Abstract
This paper presents two novel approaches to the design of two-dimensional
(2-D) optical zero reference signals (ZRSs) that are robust against diffraction
effects based on the parametric minimum cross-entropy (PMCE) method. Grating
alignment systems require a 2-D optical ZRS to perform absolute measurements.
A common method of acquiring 2-D optical ZRSs involves illuminating two identical
superimposed 2-D zero reference codes (ZRCs). The output signal is the 2-D
optical ZRS and can be represented as the autocorrelation of the 2-D ZRC transmittance.
In ultrahigh-resolution systems, diffraction distorts the shadow of the first
2-D ZRC, degrading the autocorrelation and greatly reducing the amplitude
of the 2-D optical ZRS. To improve the robustness of 2-D optical ZRSs against
diffraction effects, this paper formulates two combinatorial optimization
problems for the design of 2-D ZRCs with minimum diffraction effects: one
of which is a maximization problem, and the other a minimization problem.
Aiming at solving the two problems, this study proposes two schemes based
on the PMCE method to search for an optimal 2-D ZRC. Simulation results reveal
that there are 3.36–8.34% increases in the slope of the central peak
of a 2-D optical ZRS and that there are 16.12–20.90% increases in the
sum of the slope of the central peak and the effective signal amplitude of
a 2-D optical ZRS, as compared with those obtained by the recently proposed
cross-entropy method. The proposed PMCE-based schemes prove to search for
2-D ZRCs more effectively than existing solutions, while requiring less computational
complexity.
© 2012 IEEE
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