We recently proposed a dual-slope technique for diffuse optical spectroscopy and imaging of scattering media. This technique requires a special configuration of light sources and optical detectors to create dual-slope sets. Here, we present methods for designing, optimizing, and building an optical imaging array that features m dual-slope sets to image n voxels. After defining the m × n matrix ( S ) that describes the sensitivity of the m dual-slope measurements to absorption perturbations in each of the n voxels, we formulate the inverse imaging problem in terms of the Moore–Penrose pseudoinverse matrix of S ( S + ). This approach allows us to introduce several measures of imaging performance: reconstruction accuracy (correct spatial mapping), crosstalk (incorrect spatial mapping), resolution (point spread function), and localization (offset between actual and reconstructed point perturbations). Furthermore, by considering the singular value decomposition formulation, we show the significance of visualizing the first m right singular vectors of S , whose linear combination generates the reconstructed map. We also describe methods to build a physical array using a three-layer mesh structure (two polyethylene films and polypropylene hook-and-loop fabric) embedded in silicone (PDMS). Finally, we apply these methods to design two arrays and choose one to construct. The chosen array consists of 16 illumination fibers, 10 detection fibers, and 27 dual-slope sets for dual-slope imaging optimized for the size of field of view and localization of absorption perturbations. This particular array is aimed at functional near-infrared spectroscopy of the human brain, but the methods presented here are of general applicability to a variety of devices and imaging scenarios.

1.
F.
Scholkmann
,
S.
Kleiser
,
A. J.
Metz
,
R.
Zimmermann
,
J.
Mata Pavia
,
U.
Wolf
, and
M.
Wolf
,
Neuroimage
85
,
6
(
2014
).
2.
A.
Torricelli
,
D.
Contini
,
A.
Pifferi
,
M.
Caffini
,
R.
Re
,
L.
Zucchelli
, and
L.
Spinelli
,
Neuroimage
85
,
28
(
2014
).
3.
S.
Fantini
and
A.
Sassaroli
,
Front. Neurosci.
14
,
1
(
2020
).
4.
S.
Fantini
,
D.
Hueber
,
M. A.
Franceschini
,
E.
Gratton
,
W.
Rosenfeld
,
P. G.
Stubblefield
,
D.
Maulik
, and
M. R.
Stankovic
,
Phys. Med. Biol.
44
,
1543
(
1999
).
5.
T. J.
Barstow
,
J. Appl. Physiol.
126
,
1360
(
2019
).
6.
D.
Grosenick
,
H.
Rinneberg
,
R.
Cubeddu
, and
P.
Taroni
,
J. Biomed. Opt.
21
,
091311
(
2016
).
7.
M.
Ferrari
and
V.
Quaresima
,
Neuroimage
63
,
921
(
2012
).
8.
A. T.
Eggebrecht
,
S. L.
Ferradal
,
A.
Robichaux-Viehoever
,
M. S.
Hassanpour
,
H.
Dehghani
,
A. Z.
Snyder
,
T.
Hershey
, and
J. P.
Culver
,
Nat. Photonics
8
,
448
(
2014
).
9.
M.
Doulgerakis
,
A. T.
Eggebrecht
, and
H.
Dehghani
,
Neurophotonics
6
,
1
(
2019
).
10.
G. A.
Zimeo Morais
,
J. B.
Balardin
, and
J. R.
Sato
,
Sci. Rep.
8
,
3341
(
2018
).
11.
A.
Machado
,
O.
Marcotte
,
J. M.
Lina
,
E.
Kobayashi
, and
C.
Grova
,
J. Biomed. Opt.
19
,
026010
(
2014
).
12.
K. L.
Perdue
,
Q.
Fang
, and
S. G.
Diamond
,
Phys. Med. Biol.
57
,
2857
(
2012
).
13.
D. A.
Boas
,
K.
Chen
,
D.
Grebert
, and
M. A.
Franceschini
,
Opt. Lett.
29
,
1506
(
2004
).
14.
B. R.
White
,
J. Biomed. Opt.
15
,
026006
(
2010
).
15.
F.
Tian
,
G.
Alexandrakis
, and
H.
Liu
,
Appl. Opt.
48
,
2496
(
2009
).
16.
S.
Wijeakumar
,
J. P.
Spencer
,
K.
Bohache
,
D. A.
Boas
, and
V. A.
Magnotta
,
Neuroimage
106
,
86
(
2015
).
17.
S.
Brigadoi
,
D.
Salvagnin
,
M.
Fischetti
, and
R. J.
Cooper
,
Neurophotonics
5
,
1
(
2018
).
18.
T. J.
Huppert
,
S. G.
Diamond
,
M. A.
Franceschini
, and
D. A.
Boas
,
Appl. Opt.
48
,
D280
(
2009
).
19.
C. M.
Aasted
,
M. A.
Yücel
,
R. J.
Cooper
,
J.
Dubb
,
D.
Tsuzuki
,
L.
Becerra
,
M. P.
Petkov
,
D.
Borsook
,
I.
Dan
, and
D. A.
Boas
,
Neurophotonics
2
,
020801
(
2015
).
20.
S.
Cutini
,
P.
Scatturin
, and
M.
Zorzi
,
Neuroimage
54
,
919
(
2011
).
21.
M.
Vanegas
and
Q.
Fang
, in
OSA Technical Digest
(
OSA
,
2020
), p.
BM2C.6
.
22.
P.
Pinti
,
C.
Aichelburg
,
F.
Lind
,
S.
Power
,
E.
Swingler
,
A.
Merla
,
A.
Hamilton
,
S.
Gilbert
,
P.
Burgess
, and
I.
Tachtsidis
, “
Using fiberless, wearable fNIRS to monitor brain activity in real-world cognitive tasks
,”
J. Vis. Exp.
106
,
e53336
(
2015
).
23.
S. K.
Piper
,
A.
Krueger
,
S. P.
Koch
,
J.
Mehnert
,
C.
Habermehl
,
J.
Steinbrink
,
H.
Obrig
, and
C. H.
Schmitz
,
Neuroimage
85
,
64
(
2014
).
24.
G.
Blaney
,
A.
Sassaroli
,
T.
Pham
,
C.
Fernandez
, and
S.
Fantini
, in
OSA Technical Digest
(
OSA
,
2020
), p.
JTh2A.9
.
25.
A. Y.
Liao
,
Y.
Lai
, and
K.
Sung
, in
OSA Technical Digest
(
OSA
,
2020
), p.
JTh2A.6
.
26.
A.
Curtin
and
H.
Ayaz
,
Jpn. Psychol. Res.
60
,
374
(
2018
).
27.
M. A.
Yücel
,
J. J.
Selb
,
T. J.
Huppert
,
M. A.
Franceschini
, and
D. A.
Boas
,
Curr. Opin. Biomed. Eng.
4
,
78
(
2017
).
28.
H.
Zhao
and
R. J.
Cooper
,
Neurophotonics
5
,
1
(
2017
).
29.
M. A.
Franceschini
,
S.
Fantini
,
L. A.
Paunescu
,
J. S.
Maier
, and
E.
Gratton
,
Appl. Opt.
37
,
7447
(
1998
).
30.
M.
Dehaes
,
L.
Gagnon
,
F.
Lesage
,
M.
Pélégrini-Issac
,
A.
Vignaud
,
R.
Valabrègue
,
R.
Grebe
,
F.
Wallois
, and
H.
Benali
,
Biomed. Opt. Express
2
,
680
(
2011
).
31.
F.
Tian
,
H.
Niu
,
B.
Khan
,
G.
Alexandrakis
,
K.
Behbehani
, and
H.
Liu
,
IEEE Trans. Med. Imaging
30
,
1239
(
2011
).
32.
M.
Caldwell
,
F.
Scholkmann
,
U.
Wolf
,
M.
Wolf
,
C.
Elwell
, and
I.
Tachtsidis
,
Neuroimage
143
,
91
(
2016
).
33.
G.
Blaney
,
A.
Sassaroli
, and
S.
Fantini
, “
Dual-slope imaging in highly scattering media with frequency-domain near-infrared spectroscopy
,”
Opt. Lett.
45
,
4464
4467
(
2020
).
34.
D. M.
Hueber
,
S.
Fantini
,
A. E.
Cerussi
, and
B. B.
Barbieri
,
Proc. SPIE
3597
,
618
631
(
1999
).
35.
G.
Blaney
,
A.
Sassaroli
,
T.
Pham
,
C.
Fernandez
, and
S.
Fantini
,
J. Biophotonics
13
,
e201960018
(
2020
).
36.
A.
Sassaroli
,
G.
Blaney
, and
S.
Fantini
,
J. Opt. Soc. Am. A
36
,
1743
(
2019
).
37.
S.
Fantini
,
G.
Blaney
, and
A.
Sassaroli
,
J. Innov. Opt. Health Sci.
13
,
1930013
(
2020
).
38.
P.
Sawosz
and
A.
Liebert
,
Biomed. Opt. Express
10
,
5031
(
2019
).
39.
A.
Sassaroli
,
F.
Martelli
, and
S.
Fantini
,
J. Opt. Soc. Am. A
27
,
1723
(
2010
).
40.
MathWorks, MATLAB Document,
2020
.
41.
B.
Hallacoglu
,
A.
Sassaroli
,
E.
Guerrero-Berroa
,
M.
Schnaider Beeri
,
V.
Haroutunian
,
M.
Shaul
,
I. H.
Rosenberg
,
A.
Toren
, and
S.
Fantini
,
J. Biomed. Opt.
17
,
081406
(
2012
).
42.
X.
Xiao
,
X.
Yu
,
Z.
Zhang
,
Y.
Zhao
,
Y.
Jiang
,
Z.
Li
,
Y.
Yang
, and
C.
Zhu
,
Sci. Adv.
4
,
eaar6904
(
2018
).
43.
H.
Lu
,
L. C. W.
Lam
, and
Y.
Ning
,
CNS Neurosci. Ther.
25
,
1270
(
2019
).
44.
E.
Candes
and
J.
Romberg
, “
L1-MAGIC: Recovery of sparse signals via convex programming
,” (published online
2005
), available at http://statweb.stanford.edu/∼candes/software/l1magic/downloads/l1magic.pdf.
You do not currently have access to this content.