def get_fpimage(qubic,SOURCE_POWER=1., SOURCE_THETA=np.radians(0), SOURCE_PHI=np.radians(45),
NU=150e9,DELTANU_NU=0.25,npts=512,HORN_OPEN=None,display=True,background=True,saturation=True):
bg=0
### background power is 6 pW
if background: bg=5.95e-12
## power in watts at the location of the entry horns
## that and phi in radians
LAMBDA = c / NU # [m]
DELTANU = DELTANU_NU * NU # [Hz]
FOCAL_LENGTH = 0.3 # [m]
PRIMARY_BEAM_FWHM = 14 # [degrees]
SECONDARY_BEAM_FWHM = 14 # [degrees]
DETECTOR_OFFSET = [0, 0] # [m]
SAT_POWER = 20e-12 # [W]
NPOINT_DETECTOR_PLANE = npts**2 # number of detector plane sampling points
DETECTOR_PLANE_LIMITS = (np.nanmin(qubic.detector.vertex[..., 0]),
np.nanmax(qubic.detector.vertex[..., 0])) # [m]
if HORN_OPEN is None: HORN_OPEN = ~qubic.horn.removed #all open
########
# BEAMS
########
primary_beam = GaussianBeam(PRIMARY_BEAM_FWHM)
secondary_beam = GaussianBeam(SECONDARY_BEAM_FWHM, backward=True)
########
# HORNS
########
nhorn_open = np.sum(HORN_OPEN)
horn_vec = np.column_stack([qubic.horn.center[HORN_OPEN],
np.zeros(nhorn_open)])
#################
# DETECTOR PLANE
#################
ndet_x = int(np.sqrt(NPOINT_DETECTOR_PLANE))
a = np.r_[DETECTOR_PLANE_LIMITS[0]:DETECTOR_PLANE_LIMITS[1]:ndet_x*1j]
det_x, det_y = np.meshgrid(a, a)
det_spacing = (DETECTOR_PLANE_LIMITS[1] - DETECTOR_PLANE_LIMITS[0]) / ndet_x
det_vec = np.dstack([det_x, det_y, np.zeros_like(det_x) - FOCAL_LENGTH])
det_uvec = norm(det_vec)
det_theta = np.arccos(det_uvec[..., 2])
# solid angle of a detector plane pixel (gnomonic projection)
central_pixel_sr = np.arctan(det_spacing / FOCAL_LENGTH)**2
detector_plane_pixel_sr = -central_pixel_sr * np.cos(det_theta)**3
############
# DETECTORS
############
qubic.detector.vertex += DETECTOR_OFFSET
header = create_fitsheader((ndet_x, ndet_x), cdelt=det_spacing, crval=(0, 0),
ctype=['X---CAR', 'Y---CAR'], cunit=['m', 'm'])
detector_plane = DiscreteSurface.fromfits(header)
integ = MaskOperator(qubic.detector.removed) * \
detector_plane.get_integration_operator(qubic.detector.vertex)
###############
# COMPUTATIONS
###############
""" Phase and transmission from the switches to the focal plane. """
transmission = np.sqrt(secondary_beam(det_theta) /
secondary_beam.sr *
detector_plane_pixel_sr)[..., None]
const = 2j * pi / LAMBDA
product = np.dot(det_uvec, horn_vec.T)
modelA = ne.evaluate('transmission * exp(const * product)')
""" Phase and transmission from the source to the switches. """
source_uvec = ang2vec(SOURCE_THETA, SOURCE_PHI)
source_E = np.sqrt(SOURCE_POWER) * np.sqrt(primary_beam(SOURCE_THETA))
const = 2j * pi / LAMBDA
product = np.dot(horn_vec, source_uvec)
modelB = ne.evaluate('source_E * exp(const * product)')
E = np.sum(modelA * modelB, axis=-1)
I = np.abs(E)**2
D = integ(I)
##########
# Adding Background power
##########
nobol = D == 0
D[~nobol]+=bg
##########
# NOISE
##########
hplanck=6.62606957e-34 # [M2.kg/s]
NEPbol = 4e-17 #[W/sqrt(hz)]
N = np.sqrt(2*hplanck*NU*D + 2*D**2/DELTANU + NEPbol**2)
N[nobol]=0
##########
# SATURATION
##########
if saturation:
saturated = D >= SAT_POWER
D[saturated]=0
N[saturated]=0
##########
# DISPLAY
##########
if display:
mp.figure()
mp.imshow(np.log10(I), interpolation='nearest', origin='lower')
mp.autoscale(False)
qubic.detector.plot(transform=detector_plane.topixel)
mp.figure()
mp.imshow(D, interpolation='nearest')
mp.gca().format_coord = lambda x,y: 'x={} y={} z={}'.format(x, y, D[x,y])
mp.show()
print('Given {} horns, we get {} W in the detector plane and {} W in the detec'
'tors.'.format(nhorn_open, np.sum(I), np.sum(D)))
return(D,N)
det_uvec = norm(det_vec)
det_theta = np.arccos(det_uvec[..., 2])
# solid angle of a detector plane pixel (gnomonic projection)
central_pixel_sr = np.arctan(det_spacing / FOCAL_LENGTH) ** 2
detector_plane_pixel_sr = -central_pixel_sr * np.cos(det_theta) ** 3
############
# DETECTORS
############
qubic.detector.vertex += DETECTOR_OFFSET
header = create_fitsheader(
(ndet_x, ndet_x), cdelt=det_spacing, crval=(0, 0), ctype=["X---CAR", "Y---CAR"], cunit=["m", "m"]
)
detector_plane = DiscreteSurface.fromfits(header)
integ = MaskOperator(qubic.detector.removed) * detector_plane.get_integration_operator(qubic.detector.vertex)
########
# MODEL
########
def get_model_A():
""" Phase and transmission from the switches to the focal plane. """
transmission = np.sqrt(secondary_beam(det_theta) / secondary_beam.sr * detector_plane_pixel_sr)[..., None]
const = 2j * pi / LAMBDA
product = np.dot(det_uvec, horn_vec.T)
return ne.evaluate("transmission * exp(const * product)")
def get_model_B():
