.help gratings Mar91 noao.astutil
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NAME
gratings -- Compute and print grating parameters
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USAGE
gratings
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PARAMETERS
.ls echelle = no
Is the grating an echelle grating?  This selects whether the angle of
incidence is greater or less than blaze angle when the angle of incidence
or blaze angle are not specified.  For an echelle the angle of incidence
is generally greater than the blaze angle.
.le
.ls f = 590.
Focal length in millimeters.  Technically it is defined by the equation x =
f * tan (theta) where x is distance from the optical axis on the detector
and theta is the diffraction angle; i.e. it converts angular measures to
millimeters on the detector.  If the focal length is specified as INDEF it
is computed from the dispersion, which is required in this case, and the
other parameters.
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.ls gmm = 226.
Grating grooves per millimeter.  If specified as INDEF it is computed
from the order, which is required in this case, and the other parameters.
.le
.ls blaze = 4.5
Blaze angle in degrees.  It is always specified or printed as a positive
angle relative to the grating normal.  If specified as INDEF it is
computed from the other parameters.
.le
.ls theta = -10.5
Angle of incidence in degrees.  The angle of incidence must be in the plane
perpendicular to face of the grating.  The angle of incidence may be
specified relative to the grating normal or the blaze angle though it is
always printed relative to the grating normal.  To specify it relative to
the blaze angle add 360 degrees; for example to have an angle of 15 degrees
less than the blaze angle specify 360 - 15 = 345.  If the angle of
incidence is specified as INDEF it is computed from the other parameters.
.le
.ls order = 1
Order for which the wavelength and dispersion are specified.  If specified
as INDEF it will be computed from the grooves per mm, which is required in
this case, and the other parameters.
.le
.ls wavelength = INDEF
Blaze wavelength in Angstroms.  If specified as INDEF it will be computed
from the other parameters.
.le
.ls dispersion = INDEF
Blaze dispersion in Angstroms per millimeter.  If specified as INDEF it
will be computed from the focal length, which is required in this case,
and the other parameters.
.le
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DESCRIPTION
This task computes the grating parameters specified as INDEF from the other
grating parameters and prints the final set of self-consistent parameters.
The parameters are the focal length to the detector, the grooves per
millimeter of the grating, the blaze angle of the grating, the angle of
incidence of the incoming light to the grating (which is required to be in
the plane perpendicular to the face of the grating), the diffraction order,
and the blaze wavelength and dispersion at the blaze wavelength on the
detector for that order.  There must be five of these parameters specified
to compute the remaining two with the exceptions that the combinations
of the grooves per millimeter and the order or the focal length and
dispersion must not be simultaneously unspecified.  There are two cases in
which the computation will not succeed, if not enough parameters are
specified or when the combination of parameters is not possible.  In these
cases a warning is printed and the input parameters, including INDEF
values, are printed.

If more than the minimum number of parameters are specified then some of
the specified parameters will be adjusted to give a self-consistent set.
In particular, if all parameters are specified the input wavelength and
dispersion are ignored and new values are calculated.  If only one
parameter is not specified then the dispersion is adjusted if it is not the
dispersion the wavelength is adjusted if it is the dispersion.

When the order is not specified, the nearest integer order is computed from
the other non-integer parameters and then the wavelength and dispersion are
recomputed based on the integer order.

The basic grating equation used is

.nf
(1)	m * lambda = (sin(theta) + sin(beta)) / g
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where m is the order, lambda the wavelength, g the grooves per wavelength unit,
theta the angle of incidence to the grating normal, and beta the angle of
diffraction to the normal.  The diffraction angle relative to that
of the blaze maximum, psi, is given by

.nf
(2)	beta = psi + 2 * blaze - theta
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where blaze is the blaze angle.  The diffraction angle psi is related to
position on the detector, again measured from the blaze peak, by

.nf
(3)	x = f * tan(psi)
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where f is the effective focal length (as defined by this equation).
At the blaze maximum psi = x = 0 and the wavelength and dispersion
per millimeter on the detector are given by (1) and the derivative of (1)
with respect to x:

.nf
(4)	wavelength = 1E7*(sin(theta)+sin(2*blaze-theta))/(gmm*order)
(5)	dispersion = 1E7*cos(2*blaze-theta)/(gmm*order*f)
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where the variable names are the same as the program parameters and
the factor of 1E7 is the conversion between millimeters and Angstroms.

Equations (4) and (5) are the ones solved by this task.  There are a some
interesting points to note about the angle of incidence.  There are two
solutions of these equations one with the angle of incidence less than the
blaze angle and one greater than the blaze angle.  For an echelle the angle
of incidence is generally set greater than the blaze angle to avoid light
lost by reflections back along the angle of incidence.  The \fIechelle\fR
parameter is used to determine which side of the blaze angle the angle of
incidence will be computed in the cases in which it is not specified;
greater than the blaze angle when yes and less than the blaze angle when
no.

In spectrographs it is often the case that the angle between the
incoming beam and center of the diffracted beam, delta, is fixed where

.nf
(6)	delta = 2 * |theta - blaze|
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This fixes the angle between the blaze angle and the angle of incidence
needed to center the blaze function on the detector.  If one wants to
solve (4) and (5) for the blaze angle with this difference fixed the
angle of incidence may be specified relative to the blaze angle by
adding 360 degrees to the difference.  An example best describes this.
The Kitt Peak 4m Echelle Spectrograph has a 12 degree angle
between the incoming beam to the echelle grating and the beam to the
crossdisperser.  Then |theta - blaze| = 6 degrees.  For an echelle the
angle of incidence is greater than the blaze angle (relative to the
grating normal) so if we set the angle of incidence to 6 + 360
and the blaze angle to INDEF the resulting computation will
determine blaze and theta with a fixed 6 degree angle.
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EXAMPLES
1.  The default values are for a grating of 226 grooves per millimeter
in a 590 mm focal length camera.  For a blaze angle of 4.5 degrees
and an angle of incidence of -10.5 degrees (the angle is on the
other side of the grating normal relative to the blaze angle) the
first order wavelength and dispersion at the blaze peak is:

.nf
	cl> gratings
	Grating parameters:
	  Focal length = 590. mm
	  Grating = 226. grooves/mm
	  Blaze angle = 4.5 degrees
	  Incidence angle = -10.5 degrees
	  Order = 1
	  Blaze wavelength = 6706.696 Angstroms
	  Blaze dispersion = 70.69458 Angstroms/mm
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2.  To find nearest order and the dispersion for a wavelength of 3400
Angstroms:

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	cl> gratings order=INDEF wave=3400
	Grating parameters:
	  Focal length = 590. mm
	  Grating = 226. grooves/mm
	  Blaze angle = 4.5 degrees
	  Incidence angle = -10.5 degrees
	  Order = 2
	  Blaze wavelength = 3353.348 Angstroms
	  Blaze dispersion = 35.34729 Angstroms/mm
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3.  To find the grating parameters need to center 8000 Angstroms with
a dispersion of 90 Angstroms per millimeter:

.nf
	cl> gratings gmm=INDEF blaze=INDEF theta=345 wave=8000 disp=90
	Grating parameters:
	  Focal length = 590. mm
	  Grating = 177.8237 grooves/mm
	  Blaze angle = 4.223008 degrees
	  Incidence angle = -10.77702 degrees
	  Order = 1
	  Blaze wavelength = 8000. Angstroms
	  Blaze dispersion = 90. Angstroms/mm
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4.  What focal length should be used to get a dispersion of 20 Angstroms/mm
at 6700 Angstroms:

.nf
	cl> gratings f=INDEF wave=6700 disp=20
	Grating parameters:
	  Focal length = 2085.49 mm
	  Grating = 226. grooves/mm
	  Blaze angle = 4.5 degrees
	  Incidence angle = -10.5 degrees
	  Order = 1
	  Blaze wavelength = 6706.696 Angstroms
	  Blaze dispersion = 20. Angstroms/mm
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5.  What are the first order wavelength parameters for an echelle of
31.6 grooves per millimeter with a 63 degree blaze, and a 6 degree
angle of incidence relative to the blaze angle.  Then what are
the wavelength parameters in 80th order and what order is 6563 in.

.nf
	cl> gratings gmm=31.6 blaze=63 theta=69
	Grating parameters:
	  Focal length = 590. mm
	  Grating = 31.6 grooves/mm
	  Blaze angle = 63. degrees
	  Incidence angle = 69. degrees
	  Order = 1
	  Blaze wavelength = 560838.9 Angstroms
	  Blaze dispersion = 292.1256 Angstroms/mm
	cl> gratings gmm=31.6 blaze=63 theta=69 order=80
	Grating parameters:
	  Focal length = 590. mm
	  Grating = 31.6 grooves/mm
	  Blaze angle = 63. degrees
	  Incidence angle = 69. degrees
	  Order = 80
	  Blaze wavelength = 7010.487 Angstroms
	  Blaze dispersion = 3.651571 Angstroms/mm
	cl> gratings gmm=31.6 blaze=63 theta=69 order=INDEF wave=6563
	Grating parameters:
	  Focal length = 590. mm
	  Grating = 31.6 grooves/mm
	  Blaze angle = 63. degrees
	  Incidence angle = 69. degrees
	  Order = 85
	  Blaze wavelength = 6598.105 Angstroms
	  Blaze dispersion = 3.436772 Angstroms/mm
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SEE ALSO
artdata.mkechelle
.endhelp
