Noise analysis in Stokes parameter reconstruction for division-of-focal-plane polarimeters

Chuanbiao Bai; Zhaoxiang Jiang; Jiangcheng Zhao; Shangquan Wu; Qingchuan Zhang; Qingchuan Zhang

doi:10.1364/AO.462059

Applied Optics
Vol. 61,
Issue 24,
pp. 7084-7094
(2022)
•https://doi.org/10.1364/AO.462059

Noise analysis in Stokes parameter reconstruction for division-of-focal-plane polarimeters

Chuanbiao Bai, Zhaoxiang Jiang, Jiangcheng Zhao, Shangquan Wu, and Qingchuan Zhang

Not Accessible

Your library or personal account may give you access

Get PDF
Email
Share
Get Citation
Copy Citation Text
Chuanbiao Bai, Zhaoxiang Jiang, Jiangcheng Zhao, Shangquan Wu, and Qingchuan Zhang, "Noise analysis in Stokes parameter reconstruction for division-of-focal-plane polarimeters," Appl. Opt. 61, 7084-7094 (2022)

Export Citation
- BibTex
- Endnote (RIS)
- HTML
- Plain Text
Citation alert
Save article

Check for updates

Related Topics
Table of Contents Category
- Imaging Systems, Image Processing, and Displays
Optics & Photonics Topics
?

The topics in this list come from the Optics and Photonics Topics applied to this article.

About this Article
History
- Original Manuscript: April 26, 2022
- Revised Manuscript: July 22, 2022
- Manuscript Accepted: July 26, 2022
- Published: August 12, 2022

Abstract

The division-of-focal-plane (DoFP) polarimeter can quickly and effectively obtain the polarization information of light in real time, where Stokes parameter reconstruction is a critical issue. Many reconstruction methods have been proposed to address this; however, their performance tends to degrade in the presence of noise. Thus, it is significant to clarify the noise-induced error in Stokes parameter reconstruction. In this work, we investigate the link between the noise-introduced error and the reconstruction method and develop a simple and effective way to evaluate the noise robustness of reconstruction methods. Furthermore, a novel experimental scheme of noise measurement, to the best of our knowledge, is designed to verify the theory. Based on the criterion, our scheme guides the selection of reconstruction methods and further promotes the practical application of the DoFP technique.

Full Article | PDF Article

More Like This

Signal-to-noise analysis of Stokes parameters in division of focal plane polarimeters

Robert Perkins and Viktor Gruev
Opt. Express 18(25) 25815-25824 (2010)

Gradient-based interpolation method for division-of-focal-plane polarimeters

Shengkui Gao and Viktor Gruev
Opt. Express 21(1) 1137-1151 (2013)

Image interpolation for division of focal plane polarimeters with intensity correlation

Junchao Zhang, Haibo Luo, Bin Hui, and Zheng Chang
Opt. Express 24(18) 20799-20807 (2016)

Previous Article Next Article

Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

Cited By

You do not have subscription access to this journal. Cited by links are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

Figures (6)

You do not have subscription access to this journal. Figure files are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

Tables (6)

You do not have subscription access to this journal. Article tables are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

Equations (25)

You do not have subscription access to this journal. Equations are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

Interpolation algorithms	Interpolation convolution kernel $h = k k^{T}$
Nearest-neighbor	$k = [\begin{matrix} 1 & 1 \end{matrix}]^{T}$
Bilinear	$k = [\begin{matrix} \frac{1}{2} & 1 & \frac{1}{2} \end{matrix}]^{T}$
Bicubic	$k = [\begin{matrix} - \frac{1}{16} & 0 & \frac{9}{16} & \begin{matrix} 1 & \frac{9}{16} & 0 & - \frac{1}{16} \end{matrix} \end{matrix}]^{T}$
Natural bicubicspline $7 \times 7$	$k = [\begin{matrix} \begin{matrix} - \frac{3}{40} & 0 & \frac{23}{40} & 1 \end{matrix} & \frac{23}{40} & 0 & - \frac{3}{40} \end{matrix}]^{T}$
Natural bicubicspline $11 \times 11$	$k = [\begin{matrix} \begin{matrix} \begin{matrix} \begin{matrix} \frac{3}{152} & 0 & - \frac{9}{76} \end{matrix} & 0 & \frac{91}{152} & 1 \end{matrix} & \frac{91}{152} & 0 \end{matrix} & - \frac{9}{76} & 0 & \frac{3}{152} \end{matrix}]^{T}$

Interpolation algorithm	$H (u, v) = H (u) H (v)$
Nearest-neighbor	$H (u) = 2 \cos (π u)$
Bilinear	$H (u) = 1 + \cos (2 π u)$
Bicubic	$H (u) = 1 + \frac{9}{8} \cos (2 π u) - \frac{1}{8} \cos (6 π u)$
Natural bicubic spline $7 \times 7$	$H (u) = 1 + \frac{23}{20} \cos (2 π u) - \frac{3}{20} \cos (6 π u)$
Natural bicubic spline $11 \times 11$	$H (u) = 1 + \frac{91}{76} \cos (2 π u) - \frac{9}{38} \cos (6 π u) + \frac{3}{76} \cos (12 π u)$

Reconstruction method	$W_{0}$	$W_{+}$	$W_{-}$	$W_{1}$	$W_{2}$
Nearest-neighbor	0.2500	0.2500	0.2500	$[\begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix}]$	$[\begin{matrix} 0 & 1 \\ 1 & 0 \end{matrix}]$
Bilinear	0.1406	0.1406	0.1406	$[\begin{matrix} 0.5625 & 0 \\ 0 & 0.5625 \end{matrix}]$	$[\begin{matrix} 0 & 0.5625 \\ 0.5625 & 0 \end{matrix}]$
Bicubic	0.1682	0.1682	0.1682	$[\begin{matrix} 0.6792 & 0 \\ 0 & 0.6792 \end{matrix}]$	$[\begin{matrix} 0 & 0.6729 \\ 0.6729 & 0 \end{matrix}]$
Natural bicubic spline $7 \times 7$	0.1748	0.1748	0.1748	$[\begin{matrix} 0.6993 & 0 \\ 0 & 0.6993 \end{matrix}]$	$[\begin{matrix} 0 & 0.6993 \\ 0.6993 & 0 \end{matrix}]$
Natural bicubic spline $11 \times 11$	0.1905	0.1905	0.1905	$[\begin{matrix} 0.7618 & 0 \\ 0 & 0.7618 \end{matrix}]$	$[\begin{matrix} 0 & 0.7618 \\ 0.7618 & 0 \end{matrix}]$
Planck-taper (narrow)	0.3306	0.0381	0.0203	$[\begin{matrix} 0.1083 & 0.0085 \\ 0.0085 & 0.1083 \end{matrix}]$	$[\begin{matrix} 0.0085 & 0.1083 \\ 0.1083 & 0.0085 \end{matrix}]$
Planck-taper (wide)	0.5165	0.0596	0.0317	$[\begin{matrix} 0.1692 & 0.0133 \\ 0.0133 & 0.1692 \end{matrix}]$	$[\begin{matrix} 0.0133 & 0.1692 \\ 0.1692 & 0.0133 \end{matrix}]$

Reconstruction methods	$W_{01}$	$W_{02}$	$W_{12}$
Nearest-neighbor	$[\begin{matrix} 0.5000 & 0 \\ 0 & - 0.5000 \end{matrix}]$	$[\begin{matrix} 0 & - 0.5000 \\ 0.5000 & 0 \end{matrix}]$	0
Bilinear	$[\begin{matrix} 0.2813 & 0 \\ 0 & - 0.2813 \end{matrix}]$	$[\begin{matrix} 0 & - 0.2813 \\ 0.2813 & 0 \end{matrix}]$	0
Bicubic	$[\begin{matrix} 0.3365 & 0 \\ 0 & - 0.3365 \end{matrix}]$	$[\begin{matrix} 0 & - 0.3365 \\ 0.3365 & 0 \end{matrix}]$	0
Natural bicubic spline $7 \times 7$	$[\begin{matrix} 0.3479 & 0 \\ 0 & - 0.3479 \end{matrix}]$	$[\begin{matrix} 0 & - 0.3479 \\ 0.3479 & 0 \end{matrix}]$	0
Natural bicubic spline $11 \times 11$	$[\begin{matrix} 0.3809 & 0 \\ 0 & - 0.3809 \end{matrix}]$	$[\begin{matrix} 0 & - 0.3809 \\ 0.3809 & 0 \end{matrix}]$	0
Planck-taper (narrow)	$[\begin{matrix} - 7.578 \times 10^{- 10} & - 8.598 \times 10^{- 9} \\ 8.598 \times 10^{- 9} & 7.578 \times 10^{- 10} \end{matrix}]$	$[\begin{matrix} - 8.598 \times 10^{- 9} & - 7.578 \times 10^{- 10} \\ 7.578 \times 10^{- 10} & 8.598 \times 10^{- 9} \end{matrix}]$	0.0179
Planck-taper (wide)	$[\begin{matrix} 2.104 \times 10^{- 5} & 2.102 \times 10^{- 5} \\ - 2.102 \times 10^{- 5} & - 2.104 \times 10^{- 5} \end{matrix}]$	$[\begin{matrix} 2.102 \times 10^{- 5} & 2.104 \times 10^{- 5} \\ - 2.104 \times 10^{- 5} & - 2.102 \times 10^{- 5} \end{matrix}]$	0.0279

Reconstruction Method	${\hat{s}}_{0}$		${\hat{s}}_{1}$		${\hat{s}}_{2}$
Reconstruction Method	Theoretical	Actual	Theoretical	Actual	Theoretical	Actual
Nearest-eighbor	0.1375	0.1343	0.2749	0.2700	0.2749	0.2677
Bilinear	0.0773	0.0763	0.1546	0.1516	0.1546	0.1511
Bicubic	0.0925	0.0913	0.1867	0.1810	0.1867	0.1807
Natural bicubic spline $7 \times 7$	0.0961	0.0948	0.1922	0.1881	0.1922	0.1877
Natural bicubic spline $11 \times 11$	0.1047	0.1032	0.2094	0.2048	0.2094	0.2045
Planck-taper (narrow)	0.1818	0.1785	0.0321	0.0318	0.0321	0.0323
Planck-taper (wide)	0.2840	0.2786	0.0502	0.0496	0.0502	0.0498

Reconstruction	$\hat{DoLP}$		$\hat{AoP}$
Method	Theoretical	Actual	Theoretical	Actual
Nearest-neighbor	0.0041	0.0053	0.0186	0.0212
Bilinear	0.0023	0.0026	0.0105	0.0114
Bicubic	0.0028	0.0032	0.0125	0.0138
Natural bicubic spline $7 \times 7$	0.0029	0.0033	0.013	0.0144
Natural bicubic spline $11 \times 11$	0.0031	0.0036	0.0142	0.0158
Planck-taper (narrow)	0.0006	0.0007	0.0020	0.0023
Planck-taper (wide)	0.0010	0.0012	0.0032	0.0036

Abstract

Data availability

Cited By

Figures (6)

Tables (6)

Equations (25)

Applied Optics