Response Matrix Testing#
In this notebook, I’m testing out the ability to construct a response matrix for MOXSI
[1]:
import numpy as np
import distributed
from scipy.interpolate import interp1d
import astropy.units as u
import astropy.wcs
import matplotlib.pyplot as plt
from astropy.coordinates import SkyCoord
from sunpy.coordinates import Helioprojective, get_earth
import sunpy.map
from astropy.wcs.utils import pixel_to_pixel
from astropy.visualization import ImageNormalize, AsymmetricPercentileInterval, LogStretch
import ndcube
from synthesizAR.atomic.idl import spectrum_to_cube
from mocksipipeline.physics.spectral import SpectralModel
from mocksipipeline.detector.response import SpectrogramChannel, get_all_dispersed_channels
from overlappy.util import color_lat_lon_axes
Theory#
From CHIANTI, we can produce spectral map of the radiative loss as a function of \(\lambda\) and \(T\),
\[S(\lambda,T)\quad[\mathrm{ph}\,\mathrm{cm}^3\,\mathrm{s}^{-1}\,\mathrm{sr}^{-1}\,\mathrm{Å}^{-1}]\]
Additionally, the instrument response is a function of \(\lambda\) and \(m\) (spectral order),
\[\varepsilon(\lambda, m)\quad[\mathrm{cm}^2\,\mathrm{sr}\,\mathrm{pix}^{-1}\,\mathrm{DN}\,\mathrm{ph}^{-1}\mathrm{Å}]\]
Combining these two gives us our intermediate response matrix,
\[R^\prime(\lambda,m,T) = S(\lambda, T)\varepsilon(\lambda,m)\quad[\mathrm{DN}\,\mathrm{cm}^{5}\,\mathrm{s}^{-1}\,\mathrm{pix}^{-1}]\]
We then want to understand how to include our mapping from world pixel to detector pixel. Ultimately, we want a 3D response matrix which depends on \(p^\prime,p,T\), the pixel coordinate in the inverted frame, the pixel coordinate in the original detector, and the temperature, respectively,
\[R(p^\prime,p,T)\quad[\mathrm{DN}\,\mathrm{cm}^{5}\,\mathrm{s}^{-1}\,\mathrm{pix}^{-1}]\]
Outline of Steps#
The steps for doing this are:
Compute \(R^\prime\)
Create a WCS with equivalent scale, roll angle, reference coordinate but that is limited to the FOV of the instrument
Create WCS for each spectral order \(m\)
For the direction of the primed WCS that aligns with the dispersion, create an array that spans the every pixel in that direction (this is probably a whole row).
For every combination of \((p^\prime,\lambda, m)\), compute \(p\)
Map \(R^\prime\) into \(R\) for each \(\lambda,m,p^\prime\)
Step 1: Spectra and Instrument Response#
[2]:
spec_table = SpectralModel().spectral_table
WARNING: UnitsWarning: The unit 'Angstrom' has been deprecated in the VOUnit standard. Suggested: 0.1nm. [astropy.units.format.utils]
[3]:
fig = plt.figure(figsize=(15,5))
ax = fig.add_subplot(projection=spec_table.wcs)
vmin, vmax = AsymmetricPercentileInterval(1,98).get_limits(spec_table.data)
spec_table.plot(axes=ax,
aspect=10,
axes_units=('MK','Angstrom'),
norm=ImageNormalize(vmin=vmin, vmax=vmax, stretch=LogStretch()),
cmap='plasma')
fig.colorbar(ax.get_images()[0], label=spec_table.unit)
ax.set_title(r'$S(\lambda, T)$')
ax.set_xlim(spec_table.wcs.world_to_pixel([0.1,90]*u.Angstrom,0*u.MK)[0])
WARNING: UnitsWarning: The unit 'Angstrom' has been deprecated in the VOUnit standard. Suggested: 0.1nm. [astropy.units.format.utils]
[3]:
(0.0, 1634.5454545454545)
[4]:
all_channels = get_all_dispersed_channels()
[5]:
def compute_r_prime(spectra, channel):
f_interp = interp1d(spectra.axis_world_coords(1)[0].to_value('Angstrom'),
spectra.data,
axis=1,
bounds_error=False,
fill_value=0.0,) # Response is 0 outside of the response range
spectra_interp = f_interp(channel.wavelength.to_value('Angstrom')) * spectra.unit
response = channel.wavelength_response * channel.plate_scale * (channel.spectral_resolution*u.pix)
r_prime = spectra_interp * response
return spectrum_to_cube(r_prime, channel.wavelength, spectra.axis_world_coords(0)[0],)
[6]:
r_prime = [compute_r_prime(spec_table, chan) for chan in all_channels]
WARNING: UnitsWarning: The unit 'Angstrom' has been deprecated in the VOUnit standard. Suggested: 0.1nm. [astropy.units.format.utils]
/Users/wtbarnes/mambaforge/envs/mocksipipeline/lib/python3.9/site-packages/astropy/units/quantity.py:673: RuntimeWarning: divide by zero encountered in divide
result = super().__array_ufunc__(function, method, *arrays, **kwargs)
/Users/wtbarnes/mambaforge/envs/mocksipipeline/lib/python3.9/site-packages/astropy/units/quantity.py:673: RuntimeWarning: divide by zero encountered in divide
result = super().__array_ufunc__(function, method, *arrays, **kwargs)
/Users/wtbarnes/mambaforge/envs/mocksipipeline/lib/python3.9/site-packages/astropy/units/quantity.py:673: RuntimeWarning: invalid value encountered in multiply
result = super().__array_ufunc__(function, method, *arrays, **kwargs)
WARNING: UnitsWarning: The unit 'Angstrom' has been deprecated in the VOUnit standard. Suggested: 0.1nm. [astropy.units.format.utils]
[7]:
fig = plt.figure(figsize=(15,5*5))
for i,rp in enumerate(r_prime[4:]):
ax = fig.add_subplot(5,1,i+1,projection=rp.wcs)
vmin, vmax = AsymmetricPercentileInterval(1,99).get_limits(rp.data)
aspect_ratio = rp.axis_world_coords(1)[0].shape[0] / rp.axis_world_coords(0)[0].shape[0]
rp.plot(axes=ax,
aspect=0.5*aspect_ratio,
axes_units=('MK','Angstrom'),
norm=ImageNormalize(vmin=vmin, vmax=vmax, stretch=LogStretch()),
cmap='plasma')
fig.colorbar(ax.get_images()[0], label=rp.unit)
#ax.set_title(f'$R^\prime(\lambda, m={order}, T)$')
#ax.set_xlim(r_prime[f'{order}'].wcs.world_to_pixel([0.1,70]*u.Angstrom,0*u.MK)[0])
WARNING: UnitsWarning: The unit 'Angstrom' has been deprecated in the VOUnit standard. Suggested: 0.1nm. [astropy.units.format.utils]
WARNING: UnitsWarning: The unit 'Angstrom' has been deprecated in the VOUnit standard. Suggested: 0.1nm. [astropy.units.format.utils]
WARNING: UnitsWarning: The unit 'Angstrom' has been deprecated in the VOUnit standard. Suggested: 0.1nm. [astropy.units.format.utils]
WARNING: UnitsWarning: The unit 'Angstrom' has been deprecated in the VOUnit standard. Suggested: 0.1nm. [astropy.units.format.utils]
WARNING: UnitsWarning: The unit 'Angstrom' has been deprecated in the VOUnit standard. Suggested: 0.1nm. [astropy.units.format.utils]
WARNING: UnitsWarning: The unit 'Angstrom' has been deprecated in the VOUnit standard. Suggested: 0.1nm. [astropy.units.format.utils]
WARNING: UnitsWarning: The unit 'Angstrom' has been deprecated in the VOUnit standard. Suggested: 0.1nm. [astropy.units.format.utils]
WARNING: UnitsWarning: The unit 'Angstrom' has been deprecated in the VOUnit standard. Suggested: 0.1nm. [astropy.units.format.utils]
WARNING: UnitsWarning: The unit 'Angstrom' has been deprecated in the VOUnit standard. Suggested: 0.1nm. [astropy.units.format.utils]
[8]:
fig = plt.figure(figsize=(15,5))
t_index = 38
t_val = r_prime[0].axis_world_coords(0)[0][t_index].to('MK')
ax = fig.add_subplot()
for rp in r_prime[4:]:
ax.plot(rp.axis_world_coords(1)[0], rp[t_index, :].data)
ax.set_yscale('log')
ax.set_ylim(1e-36, 1e-28)
ax.legend(frameon=False)
ax.set_title(f'$R^\prime(\lambda,m,T={t_val:.2f})$')
WARNING: UnitsWarning: The unit 'Angstrom' has been deprecated in the VOUnit standard. Suggested: 0.1nm. [astropy.units.format.utils]
No artists with labels found to put in legend. Note that artists whose label start with an underscore are ignored when legend() is called with no argument.
[8]:
Text(0.5, 1.0, '$R^\\prime(\\lambda,m,T=7.94 MK)$')
Step 2: Create primed WCS#
[9]:
observer = get_earth('2020-11-09 18:00:00')
hpc_frame = Helioprojective(observer=observer, obstime=observer.obstime)
roll_angle = 0 * u.deg
[10]:
header = sunpy.map.make_fitswcs_header(
(450, 450),
SkyCoord(0, 0, unit='arcsec',frame=hpc_frame),
scale=all_channels[0].resolution,
rotation_angle=roll_angle,
)
wcs_prime = astropy.wcs.WCS(header=header)
[11]:
wcs_prime
[11]:
WCS Keywords
Number of WCS axes: 2
CTYPE : 'HPLN-TAN' 'HPLT-TAN'
CRVAL : 0.0 0.0
CRPIX : 225.5 225.5
PC1_1 PC1_2 : 1.0 -0.0
PC2_1 PC2_2 : 0.0 1.0
CDELT : 0.0020555555555555557 0.0020555555555555557
NAXIS : 450 450
Step 3: Create dispersed WCS#
[12]:
wcs_dispersed = [chan.get_wcs(observer, roll_angle=roll_angle) for chan in all_channels]
WARNING: FITSFixedWarning: 'datfix' made the change 'Set MJD-OBS to 59162.750000 from DATE-OBS'. [astropy.wcs.wcs]
WARNING: FITSFixedWarning: 'unitfix' made the change 'Changed units:
'angstrom' -> 'Angstrom'. [astropy.wcs.wcs]
Step 4: Create primed pixel coordinates#
[13]:
px_prime = np.arange(wcs_prime.array_shape[1])
py_prime = (wcs_prime.array_shape[0] - 1)/2
[14]:
coord_prime = wcs_prime.pixel_to_world(px_prime, py_prime)
[15]:
m_prime = sunpy.map.Map(np.nan*np.ones(wcs_prime.array_shape), wcs_prime)
[16]:
fig = plt.figure()
ax = fig.add_subplot(projection=m_prime)
m_prime.plot(axes=ax,cmap='viridis')
color_lat_lon_axes(ax)
ax.plot_coord(coord_prime,color='k')
ax.coords['hpln'].grid(lw=2)
ax.coords['hplt'].grid(lw=2)
Step 5: Map primed coordinates to dispersed coordinates#
[101]:
response_matrix = np.zeros(wcs_prime.array_shape[1:]+wcs_dispersed[0].array_shape[2:]+r_prime['0'].data.shape[:1])
for order in all_channels:
for iw, w in enumerate(all_channels[order].wavelength):
_, _, ix = wcs_dispersed[order].world_to_array_index(coord_prime, w)
ix = np.array(ix)
in_bounds = np.where(np.logical_and(ix>=0, ix<response_matrix.shape[1]))
response_matrix[px_prime[in_bounds], ix[in_bounds], :] += r_prime[f'{order}'].data[:, iw]
[103]:
plt.figure(figsize=(20,5))
plt.imshow(response_matrix[...,30], origin='lower', interpolation='none', cmap='Greys', norm=ImageNormalize(stretch=LogStretch()))
[103]:
<matplotlib.image.AxesImage at 0x2b62d8cd0>
[108]:
r_prime['0'].axis_world_coords(0)[0][25].to('MK')
[108]:
$1.7782794 \; \mathrm{MK}$
[132]:
plt.figure(figsize=(20,5))
for i_pos in [0, 225, 449]:
plt.plot(response_matrix[i_pos,:,25], label=f'$p_x={px_prime[i_pos]}$')
plt.yscale('log')
plt.ylim(1e-35, 1e-28)
plt.xlim(0,2000)
plt.legend(ncol=4,frameon=False)
[132]:
<matplotlib.legend.Legend at 0x2b96d0a90>
[166]:
all_channels[0].reference_pixel
[166]:
$[999.5,~374.5,~0] \; \mathrm{pix}$
Debugging#
trying to track down a fun bug in the cleaned up response matrix code
[34]:
dispersed_channels = get_all_dispersed_channels()
[35]:
extent = 2500 * u.arcsec
shape = tuple(np.ceil((extent / dispersed_channels[0].resolution[::-1]).to_value('pix')).astype(int))
[49]:
roll_angle = 0 * u.deg
observer = get_earth('2000-01-01 00:00:00')
hpc_frame = Helioprojective(observer=observer, obstime=observer.obstime)
reference_coordinate = SkyCoord(0, 0, unit='arcsec', frame=hpc_frame)
header = sunpy.map.make_fitswcs_header(shape,
reference_coordinate,
reference_pixel=(np.array(shape[::-1]) - 1)/2*u.pix, #dispersed_channels[0].reference_pixel[:2],
scale=dispersed_channels[0].resolution,
rotation_angle=roll_angle)
wcs_prime = astropy.wcs.WCS(header=header)
[50]:
wcs_dispersed = [chan.get_wcs(observer, roll_angle=roll_angle, dispersion_angle=0*u.deg) for chan in dispersed_channels]
WARNING: FITSFixedWarning: 'datfix' made the change 'Set MJD-OBS to 51544.000000 from DATE-OBS'. [astropy.wcs.wcs]
WARNING: FITSFixedWarning: 'unitfix' made the change 'Changed units:
'angstrom' -> 'Angstrom'. [astropy.wcs.wcs]
[51]:
px_prime = np.arange(wcs_prime.array_shape[1]) # NOTE: assume dispersive axis along the x-axis, gamma=0
py_prime = (wcs_prime.array_shape[0] - 1)/2
coord_prime = wcs_prime.pixel_to_world(px_prime, py_prime)
[53]:
coord_prime
[53]:
<SkyCoord (Helioprojective: obstime=2000-01-01T00:00:00.000, rsun=695700.0 km, observer=<HeliographicStonyhurst Coordinate (obstime=2000-01-01T00:00:00.000, rsun=695700.0 km): (lon, lat, radius) in (deg, deg, m)
(0., -2.95510448, 1.47104358e+11)>): (Tx, Ty) in arcsec
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[52]:
px_prime
[52]:
array([ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12,
13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25,
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[58]:
i_pix = wcs_dispersed[5].world_to_array_index(coord_prime, dispersed_channels[5].wavelength[1000])[2]
[59]:
i_pix
[59]:
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[33]:
wcs_dispersed[5]
[33]:
WCS Keywords
Number of WCS axes: 3
CTYPE : 'HPLN-TAN' 'HPLT-TAN' 'WAVE'
CRVAL : 0.0 0.0 0.0
CRPIX : 1000.5 375.5 1.0
PC1_1 PC1_2 PC1_3 : 1.0 0.0 -1.0
PC2_1 PC2_2 PC2_3 : 0.0 1.0 0.0
PC3_1 PC3_2 PC3_3 : 0.0 0.0 1.0
CDELT : 0.0020555555555555557 0.0020555555555555557 7.1800000000000005e-12
NAXIS : 2000 1500 1254
[40]:
coord_prime
[40]:
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(0., -2.95510448, 1.47104358e+11)>): (Tx, Ty) in arcsec
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[41]:
wcs_prime
[41]:
WCS Keywords
Number of WCS axes: 2
CTYPE : 'HPLN-TAN' 'HPLT-TAN'
CRVAL : 0.0 0.0
CRPIX : 1000.5 375.5
PC1_1 PC1_2 : 1.0 -0.0
PC2_1 PC2_2 : 0.0 1.0
CDELT : 0.0020555555555555557 0.0020555555555555557
NAXIS : 338 338
[42]:
shape
[42]:
(338, 338)
[ ]: