1. Introduction

Direct laser writing (DLW) lithography based on multiphoton absorption [1,2] has become a key additive manufacturing tool for the fabrication of polymeric structures at the micro and nanoscales. The success of DLW stems from the many advantages of this technology compared to traditional layer-by-layer approaches [3] such as the possibility, in a single processing step, to fabricate three-dimensional (3D) structures with arbitrary geometry and size. The unique capabilities of DLW are based on the non-linear interaction between photoresist and laser (two-photon absorption), which leads to a restriction of the polymerization reaction within a fraction of the focal volume [4,5]. Thus, the implementation of the micro- and nanometer-sized structures manufactured with DLW is becoming a widely ordinary routine in many innovative technological applications, e.g. nanochips for microelectronics [6], subwavelength optical elements [7], photonic crystals [8], biochemical analysis devices [9] or high-density optical and magnetic data storage [10]. However, the further exploitation of the size-dependent properties of these materials in the multiple applications lays out two technological challenges that are not completely resolved up to now: (i) the fabrication of real nanometer-sized structures with DLW and (ii) the fast and reliable characterization of the fabricated structures with optical imaging techniques.

While sub-diffraction feature sizes can be accessed by playing with the particular photoresist and its associated threshold for polymerization, laser fluctuations and other effects typically impede the fabrication of controllable deep sub-wavelength structures [4]. Recently, a change in paradigm in DLW technologies has been demonstrated inspired by the reversible saturable optical fluorescence transition (RESOLFT) concept [11,12]. The fundamental idea of these new approaches is the spatially-selective depletion of the photogenerated species that trigger the polymerization process by means of different light-induced mechanisms. More in detail, the laser beam that induces polymerization, usually called writing beam, is overlapped with a second laser beam, usually called inhibition beam, which “stops/inhibits” the polymerization reaction. Since the writing beam is typically Gaussian and the inhibition beam is normally doughnut-shaped with maximum intensities at the periphery and “zero” intensity at the centre, the polymerization process is restricted to a deep sub-diffraction-sized volume around the focal point of the writing beam [13]. Importantly, the type of photoinitiator employed, together with the wavelength of the inhibition beam, determines the mechanism responsible for the “stopping/inhibition” of the polymerization. Up to four different approaches based on different inhibition mechanisms have been proposed to operate in the two-beam (writing and inhibition beams) DLW lithography: stimulated emission depletion (STED) [14]; resolution augmentation through photo-induced deactivation (RAPID) [15]; utilization of photoinhibitors such as a radical traps [16]; and triplet state absorption (TSA) [17]. Because of the heterogeneity in either the inhibition mechanisms, resist used or two-beam DLW implementation, different values of linewidth (10-130 nm) have been reported in literature [12].

The second crucial step in DLW is the morphological characterization of the polymerized nanometer-sized structures. Indeed, the effective size and potential defects (high surface roughness, shrinkage) of the fabricated structures have a direct impact upon their overall functionality. Typically, the structures fabricated with DLW and other related lithography techniques are visualized with the help of scanning/transmission electron microscopes (SEM and TEM), or with atomic force microscopy (AFM). Unfortunately, these characterization approaches require a tedious sample preparation and/or long-time measurements [1]. Thus, innovative optical techniques are being employed to monitor the polymerization process. For example, coherent anti-Stokes Raman scattering (CARS) microscopy [18,19] has been used to characterize real-time micrometer-sized structures, but, as far as we know, it lacks the ability to characterize deep sub-wavelength structures. An attractive alternative to the previous imaging techniques is super-resolved fluorescence microscopy, which has recently demonstrated sub-diffraction nanometer resolution and large versatility [11]. Among current super-resolved methods, the RESOLFT family which includes STED microscopy and its more recent upgrade gated-STED microscopy [20], has reached a spatial resolution able to rival the resolution of TEM, SEM and AFM. Similar to the two-beam DLW system, a typical STED microscope generates sub-diffraction resolution images by overlapping a Gaussian beam with a doughnut-shaped beam. In particular, the STED microscope uses a Gaussian beam tuned in wavelength to induce excitation of the fluorophores, whilst a doughnut-shaped beam, i.e. STED beam, is tuned in wavelength in order to de-excite the excited fluorophores via stimulated emission. As a result, only the fluorophores in a sub-diffraction sized volume around the doughnut centre, where the intensity of the STED beam is null, can emit fluorescence. Scanning this sub-diffraction effective fluorescent volume through the sample yields super-resolved images.

Notably, STED microscopy maintains most of the important properties of conventional fluorescence microscopy, including the fast-recording (video-rate) [20] of images, the possibility to operate in ambient conditions and the minimally invasive character. Due to these characteristics, STED microscopy is gaining a substantial importance in life science applications [21]. Furthermore, since the basic depletion mechanism is fully compatible with inorganic materials, STED microscopy has also shown its potential in the field of material sciences [22] and it has been used to characterize nanometer-sized structures generated by electron-beam lithography [23,24]. In addition to this, other superresolution imaging approaches have been intended for characterizing nanoanchors of subdiffraction-limited diameter fabricated with two-beam DLW lithography [25]. However, to the best of our knowledge no reports exist about its use in the context of DLW lithography. As a matter of fact, provided the nanometer-sized structures generated by DLW lithography are fluorescent, straightforward visualization and characterization of the fabricated patterns can be carried out by STED microscopy. Furthermore, if the Gaussian beam serves both as writing and excitation beam, and the doughnut-shaped beam as inhibition and STED beam, the very same optical system could be potentially used to generate and characterize the nanometer-sized structures, saving time and resources with respect to the use of conventional characterization techniques.

In this article, we implemented the RESOLFT approach both for the nanofabrication and for the characterization of photopolimerized nanometer-sized structures. In particular, we applied two-beam DLW lithography on the base of the TSA mechanism, obtaining a minimum linewidth of the photopolymerized lines of ~90 nm, and we used STED microscopy to characterize the quality and linewidth of the fabricated features. Importantly, the nanometer-sized structures were fluorescently functionalized thanks to the Chromeo-488 carboxylic acid derivative fluorophore. This fluorescent dye, particularly suitable for STED microscopy, was incorporated to the resist to carry out the super-resolved fluorescence imaging. Based on the excellent agreement between the linewidths of the photopolymerized lines measured with AFM and STED fluorescence microscopy, we demonstrated the ability of the later super-resolved technique to be used as high-precision and straightforward characterization tool in DLW lithography. This state-of-the-art implementation of STED microscopy in the field of material science paves the way for the utilization of this technique as a general characterization technique for a large variety of materials.

2. Experimental section

2.1. Sample preparation and post-processing

The resist used for the polymerization was pentaerythritol triacrylate (PETA, Sigma Aldrich), a negative resist. The photoinitiator employed for triggering the polymerization was isopropyl thioxanthone (ITX, Sigma Aldrich). The fluorescent dye for STED microscopy was Chromeo 488 carboxylic acid derivative (Sigma Aldrich). All the chemicals were used without further purification. ITX (0.16 wt%) and Chromeo 488 (0.025 wt%) were dissolved in 100 μl of methanol (MeOH) and further added to 2 ml of PETA. In a typical DLW lithography experiment, a glass cover slip was placed on an oil-immersion objective lens (NA = 1.4, 100x) and a drop of the resist was deposited on top. After irradiation with the laser, the cover slip was immersed in methanol for 5 minutes and then rinsed with isopropanol to wash away the liquid monomer. Prior to characterization, a short Argon plasma treatment (10s, 20W) was used to eliminate the presence of dye in the non-polymerized areas of the substrate.

2.2. Optical DLW lithography setup combined with confocal and gated-CW-STED fluorescence microscope

The optical DLW lithography and superresolution and confocal imaging were performed on the same custom-made gated-CW-STED fluorescence microscope [26]. Different laser sources were employed for each different beam. In DLW lithography, the two-photon polymerization beam was obtained from a mode-locked Titanium-Sapphire laser (Chameleon Vision II, Coherent), which delivers pulses of ~150 fs, with a wavelength of 760 nm and at a repetition rate of 80 MHz. The inhibition beam was obtained from a high-energy (1 W) continuous wave (CW) visible fiber laser (MPB Communications, Canada) at a wavelength of 642 nm. The power of the two beams was controlled with two acoustic optic modulators (AOM, AA Optoelectronics). In STED microscopy, the excitation beam (488 nm) was provided by a supercontinuum source and the STED beam was delivered by a CW optical pumped semiconductor laser (OPSL) emitting at 577 nm (Genesis CX STM-2000, Coherent). The excitation beam was attenuated, in power, by a rotating half-wave-plate (RAC 3.3.10, Bernhard Halle Nachfl.) and a polarizing-beam-splitter (PBS251, Thorlabs). A rotating half-wave-plate (RAC 4.2.10, Bernhard Halle Nachfl.) and a rotating Glan–Thompson polarizing prism (PGT 1.10, Bernhard Halle Nachfl.) allowed the control of the power of the STED beam. Subsequently, both STED and inhibition beams passed through a polymeric mask imprinting 0–2π helical phase-ramps (VPP-A1, RPC Photonics) in order to obtain a doughnut-like diffraction pattern at the focus. The four beams were collinearly aligned using dichroic mirrors. The collinearly aligned beams were deflected by two galvanometric scanning mirrors (6215HM40B, CTI-Cambridge) and directed toward the objective lens (HCX PL APO 100x/1.40–0.70 Oil, Leica Microsystems) by the same set of scan and tube lenses as the ones used in a commercial scanning microscope (Leica TCS SP5, Leica Microsystems). The fluorescence light was collected by the same objective lens, de-scanned, and passed through the dichroic mirrors as well as through a fluorescence band pass filter (ET Bandpass 525/50 nm, AHF an.alysentechnik) before being focused (focal length 60 mm, AC254-060-A-ML, Thorlabs) into a fiber pigtailed single photon avalanche diode (SPAD) (PDF Series, MicroPhotonDevice). Photon counting and photon-arrival-time measurements were accomplished by a time-correlated-photon-counting-card (TCSPC) (SPC-830, Becker & Hickl). All acquisition operations were automated and managed by the software Imspector (Imspector, Max Planck Innovation). We implemented time-gated detection off-line using the photon-arrival-time information provided by the TCSPC card. We obtained the conventional CW-STED image by displaying all the collected fluorescent photons and the gated CW-STED image by displaying only the delay fluorescence photons (arrival time greater than T_g). We obtained confocal images by blocking the STED beam (P_STED = 0 mW).

The polarizations of all beams have been carefully settled to circular at the back-aperture of the objective lens by carefully aligning a half- and a quarter-wave plate retarders for each beam. The circular polarization for the two inhibition beams (642 nm and 577 nm) ensures a good quality of the “zero”-intensity point for the doughnut-shaped focus [27]. The circular polarization of the excitation beam (488 nm) removes any heterogeneity in the probability to excite fluorophores whose dipole is oriented randomly.

The position in the axial direction of the focal point of the writing and inhibition beams is a critical factor determining the linewidth of the polymerized lines. To achieve comparable results within all measurements, we have followed the same procedure to control the position of the focus. Firstly, the focus is adjusted manually by observing the back reflection from the coverslip with a camera, situating the focus close to the substrate surface. Then, we utilized the ascending scan method consisting in preparing different patterns of polymerized lines by moving the laser focus up above the substrate surface [28].

2.3. Atomic force microscope

AFM measurements were performed with a Nanowizard III (JPK Instruments, Germany) mounted on a Nikon optical microscope (Nikon A1R MP, Nikon Instruments Inc., Japan) using a non-contact tapping mode Monolithic silicon cantilever (NCHR AFM probes, NanoWorld, Swtizerland), a force constant ranging from 21 to 78 N/m, a resonance frequency in air ranging from 250 to 390 kHz and a tip with typical curvature radius of less than 8 nm were used.

2.4. Scanning electron microscope

The scanning electron microscopy (SEM) measurements were made with a JEOL JSM-7500FA scanning electron microscope. The microscope was equipped with a cold field emission gun. The images were acquired at 15.0 kV, which can provide a resolution of 1.0 nm.

3. Results and discussion

3.1. Characterization of the fabricated lines with AFM

One of the main critical parameters influencing the minimum linewidth attained with DLW lithography is the type of photoresist used. A recent study has reported an extraordinary linewidth of 9 nm thanks to the use of a mixture of two acrylate highly functionalized monomers which provide a higher crosslinking density and an increase of the mechanical strength of the photoresist [29]. In our work, pentaerythritol triacrylate (PETA) was used as the photoresist together with isopropyl thioxanthone (ITX) as the TSA photoinitiator. In this two-beam DLW lithography, the depletion of the triplet state of ITX due to its excitation at 642 nm to a higher triplet state prevented the formation of ITX radicals triggering the polymerization [17].

Figure 1(a) and 1(b) show non-contact AFM images of the same photopolymerized patterns (five lines) fabricated with one-beam (760 nm) and two-beam (760 nm and 642 nm) DLW lithography, respectively. The 10 μm long lines in the figures illustrate the thinnest fabricated structures obtained with each approach, where a clear decrease of the linewidth with the two-beam DLW is observed. To attain the minimum linewidth in the one-beam experiments, we reduced continuously the power of the excitation beam down to 68 mW, below which value no line was detected. For the two-beam approach, we tried different combinations of writing and inhibition powers, with the minimum linewidth obtained at a writing and inhibition power of 72 and 210 mW, respectively. Initially, we kept constant the power of the writing beam to 68 mW increasing gradually the power of the inhibition beam from 160 to 220 mW. Then, we modified the power of the writing beam in the range of 70 mW and varied the power of the inhibition beam (160-220 mW). We have used circular polarization in the writing beam to prevent the elongation of the laser-affected spot as it happens when using linear polarization due to heat diffusion [30].

 

Fig. 1 A) and B) Non-contact AFM images (height) of the thinnest photopolymerized lines fabricated with one-beam (A) and two-beam (B) DLW lithography. The image size is 10x5 μm. C) and D) Height profiles of the photopolymerized lines (dashed lines in AFM images) when using the one-beam (C) and two-beam (D) approach. The power of the writing beam was 68 mW in A) and 72 mW in B) and the inhibition power was 210 mW in B). The pixel dwell time was fixed to 0.3 ms in both cases.

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Figure 1(c) shows the AFM height profile corresponding to the dashed line drawn in Fig. 1(a) of the structure fabricated with one-beam DLW lithography. The profile is bell-shaped with a line thickness at the base of ~190 nm and a full width at half maximum (FWHM) of ~140 nm. However, to obtain the true value of the linewidth, it is necessary to perform a tip deconvolution to account for the non-negligible size of the AFM tip. Thus, the calculated value for the linewidth of the structures prepared with the one-beam approach is 155 nm [31]. This value is already well-below the diffraction limit (270 nm) as a consequence of the existence of the polymerization threshold. Interestingly, the height of the structure is barely 25 nm, which is about 6 times smaller than the linewidth. This behaviour has been previously explained based on a decrease of the polymerization threshold near the glass surface, which acts as a polymerization nuclei [32]. The axial truncation of the laser beam could also account for the small height of the polymerized lines [33]. However, the implementation of the ascending scan method in this work ensured that the presented linewidths were obtained by locating the laser focus far enough from the substrate surface and therefore the height of the structures cannot be ascribed to truncation effects [28]. Scanning electron microscopy (SEM) was also utilized to validate the estimated thickness of the lines with the AFM measurements, obtaining a linewidth of ~150 nm which matches very well with the deconvolved value from the AFM experiments. As a result, AFM was used throughout this work for the experimental measurement of the linewidth of the fabricated structures. Figure 1(d) displays the AFM height profile at the dashed line drawn in Fig. 1(b) of a structure fabricated with two-beam DLW lithography. In this case, the height of the structure was considerably lower than in one-beam DLW (~10 nm) and presented a Gaussian-shaped profile with a FWHM of 74 nm and a linewidth at the base of 110 nm (~90 nm after tip deconvolution). Note the clear improvement of the minimum linewidth (42%) when using the two-beam approach with respect to the one-beam approach (155 nm vs. 90 nm). The obtained linewidth in the two-beam approach is quite reproducible due to the good stability of the pulsed lasers. This reduction of the linewidth can be certainly attributed to the inhibition of the polymerization process due to the depletion of the ITX triplet state responsible for radicals generation. Thus, our results provide a clear demonstration of the ability of the TSA mechanism to decrease the size of the photopolymerized structures. The minimum linewidth obtained with the TSA mechanism used here is comparable with those reported with the other depletion mechanisms (55 nm with STED or 130 nm with photoinhibitors), where the deviations can be partially explained on the particular properties of the different employed photoresists.

3.2. Characterization of the fabricated lines with gated-CW-STED microscopy

In the second part of this work, we investigated the dimensions of the polymerized lines by using confocal, CW-STED and gated-CW-STED fluorescence microscopy. Since the polymer or the photoinitiator are not providing enough fluorescence signal, a high quantum yield fluorescent dye (Chromeo 488 carboxylic acid derivative) was initially added to the photoresist to perform fluorescence microscopy. Chromeo 488 and derivatives are widely used dyes for bright fluorescent labelling and STED microscopy [34]. Importantly, from the comparison of SEM images of photopolymerized lines with and without Chromeo 488 we noticed that the linewidth of the polymerized lines was not affected by the addition of the fluorescent dye to the resist. All the fluorescence images were taken after the development process where the viscous monomer was washed out with the solvents, remaining only the photopolymerized pattern on top of the coverslip.

Figure 2(a) shows a confocal fluorescence image of a detail of the polymerized lines fabricated with one-beam DLW lithography. Four lines can be identified within the image. This demonstrates the presence of fluorescent dye in the polymerized structures, and hence potential dye photodamaged by the writing and inhibition beams can be considered negligible. However, the contrast of the signal was very poor as a consequence of the high fluorescence signal coming from the background. This was ascribed to the adsorption of the dye to the surface of the coverslip which was not eliminated during the development process. The high dye concentration used with the photoresist together with the presence of the carboxylic acid group in the structure which easily can interact with the surface of the coverslip must promote the adsorption of the dye. Moreover, the background signal appears particularly high due the short height of the fabricated lines, which decreases the signal-to-noise ratio. Figure 2(c) depicts the SEM image of the photopolymerized lines shown in (A), before the plasma treatment, with a background signal very smooth. Thus, we can exclude the presence of possible residue of non-polymerized resin accounting for the detrimental fluorescence signal. The solid red fluorescence profile in Fig. 2(d) reflects the impossibility to determine the linewidth of the lines in this image due to the high level of the background signal. Several cleaning protocols were tried to selectively avoid the adsorption of the dye on the surface of the coverslip. Thus, before the writing procedure, the sample was washed with an organic solvent (acetone or ethanol), for long periods (1 hour) or heated up to 60 °C. In addition to this, a 50 nm thick layer of poly-methyl methacrylate (PMMA) was deposited onto the coverslip to change the polarity of the substrate but none of the previous methods reduced this background. Finally, we tried a plasma treatment based on ion bombardment after the development process, which is frequently employed to remove impurities and contaminants from the surface of different substrates. The fluorescence signal from the entire sample was clearly reduced after the plasma treatment but importantly, more efficiently from the surface of the coverslip. Figure 2(b) shows a confocal fluorescence image of the same pattern as in Fig. 2(a) but after plasma treatment, where an optimization of the power and duration of the treatment was performed with the aim of reducing almost completely the signal from the background without decreasing considerably the fluorescence signal from the lines. The dashed black profile in Fig. 2(d) clearly illustrates that the linewidth of the polymerized lines can be easily measured due to the excellent signal-to-background ratio.

 

Fig. 2 Confocal fluorescence images of photopolymerized lines containing a fluorescent dye (Chromeo 488) and fabricated with one-beam DLW lithography before (A) and after (B) the plasma treatment. (C) SEM image of same photopolymerized lines shown in (A), before the plasma treatment. (D) Fluorescence intensity profiles of the polymerized lines in A (solid line) and in B (dashed lines).

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Once the contrast in the fluorescence images was optimized, the polymerized lines fabricated with one-beam and two-beam DLW were characterized with fluorescence microscopy, and the corresponding linewidths were compared with those obtained with AFM. Importantly, the linewidths of the fabricated lines (90-155 nm) were well below the diffraction limited resolution (~175 nm) attainable with confocal microscopes (NA = 1.4, excitation wavelength 488 nm), and consequently it was not possible to use regular fluorescence microscopy for the appropriate characterization of the structures. Note that, similar to AFM characterization, the estimation of the linewidths could be improved by using deconvolution. However, in this case it would be necessary a precise knowledge of the point-spread-function (PSF) of the confocal system. In contrast to AFM where this information is easy to provide since it is represented by the size of the tip, the PSF can be hard to estimate [35]. Furthermore, an error into the estimation of the PSF can originate into an amplification of the error into the estimation of the linewidths. Therefore, to the measurement of the real linewidth of the structures required the use of an optical super-resolution approach. Here, we used STED super-resolved microscopy for such characterization which is a well-known imaging technique for 3D structures [36]. In particular, we used a gated-CW-STED microscope for two key reasons: (i) the two-beam DLW lithography architecture and the gated-CW-STED microscope are very similar, with the main difference between both architectures being solely the wavelength of the excitation and inhibition beams; (ii) both architectures use CW laser beams to inhibit the relative process, namely the polymerization and the fluorescence. The use of CW laser source greatly reduces the complexity of the architecture. In the case of STED microscopy the time-gated detection allows to obtain spatial resolution comparable to more complex and costly STED microscopy implementations based on pulsed lasers. Finally, changes in the degree of conversion of the polymerization process have been indicated to influence the mechanical strength and the refractive index of the photoresist [18,19]. We believe that variation of the latter two parameters should not affect the signal in STED microscopy since fluorescence is exclusively determined by the organic dye. However, special care must be paid to the formation of aggregates of the dye as a result of the changes in the material density of the photoresist since the fluorescence signal is normally affected in this situation [10].

Figure 3 (upper panel) shows fluorescence images of the thinnest photopolymerized lines fabricated with one-beam lithography obtained with confocal (A), CW-STED (B) and g-CW-STED (C) fluorescence microscopy. The fluorescence intensity is very similar within a line which demonstrates that the dye is homogeneously distributed along the structures, although some small part of the lines presented a slightly weaker signal. A fast comparison of the three images showed that the measured thickness of the lines decreased from confocal to CW-STED and more notably in g-CW-STED. Moreover, the g-CW-STED image is clearly less blurred compared with the others due to the effective resolution/contrast enhancement obtained through the time-gating detection [37]. A more quantitative analysis of the different optical characterization methods is presented in Fig. 3(d). In this case, the normalized intensity profiles corresponding to the dashed lines in Figs. 3(a)-3(c) clearly shows a reduction of the measured linewidth for g-STED microscopy. In particular, the estimated value of the linewidth of the polymerized lines obtained from the g-STED image was 170 nm, in close agreement with the 155 nm calculated with AFM. Concerning the thinnest lines prepared with two-beam DLW through the TSA depletion mechanism, Fig. 3 (lower panel) displays the confocal (E), CW-STED (F) and g-CW-STED (G) fluorescence images. Again, the g-CW-STED image presented an enhanced resolution/contrast and a reduced thickness of the lines compared with the other images. The normalized intensity profile (Fig. 3(h)) revealed a measured linewidth of 99 nm from the g-STED image, which was consistent with the 90 nm found with AFM. Based on these results, the values of the linewidths estimated with g-CW-STED microscopy are comparable with those measured with AFM. Therefore, g-CW-STED microscopy, and in general STED microscopy, can be envisioned as a rapid and reliable tool to characterize the dimensions and the morphological properties of photopolymerized structures fabricated by two-beam DLW optical lithography.

 

Fig. 3 Confocal (A and E), CW-STED (B and F) and g-CW-STED (C and G) fluorescence images of the thinnest polymerized lines fabricated with one-beam (upper panel) and two-beam (lower panel) DLW lithography. Normalized intensity profiles along the dashed lines in one-beam (D) and two-beam (H) DLW fabrication. Scale bars = 1 µm. λ_exc 485 nm, 80 MHz and 11 µW. λ_STED = 592 nm and P_STED = 300 mW; gated detection: T_g = 1 ns and ∆T = 10 ns.

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4. Conclusion

In conclusion, the combination of two-beam DLW lithography and STED microscopy is a robust and reliable strategy for the fabrication of nanometer-sized structures that allows a fast optical characterization of the polymerized system. The similarity between the two experimental architectures, namely the two-beam lithography system and the STED microscope, could allow one to implement both systems on the very same architecture with a reduction of cost and a further simplification of the entire protocol.

We expect that the characterization protocol described here can be also extended to other two-beam DLW approaches, such as those based on stimulated emission, on photo-induced deactivation or on the utilization of photoinhibitors. A critical but essential step of this protocol is the addition of specific fluorescent dyes to the resist which allowed us to perform super-resolution fluorescence microscopy to the photopolymerized sub-diffraction sized structures. Moreover, the application of a plasma treatment to improve the contrast of the lines resulted in a mandatory requisite to achieve trustworthy values of the linewidths.