10.2.1 Determination of Echelle-Order Locations

The key step in the extraction operation is the determination of the centroid of each echelle order to subpixel accuracy. In principle, the global shifting operation of ORDERG, the results of which are incorporated into the high-dispersion SI, accomplishes this same function, but this routine does not always provide the shifting accuracy needed (e.g., for images having weak continua and for extended sources). The input for this refined centroid operation is provided by the high-dispersion SI and SF, the high-dispersion noise model and a set of fiducial line positions for each order which are given in Table 10.1.

The centroid order positions in Table 10.1 were determined empirically for a collection of well-exposed images for each camera. In each case the separations of the initial determinations were compared with echelle grating theory (i.e., they should vary as 1/m_ech²). The final positions show smooth undulating departures from this distribution amounting to a few tenths of a pixel in most cases.

**Table 10.1:** Fiducial Line Positions for the Echelle Orders
Order	LWP	LWR	SWP	Order	LWP	LWR	SWP
No.	Line	Line	Line	No.	Line	Line	Line
127	131.04	119.56		96	352.28	343.82	325.32
126	136.34	127.23		95	361.82	353.34	334.43
125	141.95	133.99	128.39	94	371.56	363.11	343.73
124	147.41	139.70	132.99	93	381.50	373.01	353.24
123	153.21	144.50	137.76	92	391.68	383.19	362.95
122	158.98	150.55	142.70	91	402.06	393.50	372.88
121	164.98	156.16	147.82	90	412.71	404.20	383.02
120	171.17	162.81	153.12	89	423.60	415.06	393.40
119	177.12	168.67	158.92	88	434.78	426.14	404.01
118	183.38	175.00	164.80	87	446.18	437.41	414.86
117	189.77	181.49	170.78	86	457.78	449.12	425.96
116	196.22	187.47	176.85	85	469.68	461.04	437.32
115	202.81	194.43	183.02	84	481.90	473.26	448.95
114	209.49	200.80	189.30	83	494.42	485.74	460.85
113	216.16	207.60	195.69	82	507.20	498.52	473.04
112	223.02	214.35	202.20	81	520.30	511.59	485.53
111	229.94	221.02	208.82	80	533.71	525.15	498.32
110	236.97	228.38	215.57	79	547.48	538.83	511.43
109	244.15	235.83	222.45	78	561.57	553.07	524.87
108	251.49	243.17	229.45	77	576.02	567.50	538.65
107	259.02	250.71	236.60	76	590.80	582.49	552.79
106	266.71	258.43	243.88	75	606.01	597.78	567.30
105	274.56	266.13	251.31	74	621.65	613.48	582.19
104	282.57	274.20	258.88	73	637.76	629.57	597.47
103	290.70	282.15	266.60	72	654.42	646.08	613.18
102	298.98	290.53	274.49	71	671.34	662.99	629.31
101	307.43	299.04	282.53	70	688.88	680.35	645.89
100	316.02	307.41	290.74	69	706.53	697.89	662.94
99	324.81	316.31	299.12	68		715.36	680.48
98	333.81	325.30	307.67	67		733.63	698.53
97	342.96	334.44	316.40	66			717.11

For each of the echelle orders, fluxes are extracted from a cut in the spatial direction of the high-dispersion SI, summing the fluxes of all ``good'' (i.e., nonflagged) pixels in a swath between sample positions 150 and 450. The summed fluxes for each spatial line are normalized to a common number of contributing pixels to account for the exclusion of flagged pixels. Next, an rms scatter is computed after excluding points in the spatial profile with significant flux above an initial rms value calculated by including all profile points. A local background is also fit through the low-flux points and subtracted from the profile array. A gaussian model is then cross-correlated through the net-flux profile if there are at least two points with fluxes above the rms value. A default value (i.e., the appropriate fiducial value from Table 10.1) is assigned for the order's centroid position according to any of the following conditions: