Method for super-resolution microscopic interferometric measurement based on broadband annular radially polarized light
Disclosed in this disclosure is a method for super-resolution microscopic interferometric measurement based on broadband annular radially polarized light, where a broad-spectrum light source with an extended surface is selected; uniform illumination covering a to-be-tested FOV and having a certain aperture angle is provided using a Kohler illumination system; a two-stage relay system is designed, and amplitude and polarization of a full-FOV beam is modulated by a liquid crystal spatial light modulator and a vortex waveplate; broadband annular radially polarized light is focused based on the extended surface light source and a microscopic objective lens with a high numerical aperture to implement super-resolution microscopic interference imaging of a sample; and super-resolution topography measurement directed at a surface of a microstructure is implemented combined with phase-shifting interferometry.
1 . A method for super-resolution microscopic interferometric measurement based on broadband annular radially polarized light, comprising:
Step 1: designing a two-stage relay system, for generating broadband annular radially polarized light, wherein
the two-stage relay system comprises a light source ( 1 ), a polarizer ( 2 ), a first condenser lens ( 4 ), a first standard plane mirror ( 5 ), a liquid crystal spatial light modulator ( 6 ), a second condenser lens ( 8 ), a first cube beamsplitter ( 9 ), an analyzer ( 10 ), a third condenser lens ( 11 ), and a vortex waveplate ( 12 );
the first condenser lens ( 4 ) and the second condenser lens ( 8 ) constitute a first-stage relay lens group ( 3 );
the second condenser lens ( 8 ) and the third condenser lens ( 11 ) constitute a second-stage relay lens group ( 7 );
the light source ( 1 ), the polarizer ( 2 ), the first-stage relay lens group ( 3 ), the first standard plane mirror ( 5 ), the first cube beamsplitter ( 9 ), and the liquid crystal spatial light modulator ( 6 ) constitute a first-stage relay system;
the liquid crystal spatial light modulator ( 6 ), the second-stage relay lens group ( 7 ), the first cube beamsplitter ( 9 ), the analyzer ( 10 ), and the vortex waveplate ( 12 ) constitute a second-stage relay system;
the light source ( 1 ), the polarizer ( 2 ), the first condenser lens ( 4 ), and the first standard plane mirror ( 5 ) are arranged coaxially in sequence along a first optical axis, wherein a reflective surface of the first standard plane mirror ( 5 ) forms an angle of 45° with the first optical axis; and
the liquid crystal spatial light modulator ( 6 ), the second condenser lens ( 8 ), the first cube beamsplitter ( 9 ), the analyzer ( 10 ), the third condenser lens ( 11 ), and the vortex waveplate ( 12 ) are arranged coaxially in sequence along a second optical axis, wherein the first cube beamsplitter ( 9 ) is located on a reflection optical path of the first standard plane mirror ( 5 ), and the broadband annular radially polarized light emerges from the vortex waveplate ( 12 );
Step 2: building a system for super-resolution microscopic interferometric measurement based on broadband annular radially polarized light, wherein
the system for super-resolution microscopic interferometric measurement based on broadband annular radially polarized light comprises the two-stage relay system, a fourth condenser lens ( 14 ), a fifth condenser lens ( 15 ), a second cube beamsplitter ( 16 ), a first microscopic objective lens ( 17 ), a to-be-tested sample ( 18 ), a PZT piezoelectric ceramics ( 19 ), a second microscopic objective lens ( 20 ), a second standard plane mirror ( 21 ), a tube lens ( 22 ), and an industrial CCD camera ( 23 ), wherein the to-be-tested sample ( 18 ) is arranged on the PZT piezoelectric ceramics ( 19 );
the fourth condenser lens ( 14 ), the fifth condenser lens ( 15 ), the second cube beamsplitter ( 16 ), the first microscopic objective lens ( 17 ), and the to-be-tested sample ( 18 ) are arranged coaxially behind the vortex waveplate ( 12 ) along the second optical axis; a third optical axis passes through the second cube beamsplitter ( 16 ); the second standard plane mirror ( 21 ), the second microscopic objective lens ( 20 ), the second cube beamsplitter ( 16 ), the tube lens ( 22 ), and the industrial CCD camera ( 23 ) are distributed in sequence along the third optical axis; and the third optical axis is perpendicular to the second optical axis;
the first microscopic objective lens ( 17 ), the to-be-tested sample ( 18 ), and the PZT piezoelectric ceramics ( 19 ) constitute a test optical path, while the second microscopic objective lens ( 20 ) and the second standard plane mirror ( 21 ) constitute a reference optical path; and
the fourth condenser lens ( 14 ) and the fifth condenser lens ( 15 ) constitute a Kohler illumination lens group ( 13 );
Step 3: emitting, from the light source ( 1 ), a multi-field-of-view FOV beam, wherein: the multi-FOV beam passes through the polarizer ( 2 ) to generate a linearly polarized light; the linearly polarized light passes through the first condenser lens ( 4 ) to be converged onto the first standard plane mirror ( 5 ), and is then reflected from the first standard plane mirror ( 5 ) by 90°, onto the first cube beamsplitter ( 9 ); first reflected light reflected from the first cube beamsplitter ( 9 ) passes through the second condenser lens ( 8 ) to the liquid crystal spatial light modulator ( 6 ), the first reflected light being linearly polarized light with a polarization direction same as a long-side direction of a liquid crystal light valve of the liquid crystal spatial light modulator ( 6 ); hollow annular modulation and reflection is performed, by the liquid crystal spatial light modulator ( 6 ), on the linearly polarized light incident thereto to obtain a modulated annular beam as second reflected light; the second reflected light passes through the second condenser lens ( 8 ) to the first cube beamsplitter ( 9 ), passes through the analyzer ( 10 ), with a polarization direction perpendicular to the polarizer ( 2 ), through the first cube beamsplitter ( 9 ), and is then converged onto the vortex waveplate ( 12 ) through the third condenser lens ( 11 ), wherein the vortex waveplate ( 12 ) performs polarization modulation on a full-FOV beam to output the broadband annular radially polarized light; the broadband annular radially polarized light then passes through the Kohler illumination lens group ( 13 ) to the second cube beamsplitter ( 16 ), and is split, by the second cube beamsplitter ( 16 ), into test light and reference light, wherein the test light is transmitted to the first microscopic objective lens ( 17 ) and passes through the first microscopic objective lens ( 17 ) to illuminate the to-be-tested sample ( 18 ), and third reflected light carrying surface morphology information of the to-be-tested sample ( 18 ) reflected from the to-be-tested sample ( 18 ) passes through the first microscopic objective lens ( 17 ) to the second cube beamsplitter ( 16 ), is reflected from the second cube beamsplitter ( 16 ) into the tube lens ( 22 ), and is focused, by the tube lens ( 22 ), onto the industrial CCD camera ( 23 ), and wherein the reference light is reflected to the second microscopic objective lens ( 20 ) and passes through the second microscopic objective lens ( 20 ) to illuminate the second standard plane mirror ( 21 ), and fourth reflected light carrying surface morphology information of the second standard plane mirror ( 21 ) reflected from the second standard plane mirror ( 21 ) passes through the second microscopic objective lens ( 20 ) to the second cube beamsplitter ( 16 ), transmits into the tube lens ( 22 ) through the second cube beamsplitter ( 16 ), and is focused, by the tube lens ( 22 ), onto the industrial CCD camera ( 23 ), where meanwhile the reference light and the test light interfere with each other;
Step 4: controlling, using the PZT piezoelectric ceramics ( 19 ), micro-displacement of the to-be-tested sample ( 18 ) along a direction of an optical axis, and acquiring, by the industrial CCD camera ( 23 ), several phase-shifted interferograms of the to-be-tested sample ( 18 ) within a full-FOV range of the first microscopic objective lens ( 17 ); and
Step 5: processing, using a vertical scan interference algorithm, the acquired phase-shifted interferograms to obtain 3D topography information of the to-be-tested sample ( 18 ).
2 . The method according to claim 1 , wherein the light source ( 1 ) is a broad-spectrum light source with an extended surface, with a band range of visible light, and with a coherence length far less than a coherence length of a laser light source, wherein through modulation of an interference signal by rapid attenuation of a coherence envelope, a significant interference signal occurs just when an optical path difference between a detection light and the reference light is close to zero; and a divergence angle of the light source ( 1 ) is matched to a to-be-tested FOV at an object side, uniform illumination covering the to-be-tested FOV and having a certain aperture angle is provided through a Kohler illumination system, where a full-FOV interferogram is obtained directly without performing spot scan on the to-be-tested sample ( 18 ) using an electric displacement platform, when performing microscopic interference imaging on the to-be-tested sample ( 18 ), low efficiency brought about by conventional laser spot scan being broken.
3 . The method according to claim 2 , wherein the broadband annular radially polarized light meets that:
electric field distribution E and luminous intensity distribution I near a focal point under illumination of the broadband annular radially polarized light are expressed as:
E
=
E
r
+
E
z
,
I
=
E
·
E
¯
,
wherein E r represents a radial polarization component, E z represents an axial polarization component, and Ē represents a conjugate of E;
through simulating electric field distributions near the focal point under illumination of the broadband annular radially polarized light at different annular obscuration coefficients, a relationship among an annular obscuration coefficient, a full width at half maximum FWHM of the luminous intensity distribution near the focal point and a maximum value of luminous intensity on a focal plane is fitted using a least squares method, to obtain function expressions as follows:
x
(
m
)
=
-
0
.053
·
m
2
-
0
.
1
529
·
m
+
0
.
4
0
12
,
I
max
(
m
)
=
-
0
.
3
53
·
m
2
-
0
.
0
88
·
m
+
0
.
3
6
5
,
wherein m represents the annular obscuration coefficient, x(m) represents the FWHM of the luminous intensity distribution near the focal point, and I max (m) represents the maximum value of the luminous intensity on the focal plane.
4 . The method according to claim 3 , wherein the annular obscuration coefficient m=0.9.
5 . The method according to claim 4 , wherein a Linnik-type interference optical path is used for the system for super-resolution microscopic interferometric measurement based on broadband annular radially polarized light in Step 2; two identical microscopic objective lenses are used respectively for the test optical path and the reference optical path; and combined with illumination of the broadband annular radially polarized light, an interference signal I q,image (x, y) actually received during vertical scan is expressed as:
I
q
,
image
(
x
,
y
)
=
I
q
(
x
,
y
)
*
psf
(
x
,
y
)
,
I
q
(
x
,
y
)
=
I
′
(
1
+
exp
{
-
4
[
h
(
x
,
y
)
+
q
·
Δ
z
-
z
0
l
c
]
2
}
cos
{
4
π
λ
[
h
(
x
,
y
)
+
q
·
Δ
z
-
z
0
]
+
∅
0
}
)
wherein
I q (x, y) represents a scan interference signal without taking account of a diffraction effect;
psf(x, y) represents a point spread function, psf(x, y)=I=E·Ē;
h(x, y) represents a surface morphology function of the to-be-tested sample;
I′ represents a luminous intensity sum of a test arm and a reference arm;
z 0 represents a location where the test optical path and the reference optical path have equal optical paths, and Ø 0 represents a phase of the interference signal in case of the equal optical paths;
Δz represents a scan step size, q represents a scan step number, and a scan full length z=q·Δz;
l c represents the coherence length of the light source ( 1 ); and
λ represents a central wavelength of the light source ( 1 );
according to a calibration rule for a white light microscopic interferometer specified in guidelines VDI/VDE2655-1.1, a 3D resolution ∇ 3D (m) of a system for super-resolution microscopic interferometry is expressed as:
Λ
3
D
(
m
)
=
a
·
x
(
m
)
=
a
·
(
-
0
.
0
53
·
m
2
-
0
.
1
529
·
m
+
0
.
4
0
1
2
)
,
wherein
a represents a coefficient related to a structural characteristic of the to-be-tested sample ( 18 ); and
x(m) represents the FWHM of the luminous intensity distribution near the focal point, characterizing a lateral resolution of the system for super-resolution microscopic interferometry; and
as the annular obscuration coefficient m increases, the lateral resolution of the system for super-resolution microscopic interferometry is improved, so that the 3D resolution ∇ 3D is improved.
6 . The method according to claim 5 , wherein the light source ( 1 ) is located at a front focal plane of the first condenser lens ( 4 ), the first condenser lens ( 4 ) and the second condenser lens ( 8 ) are confocal, the liquid crystal spatial light modulator ( 6 ) is located at a back focal plane of the second condenser lens ( 8 ), the second condenser lens ( 8 ) and the third condenser lens ( 11 ) are confocal, the vortex waveplate ( 12 ) is located at a back focal plane of the third condenser lens ( 11 ), the fourth condenser lens ( 14 ) and the fifth condenser lens ( 15 ) are confocal, the fifth condenser lens ( 15 ) and the first microscopic objective lens ( 17 ) are confocal, the to-be-tested sample ( 18 ) is located at a back focal plane of the first microscopic objective lens ( 17 ), and the second standard plane mirror ( 21 ) is located at a back focal plane of the second microscopic objective lens ( 20 ).
7 . The method according to claim 6 , wherein the test optical path and the reference optical path are completely consistent, wherein a location of the to-be-tested sample ( 18 ) in the test optical path corresponds to a location of the second standard plane mirror ( 21 ) in the reference optical path.
8 . The method according to claim 7 , wherein the condenser lenses each are an achromatic lens, with a band range of a spectrum of LED, etc.
9 . The method according to claim 8 , wherein the liquid crystal spatial light modulator is an amplitude-type reflective liquid crystal spatial light modulator, configured to generate the annular beam.
10 . The method according to claim 1 , wherein the first microscopic objective lens ( 17 ) and the second microscopic objective lens ( 20 ) each are an ordinary objective lens with a numerical aperture (NA) greater than 0.85.