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include <error.h>
include <math.h>
# T_GRATINGS -- Compute grating parameters.
# Given a subset of grating parameters the remainder are computed.
procedure t_gratings()
bool e # Echelle grating?
real f # Focal length (mm)
real g # Grating grooves per mm
real b # Blaze angle (degrees)
real t # Angle of incidence (degrees)
int m # Order
real w # Blaze wavelength (Angstroms)
real d # Blaze dispersion (Angstroms / mm)
bool clgetb()
int clgeti()
real clgetr()
begin
# Input grating parameters.
e = clgetb ("echelle")
f = clgetr ("f")
g = clgetr ("gmm")
b = clgetr ("blaze")
t = clgetr ("theta")
m = clgeti ("order")
w = clgetr ("wavelength")
d = clgetr ("dispersion")
# Derive and check grating parameters.
iferr (call ast_grating (e, f, g, b, t, m, w, d))
call erract (EA_WARN)
# Print final parameters.
call printf ("Grating parameters:\n")
call printf (" Focal length = %g mm\n")
call pargr (f)
call printf (" Grating = %g grooves/mm\n")
call pargr (g)
call printf (" Blaze angle = %g degrees\n")
call pargr (b)
call printf (" Incidence angle = %g degrees\n")
call pargr (t)
call printf (" Order = %d\n")
call pargi (m)
call printf (" Blaze wavelength = %g Angstroms\n")
call pargr (w)
call printf (" Blaze dispersion = %g Angstroms/mm\n")
call pargr (d)
end
# Definitions of INDEF parameter flags.
define F 1B
define G 2B
define B 4B
define T 10B
define M 20B
define W 40B
define D 100B
# Combinations
define FG 3B
define FB 5B
define FT 11B
define FM 21B
define FW 41B
define GB 6B
define GT 12B
define GW 42B
define GD 102B
define BT 14B
define BM 24B
define BW 44B
define BD 104B
define TM 30B
define TW 50B
define TD 110B
define MW 60B
define MD 120B
define WD 140B
# AST_GRATING -- Derive and check grating parameters.
procedure ast_grating (e, f, g, b, t, m, w, d)
bool e
real f, g, b, t, w, d, x
int m
int i, flags
define err_ 10
begin
if (!IS_INDEF(f)) {
if (f <= 0.)
f = INDEF
}
if (!IS_INDEF(g)) {
if (g <= 0.)
g = INDEF
else
g = g / 1e7
}
if (!IS_INDEF(b)) {
b = DEGTORAD (b)
if (b == 0. && t == 0.)
t = INDEF
}
if (!IS_INDEF(t)) {
t = DEGTORAD (t)
if (t > PI && !IS_INDEF(b))
t = t - TWOPI + b
}
if (!IS_INDEFI(m) && m <= 0)
m = INDEFI
if (!IS_INDEF(w) && w <= 0.)
w = INDEF
if (!IS_INDEF(d) && d <= 0.)
d = INDEF
flags = 0
if (IS_INDEF(f))
flags = flags + F
if (IS_INDEF(g))
flags = flags + G
if (IS_INDEF(b))
flags = flags + B
if (IS_INDEF(t))
flags = flags + T
if (IS_INDEFI(m))
flags = flags + M
if (IS_INDEF(w))
flags = flags + W
if (IS_INDEF(d))
flags = flags + D
switch (flags) {
case 0, F, G, B, T, M, W, D:
switch (flags) {
case F:
f = cos (2 * b - t) / (g * m * d)
case G:
g = (sin (t) + sin (2 * b - t)) / (m * w)
if (g == 0.)
g = INDEF
case B:
if (t > PI) {
x = g * m * w / (2 * cos (t))
if (abs (x) > 1.)
goto err_
b = asin (x)
t = t - TWOPI + b
} else {
x = g * m * w - sin (t)
if (abs (x) > 1.)
goto err_
b = (t + asin (x)) / 2
}
case T:
x = g * m * w / (2 * sin(b))
if (abs (x) > 1.)
goto err_
if (e)
t = b + acos (x)
else
t = b - acos (x)
case M:
m = max (1, nint ((sin(t) + sin(2*b-t)) / (g * w)))
}
if (!IS_INDEF(g)) {
w = (sin (t) + sin (2 * b - t)) / (g * m)
d = cos (2 * b - t) / (f * g * m)
}
case FG:
x = (sin (t) + sin (2 * b - t)) / (m * w)
if (x == 0.)
goto err_
g = x
f = cos (2 * b - t) / (g * m * d)
case FB:
if (t > PI) {
x = g * m * w / (2 * cos (t))
if (abs (x) > 1.)
goto err_
b = asin (x)
t = t - TWOPI + b
} else {
x = g * m * w - sin (t)
if (abs (x) > 1.)
goto err_
b = (t + asin (x)) / 2
}
f = cos (2 * b - t) / (g * m * d)
case FT:
x = g * m * w / (2 * sin (b))
if (abs (x) > 1.)
goto err_
if (e)
t = b + acos (x)
else
t = b - acos (x)
f = cos (2 * b - t) / (g * m * d)
case FM:
m = nint ((sin (t) + sin (2 * b - t)) / (g * w))
f = cos (2 * b - t) / (g * m * d)
w = (sin (t) + sin (2 * b - t)) / (g * m)
d = cos (2 * b - t) / (f * g * m)
case FW:
w = (sin (t) + sin (2 * b - t)) / (g * m)
f = cos (2 * b - t) / (g * m * d)
case GB:
x = f * d / w
if (t > PI) {
b = atan (1 / (2 * x - tan (t)))
t = t - TWOPI + b
} else {
x = (tan (t) - x) / (1 + 2 * x * tan (t))
b = atan (x + sqrt (1 + x * x))
}
g = (sin (t) + sin (2 * b - t)) / (m * w)
case GT:
t = b + atan (2 * f * d / w - 1 / tan (b))
g = (sin (t) + sin (2 * b - t)) / (m * w)
case GW:
g = cos (2 * b - t) / (f * m * d)
if (g == 0.)
g = INDEF
else
w = (sin (t) + sin (2 * b - t)) / (g * m)
case GD:
x = (sin (t) + sin (2 * b - t)) / (m * w)
if (x == 0.)
goto err_
g = x
d = cos (2 * b - t) / (f * g * m)
case BT:
x = f * g * m * d
if (abs (x) > 1.)
goto err_
x = acos (x)
x = g * m * w - sin (x)
if (abs (x) > 1.)
goto err_
t = asin (x)
b = (acos (f * g * m * d) + t) / 2
case BM:
x = f * d / w
if (t > PI) {
b = atan (1 / (2 * x - tan (t)))
t = t - TWOPI + b
} else {
x = (tan (t) - x) / (1 + 2 * x * tan (t))
b = atan (x + sqrt (1 + x * x))
}
m = max (1, nint ((sin(t) + sin(2*b-t)) / (g * w)))
b = (t + asin (g * m * w - sin (t))) / 2
w = (sin (t) + sin (2 * b - t)) / (g * m)
d = cos (2 * b - t) / (f * g * m)
case BW:
b = (t + acos (f * g * m * d)) / 2
w = (sin (t) + sin (2 * b - t)) / (g * m)
case BD:
if (t > PI) {
x = g * m * w / (2 * cos (t))
if (abs (x) > 1.)
goto err_
b = asin (x)
t = t - TWOPI + b
} else {
x = g * m * w - sin (t)
if (abs (x) > 1.)
goto err_
b = (t + asin (x)) / 2
}
d = cos (2 * b - t) / (f * g * m)
case TM:
x = f * d / w
x = b + 2 * atan (x - 1 / (2 * tan (b)))
i = max (1, nint ((sin(x) + sin(2*b-x)) / (g * w)))
x = g * i * w / (2 * sin (b))
if (abs (x) > 1.)
goto err_
if (e)
t = b + acos (x)
else
t = b - acos (x)
m = i
w = (sin (t) + sin (2 * b - t)) / (g * m)
d = cos (2 * b - t) / (f * g * m)
case TW:
x = f * g * m * d
if (abs (x) > 1.)
goto err_
t = 2 * b - acos (x)
w = (sin (t) + sin (2 * b - t)) / (g * m)
case TD:
x = g * m * w / (2 * sin (b))
if (abs (x) > 1.)
goto err_
if (e)
t = b + acos (x)
else
t = b - acos (x)
d = cos (2 * b - t) / (f * g * m)
case MW:
m = max (1, nint (cos (2 * b - t) / (f * g * d)))
w = (sin (t) + sin (2 * b - t)) / (g * m)
d = cos (2 * b - t) / (f * g * m)
case MD:
m = max (1, nint ((sin(t) + sin(2*b-t)) / (g * w)))
w = (sin (t) + sin (2 * b - t)) / (g * m)
d = cos (2 * b - t) / (f * g * m)
case WD:
w = (sin (t) + sin (2 * b - t)) / (g * m)
d = cos (2 * b - t) / (f * g * m)
}
if (!IS_INDEF(g))
g = g * 1e7
if (!IS_INDEF(b))
b = RADTODEG (b)
if (!IS_INDEF(t))
t = RADTODEG (t)
if (IS_INDEF(f) || IS_INDEF(g) || IS_INDEF(b) || IS_INDEF(t) ||
IS_INDEF(m) || IS_INDEF(w) || IS_INDEF(d))
call error (1,
"Insufficient information to to determine grating parameters")
return
err_ if (!IS_INDEF(g))
g = g * 1e7
if (!IS_INDEF(b))
b = RADTODEG (b)
if (!IS_INDEF(t))
t = RADTODEG (t)
call error (2, "Impossible combination of grating parameters")
end
|
