def CDAbeam(num, div, pitch, roll, cda):
## PT.transform(*cda)
PT.pointsource(div, num)
PT.transform(0, 0, 0, pitch, 0, 0)
PT.transform(0, 0, 0, 0, 0, roll)
PT.itransform(*cda)
return
def primMaskTrace(fold, primary, woltVignette=True, foldrot=0.):
#Get Wolter parameters
alpha, p, d, e = conicsolve.woltparam(220., 8400.)
primfoc = conicsolve.primfocus(220., 8400.)
#Trace to fold mirror
#translate to center of fold mirror
PT.transform(0., 85.12, primfoc - 651.57 + 85.12, 0, 0, 0)
#rotate so surface normal points in correct direction
PT.transform(0, 0, 0, -3 * pi / 4, 0, 0)
PT.transform(0, 0, 0, 0, 0, pi)
#trace to fold flat
PT.flat()
#Introduce fold misalignment
PT.transform(*fold)
PT.zernsurfrot(foldsag, foldfig, 406. / 2, -174.659 * pi / 180 + foldrot)
PT.itransform(*fold)
PT.reflect()
PT.transform(0, 0, 0, 0, 0, -pi)
PT.transform(0, 0, 0, pi / 4, 0, 0)
#Translate to optical axis mid-plane, then down to image of
#primary focus, place primary mirror and trace
PT.transform(0, 85.12, 651.57 - 85.12, 0, 0, 0)
PT.flat()
## pdb.set_trace()
rt = conicsolve.primrad(8475., 220., 8400.)
PT.transform(0, -rt, 75., 0, 0, 0)
PT.transform(*primary)
PT.transform(0, rt, -8475., 0, 0, 0)
## PT.wolterprimary(220.,8400.)
PT.primaryLL(220., 8400., 8525., 8425., 30. * np.pi / 180., pcoeff, pax,
paz)
if woltVignette is True:
ind = logical_and(PT.z < 8525., PT.z > 8425.)
PT.vignette(ind=ind)
PT.reflect()
PT.transform(0, -rt, 8475., 0, 0, 0)
PT.itransform(*primary)
PT.transform(0, rt, -8475., 0, 0, 0)
#Move back up to mask plane and trace flat
PT.transform(0, 0, 8400. + 134.18, 0, 0, 0)
PT.flat()
## pdb.set_trace()
#Rays should now be at Hartmann mask plane
return
def setupSource(wave,N,radius=450.,focal=8000.,scatter=50e-6,\
gwidth=25.,glength=32.,pitch=0.,yaw=0.,roll=0.):
"""Set up converging beam with some scatter.
Idea is to place a grating at radius and focal length
with an incidence angle of 1.5 degrees
"""
#Setup rays over grating surface
PT.x = np.random.uniform(low=-gwidth / 2, high=gwidth / 2, size=N)
PT.y = np.random.uniform(low=-glength / 2, high=glength / 2, size=N)
PT.z = np.repeat(0., N)
PT.l = np.zeros(N)
PT.m = np.zeros(N)
PT.n = np.zeros(N)
PT.ux = np.zeros(N)
PT.uy = np.zeros(N)
PT.uz = np.repeat(1., N)
#Transform to nominal focus to set ray cosines
PT.transform(0, 0, 0, -88.5 * np.pi / 180, 0, 0)
PT.transform(0, radius, -focal, 0, 0, 0)
rad = np.sqrt(PT.x**2 + PT.y**2 + PT.z**2)
PT.l = -PT.x / rad
PT.m = -PT.y / rad
PT.n = -PT.z / rad
#Add scatter
PT.l = PT.l + scatter / 10. * np.random.normal(size=N)
PT.m = PT.m + scatter * np.random.normal(size=N)
PT.n = -np.sqrt(1. - PT.l**2 - PT.m**2)
#Go back to plane of of grating
PT.transform(0, -radius, focal, 0, 0, 0)
PT.transform(0, 0, 0, 88.5 * np.pi / 180, 0, np.pi)
#Place grating and diffract
hubdist = np.sqrt(radius**2 + focal**2) * np.cos(1.5 * np.pi / 180)
PT.flat()
PT.reflect()
PT.transform(0, 0, 0, pitch, roll, yaw)
PT.radgrat(hubdist, 160. / hubdist, 1, wave)
PT.itransform(0, 0, 0, pitch, roll, yaw)
#Go to focal plane
PT.transform(0, 0, 0, np.pi / 2, 0, 0)
PT.transform(0, 0, -hubdist, 0, 0, 0)
PT.transform(0, 0, 27.27727728 - .04904905, 0, 0, 0)
PT.flat()
#plt.plot(PT.x,PT.y,'.')
return PT.centroid()
def traceBeam(gratAlign,order=1.,wave=2.48,blaze=30.):
"""Traces a beam to grating, applies misalignment,
then traces to focal plane and returns mean
x,y position
x refers to spectral direction
"""
#Compute yaw to achieve Littrow configuration
phi0 = arccos(sin(1.5*pi/180)/cos(blaze*pi/180))
yaw = -tan(sin(blaze*pi/180)/tan(phi0))
## yaw = yaw - pi/2
## pdb.set_trace()
#Set up beam
rays = PT.pointsource(0.,10) #multiple rays to avoid Python complaints
#Rotate to nominal grating reference frame
PT.transform(rays,0,0,0,pi/2+1.5*pi/180,0,0)
#Apply misalignment
PT.transform(rays,*gratAlign)
#Trace grating
PT.flat(rays)
PT.transform(rays,0,0,0,0,0,yaw) #-1.73211678*pi/180
PT.radgrat(rays,11500.,160./11500.,order,wave)
PT.itransform(rays,0,0,0,0,0,yaw)
#Reverse misalignment
PT.itransform(rays,*gratAlign)
#Trace to focal plane
PT.transform(rays,0,11500.,0,0,0,0)
PT.transform(rays,0,0,0,pi/2,0,0)
PT.flat(rays)
#Return mean positions
return mean(rays[1]),mean(rays[2])
def traceFromMask(N,
numholes,
cda,
fold,
retro,
primary,
foldrot=0.,
retrorot=0.):
#Vignette at proper hole
h = hartmannMask()
ind = h == N
PT.vignette(ind=ind)
#Continue trace up to retro and back to CDA
PT.transform(0, -123.41, 1156.48 - 651.57 - 134.18, 0, 0, 0)
PT.flat()
PT.transform(0, 0, 0, pi, 0, 0)
PT.transform(*retro)
PT.zernsurfrot(retrosag, retrofig, 378. / 2, -8.993 * pi / 180 + retrorot)
PT.itransform(*retro)
PT.reflect()
PT.transform(0, 0, 0, -pi, 0, 0)
PT.transform(0, 123.41, -1156.48 + 651.57 + 134.18, 0, 0, 0)
PT.flat()
h = hartmannMask()
ind = h == N
PT.vignette(ind=ind)
PT.transform(0, 0, -134.18, 0, 0, 0)
rt = conicsolve.primrad(8475., 220., 8400.)
PT.transform(0, -rt, 75., 0, 0, 0)
PT.transform(*primary)
PT.transform(0, rt, -8475., 0, 0, 0)
PT.wolterprimary(220., 8400.)
ind = logical_and(PT.z < 8525., PT.z > 8425.)
PT.vignette(ind=ind)
PT.reflect()
PT.transform(0, -rt, 8475., 0, 0, 0)
PT.itransform(*primary)
PT.transform(0, rt, -8475., 0, 0, 0)
PT.transform(0,-85.12,8400.-651.57+85.12\
,0,0,0)
PT.transform(0, 0, 0, -pi / 4, 0, 0)
PT.transform(0, 0, 0, 0, 0, pi)
PT.flat()
PT.transform(*fold)
PT.zernsurfrot(foldsag, foldfig, 406. / 2, -174.659 * pi / 180 + foldrot)
PT.itransform(*fold)
PT.reflect()
PT.transform(0, 0, 0, 0, 0, -pi)
PT.transform(0, 0, 0, 3 * pi / 4, 0, 0)
PT.transform(0,-85.12,-85.12-(conicsolve.primfocus(220.,8400.)-651.57)\
,0,0,0)
PT.transform(*cda)
PT.flat()
return
def traceCyl(align):
"""Traces a cylindrical approximation to Wolter I geometry
Assumes 1 m radius of curvature in accordance with OAB samples
align is a 12 element array giving the transformations to be
applied to each mirror
Uses identical set of rays each run defined upon module import
Adds a restraint such that any vignetting over 25% results in
a huge merit function
"""
#Set up source
np.random.seed(5)
a, p, d, e = con.woltparam(1000., 10000.)
r0 = con.primrad(10025., 1000., 10000.)
r1 = con.primrad(10125., 1000., 10000.)
dphi = 100. / 1000.
PT.subannulus(r0, r1, dphi, 10**4)
PT.transform(0, 0, 0, np.pi, 0, 0)
PT.transform(0, 0, -10500., 0, 0, 0)
#Trace primary cylinder: go to tangent point at center
#of mirror and then rotate to cone angle, then move
#to new cylinder axis and tracecyl
rt = con.primrad(10075., 1000., 10000.)
PT.transform(rt, 0, 0, 0, a, 0)
PT.transform(*align[:6])
PT.transform(0, 0, 0, np.pi / 2, 0, 0)
PT.transform(-1000., 0, 0, 0, 0, 0)
PT.cyl(1000.)
#Vignette rays missing physical surface
ind = np.logical_and(abs(PT.z) < 50., abs(PT.y) < 50.)
PT.vignette(ind=ind)
#Reflect and reverse transformations
PT.reflect()
PT.transform(1000., 0, 0, 0, 0, 0)
PT.itransform(0, 0, 0, np.pi / 2, 0, 0)
PT.itransform(*align[:6])
PT.itransform(rt, 0, 0, 0, a, 0)
#Trace secondary cylinder: same principle as before
rt = con.secrad(9925., 1000., 10000.)
PT.transform(0, 0, -150., 0, 0, 0)
PT.transform(rt, 0, 0, 0, 3 * a, 0)
PT.transform(*align[6:])
PT.transform(0, 0, 0, np.pi / 2, 0, 0)
PT.transform(-1000., 0, 0, 0, 0, 0)
PT.cyl(1000.)
#Vignette rays missing physical surface
ind = np.logical_and(abs(PT.z) < 50., abs(PT.y) < 50.)
PT.vignette(ind=ind)
#Reflect and reverse transformations
PT.reflect()
PT.transform(1000., 0, 0, 0, 0, 0)
PT.itransform(0, 0, 0, np.pi / 2, 0, 0)
PT.itransform(*align[6:])
PT.itransform(rt, 0, 0, 0, 3 * a, 0)
#Go down to nominal focus
PT.transform(0, 0, -9925., 0, 0, 0)
PT.flat()
#Compute merit function
nom = PT.rmsCentroid() / 10**4 * 180. / np.pi * 60**2
nom = nom + max((9500. - np.size(PT.x)), 0.)
return nom
def fullFromMask(N, cda, fold, retro, prim, sec, foldrot=0., retrorot=0.):
## pdb.set_trace()
#Vignette at proper hole
h = hartmannMask()
ind = h == N
PT.vignette(ind=ind)
#Continue trace up to retro and back to CDA
PT.transform(0, -123.41, 1156.48 - 651.57 - 134.18, 0, 0, 0)
PT.flat()
PT.transform(0, 0, 0, pi, 0, 0)
PT.transform(*retro)
PT.zernsurfrot(retrosag, retrofig, 378. / 2, -8.993 * pi / 180 + retrorot)
PT.itransform(*retro)
PT.reflect()
PT.transform(0, 0, 0, -pi, 0, 0)
#Back to mask
PT.transform(0, 123.41, -1156.48 + 651.57 + 134.18, 0, 0, 0)
PT.flat()
h = hartmannMask()
ind = h == N
PT.vignette(ind=ind)
#Place Wolter surfaces
PT.transform(0, 0, -134.18 - 8400., 0, 0, 0)
PT.transform(0, -conicsolve.primrad(8425., 220., 8400.), 8425., 0, 0, 0)
PT.transform(*prim)
PT.itransform(0, -conicsolve.primrad(8425., 220., 8400.), 8425., 0, 0, 0)
## PT.wolterprimary(220.,8400.)
PT.primaryLL(220., 8400., 8525., 8425., 30. * np.pi / 180., pcoeff, pax,
paz)
pdb.set_trace()
ind = logical_and(PT.z < 8525., PT.z > 8425.)
PT.vignette(ind=ind)
PT.transform(0, -conicsolve.primrad(8425., 220., 8400.), 8425., 0, 0, 0)
PT.itransform(*prim)
PT.itransform(0, -conicsolve.primrad(8425., 220., 8400.), 8425., 0, 0, 0)
PT.reflect()
#Wolter secondary
PT.transform(0, -conicsolve.secrad(8325., 220., 8400.), 8325., 0, 0, 0)
PT.transform(*sec)
PT.itransform(0, -conicsolve.secrad(8325., 220., 8400.), 8325., 0, 0, 0)
PT.woltersecondary(220., 8400.)
ind = logical_and(PT.z < 8375., PT.z > 8275.)
PT.vignette(ind=ind)
PT.reflect()
PT.transform(0, -conicsolve.secrad(8325., 220., 8400.), 8325., 0, 0, 0)
PT.itransform(*sec)
PT.itransform(0, -conicsolve.secrad(8325., 220., 8400.), 8325., 0, 0, 0)
## PT.woltersecondary(220.,8400.)
## ind = logical_and(PT.z<8375.,PT.z>8275.)
## PT.vignette(ind=ind)
## PT.reflect()
#Back to fold
PT.transform(0,-85.12,8400.-651.57+85.12\
,0,0,0)
PT.transform(0, 0, 0, -pi / 4, 0, 0)
PT.transform(0, 0, 0, 0, 0, pi)
PT.flat()
PT.transform(*fold)
PT.zernsurfrot(foldsag, foldfig, 406. / 2, -174.659 * pi / 180 + foldrot)
PT.itransform(*fold)
PT.reflect()
PT.transform(0, 0, 0, 0, 0, -pi)
#Back to CDA
PT.transform(0, 0, 0, 3 * pi / 4, 0, 0)
PT.transform(0,-85.12,-85.12-8400.+651.57\
,0,0,0)
PT.transform(*cda)
PT.flat()
return