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Algorithm for Determining the Inhomogeneity Distribution Inside Beamsplitter Cubes

IP.com Disclosure Number: IPCOM000106530D
Original Publication Date: 1993-Nov-01
Included in the Prior Art Database: 2005-Mar-21
Document File: 6 page(s) / 334K

Publishing Venue

IBM

Related People

Rosenbluth, AE: AUTHOR

Abstract

Index inhomogeneities in the beamsplitter elements of lithography lenses cause non-rotational aberrations when integrated along the complex folded paths followed by the light. These aberrations are more easily avoided or corrected if the internal 3D index distribution is calculated by the algorithm described herein.

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Algorithm for Determining the Inhomogeneity Distribution Inside Beamsplitter Cubes

      Index inhomogeneities in the beamsplitter elements of
lithography lenses cause non-rotational aberrations when integrated
along the complex folded paths followed by the light.  These
aberrations are more easily avoided or corrected if the internal 3D
index distribution is calculated by the algorithm described herein.

      Beamsplitter lithography lenses, such as the SVGL Micrascan '92
printer, contain as their key element a (typically fused silica) cube
of large thickness (~100mm single pass).  When the cube
contains residual index inhomogeneities, the resulting aberrations
will be non-rotational, and therefore difficult to correct.

      Where the beamsplitter presents an unusual challenge is not in
measuring the transmission inhomogeneity, but in making use of this
information.  More familiar lens elements are typically disk-shaped
in configuration, and have modest thickness to diameter ratio.  This
makes it possible to approximately identify different sub-apertures
cut from a measured transmission interferogram with the
inhomogeneities that will be imposed on wavefronts originating from
different field directions.

      A beamsplitter can likewise be hand-figured to correct for
inhomogeneity, but it is of course impossible to clock individual
slices for symmetry.  Moreover, an interferometric test configuration
duplicating a single field position does not immediately convey
information about wavefronts from other field directions, due to the
large path lengths involved (over which small angular differences can
become significant).  Though initially gradual, the inhomogeneities
are also abruptly truncated in a completely non-rotational way at the
hypotenuse, and even modest field variations can be significant
there.

      If the 3D index distribution can be determined, the above
uncertainties can be removed by gradient index raytracing.  Such a
procedure might be undertaken to help decide how to cut prisms from
the initial fused silica piece (or pieces), and can also be repeated
to guide later hand figuring.

      Most often the inhomogeneity is investigated using three plane
wave interferograms, each integrating &Delta.n along one of the
principal axes of the cube.  Reconstruction of the cube from only
three projections is, of course, not a well-posed problem.
Fortunately, other information is available.  First, it is important
that the fused silica vendor supply material that is free of
striations, and the inhomogeneity in qualified material can then be
assumed quite gradual.  Further, the mechanisms by which
inhomogeneity arises also constrain the index gradients.  The best
optical grades of fused silica are made by CVD deposition.  During
this process the boule is rotated, typically causing a distinct axis
for the inhomogeneity.  Other inhomogeneity can arise during
re-annealing, a slow, multi-day process...