Product and Process Fingerprint for Nanosecond Pulsed Laser Ablated Superhydrophobic Surface

Superhydrophobic surfaces have attracted extensive attention over the last few decades. It is mainly due to their capabilities of providing several interesting functions, such as self-cleaning, corrosion resistance, anti-icing and drag reduction. Nanosecond pulsed laser ablation is considered as a promising technique to fabricate superhydrophobic structures. Many pieces of research have proved that machined surface morphology has a significant effect on the hydrophobicity of a specimen. However, few quantitative investigations were conducted to identify effective process parameters and surface characterization parameters for laser-ablated microstructures which are sensitive to the hydrophobicity of the microstructured surface. This paper proposed and reveals for the first time, the concepts of process and product fingerprints for laser ablated superhydrophobic surface through experimental investigation and statistical analysis. The results of correlation analysis showed that a newly proposed dimensionless functional parameter in this paper, Rhy, i.e., the average ratio of Rz to Rsm is the most sensitive surface characterization parameter to the water contact angle of the specimen, which can be regarded as the product fingerprint. It also proposes another new process parameter, average laser pulse energy per unit area of the specimen (Is), as the best process fingerprint which can be used to control the product fingerprint Rhy. The threshold value of Rhy and Is are 0.41 and 536 J/mm2 respectively, which help to ensure the superhydrophobicity (contact angle larger than 150°) of the specimen in the laser ablation process. Therefore, the process and product fingerprints overcome the research challenge of the so-called inverse problem in manufacturing as they can be used to determine the required process parameters and surface topography according to the specification of superhydrophobicity.


Introduction
Superhydrophobic surfaces are defined as those having a water contact angle larger than 150 • and sliding angle less than 10 • . Artificial superhydrophobic surfaces, created by surface structuring or coating, have received tremendous attention in recent years. It is mainly due to their capabilities of providing several interesting functions, such as self-cleaning, corrosion resistance, anti-icing and drag reduction [1][2][3][4][5][6]. Surface chemical composition and morphology are two critical factors in determining their hydrophobicity [7][8][9]. The surface chemical composition affects the intrinsic contact angle, machining parameters and surface characterization parameters can be determined according to the required hydrophobicity, i.e., contact angle. Firstly, analysis of potential process and product fingerprint candidates will be carried out. Then, the most appropriate product fingerprint will be determined from values of Spearman and Kendall rank correlation coefficients according to the experimental results. Thirdly, a new process parameter will be put forward and chosen as the best process fingerprint. Lastly, the correlation between process fingerprint and functional performance, i.e., contact angle will be explored. Figure 1 illustrates the concept of process and product fingerprints in the laser ablation process for obtaining the superhydrophobic surface with an array of Gaussian holes of designed geometry. The comparison of all the potential candidates of process and product fingerprints will be discussed in detail later. Most research performed to date has focused on the correlation A; i.e., the effect of laser machining parameters on the contact angle of specimens. However, correlation A is actually composed of correlation B and C. Correlation B refers to the relationship between contact angle and product fingerprint, which is used to explain the underlying mechanism of effect of surface topography on hydrophobicity. Correlation C can describe the relationship between the process fingerprint and product fingerprint, to explore how the process parameters affect the surface topography. Thus, product fingerprint is a bridge to connect process parameters and functional performance-contact angle.

Analysis of Process and Product Fingerprints
Micromachines 2019, 10, x FOR PEER REVIEW 3 of 15 fingerprint candidates will be carried out. Then, the most appropriate product fingerprint will be determined from values of Spearman and Kendall rank correlation coefficients according to the experimental results. Thirdly, a new process parameter will be put forward and chosen as the best process fingerprint. Lastly, the correlation between process fingerprint and functional performance, i.e., contact angle will be explored. Figure 1 illustrates the concept of process and product fingerprints in the laser ablation process for obtaining the superhydrophobic surface with an array of Gaussian holes of designed geometry. The comparison of all the potential candidates of process and product fingerprints will be discussed in detail later. Most research performed to date has focused on the correlation A; i.e., the effect of laser machining parameters on the contact angle of specimens. However, correlation A is actually composed of correlation B and C. Correlation B refers to the relationship between contact angle and product fingerprint, which is used to explain the underlying mechanism of effect of surface topography on hydrophobicity. Correlation C can describe the relationship between the process fingerprint and product fingerprint, to explore how the process parameters affect the surface topography. Thus, product fingerprint is a bridge to connect process parameters and functional performance-contact angle.   In a nanosecond pulsed laser ablation process, the absorbed energy from the laser pulse melts the stainless steel and heats it to a temperature at which the atoms gain sufficient energy to enter into a gaseous state. Due to the vapour and plasma pressure, the molten materials are partially ejected from the cavity and form surface debris. At the end of a pulse, the heat quickly dissipates into the bulk of the work material and recast layer are formed. Therefore, laser power is a good candidate of process fingerprint as it determines the laser fluence which directly affects the formation of In a nanosecond pulsed laser ablation process, the absorbed energy from the laser pulse melts the stainless steel and heats it to a temperature at which the atoms gain sufficient energy to enter into a gaseous state. Due to the vapour and plasma pressure, the molten materials are partially ejected from the cavity and form surface debris. At the end of a pulse, the heat quickly dissipates into the bulk of the work material and recast layer are formed. Therefore, laser power is a good candidate of process fingerprint as it determines the laser fluence which directly affects the formation of microstructures. The relationship between laser power, pulse repetition rate and peak power can be expressed as:

Analysis of Process and Product Fingerprints
where P is laser average power, f p is pulse repetition rate, E p is the energy of a single pulse, P peak is the peak power of laser and ∆τ is the pulse duration, respectively.

Exposure Time (t)
For substrate with periodic Gaussian holes generated by the laser ablation process, the exposure time t means the machining time for a single Gaussian hole, which determines the number of laser pulses that irradiated the surface. It has a significant effect on the dimension and morphology of Gaussian holes. As shown in Figure 2, the relationship between the number of irradiated pulse N and exposure time t can be expressed as: where T is the pulse period. Laser pulse energy per unit area of the specimen I s . I s means the average laser pulse energy irradiated on a unit area of the specimen. This parameter depends on pulse repetition rate f p and exposure time t. It can be expressed as: According to Equation (1), f p * E p = P, hence Equation (4) can be simplified as: where pitch is the distance between adjacent Gaussian holes, and L is the length of the specimen. microstructures. The relationship between laser power, pulse repetition rate and peak power can be expressed as: where P is laser average power, fp is pulse repetition rate, Ep is the energy of a single pulse, Ppeak is the peak power of laser and ∆ is the pulse duration, respectively.

Exposure Time (t)
For substrate with periodic Gaussian holes generated by the laser ablation process, the exposure time t means the machining time for a single Gaussian hole, which determines the number of laser pulses that irradiated the surface. It has a significant effect on the dimension and morphology of Gaussian holes. As shown in Figure 2, the relationship between the number of irradiated pulse N and exposure time t can be expressed as: where T is the pulse period. Laser pulse energy per unit area of the specimen Is Is means the average laser pulse energy irradiated on a unit area of the specimen. This parameter depends on pulse repetition rate fp and exposure time t. It can be expressed as: According to Equation (1), * = , hence Equation (4) can be simplified as: where pitch is the distance between adjacent Gaussian holes, and L is the length of the specimen.  In literature, two typical models have been developed to describe the behavior of a droplet on rough surfaces, i.e., the Wenzel and Cassie-Baxter models [25,26]. According to the Wenzel model, the droplet maintains contact with the structures and penetrates the asperities, and the surface contact area is increased. In addition, the contact angle θ w can be described as: cos θ w = r cos θ (6) r = actual surface area planar area (7) where, r is the roughness factor, which defined as the ratio of the actual area of the solid surface to the planar area. θ is the intrinsic contact angle of the material. Alternatively, according to the Cassie-Baxter model, the droplet is not able to penetrate the microstructure spaces. However, in order to ensure the droplet cannot connect with the bottom of the microstructures, so the sag in height of water droplet between microstructures should be smaller than the depth of microstructures. Moreover, deep microstructures will help to form stable air pockets under the water droplet. Stable air pockets underneath the water droplet help the formation of superhydrophobicity with strong resistance against transition to the Wenzel state. Hence, sufficient depth of microstructure is essential to realize Cassie-Baxter state of the water droplet. The static contact angle θ CB can be expressed as: f = actual solid and liquid contact area planar area (9) where f is the fraction of the solid-liquid contact area. The above analysis proves that the contact angles obtained in both Wenzel and Cassie-Baxter states are highly related to the vertical and horizontal feature of surface topography. Six surface characterization parameters that most probably correlated with the hydrophobicity of specimens are listed in Table 1. Sa, Sz and Sku are roughness parameters to characterize the height of the surface. Sdr, Sdq, R hy are hybrid parameters which determined from both height and horizontal parameters of the surface. For a rough surface, Sdr means the additional surface area contributed by the texture as compared to the planar definition area. Therefore, 1+Sdr has the same meaning as the roughness factor r in the Wenzel state.

Name Symbol Meaning
Arithmetical mean height Sa The difference in height of each point compared to the arithmetical mean of the surface.

Maximum height Sz
The sum of the largest peak height value and the largest pit depth value within the defined area.

Kurtosis Sku
A measure of the sharpness of the roughness profile. Sku < 3: Height distribution is skewed above the mean plane. Sku = 3: Height distribution is normal. (Sharp portions and indented portions co-exist.) Sku > 3: Height distribution is spiked.

Developed interfacial area ratio Sdr
The percentage of the definition area's additional surface area contributed by the texture as compared to the planar definition area.
Root mean square gradient Sdq Root mean square of slopes at all points in the definition area. When a surface has any slope, its Sdq value becomes larger.
Average ratio of Rz to Rsm R hy Average ratio of the maximum height of profile (Rz) and mean width of the profile elements (RSm) Theoretical analysis proved that microstructures should have a high aspect ratio to provide a larger surface area and a smaller separation distance which will help to improve the stabilization of the solid-liquid-air composite interface [27]. However, present functional parameters cannot reflect the aspect ratio of surface asperities. Hence, R hy is proposed for the first time as a dimensionless functional parameter in this research and defined as the average ratio of Rz to Rsm. The subscript "hy" is the short abbreviation of hydrophobicity. The R hy is calculated from the average value of 60 lines that evenly distributed on the structured surface horizontally and vertically. A surface with large R hy can be obtained from a large Rz or smaller Rsm, which means the features of the surface should have a large depth or smaller separation distance (i.e., high density) in the horizontal direction.

Experimental Details
Laser machining experiments were carried out on AISI 316L stainless steel by varying the process parameters in order to identify the best product and process fingerprints. All the experiments were carried out on a hybrid ultra-precision machine, as shown in Figure 3. It is equipped with a nanosecond pulsed fiber laser which has a central emission wavelength of 1064 nm. The laser source has a nominal average output power of 20 W and its maximum pulse repetition rate is 200 kHz. For a pulse repetition rate of 20 kHz, the average pulse duration is 100 ns and pulse energy is 1 mJ. The laser machining parameters are listed in Tables 2 and 3. After the laser ablation process, the specimens were cleaned ultrasonically with deionized water, acetone and ethanol successively. Then the prepared specimens were silanized in a vacuum oven using silane reagent (1H, 1H, 2H, 2H-Perfluorooctyltriethoxysilane, 97%, Alfa Aesar Ltd., Ward Hill, MA, USA), at 100 • C for 12 h to reduce their surface free energies.

Experimental Details
Laser machining experiments were carried out on AISI 316L stainless steel by varying the process parameters in order to identify the best product and process fingerprints. All the experiments were carried out on a hybrid ultra-precision machine, as shown in Figure 3. It is equipped with a nanosecond pulsed fiber laser which has a central emission wavelength of 1064 nm. The laser source has a nominal average output power of 20 W and its maximum pulse repetition rate is 200 kHz. For a pulse repetition rate of 20 kHz, the average pulse duration is 100 ns and pulse energy is 1 mJ. The laser machining parameters are listed in Table 2 and 3. After the laser ablation process, the specimens were cleaned ultrasonically with deionized water, acetone and ethanol successively. Then the prepared specimens were silanized in a vacuum oven using silane reagent (1H, 1H, 2H, 2H-Perfluorooctyltriethoxysilane, 97%, Alfa Aesar Ltd., Ward Hill, MA, USA), at 100 °C for 12 h to reduce their surface free energies.     The surface topography and varied surface characterization parameters of the laser structured surface were measured by a 3D laser scanning confocal microscope (VK-250, Keyence Corporation, Osaka, Japan). The static contact angle on surfaces was measured by a drop shape analyzer (Kruss Ltd., Hamburg, Germany). The selected water droplet volume was 5 µL. For each specimen, the contact angle of the water droplet was measured three times and the average value was adopted.

Analysis of Product Fingerprint: Sa, Sz, Sku, Sdr, Sdq, R hy
The investigation of experimental results was carried out to identify the product fingerprint from six candidates related to surface topography. The product fingerprint is the indicator that has the highest level of correlation to contact angle. In this research, the Spearman rank correlation coefficient and Kendall rank correlation coefficient were employed to determine the product fingerprint. Spearman rank correlation coefficient evaluates how strong the correlation between two variables can be defined by a monotonic function. It measures the strength and direction of the monotonic association between two variables, a perfect Spearman correlation of +1 or −1 occurs when each variable is a perfect monotone function of the other [28]. A positive Spearman correlation coefficient corresponds to an increasing monotonic trend between two variables, while a negative value means a decreasing monotonic trend. In addition, Spearman rank correlation coefficient is appropriate for data that is not normally distributed. It can be used to identify a non-linear correlation between two variables. Kendall rank correlation coefficient is a statistic used to measure the ordinal association between two variables [29]. However, unlike the Spearman coefficient, Kendall rank correlation coefficient only considers directional agreement while does not consider the difference between ranks. Therefore, this coefficient is more appropriate for discrete data. This coefficient returns a value of −1 to 1, where 0 is no correlation, 1 is a perfect positive correlation, and −1 is a perfect negative correlation. In most cases, the interpretations of Spearman and Kendall rank correlation coefficients are very similar and thus invariably lead to the same inferences. The above two coefficients were combined to determine the product fingerprint that has the maximum absolute value. The strength of the correlation between the variables can be evaluated by the absolute value of coefficients, as shown in Table 4.  Figure 4 shows scatter plots between the contact angle and the six candidates of product fingerprint. With the increase of Sa, Sz, Sdr, Sdq and R hy , the contact angle shows an increasing trend. It should be noted that a good linear relationship appears between Sz and contact angle, which is similar to the authors' previous study [15]. However, it can be observed that there is no apparent correlation between Sku and contact angle ( Figure 4c). As shown in Figure 4d, increasing Sdr from 0.02 to 4.1 leads to contact angle increase rapidly from 89.5 • to 159 • , but it has a minor impact on the contact angle when Sdr was further increased from 4.1 to 9.8. As Figure 4f indicates, the contact angle increases gradually from 89.5 • to 164 • with the value of R hy increasing from 0.06 to 0.94.
Micromachines 2019, 10, x FOR PEER REVIEW 8 of 15 Figure 4 shows scatter plots between the contact angle and the six candidates of product fingerprint. With the increase of Sa, Sz, Sdr, Sdq and Rhy, the contact angle shows an increasing trend. It should be noted that a good linear relationship appears between Sz and contact angle, which is similar to the authors' previous study [15]. However, it can be observed that there is no apparent correlation between Sku and contact angle ( Figure 4c). As shown in Figure 4d, increasing Sdr from 0.02 to 4.1 leads to contact angle increase rapidly from 89.5° to 159°, but it has a minor impact on the contact angle when Sdr was further increased from 4.1 to 9.8. As Figure 4f indicates, the contact angle increases gradually from 89.5° to 164° with the value of Rhy increasing from 0.06 to 0.94.  Figure 5 shows the variation of Spearman and Kendall rank correlation coefficient between contact angle and candidates of product fingerprint. According to the criterion in Table 4, Sz and Rhy   Figure 5 shows the variation of Spearman and Kendall rank correlation coefficient between contact angle and candidates of product fingerprint. According to the criterion in Table 4, Sz and R hy both have larger Spearman rank correlation coefficients with the contact angle, which are 0.89 and 0.92 respectively. The Kendall rank correlation coefficient among Sz, R hy and contact angle are 0.74 and 0.76. Thus, the results of Figure 5 suggest that R hy should be determined as the best product fingerprint as it has the maximum Spearman and Kendall rank correlation coefficients.
Micromachines 2019, 10, x FOR PEER REVIEW 9 of 15 both have larger Spearman rank correlation coefficients with the contact angle, which are 0.89 and 0.92 respectively. The Kendall rank correlation coefficient among Sz, Rhy and contact angle are 0.74 and 0.76. Thus, the results of Figure 5 suggest that Rhy should be determined as the best product fingerprint as it has the maximum Spearman and Kendall rank correlation coefficients. According to the results in Figure 4f, an empirical equation was deduced to correlate the experimental Rhy and contact angle. The equation is expressed as： = − * e * R hy (10) where, is contact angle; a, b and c are constant values, equal to 164, 105 and −4.9 respectively. As shown in Figure 6a, the regression curve has good precision to simulate the experimental data. We found that coefficient "a" means the maximum contact angle (164° in this research), the value of "b" is equal to the initial contact angle (105°) of 316L stainless steel after chemical modification. Thus, the contact angle of the specimen is highly related to its maximum contact angle, initial contact angle on a smooth surface and hydrophobicity functional parameter Rhy. According to Equation (10), the value of Rhy is 0.41 when = 150. Thus, 0.41 can be regarded as the threshold value of Rhy that ensure water contact angle of the specimen higher than 150°.
The dimensionless ratio Rhy is the most sensitive candidate parameter for contact angle of the specimen, which can therefore, be regarded as product fingerprint. In literature, many studies proved that a high density of microstructures and smaller period of microstructure will help decrease solidliquid contact area and increase its hydrophobicity [22,30]. With the increase of Rhy from 0.138 to 0.943 (Figure 6b), Rsm decreased from 137.0 μm to 81.8 μm. Therefore, the density of peaks shows a significant increasing trend. Moreover, the depth of microstructures shows an increasing trend, due to average Rz increased from 18.9 μm to 77.2 μm. Therefore, it can be concluded that the superhydrophobicity will benefit from the increase of Rhy. According to the results in Figure 4f, an empirical equation was deduced to correlate the experimental R hy and contact angle. The equation is expressed as: (10) where, θ A is contact angle; a, b and c are constant values, equal to 164, 105 and −4.9 respectively. As shown in Figure 6a, the regression curve has good precision to simulate the experimental data. We found that coefficient "a" means the maximum contact angle (164 • in this research), the value of "b" is equal to the initial contact angle (105 • ) of 316L stainless steel after chemical modification. Thus, the contact angle of the specimen is highly related to its maximum contact angle, initial contact angle on a smooth surface and hydrophobicity functional parameter R hy . According to Equation (10), the value of R hy is 0.41 when θ A = 150. Thus, 0.41 can be regarded as the threshold value of R hy that ensure water contact angle of the specimen higher than 150 • .
The dimensionless ratio R hy is the most sensitive candidate parameter for contact angle of the specimen, which can therefore, be regarded as product fingerprint. In literature, many studies proved that a high density of microstructures and smaller period of microstructure will help decrease solid-liquid contact area and increase its hydrophobicity [22,30]. With the increase of R hy from 0.138 to 0.943 (Figure 6b), Rsm decreased from 137.0 µm to 81.8 µm. Therefore, the density of peaks shows a significant increasing trend. Moreover, the depth of microstructures shows an increasing trend, due to average Rz increased from 18.9 µm to 77.2 µm. Therefore, it can be concluded that the superhydrophobicity will benefit from the increase of R hy .

Analysis of Process Fingerprints: P, t and Is
The above section proves that Rhy is the most appropriate product fingerprint to the laser ablated superhydrophobic structures on 316L stainless steel. In this section, further analysis of the experimental results will be performed to identify the best process fingerprint from the candidates P, t and Is, i.e., the process fingerprint which has the strongest correlation with Rhy. The control of process fingerprints helps to choose appropriate process parameter to obtain a surface with Rhy greater than the threshold value (Rhy > 0.41). The correlation among laser power, pitch of Gaussian hole and Rhy is shown in Figure 7. It shows that higher laser power and smaller pitch lead to a higher value of Rhy. Laser power and pitch of structures have combined effects on the value of Rhy.

Analysis of Process Fingerprints: P, t and I s
The above section proves that R hy is the most appropriate product fingerprint to the laser ablated superhydrophobic structures on 316L stainless steel. In this section, further analysis of the experimental results will be performed to identify the best process fingerprint from the candidates P, t and I s , i.e., the process fingerprint which has the strongest correlation with R hy . The control of process fingerprints helps to choose appropriate process parameter to obtain a surface with R hy greater than the threshold value (R hy > 0.41). The correlation among laser power, pitch of Gaussian hole and R hy is shown in Figure 7. It shows that higher laser power and smaller pitch lead to a higher value of R hy . Laser power and pitch of structures have combined effects on the value of R hy . The effect of exposure time t and pitch of Gaussian holes on the value of Rhy is presented in Figure 8. There is no significant linear correlation between exposure time and Rhy, but it does not mean exposure time has no effect on Rhy. As a whole, it can be found that the value of Rhy shows a significant increasing trend with the reduction of pitch from 150 μm to 70 μm. The above analysis shows that laser power, pitch and exposure time have a collective influence on Rhy. Focusing one of them and ignoring the other two would lead to the determined correlation only effective in certain partial conditions. For instance, the Rhy will increase with laser power, but only valid at a precondition of constant pitch and exposure time. Therefore, a comprehensive factor Is was designed to represent the combined influence of laser power, pitch and exposure time. Is means the energy intensity that irradiated on the unit area of the specimen and can be calculated by the Equation (5). Is is proportional to the laser power P and the exposure time t, but inversely proportional to the square of the pitch of the microstructures. Figure 9 reveals that the increasing Is leads Rhy The effect of exposure time t and pitch of Gaussian holes on the value of R hy is presented in Figure 8. There is no significant linear correlation between exposure time and R hy , but it does not mean exposure time has no effect on R hy . As a whole, it can be found that the value of R hy shows a significant increasing trend with the reduction of pitch from 150 µm to 70 µm. The effect of exposure time t and pitch of Gaussian holes on the value of Rhy is presented in Figure 8. There is no significant linear correlation between exposure time and Rhy, but it does not mean exposure time has no effect on Rhy. As a whole, it can be found that the value of Rhy shows a significant increasing trend with the reduction of pitch from 150 μm to 70 μm. The above analysis shows that laser power, pitch and exposure time have a collective influence on Rhy. Focusing one of them and ignoring the other two would lead to the determined correlation only effective in certain partial conditions. For instance, the Rhy will increase with laser power, but only valid at a precondition of constant pitch and exposure time. Therefore, a comprehensive factor Is was designed to represent the combined influence of laser power, pitch and exposure time. Is means the energy intensity that irradiated on the unit area of the specimen and can be calculated by the Equation (5). Is is proportional to the laser power P and the exposure time t, but inversely proportional to the square of the pitch of the microstructures. Figure 9 reveals that the increasing Is leads Rhy The above analysis shows that laser power, pitch and exposure time have a collective influence on R hy . Focusing one of them and ignoring the other two would lead to the determined correlation only effective in certain partial conditions. For instance, the R hy will increase with laser power, but only valid at a precondition of constant pitch and exposure time. Therefore, a comprehensive factor I s was designed to represent the combined influence of laser power, pitch and exposure time. I s means the energy intensity that irradiated on the unit area of the specimen and can be calculated by the Equation (5). I s is proportional to the laser power P and the exposure time t, but inversely proportional to the square of the pitch of the microstructures. Figure 9 reveals that the increasing I s leads R hy increase rapidly at first, and then level off to become asymptotic to the upper limit. The presence of upper limit means the further increased laser power, exposure time and smaller pitch cannot lead to a further increase of R hy . The correlation between I s and R hy can be expressed as Equation (11). According to the calculation result, I s should be greater than 536 J/mm 2 to ensure R hy greater than 0.41, hence the contact angle of the specimen will be larger than 150 • . R hy = 0.895 − 0.898 * 0.9985 I s (11) Micromachines 2019, 10, x FOR PEER REVIEW 12 of 15 increase rapidly at first, and then level off to become asymptotic to the upper limit. The presence of upper limit means the further increased laser power, exposure time and smaller pitch cannot lead to a further increase of Rhy. The correlation between Is and Rhy can be expressed as Equation (11).
According to the calculation result, Is should be greater than 536 J/mm 2 to ensure Rhy greater than 0.41, hence the contact angle of the specimen will be larger than 150°. R = 0.895 − 0.898 * 0.9985 (11) Figure 9. Scatter plots and fitted curve of Rhy and Is.
Therefore, the increased Is leads to rapidly increase of Rhy, the correlation between Rhy can be described by the exponential function. Is is the most sensitive parameters among the investigated three process fingerprint candidates, so it is the best process fingerprint that can be used to control surface morphology, especially the product fingerprint Rhy.

Correlation Between Laser Machining Parameters and Contact Angle
As shown in Figure 10, 3D colormaps are used to display the relationship between laser power, exposure time, pitch of structures and contact angle. To sum up, the greater contact angle benefit from larger laser power and smaller pitch of microstructures except for some outliers. Therefore, the increased I s leads to rapidly increase of R hy , the correlation between R hy can be described by the exponential function. I s is the most sensitive parameters among the investigated three process fingerprint candidates, so it is the best process fingerprint that can be used to control surface morphology, especially the product fingerprint R hy .

Correlation Between Laser Machining Parameters and Contact Angle
As shown in Figure 10, 3D colormaps are used to display the relationship between laser power, exposure time, pitch of structures and contact angle. To sum up, the greater contact angle benefit from larger laser power and smaller pitch of microstructures except for some outliers. increase rapidly at first, and then level off to become asymptotic to the upper limit. The presence of upper limit means the further increased laser power, exposure time and smaller pitch cannot lead to a further increase of Rhy. The correlation between Is and Rhy can be expressed as Equation (11).
According to the calculation result, Is should be greater than 536 J/mm 2 to ensure Rhy greater than 0.41, hence the contact angle of the specimen will be larger than 150°. Therefore, the increased Is leads to rapidly increase of Rhy, the correlation between Rhy can be described by the exponential function. Is is the most sensitive parameters among the investigated three process fingerprint candidates, so it is the best process fingerprint that can be used to control surface morphology, especially the product fingerprint Rhy.

Correlation Between Laser Machining Parameters and Contact Angle
As shown in Figure 10, 3D colormaps are used to display the relationship between laser power, exposure time, pitch of structures and contact angle. To sum up, the greater contact angle benefit from larger laser power and smaller pitch of microstructures except for some outliers.  Figure 11a shows the scatter diagram and fitted curve between contact angle and I s . The increasing I s results in a rapid increase of contact angle at first, and then level off to become asymptotic to the upper limit when I s greater than 1000 J/mm 2 . The empirical correlation between contact angle and I s can be expressed by Equation (12). When the value of R hy equals to the threshold value of 0.41, the corresponding I s is 516.6 J/mm 2 , which is very close to the value of 536 J/mm 2 obtain from Equation (11). Therefore, I s should be larger than 536 J/mm 2 in the laser ablation process, which help ensure the contact angle larger than 150 • . θ A = a − b * e d * I s (12) where, θ A is contact angle, a = 164, b = 105, d = −0.0039. Coefficients of a and b have the same meaning with Equation (10). The surface morphology and shape of water drops on specimens with a different value of I s are shown in Figure 11b. With the increase of I s , the depth and density of structures show a significant increasing trend. Thus, the surface topography and contact angle can be well controlled by choosing the appropriate process parameter I s .
Micromachines 2019, 10, x FOR PEER REVIEW 13 of 15 Figure 11a shows the scatter diagram and fitted curve between contact angle and Is. The increasing Is results in a rapid increase of contact angle at first, and then level off to become asymptotic to the upper limit when Is greater than 1000 J/mm 2 . The empirical correlation between contact angle and Is can be expressed by Equation (12). When the value of Rhy equals to the threshold value of 0.41, the corresponding Is is 516.6 J/mm 2 , which is very close to the value of 536 J/mm 2 obtain from Equation (11). Therefore, Is should be larger than 536 J/mm 2 in the laser ablation process, which help ensure the contact angle larger than 150°.
The surface morphology and shape of water drops on specimens with a different value of Is are shown in Figure 11b. With the increase of Is, the depth and density of structures show a significant increasing trend. Thus, the surface topography and contact angle can be well controlled by choosing the appropriate process parameter Is.
(a) (b) Figure 11. (a) Scatter plot and fitted curve between contact angle and Is; (b) Surface morphology and shape of water drops on specimens with a different value of Is.

Conclusions
In this study, the concepts of product and process fingerprint are put forward for the first time to reveal the correlations among process parameters, surface topography and functional performance, i.e., the contact angle of laser ablated superhydrophobic surface on 316L stainless steel.

Conclusions
In this study, the concepts of product and process fingerprint are put forward for the first time to reveal the correlations among process parameters, surface topography and functional performance,