2.1.

Preparation of Bovine Cortical Bone Sample

Bone specimens were obtained from the cortical regions of bovine femoral bone. The specimens were sectioned using a diamond saw with water as a lubricant and were wet ground to produce flat parallel surfaces using a successive series of 600-, 800-, and $1200\text{-grit}$ SiC paper so that surface scattering from inhomogeneous tissue could be minimized. The flat and parallel specimens were attached to a glass slide with double-sided tape for femtosecond laser ablation.

2.2.

Direct-Write Femtosecond Laser Ablation

Frequency doubled pulses from a mode-locked erbium-doped fiber laser intensified in a $\mathrm{Ti}:{\mathrm{Al}}_2{\mathrm{O}}_3$ regenerative amplifier laser (CPA2161, Clark-MXR) were used. The maximum output power of the laser was $P_{\mathit{av}}=2.5\mathrm{W}$ , the pulse duration was $T_p=150\mathrm{fs}$ , the pulse repetition frequency was $f_P=3\mathrm{kHz}$ , the wavelength $\lambda$ was $775\mathrm{nm}$ , and the beam diameter was $5\mathrm{mm}$ . Laser beam power was adjusted by a series of optics, including thin-film polarizing beamsplitters and half-wave plates. The attenuated laser beam was delivered by a beam mirror train through a mechanical shutter and then focused on the material. A $50\times$ infinity corrected microscope objective lens with numerical aperture $\left(\mathrm{NA}\right)=0.42$ (M Plan Apo NIR $50\times$ , Mitutoyo) was used for focusing the femtosecond laser beam. Attenuated laser power was measured by a power meter (PM100, Thorlab) placed after the laser focusing lens. The beam quality was $M^2=1.2$ in the horizontal $y$ direction and $M^2=1.3$ in the horizontal $x$ direction. A computer controlled motion system (MX80L, Parker) with a $0.5\text{-}\mu \mathrm{m}$ resolution on the $x$ , $y$ , and $z$ axes was used to position the sample and focus optic.

In order to find ablation properties of the bovine cortical bone, single-pulse and linear scanned ablation tests were performed on the bone surface at varying pulse energies and scan speeds. Dimensions of the ablated features from these tests were used in calculations described in a prior reference¹⁷ and in Sec. 6 to estimate the effective Gaussian beam radius, single-pulse ablation threshold fluence, and incubation coefficient of the bone material.

Figure 1 shows a schematic of the ablation pattern used for micropillar fabrication. A focused laser beam was scanned around concentric circular paths, with the innermost pass having a diameter equal to the programmed diameter of the pillar. In this example, $100\text{-}\mu \mathrm{m}$ -diam micropillars were fabricated by removing the surrounding material in three consecutive layers, each consisting of 45 concentric circular passes. The laser beam focus location was shifted down by $10\mu \mathrm{m}$ for each subsequent layer. Subsequently, various sizes of micropillars were made using different average laser powers and scanning speeds. The diameter and height of micropillars were measured from environmental scanning electron microscope (ESEM) images. The measured diameters at the top surface of the micropillars were compared with the diameters calculated using fluence from paraxial laser beam propagation and the bone ablation threshold and incubation factor measurements.

Fig. 1

Procedure for fabricating a micropillar by direct-write laser ablation. The innermost pass of each layer had the same programmed diameter, and the laser beam focus was shifted downward by $10\mu \mathrm{m}$ to machine successive layers. The resulting diameter of the top of the pillar was less than the programmed diameter due to the ablation width of the first pass of the first layer and further reductions by the low-fluence pulses irradiating the upper surface of the pillar during machining of the lower layers.

2.3.

Microscopy

An optical microscope (OM; MZ16, Leica) and an environmental scanning electron microscope (ESEM; XL-30, Philips) were used to characterize the ablated bone surface. The specimen was removed from the glass slide after femtosecond laser ablation and attached to an SEM mount with silver conductive paint. The single-pulse and linear scanned ablation and micromachined pillar arrays were imaged with ESEM using a gas secondary electron detector (GSED) and wet mode. This mode replaces the residual gas in the chamber with ${\mathrm{H}}_2\mathrm{O}$ (g), thereby allowing imaging of hydrated biological specimens. Image analysis software (Image J, NIH) was used to measure the diameter of single-pulse ablation, width of linear scanned microchannel, and diameter of micropillar from the ESEM images.

3.1.

Single-Pulse Ablation on Bovine Cortical Bone

To establish the proper values of pulse energy for ablation of the bovine cortical bone, single-pulse ablation spots at varying pulse energies from $5\mu \mathrm{J}\text{to}0.33\mu \mathrm{J}$ were produced by scanning the focused femtosecond laser beam over the surface of the bovine bone; examples are shown in Fig. 2 . Ablated diameters $D$ are plotted against pulse energy in Fig. 3a . Effective Gaussian beam radius $w_0$ was found to be $2.72\mu \mathrm{m}$ from the slope the curve. Next, laser fluence was calculated using the effective laser focus spot diameter and ablation squared diameter versus laser fluence was plotted as shown in Fig. 3b. It has been found that logarithmic plots of femtosecond laser ablation squared diameter versus fluence for metal generally have two slopes, which reflect a change in mechanism at high (“strong” ablation) and low (“gentle” ablation) pulse fluences.¹⁵ The same behavior is observed in the cortical bone ablation data in Fig. 3b. The two slopes indicated in the plot extrapolate to strong ablation fluence $(F_{\mathit{\text{peak}}}>2\mathrm{J}∕{\mathrm{cm}}^2)$ of $2.70\pm 0.16\mathrm{J}∕{\mathrm{cm}}^2$ and gentle ablation fluence $(F_{\mathit{\text{peak}}}<2\mathrm{J}∕{\mathrm{cm}}^2)$ of $1.67\pm 0.4\mathrm{J}∕{\mathrm{cm}}^2$ . The variation in our ablation threshold results is calculated from a curve fit correlation coefficient and is primarily due to inhomogeneity of the bone structure and pulse-to-pulse variation of laser energy and beam mode.

Fig. 2

ESEM images of single-pulse laser ablation at different pulse energies made on the bovine bone sample, (a) $E_P=0.33\mu \mathrm{J}$ ; (b) $E_P=1.33\mu \mathrm{J}$ ; and (c) $E_P=4.66\mu \mathrm{J}$ .

Fig. 3

(a) Squared ablated diameter versus laser pulse energy for single-pulse ablation trials. Effective Gaussian radius $\left(w_0\right)$ was found to be $2.72\mu \mathrm{m}$ from the slope of the curve. (b) Single-pulse ablation threshold was calculated by extrapolating the ablated diameter² versus laser fluence curve to zero diameter. Gentle ablation threshold fluence was calculated as $F_{\mathit{th}}=1.67\pm 0.4\mathrm{J}∕{\mathrm{cm}}^2$ , and strong ablation threshold fluence was calculated as $F_{\mathit{th}}=2.70\pm 0.16\mathrm{J}∕{\mathrm{cm}}^2$ .

3.2.

Scanned Ablation of Bovine Bone

Scanned ablation at different laser fluences and scanning speeds was conducted on the bovine bone, and ablated microchannel widths were measured. Two different laser fluences ( $F=2.87\mathrm{J}∕{\mathrm{cm}}^2$ and $14.34\mathrm{J}∕{\mathrm{cm}}^2$ ) at scanning speeds varying from $1.83\mathrm{mm}∕\mathrm{s}\text{to}0.02\mathrm{mm}∕\mathrm{s}$ were used to create linear microgrooves on the bone specimen. The widths of the microgrooves $D_N$ were measured from ESEM images, with examples shown in Fig. 4 . The widths of microgrooves depicted in Fig. 4 are plotted with respect to scanning speeds in Fig. 5 . At $F=2.87\mathrm{J}∕{\mathrm{cm}}^2$ , the average widths ranged from $3.5\mu \mathrm{m}\text{to}2.24\mu \mathrm{m}$ as scanning speed varied from $0.02\mathrm{mm}∕\mathrm{s}$ (corresponding to pulse number $N=783.36$ ) to $1.83\mathrm{mm}∕\mathrm{s}$ $(N=8.9)$ . The width at the scanning speed of $0.02\mathrm{mm}∕\mathrm{s}$ was much larger than the diameter of a single pulse at the same fluence because of incubation due to the larger pulse number. The solid lines in Fig. 5 represent best-fit curves of Eq. 15 for laser fluences of $F=2.87$ and $14.34\mathrm{J}∕{\mathrm{cm}}^2$ . The previously determined values of $w_0=2.72$ and $F_{\mathit{th}}=2.6\mathrm{J}∕{\mathrm{cm}}^2$ were used, and an incubation coefficient value of $\xi =0.89\pm 0.02$ minimized the error of the two curves to the corresponding data. Table 1 compares the ablation threshold for bovine cortical bone as measured in this work with that of other hard tissues such as porcine cortical bone, dentin, and enamel. The incubated gentle ablation threshold fluences are comparable to the incubated ablation threshold fluences for the other materials and are particularly close to the value reported for porcine cortical bone.¹⁴

Fig. 4

Linear grooves on the bovine bone sample produced by scanned ablation at different speeds and two laser fluences, (a) $F=2.87\mathrm{J}∕{\mathrm{cm}}^2$ , (b) $F=14.34\mathrm{J}∕{\mathrm{cm}}^2$ .

Fig. 5

Incubation coefficient, $\xi$ , was found to be $0.89\pm 0.02$ by minimizing the error between Eq. 15 and linear scanned ablation channel widths at varying scanning speeds and different laser fluences ( $F=2.87$ and $14.34\mathrm{J}∕{\mathrm{cm}}^2$ ).

Table 1

Comparison of laser ablation threshold fluence measured in this work with that of other hard tissues from the literature.

3.3.

Micropillar Fabrication by Direct-Write Femtosecond Laser Ablation

ESEM images of micropillars, which had a programmed diameter of $100\mu \mathrm{m}$ and were fabricated with three layers of pulses, are shown in Figs. 6a and 6b . An optical microscope image of these micropillars is also shown in Fig. 6c. No charring of the bone specimen is observed, similar to previous work.¹⁴ After completion of the first, second, and third layers, the average diameter of the top surface of the pillar was measured as $94\mu \mathrm{m}$ , $92.3\mu \mathrm{m}$ , and $91.9\mu \mathrm{m}$ . The ablation width for each pass (defined as the difference between the programmed and measured diameters) was $6\mu \mathrm{m}$ , $7.7\mu \mathrm{m}$ , and $8.1\mu \mathrm{m}$ . Table 2 also summarizes the different diameters of micropillars fabricated at varying average laser powers and scan speeds.

Fig. 6

Micropillars with programmed diameter of $100\mu \mathrm{m}$ and height of $30\mu \mathrm{m}$ fabricated on bovine cortical bone. Average laser power of $6\mathrm{mW}$ and scanning speed of $0.67\mathrm{mm}∕\mathrm{s}$ were used. (a) SEM image of a $3\times 3$ micropillar array. (b) Magnified SEM image of micropillar. Micropillar diameter was measured as $91\mu \mathrm{m}$ , and height was $30\mu \mathrm{m}$ . (c) Optical microscope image of micropillars. No charring of the bone surface was observed.

Table 2

Comparison of measured and predicted ablation widths for micropillars with programmed diameters ranging from 5μmto100μm .

4.1.

Comparison of Experimental and Theoretical Ablation Thresholds

It is interesting to compare the experimental single-pulse ablation threshold fluence to values predicted from theory. Ablation threshold for dielectrics was previously studied by Gamaly,²⁰ who arrived at an expression for the ablation threshold

4.2.

Comparison of Circular and Straight-Line Scanned Ablation

It is interesting to compare the pulse numbers predicted by Eq. 11 to straight-line values¹⁷ predicted using $d$ equal to measured laser focus spot diameter and $s$ equal to scan speed. Using the measured focus spot radius of $2.72\mu \mathrm{m}$ and scanning speed of $0.67\mathrm{mm}∕\mathrm{s}$ , the maximum pulse numbers calculated from Eq. 11 for various programmed radii are shown in Fig. 7 . For example, when machining around a programmed diameter of $10\mu \mathrm{m}$ with a pulse radius of $2.72\mu \mathrm{m}$ , the maximum pulse number is 25.87 versus a straight line value of 24.46. Since ablation threshold is not a very sensitive function of pulse number [see Eq. 9], there was no significant increase of the incubated ablation threshold. The ablation threshold for circular scanning was $F\left(25.87\right)=1.82$ , while the linear scanning was $F\left(24.46\right)=1.83$ , both using $\xi =0.89$ . The plot in Fig. 7 shows that the maximum pulse number for circular scanning converges to that for the linear scanning case as the radius increases. For the micropillar radiuses used in this work, it is reasonable to use the pulse number calculated for linear scanning to calculate incubated ablation threshold.

Fig. 7

Maximum pulse number for circular scanning compared to linear scanning with focus spot radius of $2.72\mu \mathrm{m}$ and various pillar radii. For the smallest pillar diameter $\left(10\mu \mathrm{m}\right)$ used in this work, the maximum pulse number predicted by circular scanning analysis was only slightly (1.25%) larger than that predicted by linear scanning.

4.3.

Comparison of Experimental and Calculated Pillar Diameters

Using the ablation relationships and material property measurements summarized earlier, it is possible to predict the pillar top diameters produced by given ablation process settings.

For a scanning speed of $s=0.67\mathrm{mm}∕\mathrm{s}$ , the number of pulses applied to a single location along the scan is $N=24.5$ . Using $\xi =0.89$ and $F_{\mathit{th}}=2.6\mathrm{J}∕{\mathrm{cm}}^2$ , the corresponding incubated ablation threshold fluence is calculated to be $F_{\mathit{th}}\left(24.5\right)=1.83\mathrm{J}∕{\mathrm{cm}}^2$ . The smaller ablation threshold implies that the channel width for scanned ablation is larger than the diameter of a single ablation spot.

When the laser beam focus was shifted down in a positive $z$ direction for machining of second and third layers, the defocused laser fluence applied to the top surface of the pillar resulted in further ablation. The fluence for a Gaussian beam that propagates along the $z$ axis can be written as²⁵

Fig. 8

Analysis of laser beam propagating in air in the $z$ direction by paraxial approximation; (a) laser beam radius: (b) laser beam fluence distribution in radial and longitudinal directions at average laser power of $P=6\mathrm{mW}$ . Beam focus spot radius $w_0=2.72\mu \mathrm{m}$ calculated from the slope of single-pulse ablation experiments was used in this calculation.

To calculate ablation of the top of the pillar by successive layers of laser pulses, threshold fluence was decreased according to the power-law relationship shown in Eq. 6, with pulse number $N=24.5$ for each layer. Figure 9 shows laser fluence distribution in the radial direction at the top surface of the bone sample $(z=0)$ for the first, second, and third passes. The peak fluences for the first and second layers were larger than $2\mathrm{J}∕{\mathrm{cm}}^2$ , so the strong ablation threshold was used to calculate incubated laser fluence. The incubated threshold fluence for the first layer was $F_{\mathit{th}}\left(24.5\right)=1.83\pm 0.12\mathrm{J}∕{\mathrm{cm}}^2$ and that of the second layer was $F_{\mathit{th}}\left(49\right)=1.69\pm 0.14\mathrm{J}∕{\mathrm{cm}}^2$ . For the third layer, the gentle ablation threshold was incubated with the same coefficient used for the strong ablation pulses, resulting in a third-pass threshold of $F_{\mathit{th}}\left(73.5\right)=1.05\pm 0.09\mathrm{J}∕{\mathrm{cm}}^2$ . It is noted that prior research has shown that incubation coefficients are the same for strong and gentle ablation thresholds for a metal material.²⁶ For analysis of ablation results, it is convenient to define ablation width as the difference in programmed and measured pillar diameter. The predicted ablation widths are compared with the experimental ablation width for each pass in Fig. 10 . Error between predicted and experimental ablation widths is within about $0.2\mu \mathrm{m}$ for each pass.

Fig. 9

Laser fluence distribution in radial direction at $z=0$ (top surface of pillar) with $w_0=2.72\mu \mathrm{m}$ , $P=6\mathrm{mW}$ . For the first pass $(z=0)$ , second pass $(z=10\mu \mathrm{m})$ , and third pass $(z=20\mu \mathrm{m})$ , the peak fluences are $F_{\mathit{\text{peak}}}=17.2$ , 5.1, and $1.63\mathrm{J}∕{\mathrm{cm}}^2$ . The incubated ablation threshold for each pass was calculated by Eq. 9 at scanning speed of $0.67\mathrm{mm}∕\mathrm{s}$ (corresponding to $N=24.5$ ) and $\xi =0.89$ . For the first, second, and third passes, each incubated ablation threshold fluence is $F_{\mathit{th}}\left(24.5\right)=1.83\pm 0.12\mathrm{J}∕{\mathrm{cm}}^2$ , $F_{\mathit{th}}\left(49\right)=1.69\pm 0.14$ , and $F_{\mathit{th}}\left(73.5\right)=1.05\pm 0.09\mathrm{J}∕{\mathrm{cm}}^2$ .

Fig. 10

Comparison of calculated and measured ablation width (programmed diameter minus the diameter of the top surface of the pillar) for successive layers. Predicted ablation width was well-matched with the measurements.

Figure 11 shows smaller micropillars with programmed diameter of $30\mu \mathrm{m}$ and measured average diameter of $23.1\mu \mathrm{m}$ . Machining of these tall pillars required nine layers of pulses at an average laser power of $4.5\mathrm{mW}$ and scanning speed of $0.67\mathrm{mm}∕\mathrm{s}$ . The final diameter of the top of the pillar was measured to be $23.1\mu \mathrm{m}$ , corresponding to an ablation width of $6.9\mu \mathrm{m}$ . Using the procedure outlined earlier, the width was predicted to be $6.4\mu \mathrm{m}$ . Still smaller micropillars with programmed diameters of $10\mu \mathrm{m}$ and $5\mu \mathrm{m}$ were also machined and predicted, and measured ablation width results are summarized in Table 2. Error between predicted and experimental final ablation widths is within about $0.6\mu \mathrm{m}$ .

Fig. 11

Micropillars fabricated on bovine cortical bone by direct-write femtosecond laser ablation. Pillars had programmed diameter of $30\mu \mathrm{m}$ and measured average diameter of $23.1\mu \mathrm{m}$ after machining with 9 layers of pulses at an average laser power of $4.5\mathrm{mW}$ and scanning speed of $0.67\mathrm{mm}∕\mathrm{s}$ .