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5 March 2019 On the equivalence of optimization metrics in Stokes polarimetry
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Abstract
Optimization of polarimeters has historically been achieved using an assortment of performance metrics. Selection of an optimization parameter is, however, frequently made on an ad hoc basis. We rigorously demonstrate that optimization strategies in Stokes polarimetry based on three common metrics, namely the Frobenius condition number of the instrument matrix, the determinant of the associated Gram matrix, or the equally weighted variance, are frequently formally equivalent. In particular, using each metric, we derive the same set of constraints on the measurement states, correcting a previously reported proof, and show that these can be satisfied using spherical 2 designs. Discussion of scenarios in which equivalence between the metrics breaks down is also given. Our conclusions are equally applicable to optimization of the illumination states in Mueller matrix polarimetry.
© 2019 Society of Photo-Optical Instrumentation Engineers (SPIE) 0091-3286/2019/$25.00 © 2019 SPIE
Matthew R. Foreman and François Goudail "On the equivalence of optimization metrics in Stokes polarimetry," Optical Engineering 58(8), 082410 (5 March 2019). https://doi.org/10.1117/1.OE.58.8.082410
Received: 26 November 2018; Accepted: 14 February 2019; Published: 5 March 2019
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