Numerical parametric lens for shifting, magnification, and complete aberration compensation in digital holographic microscopy

Tristan Colomb; Frédéric Montfort; Jonas Kühn; Nicolas Aspert; Etienne Cuche; Anca Marian; Florian Charrière; Sébastien Bourquin; Pierre Marquet; Christian Depeursinge

doi:10.1364/JOSAA.23.003177

Journal of the Optical Society of America A
Vol. 23,
Issue 12,
pp. 3177-3190
(2006)
•https://doi.org/10.1364/JOSAA.23.003177

Numerical parametric lens for shifting, magnification, and complete aberration compensation in digital holographic microscopy

Tristan Colomb, Frédéric Montfort, Jonas Kühn, Nicolas Aspert, Etienne Cuche, Anca Marian, Florian Charrière, Sébastien Bourquin, Pierre Marquet, and Christian Depeursinge

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Tristan Colomb, Frédéric Montfort, Jonas Kühn, Nicolas Aspert, Etienne Cuche, Anca Marian, Florian Charrière, Sébastien Bourquin, Pierre Marquet, and Christian Depeursinge, "Numerical parametric lens for shifting, magnification, and complete aberration compensation in digital holographic microscopy," J. Opt. Soc. Am. A 23, 3177-3190 (2006)

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- Holography
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About this Article
History
- Original Manuscript: March 20, 2006
- Revised Manuscript: June 21, 2006
- Manuscript Accepted: June 26, 2006
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Virtual Journal for Biomedical Optics Vol. 2, Iss. 1

Abstract

The concept of numerical parametric lenses (NPL) is introduced to achieve wavefront reconstruction in digital holography. It is shown that operations usually performed by optical components and described in ray geometrical optics, such as image shifting, magnification, and especially complete aberration compensation (phase aberrations and image distortion), can be mimicked by numerical computation of a NPL. Furthermore, we demonstrate that automatic one-dimensional or two-dimensional fitting procedures allow adjustment of the NPL parameters as expressed in terms of standard or Zernike polynomial coefficients. These coefficients can provide a quantitative evaluation of the aberrations generated by the specimen. Demonstration is given of the reconstruction of the topology of a microlens.

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Polynomial	Cartesian Form	Description
$Z_{0}$	1	Piston
$Z_{1}$	$\sqrt{4} x$	Tilt x
$Z_{2}$	$\sqrt{4} y$	Tilt y
$Z_{3}$	$\sqrt{3} (2 x^{2} + 2 y^{2} - 1)$	Power
$Z_{4}$	$\sqrt{6} (2 x y)$	Astig y
$Z_{5}$	$\sqrt{6} (x^{2} - y^{2})$	Astig x
$Z_{6}$	$\sqrt{8} (3 x^{2} y + 3 y^{3} - 2 y)$	Coma y
$Z_{7}$	$\sqrt{8} (3 x^{3} + 3 x y^{2} - 2 x)$	Coma x
$Z_{8}$	$\sqrt{8} (3 x^{2} y - y^{3})$	Trefoil y
$Z_{9}$	$\sqrt{8} (x^{3} - 3 x y^{2})$	Trefoil x
$Z_{10}$	$\sqrt{5} (6 x^{4} + 12 x^{2} y^{2} + 6 y^{4} - 6 x^{2} - 6 y^{2} + 1)$	Primary Spherical
$Z_{11}$	$\sqrt{10} (4 x^{4} - 3 x^{2} + 3 y^{2} - 4 y^{4})$	$2^{ary}$ Astig x
$Z_{12}$	$\sqrt{10} (8 x^{3} y + 8 x y^{3} - 6 x y)$	$2^{ary}$ Astig y
$Z_{13}$	$\sqrt{10} (x^{4} - 6 x^{2} y^{2} + y^{4})$	Tetrafoil x
$Z_{14}$	$\sqrt{10} (4 x^{3} y - 4 x y^{3})$	Tetrafoil y
$Z_{15}$	$\sqrt{12} (10 x^{5} + 20 x^{3} y^{2} + 10 x y^{4} - 12 x^{3} - 12 x y^{2} + 3 x)$	$2^{ary}$ Coma x
$Z_{16}$	$\sqrt{12} (10 x^{4} y + 20 x^{2} y^{3} + 10 y^{5} - 12 x^{2} y - 12 y^{3} + 3 y)$	$2^{ary}$ Coma y
$Z_{17}$	$\sqrt{12} (5 x^{5} - 10 x^{3} y^{2} - 15 x y^{4} - 4 x^{3} + 12 x y^{2})$	$2^{ary}$ Trefoil x
$Z_{18}$	$\sqrt{12} (15 x^{4} y + 10 x^{2} y^{3} - 5 y^{5} - 12 x^{2} y + 4 y^{3})$	$2^{ary}$ Trefoil y
$Z_{19}$	$\sqrt{12} (x^{5} - 10 x^{3} y^{2} + 5 x y^{4})$	Pentafoil x
$Z_{20}$	$\sqrt{12} (5 x^{4} y - 10 x^{2} y^{3} + y^{5})$	Pentafoil y
$Z_{21}$	$\sqrt{7} (20 x^{6} + 60 x^{4} y^{2} + 60 x^{2} y^{4} + 20 y^{6} - 30 x^{4} - 60 x^{2} y^{2} - 30 y^{4} + 12 x^{2} + 12 y^{2} - 1)$	$2^{ary}$ Spherical
$Z_{22}$	$\sqrt{14} (30 x^{5} y + 60 x^{3} y^{3} + 30 x y^{5} - 40 x^{3} y - 40 x y^{3} + 12 x y)$	$3^{ary}$ Astig y
$Z_{23}$	$\sqrt{14} (15 x^{6} + 15 x^{4} y^{2} - 20 x^{4} + 6 x^{2} - 15 x^{2} y^{4} - 15 y^{6} + 20 y^{4} - 6 y^{2})$	$3^{ary}$ Astig x

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Equations (39)

Journal of the Optical Society of America A