Dylan Brault,1
Corinne Fournier,1,*
Thomas Olivier,1
Nicolas Faure,2
Sophie Dixneuf,3
Louis Thibon,1
Loïc Mees,4
and Loïc Denis1
1Université de Lyon, Université Jean Monnet-Saint-Etienne, CNRS, Institut d’Optique Graduate School, Laboratoire Hubert Curien UMR 5516, F-42023 Saint-Etienne,Hubert Curien Laboratory, UMR CNRS 5516, France
2bioMérieux, Centre Christophe Merieux, Grenoble, France
3BIOASTER, Bioassays, Microsystems & Optical Engineering Unit, Lyon, France
Dylan Brault, Corinne Fournier, Thomas Olivier, Nicolas Faure, Sophie Dixneuf, Louis Thibon, Loïc Mees, and Loïc Denis, "Automatic numerical focus plane estimation in digital holographic microscopy using calibration beads," Appl. Opt. 61, B345-B355 (2022)
We present a new method to achieve autofocus in digital holographic microscopy. The method is based on inserting calibrated objects into a sample placed on a slide. Reconstructing a hologram using the inverse problems approach makes it possible to precisely locate and measure the inserted objects and thereby derive the slide plane location. Numerical focusing can then be performed in a plane at any chosen distance from the slide plane of the sample in a reproducible manner and independently of the diversity of the objects in the sample.
Stéphane Cuenat, Louis Andréoli, Antoine N. André, Patrick Sandoz, Guillaume J. Laurent, Raphaël Couturier, and Maxime Jacquot Opt. Express 30(14) 24730-24746 (2022)
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.
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Simulations Parameters for the Five Holograms in Fig. 1a
(1)
(2)
(3)
(4)
(5)
Radius (µm)
1
0.4
0.5
0.5
0.5
z (µm)
11
11.6
11.5
11.5
11.5
Refractive index
1.4
1.35
1.44
1.44
1.35
Transmittance
1
0.5
1
0.01
1
The transmittance parameter is defined as $t = {e^{- 2\pi {n_i}\frac{{2r}}{\lambda}}}$, where ${n_i}$ is the extinction coefficient.
Table 2.
Simulation Parameters for the Stack of 100 Holograms (illustrated in Fig. 3)a
Silica Beads (10)
Other Objects (50)
Radius mean (nm)
500
700
Range of radii (nm)
[475, 525]
[400, 1000]
Refractive index mean
1.44
1.5545
Range of refractive indices
[1.43, 1.45]
[1.519, 1.590]
Transmittance mean
1
0.5
Range of transmittance
–
[0, 1]
The bead radii and refractive indices are drawn from uniform laws. The transmittance is equal to one for the beads and is drawn from a uniform law for the other objects. The mean values and the ranges of the uniform laws are given in the table.
Table 3.
Fit Parameters Estimated from the Robust Plane Fitting on 40 Holograms with Our Inverse Problem Approach and Two State-of-the-Art Algorithms Performed on 25 Patches of Each Holograma
Parameters
IPA
GRA
ToG
Axial position () (µm)
Slope along ()
Slope along ()
The estimated values are median values on the 40 holograms, and the dispersion is evaluated with the median value of the standard error estimated during the robust fitting of the plane.
Table 4.
Median Value and Dispersion on Estimated Parameters of the Reference Planes and Focusing Planesa
Parameters
IPA
GRA
ToG
Axial position () (µm)
(degrees)
(degrees)
The dispersion is still evaluated with ${\sigma _{{\text{MAD}}}}$. ${\theta _z}$ is the angle between the $z$ axis (optical axis) and the normal to the plane surface. ${\theta _x}$ is the angle between the $x$ axis direction and the projection of the normal on the horizontal plane ($xy$ plane).
Tables (4)
Table 1.
Simulations Parameters for the Five Holograms in Fig. 1a
(1)
(2)
(3)
(4)
(5)
Radius (µm)
1
0.4
0.5
0.5
0.5
z (µm)
11
11.6
11.5
11.5
11.5
Refractive index
1.4
1.35
1.44
1.44
1.35
Transmittance
1
0.5
1
0.01
1
The transmittance parameter is defined as $t = {e^{- 2\pi {n_i}\frac{{2r}}{\lambda}}}$, where ${n_i}$ is the extinction coefficient.
Table 2.
Simulation Parameters for the Stack of 100 Holograms (illustrated in Fig. 3)a
Silica Beads (10)
Other Objects (50)
Radius mean (nm)
500
700
Range of radii (nm)
[475, 525]
[400, 1000]
Refractive index mean
1.44
1.5545
Range of refractive indices
[1.43, 1.45]
[1.519, 1.590]
Transmittance mean
1
0.5
Range of transmittance
–
[0, 1]
The bead radii and refractive indices are drawn from uniform laws. The transmittance is equal to one for the beads and is drawn from a uniform law for the other objects. The mean values and the ranges of the uniform laws are given in the table.
Table 3.
Fit Parameters Estimated from the Robust Plane Fitting on 40 Holograms with Our Inverse Problem Approach and Two State-of-the-Art Algorithms Performed on 25 Patches of Each Holograma
Parameters
IPA
GRA
ToG
Axial position () (µm)
Slope along ()
Slope along ()
The estimated values are median values on the 40 holograms, and the dispersion is evaluated with the median value of the standard error estimated during the robust fitting of the plane.
Table 4.
Median Value and Dispersion on Estimated Parameters of the Reference Planes and Focusing Planesa
Parameters
IPA
GRA
ToG
Axial position () (µm)
(degrees)
(degrees)
The dispersion is still evaluated with ${\sigma _{{\text{MAD}}}}$. ${\theta _z}$ is the angle between the $z$ axis (optical axis) and the normal to the plane surface. ${\theta _x}$ is the angle between the $x$ axis direction and the projection of the normal on the horizontal plane ($xy$ plane).
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