Move the processing code under pipeline/
Preparing to merge this repository into a combined astrophotography repo. session-scripts/ becomes pipeline/ because the scripts import layout.py from their own directory and must stay together, and because 'pipeline' says what it is rather than how it came about. observing/ stays at the top level: observing plans are not processing code.
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pipeline/sb_limits.py
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137
pipeline/sb_limits.py
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"""Step 6: how deep does the shell search actually go, and is anything there?
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Two questions:
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1. On what surface-brightness level would a shell have had to sit to be seen?
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Binning the residual to ever coarser scales shows whether the noise
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integrates down like photon noise (it does not: it is dominated by
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correlated large-scale systematics), which sets the real limit.
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2. Is there any significant azimuthal structure? The m = 1..4 Fourier
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amplitudes of the residual in each elliptical annulus are compared with
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the amplitude expected from the noise alone.
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"""
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import numpy as np
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from astropy.io import fits
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import matplotlib
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matplotlib.use('Agg')
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import matplotlib.pyplot as plt
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from sb_common import *
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XC, YC = np.load(path('_geom.npy'))
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star = fits.getdata(path('sb-mask-stars.fits')).astype(bool)
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dust = fits.getdata(path('sb-mask-dust.fits')).astype(bool)
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a_map = np.load(path('_amap.npy'))
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res = fits.getdata(path('sb-residual-flat.fits')).astype(np.float32)
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rms = float(np.load(path('_rms.npy'))[0])
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def blockstat(img, mask, B, sel):
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H, W = img.shape
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h, w = H // B, W // B
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a = img[:h * B, :w * B].reshape(h, B, w, B)
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m = (~mask)[:h * B, :w * B].reshape(h, B, w, B)
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s = sel[:h * B, :w * B].reshape(h, B, w, B)
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n = m.sum(axis=(1, 3))
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v = np.where(n > 0.35 * B * B, np.where(m, a, 0).sum(axis=(1, 3)) /
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np.maximum(n, 1), np.nan)
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keep = np.isfinite(v) & (s.mean(axis=(1, 3)) > 0.8)
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return v[keep]
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print('depth of the shell search, measured on the model-subtracted residual')
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print('(outer field, 1200 < a < 2400 px, stars and the dust lane excluded)')
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print('')
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print(' bin bin size rms 3 sigma limit ideal if noise were white')
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print(' [px] [arcsec] [ADU/px] [mag/arcsec2] [mag/arcsec2]')
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sel = (a_map > 1200) & (a_map < 2400) # outer field, beyond the measured profile
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base = None
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rows = []
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for B in [8, 16, 32, 64, 128]:
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v = blockstat(res, star | dust, B, sel)
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if v.size < 30:
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continue
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sd = float(np.std(v))
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if base is None:
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base, base_b = sd, B
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ideal = base * (base_b / B)
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print(' %4d %7.1f %8.3f %13.2f %13.2f'
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% (B, B * PIXSCALE, sd, mu(3 * sd), mu(3 * ideal)))
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rows.append((B, sd))
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print('')
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print('The rms barely falls as the bins grow (%.2f -> %.2f ADU/px from 8 to 128 px'
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% (rows[0][1], rows[-1][1]))
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print('bins, against a factor 16 if it were white), so the floor is correlated')
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print('large-scale structure -- flat-field residual plus the sky-plane')
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print('systematic -- not photon noise. Pure photon noise would reach')
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print('%.2f mag/arcsec2 at 128 px bins; the real limit is %.1f mag SHALLOWER.'
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% (mu(3 * rms / 128), mu(3 * rms / 128) - mu(3 * rows[-1][1])))
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# ------------------------------------------------------- Fourier amplitudes
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print('')
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print('azimuthal Fourier amplitudes of the residual, normalised to the model')
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resd = np.load(path('_resd16.npy'))
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a16 = np.load(path('_a16.npy'))
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H, W = resd.shape
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Y, X = np.mgrid[0:H, 0:W]
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phi = np.arctan2(Y * 16 + 8 - YC, X * 16 + 8 - XC)
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P = np.load(path('_profile.npz'))
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prof, ac = P['Luminance'], P['a']
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okp = np.isfinite(prof) & (prof > 0)
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# stop where the measured profile itself runs out: beyond that I(a) is a fill
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# value and the fractional amplitudes would be meaningless
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A_OUT = float(P['a_out'])
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edges = np.geomspace(150, A_OUT, 11)
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out = []
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print(' a range [px] I(a) m=1 m=2 m=3 m=4 noise n')
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for lo, hi in zip(edges[:-1], edges[1:]):
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m = np.isfinite(resd) & (a16 >= lo) & (a16 < hi)
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n = m.sum()
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if n < 60:
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continue
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r, ph = resd[m], phi[m]
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amp = [2 * np.abs(np.mean(r * np.exp(-1j * k * ph))) for k in (1, 2, 3, 4)]
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noise = np.std(r) * np.sqrt(2. / n) * 2
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Im = np.interp(np.sqrt(lo * hi), ac[okp], prof[okp])
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out.append((np.sqrt(lo * hi), Im, amp, noise, n))
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print(' %5.0f-%5.0f %8.2f ' % (lo, hi, Im) +
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' '.join('%6.3f' % (a / max(Im, 1e-3)) for a in amp) +
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' %6.3f %5d' % (noise / max(Im, 1e-3), n))
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print('')
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print('(amplitudes are fractional: A_m / I(a). A value is only meaningful if it')
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print(' exceeds the "noise" column, which is the amplitude a pure-noise annulus')
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print(' would produce.)')
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fig, ax = plt.subplots(figsize=(9.5, 6.4))
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aa = np.array([o[0] for o in out]) * PIXSCALE
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for k in range(4):
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ax.plot(aa, [o[2][k] / max(o[1], 1e-3) for o in out], 'o-', ms=4,
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label='m = %d' % (k + 1))
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ax.plot(aa, [o[3] / max(o[1], 1e-3) for o in out], 'k--', lw=1.6,
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label='formal noise expectation (lower bound: it assumes' + chr(10) +
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'independent bins and ignores correlated systematics)')
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ax.set_xscale('log')
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ax.set_yscale('log')
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ax.set_xlabel('semi-major axis a [arcsec]')
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ax.set_ylabel('fractional Fourier amplitude $A_m / I(a)$')
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ax.set_title('NGC 5128: azimuthal structure in the model-subtracted residual' +
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chr(10) + 'amplitudes are 4-10% of the local surface brightness at '
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'every radius' + chr(10) + 'inside ~350 arcsec this is demonstrably '
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'the dust lane; outside it, correlated systematics')
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ax.grid(alpha=.3, which='both')
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ax.legend(fontsize=8.5, loc='lower left')
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fig.tight_layout()
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fig.savefig(path('NGC5128-sb-residual-fourier.png'), dpi=140)
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plt.close(fig)
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with open(path('sb-derived-quantities.txt'), 'a') as f:
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wr = lambda t: (f.write(t + chr(10)), print(t))
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wr('')
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wr('Shell / faint-structure search depth (outer field 1200 < a < 2400 px)')
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for B, sd in rows:
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wr(' %4d px bins (%5.1f arcsec): rms %.3f ADU/px, 3 sigma = %.2f mag/arcsec^2'
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% (B, B * PIXSCALE, sd, mu(3 * sd)))
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wr(' the rms does not integrate down like photon noise: the floor is')
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wr(' correlated large-scale structure, not shot noise')
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wr(' NO shells, arcs or tidal features were detected')
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print('')
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print('wrote NGC5128-sb-residual-fourier.png')
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