n", "\n", "**Key parameter choices:**\n", "- `pixwin=True` is passed both when creating the input map\n", " (`alm2map`) and when calling `harmonic_ud_grade`. This simulates\n", " a realistic pixelised observation and allows `harmonic_ud_grade`\n", " to properly deconvolve the input pixel window and apply the output\n", " pixel window.\n", "- `fwhm_in=0` because the synthetic input has no instrumental beam." ] }, { "cell_type": "code", "execution_count": 2, "id": "7d078dd7", "metadata": { "execution": { "iopub.execute_input": "2026-05-06T04:12:35.869367Z", "iopub.status.busy": "2026-05-06T04:12:35.868633Z", "iopub.status.idle": "2026-05-06T04:12:37.367028Z", "shell.execute_reply": "2026-05-06T04:12:37.365907Z" } }, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "nside_in = 128\n", "nside_out = 32\n", "lmax_out = 3 * nside_out - 1\n", "\n", "# Single mode at ell=120\n", "alm_single = np.zeros(hp.Alm.getsize(120), dtype=np.complex128)\n", "alm_single[hp.Alm.getidx(120, 120, 0)] = 1.0\n", "# We generate the synthetic map and run downgrade methods with pixwin=True.\n", "# This simulates a realistic pixelized map and allows harmonic_ud_grade\n", "# to properly apply its pixel window correction (Eq 1).\n", "m_in = hp.alm2map(alm_single, nside=nside_in, pixwin=True)\n", "\n", "# Downgrade methods\n", "m_ud = hp.ud_grade(m_in, nside_out=nside_out)\n", "\n", "# fwhm_in is required\n", "# For this synthetic test there is no input beam → pass 0\n", "m_harm = hp.harmonic_ud_grade(\n", " m_in,\n", " nside_out=nside_out,\n", " fwhm_in=0,\n", " use_pixel_weights=False,\n", " pixwin=True,\n", " fwhm_out=0,\n", ")\n", "\n", "cl_in = hp.anafast(m_in)\n", "cl_ud = hp.anafast(m_ud)\n", "cl_harm = hp.anafast(m_harm)\n", "\n", "plt.figure(figsize=(10, 5))\n", "plt.semilogy(np.maximum(cl_in, 1e-8), label=f\"Input (Nside={nside_in})\", color=\"black\", linestyle=\"--\")\n", "plt.semilogy(np.maximum(cl_ud, 1e-8), label=f\"ud_grade (Nside={nside_out})\", alpha=0.8)\n", "plt.semilogy(np.maximum(cl_harm, 1e-8), label=f\"harmonic_ud_grade (Nside={nside_out})\", alpha=0.8)\n", "plt.axvline(lmax_out, color=\"red\", ls=\":\", label=r\"Output $\\ell_{\\max}$\")\n", "plt.xlabel(r\"$\\ell$\")\n", "plt.ylabel(r\"$C_\\ell$\")\n", "plt.xlim(0, 150)\n", "plt.ylim(1e-8, cl_in.max() * 5)\n", "plt.title(\"Aliasing of a single high-frequency mode ($\\\\ell=120$)\")\n", "plt.legend()\n", "plt.grid(alpha=0.3)\n", "plt.tight_layout()\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "c0f3f1e4", "metadata": {}, "source": [ "**Interpretation of the plot above:**\n", "\n", "- **Black dashed line (Input):** The input power spectrum has a sharp\n", " peak at $\\ell = 120$ and is essentially zero everywhere else. The\n", " satellite peaks visible around $\\ell = 120$ are due to the pixel\n", " window of the `nside_in = 128` grid.\n", "- **Orange line (`harmonic_ud_grade`):** The output spectrum is\n", " numerically zero across all multipoles — exactly the correct\n", " answer. The harmonic transform naturally band-limits the result to\n", " $\\ell \\le \\ell_{\\max}$, so the $\\ell = 120$ mode is cleanly\n", " removed.\n", "- **Blue line (`ud_grade`):** Significant spurious power appears\n", " across the *entire* output multipole range. This is **aliasing**:\n", " because pixel-space averaging has no frequency cutoff, the\n", " high-$\\ell$ mode is \"folded\" back into the lower multipoles,\n", " corrupting the output with an oscillating pattern.\n", "- **Red dotted line:** The output bandlimit $\\ell_{\\max} = 95$.\n", "\n", "The RMS values below quantify this: `ud_grade` retains about 43 % of\n", "the original map RMS as pure aliasing artefact, while\n", "`harmonic_ud_grade` suppresses it to the numerical noise floor." ] }, { "cell_type": "code", "execution_count": 3, "id": "8d2ca21d", "metadata": { "execution": { "iopub.execute_input": "2026-05-06T04:12:37.370049Z", "iopub.status.busy": "2026-05-06T04:12:37.369728Z", "iopub.status.idle": "2026-05-06T04:12:37.377417Z", "shell.execute_reply": "2026-05-06T04:12:37.376229Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Input map RMS: 2.705287e-01\n", "ud_grade output RMS: 1.154352e-01 <-- aliasing\n", "harmonic_ud_grade RMS: 6.952337e-04 <-- suppressed\n" ] } ], "source": [ "print(f\"Input map RMS: {np.std(m_in):.6e}\")\n", "print(f\"ud_grade output RMS: {np.std(m_ud):.6e} <-- aliasing\")\n", "print(f\"harmonic_ud_grade RMS: {np.std(m_harm):.6e} <-- suppressed\")" ] }, { "cell_type": "markdown", "id": "2e4ae8d5", "metadata": {}, "source": [ "## 2. Power-Spectrum Recovery — Why It Matters\n", "\n", "The single-mode test above is deliberately extreme. Real sky maps\n", "contain power at **all** multipoles, so aliasing from `ud_grade`\n", "is spread across the full spectrum, making it harder to spot by\n", "eye but no less damaging to science.\n", "\n", "In this section we synthesise a realistic broadband signal with\n", "$C_\\ell \\propto \\ell^{-2}$ (a spectrum often used for test\n", "purposes) at `nside_in = 256`, downgrade to `nside_out = 64`,\n", "and compare the recovered power spectrum against a **ground-truth\n", "reference**.\n", "\n", "The reference is built by truncating the original $a_{\\ell m}$ to\n", "$\\ell_{\\max}^{\\rm out}$ and synthesising directly at the output\n", "resolution, so both the reference and the downgraded maps contain\n", "the same pixel-window effects. Any difference between them is\n", "therefore purely due to the downgrade method." ] }, { "cell_type": "code", "execution_count": 4, "id": "4269e324", "metadata": { "execution": { "iopub.execute_input": "2026-05-06T04:12:37.380889Z", "iopub.status.busy": "2026-05-06T04:12:37.380286Z", "iopub.status.idle": "2026-05-06T04:12:38.041860Z", "shell.execute_reply": "2026-05-06T04:12:38.040469Z" } }, "outputs": [], "source": [ "nside_in = 256\n", "nside_out = 64\n", "lmax_in = 3 * nside_in - 1\n", "lmax_out = 3 * nside_out - 1\n", "\n", "np.random.seed(42)\n", "ell = np.arange(lmax_in + 1, dtype=float)\n", "cl_in = np.zeros(lmax_in + 1)\n", "cl_in[2:] = ell[2:] ** (-2.0)\n", "elm = hp.synalm(cl_in, lmax=lmax_in)\n", "m_in = hp.alm2map(elm, nside=nside_in, lmax=lmax_in, pixwin=True)\n", "\n", "# Ground-truth reference: directly synthesise at output resolution\n", "elm_ref = hp.resize_alm(elm, lmax_in, lmax_in, lmax_out, lmax_out)\n", "m_ref = hp.alm2map(elm_ref, nside=nside_out, lmax=lmax_out, pixwin=True)\n", "\n", "m_ud = hp.ud_grade(m_in, nside_out=nside_out)\n", "\n", "# fwhm_in=0 for this synthetic simulation with no beam\n", "m_harm = hp.harmonic_ud_grade(\n", " m_in,\n", " nside_out=nside_out,\n", " fwhm_in=0,\n", " use_pixel_weights=False,\n", " pixwin=True,\n", " fwhm_out=0,\n", ")\n", "\n", "# Measure spectra\n", "cl_ref = hp.anafast(m_ref, lmax=lmax_out)\n", "cl_ud = hp.anafast(m_ud, lmax=lmax_out)\n", "cl_harm = hp.anafast(m_harm, lmax=lmax_out)\n", "ell_out = np.arange(lmax_out + 1)" ] }, { "cell_type": "code", "execution_count": 5, "id": "8c01508b", "metadata": { "execution": { "iopub.execute_input": "2026-05-06T04:12:38.045870Z", "iopub.status.busy": "2026-05-06T04:12:38.044600Z", "iopub.status.idle": "2026-05-06T04:12:39.115932Z", "shell.execute_reply": "2026-05-06T04:12:39.114916Z" } }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, axes = plt.subplots(1, 2, figsize=(12, 4))\n", "\n", "axes[0].loglog(ell_out[2:], cl_ref[2:], \"k--\", lw=2, label=\"Reference $C_\\ell$ (truth)\")\n", "axes[0].loglog(ell_out[2:], cl_ud[2:], alpha=0.8, label=\"ud_grade\")\n", "axes[0].loglog(ell_out[2:], cl_harm[2:], alpha=0.8, label=\"harmonic_ud_grade\")\n", "axes[0].axvline(lmax_out, color=\"red\", ls=\":\", label=r\"$\\ell_{\\max}$\")\n", "axes[0].set_xlabel(r\"$\\ell$\")\n", "axes[0].set_ylabel(r\"$C_\\ell$\")\n", "axes[0].set_title(\"Power spectra after downgrade\")\n", "axes[0].legend()\n", "axes[0].grid(alpha=0.3)\n", "\n", "# Fractional error\n", "frac_ud = (cl_ud[2:] - cl_ref[2:]) / cl_ref[2:]\n", "frac_harm = (cl_harm[2:] - cl_ref[2:]) / cl_ref[2:]\n", "\n", "axes[1].plot(ell_out[2:], frac_ud * 100, alpha=0.8, label=\"ud_grade\")\n", "axes[1].plot(ell_out[2:], frac_harm * 100, alpha=0.8, label=\"harmonic_ud_grade\")\n", "axes[1].axhline(0, color=\"k\", lw=0.5)\n", "axes[1].axvline(lmax_out, color=\"red\", ls=\":\")\n", "axes[1].set_xlabel(r\"$\\ell$\")\n", "axes[1].set_ylabel(\"Fractional error [%]\")\n", "axes[1].set_title(\"Spectral error vs truth\")\n", "axes[1].legend()\n", "axes[1].grid(alpha=0.3)\n", "\n", "plt.tight_layout()\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "76e55b9c", "metadata": { "lines_to_next_cell": 0 }, "source": [ "**Interpretation of the plots above:**\n", "\n", "**Left panel — Power spectra after downgrade:**\n", "All three curves agree well at low $\\ell$, but diverge at high\n", "multipoles. The reference (black dashed) and `harmonic_ud_grade`\n", "(orange) both roll off smoothly beyond $\\ell \\approx 100$: this is\n", "the expected damping from the pixel window of the `nside_out = 64`\n", "grid. `ud_grade` (blue), by contrast, shows a visible *excess* of\n", "power in this regime because aliased high-frequency structures from\n", "above $\\ell_{\\max}$ have been folded back into the output.\n", "\n", "**Right panel — Fractional spectral error relative to truth:**\n", "This panel makes the aliasing bias quantitative.\n", "- `harmonic_ud_grade` (orange) sits flat on 0 % error — it matches\n", " the truth map almost perfectly.\n", "- `ud_grade` (blue) is systematically **positive**, meaning it\n", " **over-estimates** the power. This is expected: aliasing can only\n", " *add* power, never subtract it. The error grows rapidly toward\n", " $\\ell_{\\max}$, reaching 50–70 % near the bandlimit.\n", "\n", "Because both the reference and the downgraded maps include the same\n", "pixel window, window effects cancel exactly in the ratio. The\n", "residual is pure aliasing.\n", "\n", "The RMS fractional error below summarises this over the \"safe\"\n", "multipole band $\\ell \\in [2,\\, 2 N_{\\rm side}^{\\rm out}]$:" ] }, { "cell_type": "code", "execution_count": 6, "id": "60a362c0", "metadata": { "execution": { "iopub.execute_input": "2026-05-06T04:12:39.118762Z", "iopub.status.busy": "2026-05-06T04:12:39.118474Z", "iopub.status.idle": "2026-05-06T04:12:39.123758Z", "shell.execute_reply": "2026-05-06T04:12:39.123109Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "RMS frac. error over safe band ℓ ∈ [2, 128]:\n", " ud_grade: 2.34%\n", " harmonic_ud_grade: 0.00%\n" ] } ], "source": [ "safe = slice(2, 2 * nside_out + 1)\n", "print(\n", " f\"RMS frac. error over safe band ℓ ∈ [2, {2*nside_out}]:\\n\"\n", " f\" ud_grade: {np.sqrt(np.mean(frac_ud[safe]**2))*100:.2f}%\\n\"\n", " f\" harmonic_ud_grade: {np.sqrt(np.mean(frac_harm[safe]**2))*100:.2f}%\"\n", ")" ] }, { "cell_type": "markdown", "id": "7db1fa57", "metadata": {}, "source": [ "## 3. Noise Aliasing — The Real-World Failure Mode\n", "\n", "The tests above used noiseless inputs, but real observational data\n", "always contain instrumental noise. In CMB data processing a\n", "particularly important case is **blue noise** — noise whose power\n", "spectrum *grows* with $\\ell$ (e.g., $C_\\ell^{\\rm noise} \\propto\n", "\\ell^{2}$). This commonly arises when a map is beam-deconvolved:\n", "dividing out the beam's Gaussian roll-off amplifies the\n", "high-frequency noise enormously.\n", "\n", "Because `ud_grade` operates in pixel space with no frequency cutoff,\n", "**all** of that amplified high-$\\ell$ noise above\n", "$\\ell_{\\max}^{\\rm out}$ is aliased back into the signal band,\n", "dramatically raising the noise floor. `harmonic_ud_grade` avoids\n", "this by band-limiting the map before downgrading.\n", "\n", "Below we construct a signal + blue-noise map at `nside_in = 512`,\n", "downgrade to `nside_out = 64` (a factor-8 step), and isolate the\n", "noise contribution in each output. The larger resolution ratio\n", "means there is a vast reservoir of high-$\\ell$ noise power above\n", "$\\ell_{\\max}^{\\rm out} = 191$ that can potentially alias back." ] }, { "cell_type": "code", "execution_count": 7, "id": "9a4ddd3c", "metadata": { "execution": { "iopub.execute_input": "2026-05-06T04:12:39.126869Z", "iopub.status.busy": "2026-05-06T04:12:39.126611Z", "iopub.status.idle": "2026-05-06T04:12:45.117546Z", "shell.execute_reply": "2026-05-06T04:12:45.115875Z" } }, "outputs": [], "source": [ "nside_in = 512\n", "nside_out = 64\n", "lmax_out = 3 * nside_out - 1\n", "\n", "np.random.seed(42)\n", "ell_in = np.arange(3 * nside_in + 1, dtype=float)\n", "cl_signal = np.zeros(3 * nside_in + 1)\n", "cl_signal[2:] = ell_in[2:] ** (-2.0)\n", "map_signal = hp.synfast(cl_signal, nside_in, lmax=3 * nside_in, new=True, pixwin=True)\n", "\n", "# Blue noise: noise dominates at high ℓ (e.g. beam deconvolved noise)\n", "ell_knee = 50\n", "cl_noise = np.zeros(3 * nside_in + 1)\n", "cl_noise[2:] = cl_signal[ell_knee] * (ell_in[2:] / ell_knee) ** 2\n", "map_noise = hp.synfast(cl_noise, nside_in, lmax=3 * nside_in, new=True, pixwin=True)\n", "map_noisy = map_signal + map_noise\n", "\n", "# Reference: downgrade signal-only with harmonic\n", "m_ref_signal = hp.harmonic_ud_grade(\n", " map_signal,\n", " nside_out=nside_out,\n", " fwhm_in=0,\n", " use_pixel_weights=False,\n", " pixwin=True,\n", " fwhm_out=0,\n", ")\n", "\n", "# Downgrade methods\n", "m_ud = hp.ud_grade(map_noisy, nside_out=nside_out)\n", "m_harm = hp.harmonic_ud_grade(\n", " map_noisy,\n", " nside_out=nside_out,\n", " fwhm_in=0,\n", " use_pixel_weights=False,\n", " pixwin=True,\n", " fwhm_out=0,\n", ")\n", "\n", "# Isolate noise contribution\n", "cl_noise_ud = hp.anafast(m_ud - hp.ud_grade(map_signal, nside_out=nside_out), lmax=lmax_out)\n", "cl_noise_harm = hp.anafast(m_harm - m_ref_signal, lmax=lmax_out)\n", "cl_signal_out = hp.anafast(m_ref_signal, lmax=lmax_out)" ] }, { "cell_type": "code", "execution_count": 8, "id": "a6638e63", "metadata": { "execution": { "iopub.execute_input": "2026-05-06T04:12:45.122183Z", "iopub.status.busy": "2026-05-06T04:12:45.121914Z", "iopub.status.idle": "2026-05-06T04:12:46.079257Z", "shell.execute_reply": "2026-05-06T04:12:46.078257Z" } }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(8, 5))\n", "\n", "plt.loglog(ell_out[2:], cl_signal_out[2:], \"k--\", lw=2, label=\"Signal (truth)\")\n", "plt.loglog(ell_out[2:], cl_noise[:lmax_out + 1][2:], \"gray\", ls=\":\", lw=2, label=\"Input Noise\")\n", "plt.loglog(ell_out[2:], cl_noise_ud[2:], alpha=0.8, label=\"Noise in ud_grade\")\n", "plt.loglog(ell_out[2:], cl_noise_harm[2:], alpha=0.8, label=\"Noise in harmonic_ud_grade\")\n", "plt.xlabel(r\"$\\ell$\")\n", "plt.ylabel(r\"$C_\\ell$ (noise)\")\n", "plt.title(\"Noise contamination after downgrade\")\n", "plt.legend()\n", "plt.grid(alpha=0.3)\n", "plt.tight_layout()\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "c6971a73", "metadata": {}, "source": [ "**Interpretation of the plot above:**\n", "\n", "This plot isolates the **noise-only** component after downgrading\n", "from `nside = 512` to `nside = 64` (a factor-8 resolution step).\n", "Each curve has a specific meaning:\n", "\n", "- **Black dashed (Signal truth):** The true signal power spectrum at\n", " the output resolution. It is shown for context so you can judge\n", " where noise starts to dominate over signal.\n", "- **Grey dotted (Input Noise):** The raw analytic noise spectrum\n", " $C_\\ell^{\\rm noise} \\propto \\ell^{2}$ as injected into the\n", " input map. It crosses the signal near $\\ell \\approx 50$\n", " (the chosen knee multipole) and grows steeply beyond.\n", "- **Orange (`harmonic_ud_grade`):** The noise residual after\n", " harmonic downgrading. It tracks the input noise closely at low\n", " $\\ell$ and rolls off above $\\ell \\approx 100$ due to the target\n", " pixel window — exactly as expected.\n", "- **Blue (`ud_grade`):** The noise residual after pixel-space\n", " downgrading. Across the full multipole range, the `ud_grade`\n", " noise is roughly **5–10× higher** than the `harmonic_ud_grade`\n", " noise. This excess is entirely due to aliased high-$\\ell$ noise\n", " being folded into the signal band. The effect grows with the\n", " resolution ratio: a larger step (here 8×) means more high-$\\ell$\n", " modes available to alias, producing a larger noise floor uplift.\n", "\n", "**Why this matters in practice:** When analysing real CMB or\n", "astrophysical data, any aliased noise that leaks into the low-$\\ell$\n", "modes will bias power-spectrum estimates, cross-correlations, and\n", "component-separation results. `harmonic_ud_grade` prevents this by\n", "applying a strict harmonic bandlimit before re-gridding to the\n", "output resolution." ] }, { "cell_type": "markdown", "id": "00743559", "metadata": {}, "source": [ "## 4. When `ud_grade` Wins: Point Sources and Gibbs Ringing\n", "\n", "The previous sections show that `harmonic_ud_grade` is clearly\n", "superior for broadband or noisy signals. But there is an important\n", "case where **`ud_grade` is the better choice**: maps dominated by\n", "**compact, localised features** such as point sources or binary\n", "masks.\n", "\n", "A point source is a delta function on the sky, which means it has\n", "power at *all* multipoles. When `harmonic_ud_grade` band-limits\n", "the map to $\\ell_{\\max}^{\\rm out}$, it truncates the harmonic\n", "expansion abruptly, producing oscillating **Gibbs ringing** around\n", "each source. `ud_grade`, operating purely in pixel space, simply\n", "averages the sub-pixels and preserves the compact, positive-definite\n", "nature of the source.\n", "\n", "To make this test realistic, we simulate point sources **as an\n", "instrument would observe them**: we paint a Gaussian beam profile\n", "directly in pixel space at each source position, using the\n", "Planck-suggested FWHM for the input resolution. We then compare\n", "three downgrade strategies:\n", "1. `ud_grade` — pixel-space averaging.\n", "2. `harmonic_ud_grade` with `fwhm_out = 0` — band-limit only, no\n", " additional smoothing.\n", "3. `harmonic_ud_grade` with default `fwhm_out` — Planck-scaled\n", " output beam." ] }, { "cell_type": "code", "execution_count": 9, "id": "41c41ffa", "metadata": { "execution": { "iopub.execute_input": "2026-05-06T04:12:46.082215Z", "iopub.status.busy": "2026-05-06T04:12:46.081902Z", "iopub.status.idle": "2026-05-06T04:12:47.124749Z", "shell.execute_reply": "2026-05-06T04:12:47.115356Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Nside_in = 256, fwhm_in = 40.0 arcmin (Planck ratio)\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "ud_grade: min=0.0000, max=46.04, negative pixels: 0\n", "harmonic (no smooth): min=-3.9391, max=35.83, negative pixels: 24614\n", "harmonic (Planck): min=-0.0003, max=5.87, negative pixels: 24342\n" ] } ], "source": [ "nside_in = 256\n", "nside_out = 64\n", "\n", "# Planck-suggested beam for this resolution\n", "fwhm_in_pts = PLANCK_K * hp.nside2resol(nside_in)\n", "sigma_in = fwhm_in_pts / (2 * np.sqrt(2 * np.log(2)))\n", "print(f\"Nside_in = {nside_in}, fwhm_in = {np.degrees(fwhm_in_pts)*60:.1f} arcmin \"\n", " f\"(Planck ratio)\")\n", "\n", "# Simulate point sources as an instrument would see them:\n", "# paint a Gaussian beam profile directly in pixel space.\n", "m_pts = np.zeros(hp.nside2npix(nside_in))\n", "np.random.seed(123)\n", "src_pixels = np.random.choice(hp.nside2npix(nside_in), size=5, replace=False)\n", "src_vecs = np.array(hp.pix2vec(nside_in, src_pixels)).T # (5, 3)\n", "all_vecs = np.array(hp.pix2vec(nside_in, np.arange(hp.nside2npix(nside_in)))).T\n", "\n", "for src_vec in src_vecs:\n", " cos_dist = np.dot(all_vecs, src_vec)\n", " cos_dist = np.clip(cos_dist, -1, 1)\n", " ang_dist = np.arccos(cos_dist)\n", " m_pts += 100.0 * np.exp(-0.5 * (ang_dist / sigma_in) ** 2)\n", "\n", "# Downgrade: three methods\n", "m_pts_ud = hp.ud_grade(m_pts, nside_out=nside_out)\n", "\n", "# harmonic_ud_grade with NO additional smoothing (band-limit only)\n", "m_pts_harm_nosmooth = hp.harmonic_ud_grade(\n", " m_pts,\n", " nside_out=nside_out,\n", " fwhm_in=fwhm_in_pts,\n", " use_pixel_weights=False,\n", " pixwin=True,\n", " fwhm_out=0,\n", ")\n", "\n", "# harmonic_ud_grade with Planck default output beam\n", "m_pts_harm_smooth = hp.harmonic_ud_grade(\n", " m_pts,\n", " nside_out=nside_out,\n", " fwhm_in=fwhm_in_pts,\n", " use_pixel_weights=False,\n", " pixwin=True,\n", ")\n", "\n", "print(f\"ud_grade: min={m_pts_ud.min():.4f}, max={m_pts_ud.max():.2f}, \"\n", " f\"negative pixels: {(m_pts_ud < 0).sum()}\")\n", "print(f\"harmonic (no smooth): min={m_pts_harm_nosmooth.min():.4f}, \"\n", " f\"max={m_pts_harm_nosmooth.max():.2f}, \"\n", " f\"negative pixels: {(m_pts_harm_nosmooth < 0).sum()}\")\n", "print(f\"harmonic (Planck): min={m_pts_harm_smooth.min():.4f}, \"\n", " f\"max={m_pts_harm_smooth.max():.2f}, \"\n", " f\"negative pixels: {(m_pts_harm_smooth < 0).sum()}\")" ] }, { "cell_type": "code", "execution_count": 10, "id": "b66cbf3d", "metadata": { "execution": { "iopub.execute_input": "2026-05-06T04:12:47.128067Z", "iopub.status.busy": "2026-05-06T04:12:47.127699Z", "iopub.status.idle": "2026-05-06T04:12:48.226367Z", "shell.execute_reply": "2026-05-06T04:12:48.225383Z" } }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Zoom in on one source with gnomview\n", "theta, phi = hp.pix2ang(nside_in, src_pixels[0])\n", "rot = (np.degrees(phi), 90 - np.degrees(theta))\n", "\n", "fig = plt.figure(figsize=(16, 4))\n", "\n", "ax1 = fig.add_subplot(141)\n", "hp.gnomview(m_pts, rot=rot, reso=5, xsize=200,\n", " title=f\"Input (Nside={nside_in})\", hold=True, notext=True)\n", "\n", "ax2 = fig.add_subplot(142)\n", "hp.gnomview(m_pts_ud, rot=rot, reso=5, xsize=200,\n", " title=f\"ud_grade (Nside={nside_out})\", hold=True, notext=True)\n", "\n", "ax3 = fig.add_subplot(143)\n", "hp.gnomview(m_pts_harm_nosmooth, rot=rot, reso=5, xsize=200,\n", " title=\"harmonic (no smooth)\", hold=True, notext=True)\n", "\n", "ax4 = fig.add_subplot(144)\n", "hp.gnomview(m_pts_harm_smooth, rot=rot, reso=5, xsize=200,\n", " title=\"harmonic (Planck beam)\", hold=True, notext=True)\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "6f503d8b", "metadata": {}, "source": [ "**Interpretation of the plots above:**\n", "\n", "The four panels zoom in on one point source that was simulated with\n", "a realistic Gaussian beam painted directly in pixel space (FWHM\n", "≈ 40 arcmin for Nside = 256).\n", "\n", "- **Panel 1 (Input):** The beam-convolved point source at the input\n", " resolution — a smooth Gaussian profile, as an instrument would\n", " observe it.\n", "- **Panel 2 (`ud_grade`):** Pixel-space averaging preserves the\n", " smooth, positive-definite profile of the beam. No ringing, no\n", " negative pixels.\n", "- **Panel 3 (`harmonic_ud_grade`, no smoothing):** Band-limiting to\n", " $\\ell_{\\max} = 191$ without additional smoothing produces visible\n", " **Gibbs ringing** — oscillations with negative values around the\n", " source. Even though the input is beam-convolved (not a true\n", " delta), the beam is narrow enough that significant power remains\n", " above $\\ell_{\\max}^{\\rm out}$, and truncating it causes ringing.\n", "- **Panel 4 (`harmonic_ud_grade`, Planck beam):** The default\n", " Planck-scaled output beam adds extra smoothing that suppresses the\n", " ringing significantly. This is the recommended harmonic approach\n", " for diffuse science — but for point-source work, `ud_grade` still\n", " produces a cleaner, more compact result.\n", "\n", "**Takeaway:** `harmonic_ud_grade` is optimal for **band-limited**\n", "signals (CMB, diffuse emission). `ud_grade` is preferable for\n", "**pixel-localised** features (point sources, binary masks,\n", "hit-count maps)." ] }, { "cell_type": "markdown", "id": "e3273ea8", "metadata": {}, "source": [ "## 5. Required `fwhm_in`\n", "\n", "`harmonic_ud_grade` requires `fwhm_in` so the resolution scaling\n", "is always explicit. The default `fwhm_out` preserves the Planck\n", "FWHM-to-pixel ratio across resolutions.\n", "\n", "### 5.1 Default beam scaling" ] }, { "cell_type": "code", "execution_count": 11, "id": "7e63835f", "metadata": { "execution": { "iopub.execute_input": "2026-05-06T04:12:48.228942Z", "iopub.status.busy": "2026-05-06T04:12:48.228526Z", "iopub.status.idle": "2026-05-06T04:12:53.919568Z", "shell.execute_reply": "2026-05-06T04:12:53.918174Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Nside_in = 2048, Nside_out = 64\n", " fwhm_in = 5.0 arcmin\n", " expected fwhm_out = 160.0 arcmin ← matches Planck Nside=64\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ " ✓ harmonic_ud_grade accepted the call with default fwhm_out\n" ] } ], "source": [ "nside_in = 2048\n", "nside_out = 64\n", "\n", "# Planck beam at Nside=2048 is 5 arcmin\n", "fwhm_in = np.radians(5 / 60)\n", "\n", "m_input = np.zeros(hp.nside2npix(nside_in))\n", "\n", "# fwhm_out is auto-computed to preserve the ratio\n", "# fwhm_out = fwhm_in * (resol_out / resol_in)\n", "expected_fwhm_out = fwhm_in * (\n", " hp.nside2resol(nside_out) / hp.nside2resol(nside_in)\n", ")\n", "\n", "# This should equal 160 arcmin (Planck Nside=64 beam)\n", "print(f\"Nside_in = {nside_in}, Nside_out = {nside_out}\")\n", "print(f\" fwhm_in = {np.degrees(fwhm_in)*60:.1f} arcmin\")\n", "print(f\" expected fwhm_out = {np.degrees(expected_fwhm_out)*60:.1f} arcmin ← matches Planck Nside=64\")\n", "\n", "# Verify by running the function (it will work even on zeros)\n", "m_out = hp.harmonic_ud_grade(\n", " m_input,\n", " nside_out=nside_out,\n", " fwhm_in=fwhm_in,\n", " use_pixel_weights=False,\n", " pixwin=True,\n", ")\n", "print(f\" ✓ harmonic_ud_grade accepted the call with default fwhm_out\")" ] }, { "cell_type": "markdown", "id": "14f6a236", "metadata": {}, "source": [ "## 6. Performance\n", "\n", "`harmonic_ud_grade` is more expensive than `ud_grade` because it\n", "requires a full spherical-harmonic transform (SHT) of the input\n", "map. Below we benchmark both methods at `nside_in = 512` →\n", "`nside_out = 128` (10 iterations each)." ] }, { "cell_type": "code", "execution_count": 12, "id": "5cee3b10", "metadata": { "execution": { "iopub.execute_input": "2026-05-06T04:12:53.922317Z", "iopub.status.busy": "2026-05-06T04:12:53.922020Z", "iopub.status.idle": "2026-05-06T04:13:00.621740Z", "shell.execute_reply": "2026-05-06T04:13:00.620416Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "ud_grade: 157.4 ms\n", "harmonic_ud_grade: 461.6 ms\n", "slowdown: 2.9x\n" ] } ], "source": [ "nside_in = 512\n", "nside_out = 128\n", "np.random.seed(42)\n", "m = hp.synfast(np.ones(3 * nside_in), nside_in, new=True)\n", "\n", "# ud_grade\n", "t0 = time.perf_counter()\n", "for _ in range(10):\n", " _ = hp.ud_grade(m, nside_out=nside_out)\n", "t_ud = (time.perf_counter() - t0) / 10\n", "\n", "# harmonic_ud_grade\n", "t0 = time.perf_counter()\n", "for _ in range(10):\n", " _ = hp.harmonic_ud_grade(\n", " m,\n", " nside_out=nside_out,\n", " fwhm_in=0,\n", " use_pixel_weights=False,\n", " pixwin=True,\n", " fwhm_out=0,\n", " )\n", "t_harm = (time.perf_counter() - t0) / 10\n", "\n", "print(f\"ud_grade: {t_ud*1000:.1f} ms\")\n", "print(f\"harmonic_ud_grade: {t_harm*1000:.1f} ms\")\n", "print(f\"slowdown: {t_harm/t_ud:.1f}x\")" ] }, { "cell_type": "markdown", "id": "d97c4969", "metadata": {}, "source": [ "## Summary\n", "\n", "The table below summarises the key differences between the two\n", "downgrading methods demonstrated in this notebook.\n", "\n", "| Feature | `ud_grade` | `harmonic_ud_grade` |\n", "|---------|------------|---------------------|\n", "| **Domain** | Pixel space (sub-pixel averaging) | Spherical-harmonic space (SHT) |\n", "| **Aliasing** | Heavy leakage at all $\\ell$ | Suppressed to numerical noise floor |\n", "| **Spectrum fidelity** | Corrupted — aliased power adds positive bias | Correct within the output band |\n", "| **Pixel-window handling** | Ignored | Deconvolved/re-applied (Planck 2015 XVI Eq. 1) |\n", "| **Beam scaling** | Not handled | Auto-scales FWHM (required `fwhm_in`) |\n", "| **Gibbs ringing** | None — preserves positivity | Ringing around compact sources |\n", "| **Typical speed** | Fast (≈ ms) | ~5–15× slower (dominated by SHT) |\n", "\n", "**Important note:** `harmonic_ud_grade` **smoothes the output by\n", "default** via `fwhm_out = PLANCK_K * nside2resol(nside_out)`. The\n", "beam transfer deconvolves `fwhm_in` and applies `fwhm_out`; passing\n", "the wrong `fwhm_in` (or forgetting it) will silently give an\n", "incorrect smoothing. See the `fwhm_in` parameter discussion above.\n", "\n", "**Recommendation:**\n", "- Use **`harmonic_ud_grade`** whenever scientific accuracy matters:\n", " power-spectrum estimation, component separation, map-level\n", " comparisons, or any analysis involving noisy or beam-deconvolved\n", " data.\n", "- Use **`ud_grade`** when working with point-source maps, binary\n", " masks, hit-count maps, or when speed is critical and aliasing\n", " artefacts are acceptable." ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.11.2" } }, "nbformat": 4, "nbformat_minor": 5 }