1. Introduction
Laser 3D imaging represents an active imaging detection technology unaffected by ambient light and atmospheric conditions, enabling rapid and comprehensive acquisition of target size and structural information [
1,
2,
3,
4,
5]. This technology finds diverse applications in target observation and recognition [
6,
7,
8,
9,
10,
11]. The area array detector is used as an imaging device in laser three-dimensional imaging technology, which can obtain target information in a single imaging. It has the advantages of fast imaging and high resolution [
1,
12,
13]. The traditional area array laser 3D imaging technology selects an Intensified Charge-Coupled Device (ICCD) with a gating function as the imaging detector device. However, ICCD cameras need to go through the conversion of “optical–electrical–optical–electrical” signals during the imaging process, which leads to a low quantum efficiency of the camera, usually less than 50%, which reduces the imaging quality [
14]. In recent years, laser 3D imaging based on polarization modulation has gradually become a research hotspot for area array laser 3D imaging by using large-area array and high-sensitivity industrial cameras (EMCCD: Electron Multiplying Charge-Coupled Device, high-performance CCD, etc.) instead of an ICCD as detectors [
15,
16,
17,
18,
19]. Polarization modulation refers to a way to modulate a laser to change the polarization state of the laser. Because the detector selected for polarization-modulated 3D imaging reconstruction does not have the gating function or the global shutter gate width is too wide (generally in the order of ms), it is challenging to achieve high-precision distance resolution. Therefore, it is necessary to place an electro-optical crystal at the front end of the detector, which means that a voltage is applied to both ends of the crystal to make it an electro-optical modulator. The electro-optical effect of the crystal is used to realize the gating function of high repetition frequency and narrow pulse width.
In 2016, Sungeun Jo, a scholar at the Korean Academy of Science and Technology, developed a polarization-modulated 3D imaging reconstruction system based on a split focal plane [
20]. This innovative system incorporated four micro polarizer arrays aligned in the polarization direction in front of a detector. It calculated the distance information of the target using the polarization data from the laser echo, achieving an impressive lateral resolution of 200 × 200. In 2018, Chen Zhen et al. from the Chinese Academy of Sciences selected an EMCCD as an imaging detector [
16] and used a KDP crystal to construct a polarization-modulated 3D imaging reconstruction system. The system has a detector lateral resolution of 1024 × 1024 and a modulation gate width of 0.32 μs, with a range resolution of around 1 m when imaging targets up to 960 m away. In 2020, Song of the University of Aerospace Engineering selected a KTN crystal as the electro-optical modulator [
21] to achieve polarization-modulated 3D imaging reconstruction with a large field of view of 20°, with a distance error of 4.8 cm and a distance accuracy of 4.4 cm at 15 m. However, the growth of the KTN crystal is poor, and the clearance diameter of the crystal is only 5 mm, which will waste a lot of target echo information and reduce the imaging quality. In 2023, our group conducted a preliminary study on 3D imaging reconstruction based on electro-optical crystal modulation, and we analyzed the source of the non-uniformity error caused by an electro-optical crystal and calculated the mathematical expression of the non-uniformity of the crystal. Based on the above analysis, a compensation method was proposed to improve the imaging accuracy [
22].
At present, 3D imaging reconstruction technology based on polarization modulation uses electro-optical crystals to modulate the laser echo, carrying the target information. It uses the correspondence between the electro-optical crystal modulation state and the flight time to calculate the target distance information, which requires linear modulation of the crystal [
23]. However, crystals with high stability and good electro-optical performance, such as KDP and LN crystals, have half-wave voltages of thousands of volts, and the crystals will introduce huge electro-optical modulation errors in the process of high-voltage linear modulation, which will reduce the imaging accuracy of the system. Therefore, in this paper, pulse modulation is first used to realize the two modulation states of electro-optical crystals, “on” and “off.” Then, the detector is used to obtain the target laser gray image with a specific distance and depth of field. Finally, the relevant algorithm is used to recover the distance information of the target to achieve high-resolution laser three-dimensional imaging.
2. Comparison of the Related Research Works
Three-dimensional imaging reconstruction is a popular field that has been studied by many scholars; in this section, we will compare previous related research works. In order to distinguish this research from earlier contributions and studies, it is necessary to elaborate from two aspects: one is the difference between the work in this paper and the method of imaging using an ICCD, and the other is the difference between the work of this paper and the method of imaging using an EMCCD. Below we will elaborate on the differences between the three separately.
The imaging camera used in this paper is an SCMOS (edge 5.5, produced by PCO in Kelheim, Germany), and we compare the performance of another ICCD (PI-MAX4: 1024i, manufactured by Teledyne Corporation, Thousand Oaks, CA, USA) camera in the same price range, as shown in
Table 1.
In
Table 1, SCMOS cameras in the same price range perform better than the ICCD and therefore also have higher imaging potential. In
Table 1, the SCMOS has a high quantum efficiency (80%) and low readout noise (<1.0 e
−), allowing it to capture sharper images in low light. Furthermore, the SCMOS has a high sensitivity and is suitable for applications that require a high signal-to-noise ratio. The ICCD, on the other hand, has a low quantum efficiency (25%), and the ICCD uses electronic enhancement technology to amplify low-intensity light signals to improve imaging sensitivity. The ICCD amplifies the optical signal while simultaneously amplifying the noise, thus introducing imaging errors. In addition, due to the difference in manufacturing process, the SCMOS (pixel counts: 2560 × 2160) also has a higher pixel count than the ICCD (pixel counts: 1024 × 1024), which is more conducive to high-resolution imaging. However, the ICCD has its own shutter and has the function of gating a target at a specific distance, and the SCMOS imaging performance is high, but it does not have the gating function, so the electro-optical effect of the crystal is used to realize the gating function of the SCMOS. In the laboratory experiment, the root mean square error of the SCMOS imaging at the distance of 20 m can reach 3.2 cm, and the root mean square error of the ICCD is around 5 cm under the same imaging environment.
Some scholars use an EMCCD for 3D imaging restoration studies. Both our imaging method and the EMCCD imaging method use the electro-optical effect of the crystal to achieve the 3D imaging function of the target. However, the imaging principle of the two methods is different, so the modulation of the crystal is also different.
Figure 1 illustrates the modulation process of a crystal using an EMCCD.
The EMCCD imaging method uses an EMCCD to obtain the polarization light intensity information of the target by linear modulation of the crystal, and calculates the distance information of the target by solving the relationship between the polarization state of the crystal modulation and the time of flight. As can be seen from
Figure 1, the modulation uniformity of the crystal is good at
V(
t) = 0 and
V(
t) =
Vπ during modulation, while the uniformity of the crystal is poor in other modulation processes. Due to the inhomogeneity of the crystal, distance errors in imaging are introduced. Therefore, in this paper, the modulation mode of the crystal is changed from linear modulation to pulse modulation, and the two modulation states of
V(
t) = 0 and
V(
t) =
Vπ of crystal modulation are used to gate the target, and then the algorithm introduced in
Section 3.2 of the manuscript is used to recover the distance information of the target, which can reduce the modulation error of the crystal and improve the imaging accuracy.
4. Analysis of Polarization Modulation Characteristics of Electro-Optical Crystals
In the 3D imaging reconstruction of electro-optical crystal polarization modulation, the electro-optical crystal provides the detector with a high repetition frequency and narrow pulse width gating function, and the polarization modulation characteristics of the electro-optical crystal affect the 3D imaging reconstruction quality. The lithium niobate (LiNbO3, LN) crystal selected in this paper was used for electro-optical polarization modulation research, and the LN crystal belongs to the C3v − 3 m crystal class, which has the characteristics of a large electro-optical coefficient and low half-wave voltage and is a crystal material with excellent electro-optical properties. In this paper, we will analyze the electro-optical modulation characteristics of crystals under arbitrary incidence conditions according to the refractive index ellipsoid theory and explore the effective field of view of electro-optical crystal modulation in 3D imaging reconstruction systems.
In the absence of an external electric field, the refractive index ellipsoidal equation of an LN crystal can be expressed as follows:
where
X,
Y, and
Z are the main refractive index axes of the crystal and
and
are the refractive indices of ordinary light and abnormal light, respectively. Now, the crystal is uniaxial, and the optical axis of the crystal is along the
Z-axis.
When the LN crystal is used for electro-optical modulation, if the direction of the light is along the optical axis (Z axis), and if the direction of the external electric field is also along the optical axis, the two refracted rays corresponding to the perpendicular incident light have the same refractive index. There is no phase difference in the propagation process of the crystal, so it is not easy to achieve a practical modulation effect. Therefore, when the direction of light is along the Z-axis, the direction of the electric field should be along the X-axis or Y-axis, and the modulation effect of the two methods is the same. When an electric field is applied along the X-axis, the refractive index ellipsoidal coordinate system will rotate 45° about the Z-axis to become an O-X’Y’Z’ coordinate system.
The propagation of light in the crystal is shown in
Figure 8. In the
O-
XYZ coordinate system, the light vector
enters the crystal at the angle of incidence
and the azimuth angle
. Due to the birefringence effect,
is refracted on the surface of the crystal into two light vectors,
and
. The intersection points of
and
with the exit surface of the crystal are
M and
N, respectively. In the 3D coordinate system
O-
XYZ, the incident light
can be expressed as
.
Since the incident light vector
enters the crystal, and the birefringence effect will produce two light vectors
and
in the crystal, we have analyzed in Reference [
24] that the average value
of the two refracted light vectors can be used as the refracted light vector for study. The influence of this simplified research method on the modulation performance of the electro-optical crystal is negligible. When the direction of light is along the optical axis, the phase delay caused by the electro-optical effect can be expressed as follows:
where
is the voltage applied at both ends of the crystal, and d is the thickness of the crystal in the direction of the external electric field. When
,
, it is called a half-wave voltage
.
Calculating the interference light intensity requires the phase difference
of the birefringent ray and the polarization direction
of the refracted light. The expression for phase difference
is as follows:
where
is the angle of refraction of the refracted ray,
.
To find the polarization direction of the refracted ray,
, requires the help of a refractive index ellipsoid, which is shown in
Figure 9. An ellipsoid has two circular cross-sections, C
1 and C
2, passing through the center of the sphere, and the normals of these two cross-sections,
N1 and
N2, are called the optical axis of the crystal;
N1 and
N2 are in the
X’
OZ’ plane, and in the
O-
XYZ coordinate system, the unit typical of the optical axis surface is
. For a ray
, propagating in a non-optical axis direction, the center of the super refractive index ellipsoid is a plane
Q perpendicular to
, and its cross-section with the ellipsoid is an ellipse. The plane
Q intersects the circle C
1 and C
2 at
and
, which are of equal length, so the principal axis direction of the ellipse
Q is the direction of the angular bisector of
and
, which is also the direction of polarization
of the ray
.
The three-dimensional coordinates of the unit direction vectors of the optical axis
N1 and
N2 are
and
, respectively.
is the angle between the optical axis and the
Z axis, and the expression of
is given directly:
Since
is perpendicular to
and
N1,
can be found, and similarly,
can be found
The direction of polarization of the light rays is
. The angle between the polarization direction and the optical axis surface can be expressed as follows:
Knowing the phase difference
θ(
α,
β) and the polarization direction
ϕ(
α,
β), the light intensity formula can be expressed as follows:
According to Equation (8), the light intensity distribution under electro-optical crystal modulation can be calculated, and the result is shown in
Figure 10.
As shown in
Figure 10,
Figure 10a shows the light intensity distribution of the electro-optical crystal in the “off” state, the lower part of
Figure 10a is the magnification of the central region of the upper half,
Figure 10b is the light intensity distribution of the electro-optical crystal in the “on” state, and the lower part of
Figure 10b is the magnification of the central region of the upper half.
To achieve high-precision electro-optical crystal polarization modulation, the modulation effect is measured according to the light intensity, brightness, and uniformity of the electro-optical crystal modulation, and the field of view of electro-optical crystal polarization modulation is determined. LN was selected as the electro-optical modulation crystal, and the clear aperture of the crystal was 9 mm × 9 mm, and the modulation length was 18.8 mm. Assuming that the brightest light intensity of the central field of view is 1 during the crystal polarization modulation when the average light intensity of the modulation region is greater than 0.95, and the lowest light intensity is less than 0.9, it is considered that the polarization modulation light intensity of the electro-optical crystal has good uniformity. The field of view of the electro-optical crystal polarization modulation is around 0.5 degrees when the above conditions are met.
Figure 11 is a schematic diagram of crystal polarization modulation. In
Figure 11, the laser echo scattered by the target passes through the diaphragm and enters a crystal polarization modulator, which consists of two polarizers with perpendicular polarization directions, two lenses, and a crystal. The high-voltage power supply provides voltage to the crystal, the stepper motor drives the turntable, and the crystal placed on the turntable can achieve high-precision three-dimensional angle control. The laser echo carrying the target information is modulated by a modulator and then received by the Scientific Complementary Metal-Oxide Semiconductor (SCMOS) camera.
According to the polarization-modulated light intensity distribution of the electro-optical crystal, the central region of the electro-optical modulation interference pattern can be used to realize the three-dimensional laser imaging of polarization modulation, which requires the returned laser echo to be in the middle region of the crystal interference pattern. For short-range targets, the field of view of 3D imaging reconstruction based on electro-optical crystal polarization modulation will be limited to a slight angle. However, for long-distance targets, the divergence angle of the laser echo is slight, and the energy of the laser device will become a significant limitation of the 3D imaging of this system. Therefore, it is necessary to optimize the reasonable balance between the field of view of electro-optical crystal modulation and the laser energy to build a 3D imaging reconstruction system with the best performance.