Focusing anomalies with binary diffractive optical elements

O. Bouzid; S. Haddadi; M. Fromager; E. Cagniot; K. Ferria; A. Forbes; K. Ait-Ameur

doi:10.1364/AO.56.009735

Applied Optics
Vol. 56,
Issue 35,
pp. 9735-9741
(2017)
•https://doi.org/10.1364/AO.56.009735

Focusing anomalies with binary diffractive optical elements

O. Bouzid, S. Haddadi, M. Fromager, E. Cagniot, K. Ferria, A. Forbes, and K. Ait-Ameur

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O. Bouzid, S. Haddadi, M. Fromager, E. Cagniot, K. Ferria, A. Forbes, and K. Ait-Ameur, "Focusing anomalies with binary diffractive optical elements," Appl. Opt. 56, 9735-9741 (2017)

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Abstract

Binary diffractive optics have been extensively studied to date as tools for arbitrary laser beam shaping and experimentally implemented with etched transparent optics and spatial light modulators. Here we demonstrate that a simple one-step binary optic is able to enhance the intensity of a focused beam, displaying some counterintuitive focusing anomalies. We explain these effects by considering the optical aberrations in binary diffractive optics and outline how this may be exploited for further improvements in refractive/diffractive combinations for super-resolution microscopy.

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$j$	$Z_{j}$	Type of Aberration
1	1	Piston
4	$\sqrt{3} (2 {\bar{ρ}}^{2} - 1)$	Defocus
11	$\sqrt{5} (6 {\bar{ρ}}^{4} - 6 {\bar{ρ}}^{2} + 1)$	Primary spherical
22	$\sqrt{7} (20 {\bar{ρ}}^{6} - 30 {\bar{ρ}}^{4} + 12 {\bar{ρ}}^{2} - 1)$	Secondary spherical
37	$3 (70 {\bar{ρ}}^{8} - 140 {\bar{ρ}}^{6} + 90 {\bar{ρ}}^{4} - 20 {\bar{ρ}}^{2} + 1)$	Tertiary spherical

$N$	$A_{4}$	$A_{11}$	$A_{22}$	$A_{37}$
1	$16.23 \times 10^{- 2}$	$- 10.48 \times 10^{- 2}$	$1.55 \times 10^{- 2}$	$4.39 \times 10^{- 2}$
2	$10.14 \times 10^{- 2}$	$8.18 \times 10^{- 2}$	$- 3.57 \times 10^{- 2}$	$- 12.26 \times 10^{- 2}$
3	$7 \times 10^{- 2}$	$7.57 \times 10^{- 2}$	$3.95 \times 10^{- 2}$	$- 4.14 \times 10^{- 2}$
4	$5.32 \times 10^{- 2}$	$6.23 \times 10^{- 2}$	$5.12 \times 10^{- 2}$	$1.016 \times 10^{- 2}$
5	$4.28 \times 10^{- 2}$	$5.20 \times 10^{- 2}$	$4.96 \times 10^{- 2}$	$2.88 \times 10^{- 2}$
6	$3.58 \times 10^{- 2}$	$4.43 \times 10^{- 2}$	$4.54 \times 10^{- 2}$	$3.45 \times 10^{- 2}$

$j$	$Z_{j}$	Type of Aberration
1	1	Piston
4	$\sqrt{3} (2 {\bar{ρ}}^{2} - 1)$	Defocus
11	$\sqrt{5} (6 {\bar{ρ}}^{4} - 6 {\bar{ρ}}^{2} + 1)$	Primary spherical
22	$\sqrt{7} (20 {\bar{ρ}}^{6} - 30 {\bar{ρ}}^{4} + 12 {\bar{ρ}}^{2} - 1)$	Secondary spherical
37	$3 (70 {\bar{ρ}}^{8} - 140 {\bar{ρ}}^{6} + 90 {\bar{ρ}}^{4} - 20 {\bar{ρ}}^{2} + 1)$	Tertiary spherical

$N$	$A_{4}$	$A_{11}$	$A_{22}$	$A_{37}$
1	$16.23 \times 10^{- 2}$	$- 10.48 \times 10^{- 2}$	$1.55 \times 10^{- 2}$	$4.39 \times 10^{- 2}$
2	$10.14 \times 10^{- 2}$	$8.18 \times 10^{- 2}$	$- 3.57 \times 10^{- 2}$	$- 12.26 \times 10^{- 2}$
3	$7 \times 10^{- 2}$	$7.57 \times 10^{- 2}$	$3.95 \times 10^{- 2}$	$- 4.14 \times 10^{- 2}$
4	$5.32 \times 10^{- 2}$	$6.23 \times 10^{- 2}$	$5.12 \times 10^{- 2}$	$1.016 \times 10^{- 2}$
5	$4.28 \times 10^{- 2}$	$5.20 \times 10^{- 2}$	$4.96 \times 10^{- 2}$	$2.88 \times 10^{- 2}$
6	$3.58 \times 10^{- 2}$	$4.43 \times 10^{- 2}$	$4.54 \times 10^{- 2}$	$3.45 \times 10^{- 2}$

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Applied Optics