US 2026/0187768 A1 · METHODS AND SYSTEMS FOR CHROMATIC ABERRATION COMPENSATION IN DUAL-WAVELENGTH DIGITAL HOLOGRAPHY

Abstract

A method for chromatic aberration compensation in dual-wavelength digital holography is provided. The method includes: obtaining a dual-wavelength interferogram simultaneously containing two wavelengths; obtaining complex amplitudes of the two different wavelengths at a camera plane; performing numerical propagation on object wavefronts of the two wavelengths within a defocus range to obtain complex amplitudes of the two wavelengths at different axial propagation positions within the defocus range using an angular spectrum method; calculating single-wavelength phase distributions corresponding to the axial propagation positions within the defocus range; calculating, for all combinations of different axial propagation positions for the two wavelengths, dual-wavelength synthetic phase distributions; obtaining a chromatic-aberration-compensated dual-wavelength synthetic phase by identifying a combination of optimal axial propagation positions at which the gradient value of the corresponding dual-wavelength synthetic phase distribution reaches a minimum, and subtracting two single-wavelength phases corresponding to the identified axial propagation positions.

A method for chromatic aberration compensation in dual-wavelength digital holography, comprising:

obtaining a dual-wavelength interferogram simultaneously containing two different wavelengths;
receiving the dual-wavelength interferogram and obtaining complex amplitudes of the two wavelengths at a camera plane through calculation;
based on the complex amplitudes of the two wavelengths at the camera plane, performing numerical propagation on object wavefronts of the two wavelengths within a set defocus range by using an angular spectrum propagation algorithm, to obtain, for each of the two wavelengths, complex amplitudes at different axial propagation positions within the defocus range;
for each of the two wavelengths:
calculating, at each of the different axial propagation positions within the defocus range, a single-wavelength phase distribution corresponding to the axial propagation position based on the complex amplitude at the axial propagation position;
based on the single-wavelength phase distributions at the different axial propagation positions corresponding to each of the two wavelengths, calculating, for all combinations of different axial propagation positions for the two wavelengths, dual-wavelength synthetic phase distributions;
obtaining gradient values of the dual-wavelength synthetic phase distributions when the two wavelengths are at the different axial propagation positions by calculating gradients for all the dual-wavelength synthetic phase distributions;
obtaining a chromatic-aberration-compensated dual-wavelength synthetic phase by identifying a combination of axial propagation positions at which the gradient value of the corresponding dual-wavelength synthetic phase distribution reaches a minimum among all the dual-wavelength synthetic phase distributions, and subtracting two single-wavelength phases corresponding to the identified combination of axial propagation positions;
performing, for each of the two wavelengths, a two-dimensional Fourier transform on an initial complex amplitude of an optical field of the wavelength and converting the initial complex amplitude into a frequency domain;
introducing a phase factor related to a propagation distance into the frequency domain to represent an influence of different propagation distances, and performing an inverse Fourier transform to return to a spatial domain to obtain object complex amplitudes
U
d
m
λ
1
⁢
and
⁢
U
d
n
λ
2
at different defocused planes:
U
d
m
λ
1
=
F
-
1
⁢
{
F
⁢
{
U
0
λ
1
}
·
exp
[
j
⁢
2
⁢
π
λ
1
⁢
d
m
⁢
1
-
(
λ
1
⁢
u
)
2
-
(
λ
1
⁢
v
)
2
]
}
,
U
d
n
λ
2
=
F
-
1
⁢
{
F
⁢
{
U
0
λ
2
}
·
exp
[
i
⁢
2
⁢
π
λ
2
⁢
d
n
⁢
1
-
(
λ
2
⁢
u
)
2
-
(
λ
2
⁢
v
)
2
]
}
,
wherein
U
0
λ
1
denotes complex amplitudes of a wavelength λ1 at the different axial propagation positions within the defocus range;
U
0
λ
2
denotes complex amplitudes of a wavelength λ2 at the different axial propagation positions within the defocus range;
F{ } denotes the Fourier transform;
F−1{ } denotes the inverse Fourier transform;
(u,v) denotes frequency domain coordinates corresponding to spatial coordinates;
and subscripts m, n=1, 2, . . . , M denote propagation position indices;
the propagation position indices satisfy:
M
=
floor
[
(
d
m
-
d
0
)
/
step
]
+
1
,
wherein floor denotes a floor function, and M=41;
subtracting the single-wavelength phase distributions of the wavelength λ2 at all the different axial propagation positions from each single-wavelength phase distribution of the wavelength λ1 to obtain M2 dual-wavelength synthetic phase distributions φm,n:
φ
m
,
n
=
φ
d
m
λ
1
-
φ
d
n
λ
2
,
wherein
φ
d
m
λ
1
denotes the single-wavelength phase distribution corresponding to the wavelength λ1, and
φ
d
n
λ
2
denotes the single-wavelength phase distribution corresponding to the wavelength λ2;
and
calculating gradient values for all the dual-wavelength synthetic phase distributions φm,n to obtain the gradient values Gm,n of the dual-wavelength synthetic phase distributions when the two wavelengths are at the different axial propagation positions m, n:
G
m
,
n
=
∑
x
=
2
X
∑
y
=
2
Y
(
φ
m
,
n
(
x
,
y
)
-
φ
m
,
n
(
x
-
1
,
y
)
)
2
+
(
φ
m
,
n
(
x
,
y
)
-
φ
m
,
n
(
x
,
y
-
1
)
)
2
,
wherein X, Y denote a count of pixels of an image along a longitudinal direction and a transverse direction, respectively.

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Methods and systems for chromatic aberration compensation in dual-wavelength digital holography

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Methods and systems for chromatic aberration compensation in dual-wavelength digital holography

Life of this patent

Abstract

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