Reconstruction method based on the Hilbert fractal curve recovery sequence in a Fourier ptychography microscope

Xin Chen; Haobo Cheng; Yongfu Wen; Hengyu Wu; Yingwei Wang

doi:10.1364/AO.58.000517

Applied Optics
Vol. 58,
Issue 3,
pp. 517-527
(2019)
•https://doi.org/10.1364/AO.58.000517

Reconstruction method based on the Hilbert fractal curve recovery sequence in a Fourier ptychography microscope

Xin Chen, Haobo Cheng, Yongfu Wen, Hengyu Wu, and Yingwei Wang

Not Accessible

Your library or personal account may give you access

Get PDF
Email
Share
Get Citation
Copy Citation Text
Xin Chen, Haobo Cheng, Yongfu Wen, Hengyu Wu, and Yingwei Wang, "Reconstruction method based on the Hilbert fractal curve recovery sequence in a Fourier ptychography microscope," Appl. Opt. 58, 517-527 (2019)

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

Check for updates

Related Topics
Table of Contents Category
- Medical Optics, Microscopy, and Biotechnology
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: September 27, 2018
- Revised Manuscript: December 5, 2018
- Manuscript Accepted: December 6, 2018
- Published: January 11, 2019

Abstract

Many Fourier ptychography microscopy techniques have been proposed to achieve higher recovery accuracy in the past few years, yet it is little known that their reconstructed quality is also dependent on the choice of recovery sequence, which is important for fast solution convergence during the Fourier ptychography reconstruction process. In this paper, we propose to use the Hilbert fractal curve, which is one of the most representative of classic space-filling curves, as a new kind of recovery sequence of mesh LED arrays and validate its effectiveness and robustness with both simulated and real experiments. Results show that the Hilbert fractal curve as the recovery sequence is a better choice for periodic LED arrays, compared with raster line, spiral line, and wave-shaped-curve three-recovery sequences.

Full Article | PDF Article

More Like This

Sparse aperture arrangement for periodic LED array sampling in a Fourier ptychography microscopy system

Haobo Cheng, Xin Chen, Yongfu Wen, Huaying Wang, and Hui Li
Appl. Opt. 58(32) 8791-8801 (2019)

Fourier ptychographic reconstruction based on augmented Lagrangian method and sparse approximations for phase and magnitude

Xin Chen, Haobo Cheng, Yongfu Wen, and Yunpeng Feng
Appl. Opt. 60(9) 2471-2482 (2021)

Apodized coherent transfer function constraint for partially coherent Fourier ptychographic microscopy

Xiong Chen, Youqiang Zhu, Minglu Sun, Dayu Li, Quanquan Mu, and Li Xuan
Opt. Express 27(10) 14099-14111 (2019)

Previous Article Next Article

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 (13)

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 (4)

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 (10)

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

Symbol	Definition
$F$	Move forward a step of length $d$ . The state of the turtle changes to ( $x^{'}, y^{'}, α$ ), where $x^{'} = x + d \times \cos α$ and $y^{'} = y + d \times \sin α$ . A line segment between points ( $x$ , $y$ ) and $(x^{'}, y^{'})$ is drawn.
$X$ , $Y$	Move forward a step of length $d$ without drawing a line.
$+$	Turn right by angle $δ$ . The next state of the turtle is ( $x$ , $y$ , $α + δ$ ). (Here we assume that the positive orientation of angles is clockwise.)
−	Turn left by angle $δ$ . The next state of the turtle is ( $x$ , $y$ , $α - δ$ ).
$\|$	Turn away. The state of the turtle changes to ( $x$ , $y$ , $α + 180 °$ ).

Curve Type	Initial Character	Angle	Rewriting Rule
Hilbert	$X$	90	$X = + Y F - X F X - F Y +$ ; $Y = - X F + Y F Y + F X -$

Alpha	Amplitude SSIM	Intensity SNR	Phase SNR
0.1	0.9764	18.1941	6.9947
0.5	0.9140	6.3012	4.7316
0.8	0.8838	4.7477	3.7603
1	0.1421	3.963	0.6865

	Amplitude SSIM		Intensity SNR		Phase SNR
Recovery Sequence	Without Noise	With Noise	Without Noise	With Noise	Without Noise	With Noise
Hilbert fractal curve	0.9812	0.9441	33.7614	7.0421	7.866	3.0154
Raster lines	0.9764	0.9328	18.1941	6.0822	6.9947	2.5484
Spiral lines	0.9745	0.9198	19.3987	6.1489	7.4104	2.9509
Wave-shaped curve	0.9733	0.9182	18.2777	6.2547	7.3036	3.0102

Symbol	Definition
$F$	Move forward a step of length $d$ . The state of the turtle changes to ( $x^{'}, y^{'}, α$ ), where $x^{'} = x + d \times \cos α$ and $y^{'} = y + d \times \sin α$ . A line segment between points ( $x$ , $y$ ) and $(x^{'}, y^{'})$ is drawn.
$X$ , $Y$	Move forward a step of length $d$ without drawing a line.
$+$	Turn right by angle $δ$ . The next state of the turtle is ( $x$ , $y$ , $α + δ$ ). (Here we assume that the positive orientation of angles is clockwise.)
−	Turn left by angle $δ$ . The next state of the turtle is ( $x$ , $y$ , $α - δ$ ).
$\|$	Turn away. The state of the turtle changes to ( $x$ , $y$ , $α + 180 °$ ).

Abstract

Cited By

Figures (13)

Tables (4)

Equations (10)

Applied Optics