US 2026/0309970 A1 · METHOD FOR GENERATING A SUPER-RESOLVED RECONSTRUCTED IMAGE OF A FLUORESCENT SAMPLE AND STRUCTURED ILLUMINATION MICROSCOPY METHOD

Abstract

A digital imaging process that can be used in structured illumination microscopy to obtain super-resolved images of samples having a distribution of fluorophores that emit light when illuminated by excitation light beams uses an innovative algorithm in which a super-resolved image, in a secant plane of the sample in which the excitation light beams are focused, is reconstructed also taking into account the light contributions coming from fluorophores located in out-of-focus planes. The digital image processing methods of this disclosure can be implemented through a program run by a computer and can be used in a related structured illumination microscopy method (SIM).

A computer-implemented method of generating a super-resolution reconstructed image of a fluorescent sample comprising fluorophores that emit light when illuminated with an excitation light beam, wherein said sample is illuminated with a plurality of excitation light beams focused in a secant plane traversing said sample to excite at least part of said sample fluorophores, said method comprising the following steps:

providing a plurality of N two-dimensional images dj in a secant plane traversing said sample wherein each two-dimensional image dj in said secant plane of said plurality of images was captured by illuminating said fluorescent sample with a corresponding j-th beam of excitation light focused in said secant plane,
being known a generic distribution of light intensity pj,z′=pj(r;z′) irradiated in three-dimensional space r by each excitation light beam focused in a generic secant plane of coordinate z′ and being known a three-dimensional emission Point Spread Function
h
em
(
3
⁢
d
)
(
r
)
and a corresponding three-dimensional transposed Point Spread Function
h
em
(
3
⁢
d
)
⁢
t
(
r
)
of the excited fluorophores of the sample, iteratively computing an approximate three-dimensional distribution of fluorophore
ρ
f
(
k
+
1
)
(
r
)
at a (k+1)-th iteration step as the product of a k-th three-dimensional update operator {circumflex over (└)}(k)(r) and an approximate three-dimensional distribution of fluorophores
ρ
f
(
k
)
(
r
)
at a (k)-th iteration step:
ρ
f
(
k
+
1
)
(
r
)
≡
∏
^
(
k
)
(
r
)
⁢
ρ
f
(
k
)
(
r
)
wherein the k-th three-dimensional update operator {circumflex over (└)}(k)(r) is given by
∑
j
∫
d
3
⁢
r
′
(
d
j
(
r
′
)
+
σ
2
μ
j
(
k
)
(
r
′
)
+
σ
2
)
⁢
p
j
(
r
;
z
′
)
⁢
h
em
(
3
⁢
d
)
⁢
t
(
r
-
r
′
)
≡
∏
^
(
k
)
(
r
)
,
wherein σ2 is a variance of a Gaussian noise and where a reconstructed k-th two-dimensional image
μ
j
(
k
)
(
x
,
y
,
z
0
)
in a secant plane of coordinate z0, which ideally would be obtained from the approximate three-dimensional distribution of the fluorophores
ρ
f
(
k
)
(
r
)
determined at a generic k-th iteration step by focusing the j-th beam of excitation light in said secant plane of coordinate z0 which passes through said sample, is given by:
μ
j
[
ρ
f
(
k
)
]
≡
μ
j
(
k
)
(
x
,
y
,
z
0
)
=
[
(
ρ
f
(
k
)
·
p
j
,
z
0
)
⊗
3
⁢
d
h
em
(
3
⁢
d
)
]
⁢
(
x
,
y
,
z
0
)
wherein ⊗3d denotes a convolution product in three-dimensional space;
determining a final three-dimensional distribution of the fluorophores {circumflex over (ρ)}f as an approximate three-dimensional distribution of the fluorophore
ρ
f
(
k
)
(
r
)
at a generic k-th iteration step minimizing a maximum likelihood function calculated as:
L
[
ρ
f
]
=
∑
j
∫
∫
∫
dxdydz
[
(
μ
j
[
ρ
f
]
+
σ
2
)
-
(
d
j
+
σ
2
)
⁢
log
⁡
(
μ
j
[
ρ
f
]
+
σ
2
)
+
log
⁢
(
Γ
⁡
(
d
j
+
σ
2
+
1
)
)
]
;
generating with said computer a file of a super-resolution reconstructed image of said sample as a summation of reconstructed images μj[{circumflex over (ρ)}f] for each j-th beam of focused excitation light which theoretically would be obtained from the final three-dimensional distribution of fluorophores {circumflex over (ρ)}f, in which each reconstructed image μj[{circumflex over (ρ)}f] is obtained as:
μ
j
[
ρ
^
f
]
=
[
(
ρ
^
f
·
p
j
,
z
0
)
⊗
3
⁢
d
h
em
(
3
⁢
d
)
]
.

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Method for generating a super-resolved reconstructed image of a fluorescent sample and structured illumination microscopy method

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Method for generating a super-resolved reconstructed image of a fluorescent sample and structured illumination microscopy method

Life of this patent

Abstract

Claims9