In the absence of systematic errors, the centering accuracy on wavelength
calibration lines is random noise limited. Brown (1990)
derived that the photon-noise limited accuracy of centering
may be estimated as:
where 
is the variance on the position of the line centre in
wavelength squared units,
Ii is the observed intensity at pixel i and the sum extends
over the window used for centering. The lines are assumed
sufficiently strong to make read-out noise negligible; the generalisation
to faint lines is however straightforward.
A useful estimate of 
] is obtained using a Gaussian
line profile and neglecting (for simplicity)
discretisation and edge effects, integrating over an infinite interval
rather than summing over a finite one gives:
Many lines are usually available with 
detected
electrons on their
central pixel. In the case of
critically sampled lines (full-width at half
maximum
FWHM < 2 pix), the photon-noise limit is thus close to
0.002 pix (
), 0.006 pix (
) or
0.018 pix (
) depending on the line strength. Hence a
positional accuracy on individual calibration lines of the order of
is in principle attainable. This conclusion remains
valid after taking into account the model-mismatch errors discussed by
David
& Verschueren (1995), when the proper precautions are made.
In practice, however, the residuals of the lines to a best fit are significantly larger. This is mainly due to the fact that laboratory input data are used at face value, without concern for the effects of line blending at the actual resolution of the astrophysical instrument.
Intuitively, it appears that the adverse influence of blending may be eliminated by rejecting the outlying residuals through a clipping algorithm. Hensberge & Verschueren (1990) showed for Th, why clipping algorithms are rather inefficient: the distribution of the centering bias due to blending is monotonously decreasing rather than multi-modal, and the larger part of the distribution extends to biases largely exceeding the random noise. Hence, a clipping algorithm only eliminates the most obviously blended lines. One should keep in mind that apparently weak blends, not easily noticeable on an individual measure with the instrument's optimal S/N, can still produce systematic centering errors which are an order of magnitude above the noise limit (see De Cuyper & Hensberge 1995). A stringent selection of useful lines is needed for critical applications: the residuals of a fit to the measured line positions will be useful for testing the suitability of the fit formula only when the rms induced by blending is negligible with respect to the contribution of random noise.