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/*m*_{echelle} 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/*m*_{ech}. Since the
*y* positions of the orders are distributed as 1/*m*_{ech}, this
axis may be thought as mapping a continuous (floating-point) parameter,
1/m_{ech} (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 m_{ech} 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 m_{ech} 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.