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diff --git a/noao/astutil/doc/gratings.hlp b/noao/astutil/doc/gratings.hlp new file mode 100644 index 00000000..593ddd62 --- /dev/null +++ b/noao/astutil/doc/gratings.hlp @@ -0,0 +1,252 @@ +.help gratings Mar91 noao.astutil +.ih +NAME +gratings -- Compute and print grating parameters +.ih +USAGE +gratings +.ih +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. +.le +.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 +.ih +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 +.fi + +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 +.fi + +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) +.fi + +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) +.fi + +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| +.fi + +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. +.ih +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 +.fi + +2. To find nearest order and the dispersion for a wavelength of 3400 +Angstroms: + +.nf + 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 +.fi + +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 +.fi + +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 +.fi + +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 +.fi +.ih +SEE ALSO +artdata.mkechelle +.endhelp |