The differential rotation (``splaying'') of individual echelle orders results from the combined effects of the echelle and cross-dispersing elements. The ratio of these two components of dispersion is proportional to the ratio of the grating orders and can be expressed as 1/mechelle times a constant. The change in this ratio from one order to the next causes the orders to be differentially rotated (``splayed'') on the detector. The de-splaying angle for each camera was determined after first rotating the raw space image in the GEOM module and recognizing conceptually that the y coordinate of the rotated image may be replaced with the parameter 1/mech. Since the y positions of the orders are distributed as 1/mech, this axis may be thought as mapping a continuous (floating-point) parameter, 1/mech (Smith 1990a, 1990b). A single differential rotation constant may then be incorporated which is used ultimately to detilt each of the y pixel-lines with respect to a reference (``horizontal") line position. This detilting is in fact a de-splaying of each of the lines in the image with respect to a reference order: a single constant which properly takes into account the variation of the splaying-tilt with mech across the image field. The de-splaying angle is determined empirically and by means of a virtual-coordinate artifice rather than from grating parameters of the spectrograph because NEWSIPS does not yet ``know" what mech value will correspond to each y line in the rotated raw-image space in which the de-splaying corrections are computed. The de-splaying correction performed in NEWSIPS processing is such that pixels which lie along ``central'' x-y axes (positioned about the center of the target area) have no correction applied. Pixels which lie off of the ``central'' axes have a de-splaying correction applied that is directly proportional to the displacement of the pixel's position from the origin of the ``central'' axes. The de-splaying correction corresponds to a shift in the y (i.e., line) direction only.
Determination of the splaying constants was done iteratively for a collection of continuum images for each camera until values were found which forced all the orders to fall along constant pixel lines. In practice, the ``wiggles" of the orders (Chapter 7.3.3) limited the accuracy to which the de-splaying constants could be determined. However, small residual errors in these constants were presumed to be incorporated as residual slopes in the wiggle vectors.