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Legendre polynomials rather than other
types, as the x- and y-based Legendre
polynomials are orthogonal with respect
to a rectangle while, for example, radial
Zernike polynomials aren’t. Certain low-order terms of the orthonormal Legendre
polynomials are directly related to
common aberrations such as piston, x and
y tilt, x and y defocus, x and y primary
coma, and so on. The researchers aim
was to test their new algorithm against an
older iterative nonpolynomial algorithm
that, although accurate, was slow.
To numerically test their algorithm, the
researchers generated an arbitrary wavefront consisting of six orders ( 28 terms) of
Legendre polynomials with random coefficients; the modeled CRSI had both radial
and lateral (in both x and y) shear. The
peak-to-valley residual error between the
generated and reconstructed wavefront
was very small—on the order of 10–14 nm.
The researchers then experimen-
tally tested the algorithm on a real CRSI,
For the future, the group plans to
increase the number of polynomial
terms as much as possible (although this
increases noise), while using as small
a shear as they can (which reduces
1. E. Kewei et al., Opt. Express (2015);
doi: 10.1364/OE. 23.020267.
and phosphors for
A U.S. patent granted to VerLASE
(Winooski, VT) describes new wave-length-conversion materials based on
two-dimensional (2D) semiconductor structures that overcome most
technical issues associated with traditional phosphors and even overcome
emerging hurdles to adoption of
quantum dots (QDs). 1
Compared to traditional phosphors,
these 2D converters have a narrower
spectral profile and better color saturation. And compared to both QDs and
phosphors, the new materials have better