Accurate measurement for damage evolution of ceramics caused by nanosecond laser pulses with polarization spectrum imaging

Ying Ye; Yong Tan; Guangyong Jin

doi:10.1364/OE.27.016360

1. Introduction

The research on the interaction between laser and matter is mainly focused on the engineering fields of cutting, welding and surface thermal treatment of metal materials [1]. In recent years, composite ceramics have been widely used as an alternative to traditional metal materials in extreme environments and special cases. For example, deep well drilling, aircraft surface, etc., so laser protection and laser damage have been attracting more and more attentions of researchers [2]. The ceramic damage morphology and mechanism caused by the interaction between laser and material are widely related to the physical parameters of the laser and the surface structure of the material, so the thermal and mechanical changes involved are more complicated [3,4]. However, in order to have the in-depth understanding to damage process, it is very necessary to use a technical metrology to obtain the relevant damage information [5]. At present, the microscopic morphology changes of laser caused damage of materials are used to enhance the efficiencies of the traditional microscopic imaging methods, electron microscopy and other techniques to analyze the damage characteristics of materials under laser irradiation, but all these techniques are only used for an offline detection [6,7], the dynamic process of material damage cannot be recorded. Thereby, in the past years many online detection methods are invented and developed, including the light scattering [8], plasma flash [9–11], photothermal deflection imaging [12–15], acousto-optic discrimination [16,17], optical interference [18], photodetection method [19], etc., each of them has its advancements and limitations in applications. For instance, the plasma flash method can be used for online detections, but it has an high uncertainties from the human eye observation and human operation discrepancies, the acousto-optic discrimination method cannot reflect the degree of damage, the photothermal deflection imaging and the photoelectric detection imaging can record the damage process in real time through the visual image, but the images of the microscale damage details are always not clear enough. Therefore, it is one of the key steps to develop a more sensitive and accurate detection method for laser damage observation.

Polarization spectral imaging detection technology is an emerging detection technology and has been developed rapidly in recent years since it effectively combines the spectral imaging technology and the polarization imaging technology to acquire seven-dimensional information of space targets [20]. Polarization spectral imaging technology has a wide range of applications and prospects, such as military concealment recognition [21], clear imaging of microscale structures [22], crop micro-damage screening and lesion detection [23], atmospheric aerosol measurement [24], biomedical diagnosis [25] etc. At present, there are two kinds of spectral polarization analysis methods: the experimental analysis and the theoretical modeling analysis. In applications, the experimental analysis method requires the high-cost experimental equipment and the critical conditions, and the research of polarization spectral imaging system is a key technology and has become a hot spot in research, it has especially become a trend to gradually optimize and improve from mechanical manual equipment to liquid crystal tuned automatic equipment. M. Vedel et al. invented a full Stokes polarization imaging camera based on a dual-ferroelectric liquid crystal wave plate (FLC) to analyze the polarization characteristics of targets of different materials and then concluded that the polarization imaging system can achieve the low-contrast target detection, remove the background stray light, perform 3D the reconstruction of target, and finally achieve the material surface stress measurement [26]. Polarization detection is generally directed at the object of the ground object, and the circular polarization component of the object scattering light is weak, so it is usually ignored by the researcher. In recent years, research shows that information of the circular polarization component has an advantage in obtaining the clear image of a dust and a fog, especially this advantage is more observable when the target has more moisture and humidity [27]. Therefore, in order to fully and truly reflect the polarization information of the target, it is necessary to obtain the full polarization components and establish a perfect model relating the polarization characteristics to the imaging properties of the target.

As well known, the theoretical modeling is generally a commonly adopted step to obtain the intrinsic relationship between each key variable and the target polarization characteristics, but most of the current theoretical models only consider specular reflection, while rarely consider or even completely ignore the influence of diffuse reflection. Here, a further development of the semi-empirical model with respect to polarization and originally applied to painted surfaces was the Maxwell-Beard model [28]. One class of semi-empirical models that is based on geometrical optics and statistical description of surface facet slope distributions can be represented by the Torrance-Sparrow model [29]. In order to sufficiently analyze the polarization reflection characteristics of the target object, it is necessary to combine the measured polarization information with the polarization model for appropriately understanding the polarization reflection characteristics of the target object and accurately identifying the target in a complex background [30,31].

In this article, a polarization spectrum imaging system composed of a liquid crystal tunable filter (LCTF), a liquid crystal polarization rotator (LCPR), a liquid crystal phase retarder (LCVR) and a charge-coupled device (CCD) detector is developed to detect nanosecond laser ablated ceramics. The system has the characteristics of small field of view and large aperture, which is equivalent to a 69 times magnification microscope for a long-distance camera. In theory, the fully polarized bidirectional reflection distribution function (pBRDF) model of micro-surface is gained, the full Stokes vector transfer equation is deduced based on the polarization spectrum imaging system and the relevant image fusion processing technology. The experimental results show that the “on-line detection of damage identification based on polarization spectrum imaging” method can obtain the spatial evolution process of laser-substance interaction in real-time online under full polarization state, and it can clearly highlight the complex environmental background during the action of laser and matter. Concealed information and its critical edge state and evolutionary process that are not detected by other detection methods such as low-contrast surface, shadow damage morphology, etc., polarization intensity value, degree of polarization (DOP), average output polarization (AOP) can reflect the physical and chemical properties of the target surface. The image processing technology makes the evolution process of damage morphology intuitive and effective so order to reveal more easily the mechanism of laser damage. Combined with the theoretical model, the relationship between polarization spectra data and damage information can be deeply established. In brief, the polarization spectrum imaging detection technology provides a new method for further research on the mechanism of laser-substance interaction, which is not replaceable by the existing laser damage detection methods.

2. Experimental procedure

2.1. Experimental device and conditions

The experimental setup of polarization spectrum imaging for measuring the laser damage of ceramics is shown in Fig. 1 that is composed of four parts: the pulse laser source part, the illuminative laser source part, the laser-material interaction part and the imaging/analyzing part. The pulse laser source part is composed of a Nd: YAG solid-state pulsed laser with an output of a pulse width of 12 ns at the wavelength of 1064 nm, a beam splitter (2:23) and an aperture, and the laser beam is focused by a lens to the surface of the target. The spot diameter of laser beam at the focused point is 3.5 mm, and the output stability of energy is ± 3%. During an experiment, the energy is monitored by the energy meter after the beam splitter in real time. In order to reduce the influence of the surface defects of the material itself, the laser energy used in the experiment is set to be much higher than the initial damage threshold for the composite ceramic surface. As shown in Fig. 1, in the laser-material interaction part, the sample under studying is fixed on a three-dimensional (3D) movable platform to precisely control the position of the damaged point in the X-Y plane. With a liquid crystal tunable filter (LCTF, VIS-10 51997) produced by CRI of America, a liquid crystal polarization rotator (LCPR) and a liquid crystal phase retarder (LCVR) produced by Meadowlark of America, a CCD detector (Camera MV-VEM200SM) by Microvision company of China, a fully polarized hyperspectral imaging system is developed to realize the hyperspectral full polarization imaging detection and identification of target damage characteristics in a spectrum range of 400-720nm. Figure 2 shows a nanosecond laser damage spectrum of ceramic recorded by a fiber optic spectrometer (Ocean Optics, QE65Pro) for active spectral curve. According to Fig. 2, the ceramic plasma irradiated by laser cover about 20 nm from 567 nm to 589 nm which is superposed upon the thermal radiation spectrum. In order to see the material body covered by plasma and thermal radiation spectrum, the center wavelength of an LED illumination source is selected as 580 nm which 0° linearly polarized orientation is determined by the polarizer as the X-axis, the kind of wavelength multiple frame polarization spectroscopy images with different polarization angle for the same target are acquired to form full Stokes vector. To ensure the optimal imaging results and consistent image damage, the angle $θ_{i}$ between the incident direction of the LED beam and the target normal is 45° and the angle $θ_{r}$ between the fixed camera and the normal of target surface is 5°, corresponding $ϕ_{i}$ = 0° and $ϕ_{r}$ = 180°, the positional relationship between illumination and detection refers to the rule of the bidirectional reflection distribution function (BRDF), as shown in the upper right corner of Fig. 1. The composite ceramic materials are required to be cleaned before the experiment to avoid the influence of surface pollutants on the damage characteristics of the materials. The damage morphology was recorded by metallographic microscope before and after the experiment so that their contrast analysis is carried out.

Fig. 1 Schematic (left) and pBRDF physical model (right) of the laser ablating composite ceramic materials.

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Fig. 2 Nanosecond laser damage composite ceramic spectrum.

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2.2. Polarization spectrum imaging detection and analysis method

Based on a polarization spectral imaging system, a kind of detection method about laser-material interaction is proposed to achieve spectral full polarization detection in this work. With the LCPR and LCVR in the polarized imaging/detecting system at the left-corner of Fig. 1, three linear polarizations and one circular polarization can be obtained by precisely controlling the phase delay amount and the polarization direction by the electronically controlled liquid crystal polarization modulator, and the reflection characteristics of the material surface can be fully characterized by polarized bidirectional reflection distribution function (pBRDF). In order to reflect the polarization characteristics of the material before and after being damaged, the Fresnel reflection Muller matrix and the Torrance-Sparrow BRDF (TS-BRDF) model based on the micro-surface theory are used to represent the transmission relationship between incident radiation and reflected radiation. Then pBRDF can be obtained by the action of a scalar TS-BRDF model and 4 × 4 Fresnel reflection Muller matrix as [31,32]:

f (θ_{i}, ϕ_{i}, θ_{r}, ϕ_{r}, λ) = \frac{1}{2 π} \frac{1}{4 σ^{2}} \frac{1}{\cos^{4} α} \frac{\exp (- (\tan^{2} α / 2 σ^{2}))}{\cos (θ_{i}) \cos (θ_{r})} Μ (θ_{i}, θ_{r}, ϕ_{i}, ϕ_{r}, λ),

_{$Μ (θ_{i}, θ_{r}, ϕ_{i}, ϕ_{r})$} is the Fresnel reflection Muller matrix that is given by [33]:

(\begin{matrix} \frac{1}{2} ({| S_{11} |}^{2} + {| S_{12} |}^{2} + {| S_{22} |}^{2} + {| S_{21} |}^{2}) & \frac{1}{2} ({| S_{11} |}^{2} - {| S_{12} |}^{2} - {| S_{22} |}^{2} + {| S_{21} |}^{2}) & Re (S_{11} S_{12}^{*} + S_{21} S_{22}^{*}) & - Im (S_{11} S_{12}^{*} + S_{21} S_{22}^{*}) \\ \frac{1}{2} ({| S_{11} |}^{2} + {| S_{12} |}^{2} - {| S_{22} |}^{2} - {| S_{21} |}^{2}) & \frac{1}{2} ({| S_{11} |}^{2} - {| S_{12} |}^{2} + {| S_{22} |}^{2} - {| S_{21} |}^{2}) & Re (S_{11} S_{12}^{*} - S_{21} S_{22}^{*}) & - Im (S_{11} S_{12}^{*} - S_{21} S_{22}^{*}) \\ Re (S_{11} S_{21}^{*} + S_{12} S_{22}^{*}) & Re (S_{11} S_{21}^{*} - S_{12} S_{22}^{*}) & Re (S_{11} S_{22}^{*} + S_{12} S_{21}^{*}) & - Im (S_{11} S_{22}^{*} - S_{12} S_{21}^{*}) \\ Im (S_{11} S_{21}^{*} + S_{12} S_{22}^{*}) & Im (S_{11} S_{21}^{*} - S_{12} S_{22}^{*}) & Im (S_{11} S_{22}^{*} + S_{12} S_{21}^{*}) & Re (S_{11} S_{22}^{*} - S_{12} S_{21}^{*}) \end{matrix}) .

Then, the directional hemispherical reflectivity (DHR) of the measured surface is recognized by [34–36]:

D H R (θ_{i}) = \int f (θ_{i}, θ_{r}, ϕ_{i}, ϕ_{r}, λ) \cos θ_{r} d Ω_{r},

In the formula

d Ω_{r} = \sin θ_{r} d θ_{r} d ϕ_{r}

,

θ_{i}

is the incident angle,

θ_{r}

is the reflection angle,

ϕ_{i}

is the incident azimuth angle,

ϕ_{r}

is the reflection azimuth angle,

α

is the angle between the micro-surface normal

n

and the target surface normal

z

, and

γ

between the incident ray and the micro-surface normal

n

,

\cos α = (\cos θ_{i} + \cos θ_{r}) / \cos γ

.

σ

is the roughness of the target surface. The Stokes vector is usually used to represent the incident and reflected directions, thus according to the Stokes vector

S^{i}

of the incident interface, the reflected Stokes vector

S^{r}

can be obtained with Eq. (3) as:

(\begin{matrix} S_{0}^{r} \\ S_{1}^{r} \\ S_{2}^{r} \\ S_{3}^{r} \end{matrix}) = (\begin{matrix} \int f_{00} \cos θ_{r} d Ω_{r} & \int f_{01} \cos θ_{r} d Ω_{r} & \int f_{02} \cos θ_{r} d Ω_{r} & \int f_{03} \cos θ_{r} d Ω_{r} \\ \int f_{10} \cos θ_{r} d Ω_{r} & \int f_{11} \cos θ_{r} d Ω_{r} & \int f_{12} \cos θ_{r} d Ω_{r} & \int f_{13} \cos θ_{r} d Ω_{r} \\ \int f_{20} \cos θ_{r} d Ω_{r} & \int f_{21} \cos θ_{r} d Ω_{r} & \int f_{22} \cos θ_{r} d Ω_{r} & \int f_{23} \cos θ_{r} d Ω_{r} \\ \int f_{30} \cos θ_{r} d Ω_{r} & \int f_{31} \cos θ_{r} d Ω_{r} & \int f_{32} \cos θ_{r} d Ω_{r} & \int f_{33} \cos θ_{r} d Ω_{r} \end{matrix}) (\begin{matrix} S_{0}^{i} \\ S_{1}^{i} \\ S_{2}^{i} \\ S_{3}^{i} \end{matrix}),

It can be noticed that the Stokes vector of the visible light polarization reflection model can be expressed as (ignoring the atmospheric radiation in the transmission path):

S^{i n} = S^{r} = \int f (θ_{i}, ϕ_{i}, θ_{r}, ϕ_{r}, λ) \cos θ_{r} d Ω_{r} \cdot S^{i},

Where

S^{i n}

is the incident light Stokes vector of the initial beam entering the active imaging system, but 0° linearly polarization direction

S^{i}

is set in the same X-Z plane as polarization direction of LED light, when

S^{i} = {[\begin{matrix} 1 & 1 & 0 & 0 \end{matrix}]}^{T}

, according to Eqs. (2) and (5), the Stokes vector

S^{i n}

is closely related to

f_{00}

,

f_{10}

,

f_{20}

and

f_{30}

. Then,

f_{00}

,

f_{10}

,

f_{20}

and

f_{30}

can be calculated from

m_{00}

,

m_{10}

,

m_{20}

,

m_{30}

and

m_{01}

,

m_{11}

,

m_{21}

,

m_{31}

in the Fresnel reflection Muller matrix

Μ (θ_{i}, θ_{r}, ϕ_{i}, ϕ_{r})

. It is existed that

m_{00} \neq m_{11}

for this case is indicative of the fact that there is depolarization in actual model. M matrix of interest is [37]:

(\begin{matrix} \begin{matrix} m_{00} \\ m_{10} \\ m_{20} \\ m_{30} \end{matrix} & \begin{matrix} m_{01} \\ m_{11} \\ m_{21} \\ m_{31} \end{matrix} \end{matrix}) = (\begin{matrix} \begin{matrix} \frac{1}{2} ({| S_{11} |}^{2} + {| S_{12} |}^{2} + {| S_{22} |}^{2} + {| S_{21} |}^{2}) \\ \frac{1}{2} ({| S_{11} |}^{2} + {| S_{12} |}^{2} - {| S_{22} |}^{2} - {| S_{21} |}^{2}) \\ Re (S_{11} S_{21}^{*} + S_{12} S_{22}^{*}) \\ Im (S_{11} S_{21}^{*} + S_{12} S_{22}^{*}) \end{matrix} & \begin{matrix} \frac{1}{2} ({| S_{11} |}^{2} - {| S_{12} |}^{2} - {| S_{22} |}^{2} + {| S_{21} |}^{2}) \\ \frac{1}{2} ({| S_{11} |}^{2} - {| S_{12} |}^{2} + {| S_{22} |}^{2} - {| S_{21} |}^{2}) \\ Re (S_{11} S_{21}^{*} - S_{12} S_{22}^{*}) \\ Im (S_{11} S_{21}^{*} - S_{12} S_{22}^{*}) \end{matrix} \end{matrix}),

When the incident electric field is described in the second coordinate system,

{\vec{E}}_{r} = a {\vec{E}}_{i}

, where

a

is a complex diagonal 2 × 2 matrix, it can be written by

(\begin{matrix} a_{s s} & 0 \\ 0 & a_{p p} \end{matrix})

,with the aid of the angles

η_{i}

and

η_{r}

, and rotation matrices, this can be given as [37]:

\begin{array}{l} (\begin{matrix} E_{s}^{r} \\ E_{p}^{r} \end{matrix}) = (\begin{matrix} \cos (η_{r}) & \sin (η_{r}) \\ - \sin (η_{r}) & \cos (η_{r}) \end{matrix}) (\begin{matrix} a_{s s} & 0 \\ 0 & a_{p p} \end{matrix}) (\begin{matrix} \cos (η_{i}) & - \sin (η_{i}) \\ \sin (η_{i}) & \cos (η_{i}) \end{matrix}) (\begin{matrix} E_{s}^{i} \\ E_{p}^{i} \end{matrix}) \\ (\begin{matrix} E_{s}^{r} \\ E_{p}^{r} \end{matrix}) = (\begin{matrix} S_{11} & S_{12} \\ S_{21} & S_{22} \end{matrix}) (\begin{matrix} E_{s}^{i} \\ E_{p}^{i} \end{matrix}), \end{array}

Where the calculation expressions of

η_{i}

and

η_{r}

are written as:

\cos (η_{i}) = {[\cos (θ_{i}) + \cos (θ_{r})] / [2 \cos (γ)] - \cos (θ_{i}) \cos (γ)} / \sin (θ_{i}) \sin (γ),

\cos (η_{r}) = {[\cos (θ_{i}) + \cos (θ_{r})] / [2 \cos (γ)] - \cos (θ_{r}) \cos (γ)} / \sin (θ_{r}) \sin (γ),

So, M matrix can be reduced as:

(\begin{matrix} \begin{matrix} m_{00} \\ m_{10} \\ m_{20} \\ m_{30} \end{matrix} & \begin{matrix} m_{01} \\ m_{11} \\ m_{21} \\ m_{31} \end{matrix} \end{matrix}) = \frac{1}{2} (\begin{matrix} \begin{matrix} ({| a_{s s} |}^{2} + {| a_{p p} |}^{2}) \\ \cos (2 η_{r}) ({| a_{s s} |}^{2} - {| a_{p p} |}^{2}) \\ \sin (2 η_{r}) ({| a_{s s} |}^{2} - {| a_{p p} |}^{2}) \\ 0 \end{matrix} & \begin{matrix} \cos (2 η_{i}) ({| a_{s s} |}^{2} - {| a_{p p} |}^{2}) \\ \cos (2 η_{r}) \cos (2 η_{i}) ({| a_{s s} |}^{2} + {| a_{p p} |}^{2}) \\ \cos (2 η_{r}) \sin (2 η_{i}) (a_{s s} a_{p p}^{*} + c . c .) - \sin (2 η_{r}) \sin (2 η_{i}) ({| a_{s s} |}^{2} - {| a_{p p} |}^{2}) \\ 2 i \sin (2 η_{i}) (a_{s s} a_{p p}^{*} - a_{s s}^{*} a_{p p}) \end{matrix} \end{matrix}),

Where

R_{s}

and

R_{p}

is the vertical (y direction) and parallel component (x direction) of Fresnel reflectivity, respectively. So

S^{i n}

can be expressed as:

(\begin{matrix} I \\ Q \\ U \\ V \end{matrix}) = (\begin{matrix} S_{0}^{i n} \\ S_{1}^{i n} \\ S_{2}^{i n} \\ S_{3}^{i n} \end{matrix}) = [\begin{matrix} \frac{1}{8 π σ^{2}} \int \frac{1}{\cos^{4} α} \frac{\exp (- (\tan^{2} α / 2 σ^{2}))}{\cos (θ_{i})} [2 \cos^{2} (η_{i}) {| a_{s s} |}^{2} + 2 \sin^{2} (η_{i}) {| a_{p p} |}^{2}] d Ω \cdot I_{b g} \\ \frac{1}{8 π σ^{2}} \int \frac{1}{\cos^{4} α} \frac{\exp (- (\tan^{2} α / 2 σ^{2}))}{\cos (θ_{i})} \cos (2 η_{r}) [2 \cos^{2} (η_{i}) {| a_{s s} |}^{2} - 2 \sin^{2} (η_{i}) {| a_{p p} |}^{2}] d Ω \cdot I_{b g} \\ \frac{1}{8 π σ^{2}} \int \frac{1}{\cos^{4} α} \frac{\exp (- (\tan^{2} α / 2 σ^{2}))}{\cos (θ_{i})} {\begin{cases} \sin (2 η_{r}) [2 \sin^{2} (η_{i}) {| a_{s s} |}^{2} + 2 \cos^{2} (η_{i}) {| a_{p p} |}^{2}] \\ + \cos (2 η_{r}) \sin (2 η_{i}) (a_{s s} a_{p p}^{*} + a_{s s}^{*} a_{p p}) \end{cases}} d Ω \cdot I_{b g} \\ \frac{1}{8 π σ^{2}} \int \frac{1}{\cos^{4} α} \frac{\exp (- (\tan^{2} α / 2 σ^{2}))}{\cos (θ_{i})} [2 i \sin (2 η_{i}) (a_{s s} a_{p p}^{*} - a_{s s}^{*} a_{p p})] d Ω \cdot I_{b g} \end{matrix}],

Where I, Q, U, and V represent the four parameters of the Stokes vector of the incident light, namely,

I

represents the radiant energy of the incident light passing through the unit area, both Q and U represent the direction and intensity of the linear polarization, V is the circular polarization component in the incident light, and

I_{b g}

is the background light intensity when natural light is incident.

As a result, the polarization state of the object can be concluded that is not only related to various physical factors such as surface refractive index, incident angle, reflection angle, roughness, etc., but also closely related to the intensity of the background. DOP and AOP can usually highlight material characteristics under background light interference. DOP and AOP are obtained as functions of parameters such as roughness, refractive index, and incident angle too. The mathematical model of DOP and AOP based on BRDF model can be derived from Eq. (11) as:

D O P = \frac{\sqrt{Q^{2} + U^{2} + V^{2}}}{I},

A O P = \frac{1}{2} arc \tan (\frac{U}{Q}),

In the above formulas, there are

σ

,

α

and

γ

,

a_{s s}

and

a_{p p}

that characterize the material real time characteristics. These parameters are unknown in actual detection. Through the established Stokes vector parameter measurement system, the four components of the Stokes vector can be obtained by matrix inversion which can give the five parameters. The DOP and AOP images can be reconstructed after calculation.

3. Experimental results and discussion

Figure 3 shows the comparisons of 580 nm spectral image Fig. 3(a) and metallographic microscopy image Fig. 3(b) of origin ceramic surface that is shaped by the “dry-pressed” processing method and which roughness measurement of the surface (RMS) is small. The calibration size of optical imaging system is 50 μm and the filter is set to 580 nm in Fig. 3(a), and the image scale of the metallographic microscope is 50 μm in Fig. 3(b), but the resolution of both CCD detectors is different, so the scale length display of both are different too. When the laser beam interacts with the composite ceramic material, the energy, pulse mode and experimental environment of laser are not only important, but also the physical and chemical properties of materials play important roles, so damage mechanism is complex.

Fig. 3 Ceramic surface topography when not damaged. (a) 580 nm spectral image of ceramic undamaged surface; (b) metallographic microscopy image.

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In this paper, a kind of metrology about on-line detection of damage identification based on polarization spectral imaging can strip away some complex problems and reveal some essence. A single wavelength spectrum of 580 nm is selected to illuminate the laser damage morphology and the four different sets of polarization states of polarization spectral images are applied to characterize damage evolutionary process. The four different sets of polarization states are I (0°, 0°), I (45°, 0°), I (90°, 0°), I (135°, 90°) where the first three values stand for linear polarization states at polarization angle $β$ = 0°, 45°, 90° respectively and phase retarder angle $δ$ = 0°, but where the last one is a circle polarization state at $β$ = 135° and $δ$ = 90°. Every kind of evolution belongs to the different laser pulse number N and different laser energy. As shown in Fig. 4, the partial evolution process of the composite ceramic damaged in the circular polarization state which 63 pictures are listed as a representative in the continuous dynamics data from four different polarization parameters with laser energy of 217.94 mJ and 40 pulses due to the large amount of experimental data. The results show gradual evolution of damage morphology where degree of damage increases obviously with time.

Fig. 4 Evolution of damage morphology of composite ceramics with time under circular polarization I (135°, 90°).

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On the other hand, the characteristic images of four different polarization parameters with the laser energy of 217.94 mJ are selected as shown in Fig. 5 to analyze the dependence of laser damage spectral image of ceramics on both the pulse number and polarization state. Figure 5 shows that the laser damage spectral image shows the different damage morphology and information under different polarization state. For instance, at the 0° linear polarization state, the damage morphology of the material surface can be seen irrespective of the number of pulses, but with increase of the pulse numbers N, the ablation area increases and become gradually clear, a dark ring is formed between the ablation and non-ablative zone. When N = 14, a certain depth of ablation pit appears, and a slight uneven change occurs on the surface of the material outside the dark ring. As shown in Fig. 6, along the yellow dashed line, as the number of pulses increases, the area of uneven variation gradually expands, implying a topographic map of stress change in various regions, that is, this kind of detection technology can find the material has uneven undulations on the surface under laser action mainly due to thermal stress effects that is different from other methods. Two additional impressive trends of images can be found from Fig. 5: (i) at the same number of laser pulses, as far as the linear polarization images are concerned, the gray level of the images decrease with the increase of polarization angles, therefore, no matter how many laser pulses are, the damage morphology becomes difficult to detect under the 90° linear polarization state, that is, when a pulsed laser irradiates the surface of the ceramic, the damage morphology under the 90° linear polarization state manifests as a dark spot of uniform spot size. As the number of laser pulses increases, the dark spots gradually fade away from the center of the damaged area that shows some significant polarization characteristics, in other words, that indicates that the physical and chemical properties between dark spots and faded areas are different. The physicochemical properties of the faded areas are consistent with them outside the laser action zone. From the perspective of the shrinking process of dark spots, the hot melt effect gradually becomes dominant, which is due to the disappearance of micro-particles and the disappearance of out-of-flatness on the surface of the material. Considering that the laser beam is Gaussian type and its incident-angle to the surface of the ceramic is not vertical, the energies of different irradiated areas are different, so distribution of hot melt zone and strain zone is separated; and (ii) the circle polarization state images become clearer than the cases of linear polarization state. As the number of pulses increases, the deeper areas gradually become bright from the dark states. Note from Fig. 5 that, (i) when N = 5, the damage state change significantly from the case of N = 3, and the dark spot area becomes weak and completely disappears until N = 120; (ii) each image has a bright improvement when N is doubled irrespective of the polarization state of imaging light, for which the evidence is the case from N = 14 to N = 20, the only non-doubled increase of N in this test, the image change is not so obviously clear.

Fig. 5 Ceramic materials with four different polarization parameters collected at a single wavelength of 580 nm with varying pulse number N damage polarization source image.

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Fig. 6 Uneven changes in the surface of composite ceramics as the number of pulses increases. (a) N = 14; (b) N = 20; (c) N = 40 and (d) N = 120.

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In order to analyze the mechanism of laser damage of the ceramic material from the polarization spectrum image acquired by the polarization spectrum camera, the scattered light of material is traced and analyzed with the optical signal after passing through multiple devices in the detection process. Owing to the function of the detector in Fig. 1, the evolution of the polarization state $S^{i n}$ of the scattered light of the material is obtained by Muller matrix and Stokes parameters, which can be calculated with the relationship of $S_{o u t} = M_{s y s t e m} S^{i n} = M_{α} M_{45^{\circ}, δ} M_{45^{\circ}, δ} S^{i n}$ . Based on full Stokes parameter measurement principle of the system's LCPR, LCVR and LCTF, the incident light propagates along the Z-axis and the LCPR and LCVR fast axes are fixed at an angle of $β_{1}$ and $β_{2}$ to the X-axis, respectively. Then, the LCTF fast axis with the line-off characteristic has an angle of $α$ with the X-axis. The Muller matrix of any device with a phase delay of $δ$ and an angle of $β_{i}$ ( $i$ = 1, 2) between the fast axis and the X-axis is:

M_{β_{i}, δ} = {[\begin{matrix} 1 & 0 & 0 & 0 \\ 0 & \cos 2 β_{i} & \sin 2 β_{i} & 0 \\ 0 & - \sin 2 β_{i} & \cos 2 β_{i} & 0 \\ 0 & 0 & 0 & 1 \end{matrix}]}^{T} \cdot [\begin{matrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & \cos δ & \sin δ \\ 0 & 0 & - \sin δ & \cos δ \end{matrix}] \cdot [\begin{matrix} 1 & 0 & 0 & 0 \\ 0 & \cos 2 β_{i} & \sin 2 β_{i} & 0 \\ 0 & - \sin 2 β_{i} & \cos 2 β_{i} & 0 \\ 0 & 0 & 0 & 1 \end{matrix}],

The Muller matrix of a linear polarizer that is ._. with the X-axis is:

M_{α} = [\begin{matrix} 1 & \cos 2 α & 0 & 0 \\ \cos 2 α & \cos^{2} 2 α & \cos 2 α \sin 2 α & 0 \\ \sin 2 α & \cos 2 α \sin 2 α & \sin^{2} 2 α & 0 \\ 0 & 0 & 0 & 0 \end{matrix}],

The four parameters of Stokes are solved via the phase delay combination of four groups of LCPR. In this model, the function of LCVR is considered as: _{${\begin{matrix} δ_{1} = 3 π / 2 \\ δ_{1} = 2 π \end{matrix}, {\begin{matrix} δ_{2} = 3 π / 2 \\ δ_{2} = π \end{matrix}, {\begin{matrix} δ_{3} = π \\ δ_{3} = 3 π / 2 \end{matrix}, {\begin{matrix} δ_{4} = 3 π / 2 \\ δ_{4} = 3 π / 2 \end{matrix} .$} Considering the experimental conditions further, the fixed LCPR, LCVR, LCTF and X-axis angles that are _{$β_{1}$} = 0°, _{$β_{2}$} = 45°, _$α$ = 0°, respectively, are brought into the Muller matrix of the entire optical system. Finally, we obtain the original Stokes parameters of the incident light as:

S_{i n} = [\begin{array}{l} I \\ Q \\ U \\ V \end{array}] = \frac{1}{2} [\begin{matrix} 1 & 1 & 0 & 0 \\ 1 & - 1 & 0 & 0 \\ - 1 & - 1 & 0 & 2 \\ 1 & 1 & - 2 & 0 \end{matrix}] [\begin{array}{l} I_{1} \\ I_{2} \\ I_{3} \\ I_{4} \end{array}] .

In general, the single slight difference of the polarization image cannot integrally reflect the details of the target. In order to more clearly identify the damage topography, the polarization dependence of I, Q, U or V image is obtained based on the optical transfer model of the system and the image fusion processing technology. And DOP, AOP, degree of linear polarization (DOLP), and degree of circular polarization (DOCP) images are processed to obtain a typical damage situation where the laser energy of 155.54 mJ and 217.94 mJ is selected cyclically at N = 1 and N = 14, as shown in Figs. 7–10. Comparisons of all the images among these four cases show that each of the four components of Stokes vector: I, Q, U or V image have more dual dependence on the pulse number and energy than the origin polarized images, but the image differences among the four components of Stokes vector are not so obvious as the DOP, AOP, DOLP and DOCP.

Fig. 7 Normalized polarization characteristic matching image N = 1, energy is 155.44 mJ.

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Fig. 8 Normalized polarization characteristic matching image N = 1, energy is 217.94 mJ.

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Fig. 9 Normalized polarization characteristic matching image N = 14, energy is 155.44 mJ.

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Fig. 10 Normalized polarization characteristic matching image N = 14, energy is 217.94 mJ.

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Thereby, the metallographic microscopic images are taken for N = 1, 3, 14 and 20, as shown in Figs. 11(a), 11(b), 11(c) and 11(d), respectively. When the energy is 155.54mJ, at N = 1, the micro-damage phenomenon appears on the surface of the composite ceramic. The damaged metallographic microscopic morphology is as shown in Fig. 11(a), which looks more like the laser spot on the surface, which is similar to that of the Stokes intensity vector I. The polarization intensity Q and U images can show the contour features of the edge of the damaged area. They are like to the spot damage structure displayed on the metallographic microscope. In principle, there is a little “material removal” on the material surface, but this removal is only limited to the skin layer. The polarization intensity V image supplements the contour information not shown by the Q and U images which shows the specific ablated region; as the number of laser pulses N and the laser energy increase, a large amount of material ablation begins to appear on the surface of the material. Note from the polarization degree image that the damage state of the material surface has changed, and that the feature extraction of the damage edge contour by the polarization angle image can clearly see that a material like the dragon fruit spot is removed in the area around the ablation pit. Phenomenon, with the increase of the number of laser pulses N and the increase of laser energy, the tendency of such spotting increases, and the area of the ablation pit is enlarged. When expanded to a certain extent, the size of the damage is in a dynamic equilibrium state, around the ablation pit. The surface still has a change in shape.

Fig. 11 Metallographic microscopic image of the damage morphology with the number of laser pulses N at an energy of 155.54 mJ. (a) N = 1; (b) N = 3; (c) N = 14 and (d) N = 20.

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In order to further analyze the relationship between the laser damage state of the composite ceramics and the degree of polarization, the different damage areas of the morphology are divided as depicted in Fig. 12, they are divided into shock wave action area, ablation ring outer edge area, ablation ring inner edge area, laser point action area, central ablation edge area and central ablation area, which is helpful for recognizing the distribution property of laser damage morphology of ceramic material. Further, the relationship between the polarization degree of different regions and the laser pulse is calculated as shown in Fig. 13. That is, the polarization bidirectional reflection distribution model established by the micro-face theory can transfer the optical constants and roughness parameters well. From Eq. (5), it is known from the experimental conditions that when the incident angle is 45°, the reflection angle of the detection is 5°, the center wavelength is fixed at _$λ$ = 580 nm, the roughness of a target surface is a parameter affecting the degree of polarization. The larger the surface roughness is, the stronger the diffuse reflection component in the reflected light and the larger the degree of polarization are, because the anisotropy of reflected light is more obvious according to Eqs. (11) and (12). The polarization degree of the central region of the laser applied on composite ceramic surface has a decreasing tendency, and the region 1 is initially stable. As the number of pulses increases, there is a tendency to change the near three regions, while the edge region 5 maintains at the initial damage state. The transition phase of the damage state is particularly obvious. The state of the central region tends to be stable after the occurrence of the ablation pit, the ablation polarization is much smaller than the initial damage phase, and the edge region 2 changes with the same as the region 5, but the degree of polarization is slightly lower than edge region 5. In this region, the changing trends of the region 3 and region 4 are similar, and the region 4 is slightly larger than that of the region 3.

Fig. 12 Schematic diagram of the area after the energy 155.54 mJ 20 pulses damage morphology is divided. Region 1 represents the shock wave action zone; region 2 represents the ablation of the outer edge of the ring; region 3 represents the ablation of the inner edge of the ring; region 4 represents the laser spot area; region 5 represents the edge of the central ablation zone and region 6 represents the central ablation zone.

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Fig. 13 The relationship between the mean value of polarization and the number of pulses in different damage areas of composite ceramic damage morphology after the energy 155.54 mJ damage.

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The polarization degree visual heightening images of the damaged composite ceramic morphology are produced in Fig. 14 where the damaged states for six different pulse number N values are characterized by the polarization degree dependent images at the pulse energy of 217.94 mJ. The multiple damage results are compared and analyzed, thermal and shock wave damage are the main causes for composite ceramics on the whole. In the initial stage, the ablation appearance is similar to the spot shape, and many slight ablation pits appear in Figs. 14(a) and 14(b), so that the roughness increases in the ablated area compared with the origin material surface. As the number of pulses increases, the peripheral part of the ablation pit is covered by the particulate matter, DOP in the peripheral part is larger, that is, the material in beam center absorbed photons and partially converted their energy into heat where the local temperature is rapidly increased to cause melting or even gasification and to form an ablation pit. As the photons continues to be absorbed, the vapor in the ablation pit rapidly expands, ejecting the melt at a high velocity, and simultaneously generating a highly directional shock wave, so that a new ablation melting region appears in the direction of the shock wave around the region, and is gradually enlarged in a circular way, finally, a new ablation ring is formed, which forms a double ring structure with the initial melting pit, as shown in Figs. 14(c)–14(f), this double-ring structure also reflects the different stress distribution. At this time, the removal of the central material is mainly caused by melt vaporization, and the front end of the laser action point is still dominated by thermal damage until the damage morphology of a double ring structure reaches a dynamic equilibrium. Finally, it is found from the six images that the damage effect of the composite ceramic surface with the number of pulses or duration of pulses can be analyzed by using the polarization degree and polarization angle of the image.

Fig. 14 The polarization degree visual heightening image of the damage composite ceramic morphology under the different pulse number N of 217.94mJ energy. (a) N = 1; (b) N = 3; (c) N = 20; (d) N = 60; (e) N = 100 and (f) N = 120.

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4. Summary

This paper aims to explore the online real-time detection method of damage evolution of nanosecond laser ablation composite ceramics, the polarization spectrum camera is used to observe the damage evolution of composite materials with the pulse number and energy change online which results embody the damage law and mechanism. Firstly, a set of theoretical methods has been proposed from the full pBRDF model to the full Stokes vector transfer equation combined with the fusion processing technology of polarization spectrum images. Based on that, a kind of corresponding detection device is built and applied. As a result, the experimental data prove that the Stokes vectors can reflect the severity of laser damage with changes of pulse number and energy, and that fusion parameters of Stokes vectors including of DOP, AOP, DOLP and DOCP are used to evolution difference of damage. The overall shape of the detection target in the low contrast background clearly identifies the detailed texture information of the minor damage with the image fusion processing technology, without doubt, the visual performance benefits from the selection of feature detection spectra too. Based on the detailed understanding, the on-line detection of damage identification via the polarization spectrum imaging is used to reflect the microscopic properties and concealment performances of the target damage process, which provides a new research method for the further investigation of the interaction between laser and matter, which would be conducive to correct the model of thermal stress and shock wave in the laser damage process.

Funding

National Natural Science Foundation of China (41404109); Qingdao National Laboratory for Marine Science and Technology of China (2018ASKJ01).

Acknowledgments

The authors would like to thank Prof. Sun DeGui of the School of Science at the CUST, China, for his help in carrying out these experiments.

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Accurate measurement for damage evolution of ceramics caused by nanosecond laser pulses with polarization spectrum imaging

Abstract

1. Introduction

2. Experimental procedure

2.1. Experimental device and conditions

2.2. Polarization spectrum imaging detection and analysis method

3. Experimental results and discussion

4. Summary

Funding

Acknowledgments

References

Cited By

Figures (14)

Equations (16)

Optics Express