The field of the undulator for the VUV-FEL at the TESLA Test Facility has t
o meet very tough tolerances in order to guarantee a close overlap between
the electron beam and the laser field. Consequently the undulator was desig
ned to have height-adjustable poles in order to allow for fine tuning of th
e vertical undulator fit ld in such a way that the trajectory is straighten
ed. The signature of local pole height and gap changes on the field distrib
ution was investigated. It was seen that changes are not restricted to the
pole itself. its effect can be seen up to the next eight neighboring poles,
in this contribution we describe an algorithm in detail, which allows the
prediction of required pole height changes in order to correct for field er
rors. As input data field errors deduced from precise magnetic field measur
ements are used together with the signatures of pole movements. A band diag
onal system of linear equations has to be solved to obtain the pole height
corrections. For demonstration of the method the field of the 0.9 m long pr
ototype structure was optimized to have a straight trajectory. Since only a
sparse band diagonal system of equations has to be solved, the method has
the potential to be used in very long undulators having 600 -1000 poles. (C
) 1999 Elsevier Science B.V. All rights reserved.