FWHM response to annular Zernike wavefront error contribution

dFWHMdZ.ipynb

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   "source": [
    "import numpy as np\n",
    "import galsim"
   ]
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    "def dFWHMdZ(R_outer, R_inner, jmax):\n",
    "    \"\"\"\n",
    "    Params\n",
    "    ------\n",
    "    R_outer : float\n",
    "        Outer radius of entrance pupil annulus in meters\n",
    "    R_inner : float\n",
    "        Inner radius of entrance pupil annulus in meters\n",
    "    jmax : int\n",
    "        Maximum Noll index for which to compute dFWHM/dZ\n",
    "        \n",
    "    Returns\n",
    "    -------\n",
    "    dFWHMdZ : array of float\n",
    "        Derivative of FWHM wrt wavefront error given by annular Zernike coefficient.\n",
    "        Units are arcsec per micron.  Indices run from 0 to jmax inclusive, though\n",
    "        results for indices 0-3 are not meaningful.\n",
    "    \"\"\"\n",
    "    out = np.zeros((jmax+1,))\n",
    "    for j in range(4, jmax+1):\n",
    "        coefs = [0]*j + [1]\n",
    "        Z = galsim.zernike.Zernike(coefs, R_outer=R_outer, R_inner=R_inner) \n",
    "        # (Annular) Zernikes are normalized to have rms of 1 over their domain\n",
    "        # So to get rms of Zernike series, just need the RSS of the coefficients. \n",
    "        # For the rms of the tilts, this is the RSS of the coefficients of the\n",
    "        # X/Y gradients expressed as Zernike series.\n",
    "        rms_tilt = np.sqrt(np.sum(Z.gradX.coef**2 + Z.gradY.coef**2)/2) \n",
    "        # Results are in radians per meter right now.  Convert to arcsec per micron.\n",
    "        rms_tilt = np.rad2deg(rms_tilt*1e-6)*3600\n",
    "        # rms -> fwhm\n",
    "        fwhm_tilt = rms_tilt*2*np.sqrt(2*np.log(2))\n",
    "        out[j] = fwhm_tilt\n",
    "    return out"
   ]
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     "text": [
      " 4    3.395\n",
      " 5    1.969\n",
      " 6    1.969\n",
      " 7    4.374\n",
      " 8    4.374\n",
      " 9    2.802\n",
      "10    2.802\n",
      "11    7.592\n",
      "12    5.726\n",
      "13    5.726\n",
      "14    3.620\n",
      "15    3.620\n",
      "16    8.696\n",
      "17    8.696\n",
      "18    7.146\n",
      "19    7.146\n",
      "20    4.434\n",
      "21    4.434\n",
      "22   12.704\n",
      "23   10.214\n",
      "24   10.214\n",
      "25    8.566\n",
      "26    8.566\n",
      "27    5.246\n",
      "28    5.246\n",
      "29   13.934\n",
      "30   13.934\n",
      "31   11.941\n",
      "32   11.941\n",
      "33    9.980\n",
      "34    9.980\n",
      "35    6.058\n",
      "36    6.058\n",
      "37   18.597\n"
     ]
    }
   ],
   "source": [
    "# AuxTel\n",
    "for j, coef in enumerate(dFWHMdZ(0.6, 0.3525*0.6, 37)):\n",
    "    if j < 4: \n",
    "        continue\n",
    "    print(f\"{j:2d}   {coef:6.3f}\")"
   ]
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     "text": [
      " 4    0.751\n",
      " 5    0.271\n",
      " 6    0.271\n",
      " 7    0.819\n",
      " 8    0.819\n",
      " 9    0.396\n",
      "10    0.396\n",
      "11    1.679\n",
      "12    0.937\n",
      "13    0.937\n",
      "14    0.517\n",
      "15    0.517\n",
      "16    1.755\n",
      "17    1.755\n",
      "18    1.089\n",
      "19    1.089\n",
      "20    0.635\n",
      "21    0.635\n",
      "22    2.810\n",
      "23    1.869\n",
      "24    1.869\n",
      "25    1.263\n",
      "26    1.263\n",
      "27    0.752\n",
      "28    0.752\n",
      "29    2.894\n",
      "30    2.894\n",
      "31    2.015\n",
      "32    2.015\n",
      "33    1.450\n",
      "34    1.450\n",
      "35    0.869\n",
      "36    0.869\n",
      "37    4.113\n"
     ]
    }
   ],
   "source": [
    "# Rubin\n",
    "for j, coef in enumerate(dFWHMdZ(4.18, 4.18*0.61, 37)):\n",
    "    if j < 4: \n",
    "        continue\n",
    "    print(f\"{j:2d}   {coef:6.3f}\")"
   ]
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