Following the successful completion of Step 1, an attempt is made to refine the order shifts by determining systematic differential shifts across the image, e.g., due to an expansion/contraction term. A failure in the Step 2 tests described below results in the adoption of the global fit determined from Step 1. Differential shifts cannot be computed for these cases.

Order centroid positions and weights found above are used in Step 2.
This step differs from Step 1 in two important respects. First, a
sufficient number of orders containing flux must be found both in the
short- and long-wavelength (spatial) ends of the camera. If this
distribution test fails, the global shift from Step 1 is adopted and
applied to all lines in the image. A second difference from Step 1 is
that Step 2 computes order spacings from the found centroids. A
least-squares solution is then determined from the differences of the
logarithms of these spacings versus echelle order number (because of the
expected 1/*m ^{2}*-dependence in order separation) and the logarithms of
the corresponding order spacings for the fiducial image. A quadratic
least-squares solution is attempted for SWP images because a curvature
term is sometimes necessary. For LWP images the least-squares solution
is linear, while for LWR images the solution is two joined line segments
across the camera. As a quality-control check,

The found shifts resulting from Step 2 are defined literally only for the order centroid positions. As a practical matter, the final shift for a given order is applied uniformly to all lines associated with that order, including the adjacent lines containing background fluxes. Note that this can produce small shift discontinuities for lines located midway between the orders.