All Figures

$\begin{figure} \par {\includegraphics[width=18cm]{3818fig1.eps} } \end{figure}$ Figure 1: Conventional velocities as a function of true radial velocity for selected values of the transverse velocity. The apparent radial velocity $\varv /c$ is plotted in the left panel, the radio velocity V/c is plotted in the center panel, and the optical velocity Z/c is plotted in the right panel. Note that, at a transverse velocity of 0.9 c, the red shift z always exceeds 1. Note that each family of curves intersects the axis of zero velocity measure at the same values of $\varv _{\rm t}$ because the redshift is zero for these combinations of $\varv _{\rm t}$ and $\varv _{\rm r}$ . Thus, regardless of the value of $\varv _{\rm t}$ , for any given redshift the velocity measures agree on whether the object appears to be receding or approaching. However, the object may appear to be receding at high speed even when it is actually approaching at high speed, though the converse is never true. At transverse velocities of $\varv _{\rm t} / c > \sqrt {2} / 2 ({\approx }0.71)$ all of the velocity measures are positive (receding) regardless of whether the object is actually receding or approaching. Furthermore, for $\varv _{\rm r} / c$ below -0.5, the faster the object approaches, the smaller the transverse velocity required to make it appear to be receding!
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In the text

$\begin{figure} {\includegraphics[width=18cm]{3818fig2.ps} } \end{figure}$ Figure 2: Geometry of gratings, prisms, and grisms. This simplified representation omits the collimation and focusing optics. Dashed lines mark ray paths in the plane of the figure - the "dispersion plane''. The normal to the grating/exit prism face and the normal to the detector plane are each projected onto the dispersion plane, and angles $\alpha$ , $\gamma$ , and $\theta$ are measured with respect to these projected normals. Usually the incident ray for a prism or grism is perpendicular to the entry face so that $\alpha$ is equal to the prism angle, $\rho$ . Angle $\gamma$ is wavelength-dependent, and consequently so is the offset $\xi$ in the dispersion direction on the detector. The intermediate spectral world coordinate, w, is proportional to $\xi$ . Reference wavelength $\lambda _{\rm r}$ follows the reference ray defined by $\gamma _{\rm r}$ and illuminates the reference point at $w= \xi = 0$ . The normal to the detector plane is shown tilted by angle $\theta$ from the reference ray though typically this angle is zero. The grating spacing G^-1 is indicated.
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In the text

$\begin{figure} {\includegraphics[width=8cm]{3818fig3.ps} } \verb*!CTYPE1 = \lq AWAV... ...Diffraction order! \\ \verb*!PV1_2 = 13.9 / [deg] Incident angle! \end{figure}$ Figure 3: KPNO Coudé Feed spectrograph with a long focal length and a 3K CCD.
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In the text

$\begin{figure} {\includegraphics[width=8cm]{3818fig4.ps} } \verb*!CTYPE1 = \lq AWAV... ...Diffraction order! \\ \verb*!PV1_2 = 64.8 / [deg] Incident angle! \end{figure}$ Figure 4: KPNO Hydra Fiber Bench Spectrograph using an echelle grating in $11{\rm th}$ order with a 2K CCD.
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In the text

$\begin{figure} {\includegraphics[width=8cm]{3818fig5.ps} } \verb*!CTYPE1 = \lq AWAV... ...fraction! \\ \verb*!PV1_4 = -1.077E6 / [m^(-1)] Refraction deriv! \end{figure}$ Figure 5: KPNO MARS spectrograph with a 450 lines/mm volume phase holographic grism and a 2K CCD.
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In the text

$\begin{figure} \includegraphics[width=8.8cm]{3818f6.eps}\par \end{figure}$ Figure 6: -TAB logic flow with and without an indexing vector. The coordinate array subscript m associated with intermediate world coordinate axis i is specified with keyword PV i_ ${\tt 3}$ . In the case of an independent -TAB axis it would have value 1. Note that $\psi _m$ is computed either with the CD i_j form of the linear transformation matrix or the PC i_j plus CDELT i form.
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In the text

$\begin{figure} \includegraphics[width=8.8cm]{3818f7.eps}\end{figure}$ Figure 7: Example taken from radio interferometry using -TAB with an indexing vector. The FITS keywords shown are suitable for the random groups format. The observation is made at a number of frequencies, with a number $N_\ell$ of regularly spaced $\delta _\ell$ spectral channels beginning from each of a number of arbitrary base frequencies $\nu _\ell$ . The use of an indexing vector reduces the number of values in the table from one array of 30 to two arrays of 10 each. In a real case the number of spectral channels would be significantly larger, making the space savings significant. In this example, pixel p_j = 6 produces $\psi _m = 6$ . This lies at $\Upsilon_m = 1\frac{5}{6}$ . The resulting coordinate is then $\frac{1}{6}\nu_1 + \frac{5}{6}\left( \nu_1 + 6\delta_1 \right)$ which, as one would expect, equals $\nu _1 + 5\delta _1$ . Note that this example involves only a single independent -TAB axis, so that PV i_ ${\tt 3}$ $= m \equiv 1$ .
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In the text

$\begin{figure} {\includegraphics[width=8cm]{3818fig3.ps} } \verb!CTYPE1 = \lq AWAV... ...Diffraction order! \\ \verb!PV1_2 = 13.9 / [deg] Incident angle! \end{figure}$	Figure 3: KPNO Coudé Feed spectrograph with a long focal length and a 3K CCD.
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$\begin{figure} {\includegraphics[width=8cm]{3818fig4.ps} } \verb!CTYPE1 = \lq AWAV... ...Diffraction order! \\ \verb!PV1_2 = 64.8 / [deg] Incident angle! \end{figure}$	Figure 4: KPNO Hydra Fiber Bench Spectrograph using an echelle grating in $11{\rm th}$ order with a 2K CCD.
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$\begin{figure} {\includegraphics[width=8cm]{3818fig5.ps} } \verb!CTYPE1 = \lq AWAV... ...fraction! \\ \verb!PV1_4 = -1.077E6 / [m^(-1)] Refraction deriv! \end{figure}$	Figure 5: KPNO MARS spectrograph with a 450 lines/mm volume phase holographic grism and a 2K CCD.
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