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Since its emergence in the 1990s, multi-photon 3D direct laser writing (DLW), also known as 3D laser printing, has evolved from a scientific curiosity to an important 3D micro- and nanofabrication technique1, 2. Today, applications range from metamaterials3, 4 and biomimetics5 to microoptical components6, 7 and photonic interconnects8, 9.
However, challenges exist in that the physical 3D microstructures obtained from 3D printing often differ significantly from the underlying 3D computer models. Typically, shape distortions of readily printed 3D microstructures can, for example, result from the proximity effect10, volume shrinkage of the polymerised photoresist during polymerisation11, sample development12, or from a limited printing resolution13. Therefore, the 3D printing process must usually be optimised iteratively until the targeted 3D structure is reproduced with the required accuracy and quality. To date, this optimisation procedure has typically been based on imaging techniques, such as scanning electron microscopy14, holographic tomography15, X-ray tomography16, confocal fluorescence microscopy17, 18, confocal laser profilometry19, optical coherence tomography20, 21 and atomic force microscopy22.
These methods are carried out on the finished 3D printed parts using ex-situ approaches, that is, after the unpolymerised photoresist has been washed out using organic solvents. Hence, the optimisation processes relying on such ex-situ methods are comparatively slow.
An in-situ inspection method routinely used in the context of DLW is wide-field optical microscopy. Herein, one observes two-dimensional snapshots of light scattering from the momentary refractive-index distribution due to the unpolymerised and polymerised parts23. Reconstruction of the overall polymerised 3D microstructure from these data points is presently elusive and perhaps not even conceptually possible without deriving the phase or intensity information from the image. Another in-situ approach is coherent anti-Stokes Raman scattering (CARS) microscopy24, which allows for a spectroscopic determination of the local cross-linking density. However, this approach is relatively slow and cannot be used as a routine on-the-fly diagnostic tool. Thus, non-invasive in-situ 3D monitoring techniques that enable a fast and routine identification of printing defects during the printing process are missing to date. For example, X-rays would polymerise the monomer around the already printed (polymerised) regions and would therefore completely change the part to be inspected.
An ideal in-situ imaging modality should 1) be fast with respect to the printing process, so that the monitoring does not significantly increase the printing time; 2) give at least micrometer-scale 3D resolution; and, importantly, 3) not influence the printing process, i.e., not introduce any polymerisation or other unwanted chemical modifications of the photoresist.
Optical coherence tomography (OCT) is a promising candidate for in-situ inspection during multi-photon 3D laser printing. OCT relies on the interferometric detection of backscattered light from a sample. In the scope of in-situ DLW process monitoring, backscattering from the sample occurs because of the very small refractive-index differences between the polymerised and unpolymerised regions in the photoresist on the scale of
$ \Delta n \approx 10^{-2} $ and below25. Fourier-domain OCT systems can combine fast acquisition speeds and micrometer-scale resolution26 with high sensitivities exceeding$ 100 $ dB and are hence able to detect such small refractive index differences. Finally, polymerisation of the monomer used for printing by an OCT light source is obviously unwanted. For printing via two-photon absorption, we use tightly focused mode-locked femtosecond laser pulses centred at around$ 780 $ nm wavelength. Therefore, a continuous-wave OCT light source at a similar wavelength does not lead to two-photon or one-photon absorption. However, a continuous-wave OCT light source with significant power at approximately half of the 780 nm wavelength polymerises the monomer by one-photon absorption. Various continuous-wave OCT light sources are potentially compatible with these conditions. We choose superluminescent diodes, which are compact, readily available with similar wavelengths as the printing laser, and provide sufficiently large emission powers in the range of a few milliwatts.In the context of other 3D printing methods, in-situ 3D diagnostics using OCT have already been demonstrated in combination with extrusion-based bioprinting27, 28. Using gauging software, deviations from the original 3D computer model were revealed in a 3D OCT reconstruction. Furthermore, several studies on metal additive manufacturing used OCT for the in-situ monitoring of surface defects, layer roughness, and time-dependent thickness of the sintered metal29-31. In addition, the use of OCT for visualising the curing process in semi-transparent polymer droplets has been described recently32.
In this paper, we examine and demonstrate the feasibility of Fourier-domain optical coherence tomography (FD-OCT) as an in-situ diagnostic tool for multi-photon 3D laser printing. We start with OCT imaging of photoresists before 3D printing. Next, we investigate the polymer-substrate interface and the polymer-monomer interface of the printed structures. Thereafter, OCT imaging is applied to various 3D example architectures. To mimic the in-situ situation, these architectures are examined after laser printing, but before development. Several structures are inspected after development, followed by re-immersion in the same photoresist. We observe a time-dependent behaviour of the reflectivity at the polymer-monomer interfaces, which we model using graded-index profiles and a transfer-matrix approach. Subsequently, we examine the effective numerical aperture of our setup on a custom-printed 3D test target. Finally, we discuss the influence of different printing process parameters on the imaging contrast and show the OCT reconstructions recorded for a variety of 3D printed microstructures.
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Sensitivity characterization To calculate the signal-to-noise ratio (SNR) of the OCT setup, we use the method of specular surface reflection described in Ref. 35 with a fused silica substrate as a specular reflector and immersion oil as a medium. SNR is calculated as follows:
$$ \mathrm{SNR}_{\mathrm{max}} (\mathrm{dB}) = 20\,\mathrm{log}\left(\dfrac{I_{\mathrm{sub}}}{\sigma_{\mathrm{bg}}}\right)-10\,\mathrm{log}(R_{\mathrm{sub}}) $$ (1) where
$ I_\mathrm{sub} $ is the OCT intensity of the oil-substrate interface,$ \sigma_{\mathrm{bg}} $ is the standard deviation of the background intensity away from the substrate, and$ R_{\mathrm{sub}} $ is the Fresnel intensity reflection coefficient of the oil-substrate interface. The known refractive index of the glass substrate of$ 1.4525 $ and that of the used immersion oil of$ 1.510 $ lead to$ R_{\mathrm{sub}} = 3.77\times10^{-4} $ , which is equivalent to an OCT intensity of$ -34.24 $ dB. The sensitivity$ \mathrm{SNR}_{\mathrm{max}} $ of$ 105 $ dB quoted in the main text refers to a frame rate of$ 25 $ kHz and a single measurement. Averaging further improves this value.Multi-photon 3D laser printing Laser printing is performed using a commercially available DLW apparatus Nanoscribe Professional GT with a
$ 63\times $ /NA$ 1.4 $ objective lens in the dip-in mode. All samples are printed using IP-Dip (Nanoscribe) photoresist. In addition, we print cube samples in IP-Dip and IP-S (Nanoscribe) photoresists using a$ 25\times $ /NA$ 0.8 $ objective lens. For a two-photon absorption and an ideal photoresist, the resolution of the printing process can be estimated from the full width at half maximum (FWHM) of the squared focus intensity profile along the lateral (and axial) directions. For the$ 25\times $ objective lens, we obtain$ 400 $ nm (and$ 2300 $ nm) for the$ 63\times $ objective lens$ 250 $ nm (and$ 600 $ nm).OCT measurements The printed samples are measured on the OCT setup immediately after printing unless stated otherwise. We perform OCT measurements in the same photoresist used for laser printing as an immersion medium. To eliminate undesired air-glass specular reflections, we add a drop of immersion oil on top of the substrate. For all experiments reported herein, the power from the superluminescent diode, measured at the entrance pupil of the microscope objective lens, is approximately
$ 4.1 $ mW). The$ 1/e^2 $ intensity diameter of the OCT beam at the same point is$ 1.2 $ mm). Assuming a$ 70\% $ optical intensity transmission of the microscope lens, we estimate the light intensity in the focal plane to be$ 60 $ kW/cm2. This intensity level do not lead to a polymerisation of previously unpolymerised parts in our experiments. To convert the OCT data into an absolute z axis, one needs to make an assumption regarding the group index. Because the materials involved in our work are only weakly dispersive, we assume that the group index is equal to the refractive index at the centre wavelength of the OCT superluminescent diode. For the unpolymerised monomer, we use$ n_{\mathrm{mon}} = 1.51 $ ; for the polymer, we use$ n_{\mathrm{pol}} = 1.545 $ .Focus distortion calculations To calculate the possible influence of the detected refractive index inhomogeneities on the focus, we describe the system as follows: the illumination is approximated by a monochromatic circularly polarized plane wave with a wavelength of
$ 790 $ nm. This wave is refracted into the photoresist containing the described scatterers by an objective lens with a numerical aperture of$ 1.4 $ and a focal length of$ 4.125 $ μm.Simulating the focal spot, including the perturbations induced by the scatterers, is a computational challenge for many numerical methods owing to the large volume of computational domain needed. The relevant domain is the cone-shaped volume between the lens and the focal spot. Therefore, we simulate the scattering using the T-matrix method46, in which simulations are limited not by the total size of the volume, but by the size and number of the individual scatterers. To include focusing by the objective lens into the simulations, we use the method of47 before the T-matrix calculations. Therefore, the simulation can be summarised as a three-step process. First, the angular spectrum representation of the focused light behind the lens is calculated. This field is the background field for the following scattering calculations. Second, a random arrangement of scatterers is generated in a cone shaped volume and, finally, the scattered field is calculated.
Details of the calculation of the focal field can be found in the Ref. 47. In short, the electric field of the incoming beam is refracted at the lens onto a spherical sector centred at the focal spot. The radius and opening angle of the spherical sector are determined by the focal length and numerical aperture of the lens. The refracted field is then converted to an angular spectrum representation of the field in the focal plane. The angular spectrum representation can be propagated to an arbitrary point within the resist by applying suitable phase factors. Thus, we obtain the background field at the position of each scatterer.
After obtaining the background field, the next step is to generate a random arrangement of refractive index inhomogeneities. For this, we generate random positions within the cone between the lens and the focal spot. Random positions are only added to a simulated sample if a newly added scatterer does not overlap with existing scatterers. To improve the efficiency of the subsequent T-matrix calculation, the scatterers are approximated by spheres of a fixed diameter. We deduced the diameter and volume distribution of the scatterers from the OCT measurements, as described in the main text.
The T-matrix of spherical scatterers can be calculated analytically48. Typically, the next step is to calculate the interactions between particles. However, owing to the high number of particles, multi-scattering processes are extremely resource-demanding in computational terms. Therefore, we approximate the total scattering by neglecting this interaction. We evaluate the scattered field around the focal spot for each scatterer. Finally, we consider the coherent sum of the individual scattering of each particle.
Refractive-index calculations We treat the polymer-substrate interface signal in terms of the Fresnel reflectivity, taking the monomer-substrate interface signal as the reference value for the recalculation from the OCT intensity to the Fresnel coefficient. We extract the refractive index of the polymer from the OCT data according to the following equation:
$$ n_\mathrm{pol} = n_\mathrm{sub}\dfrac{1+\sqrt{\dfrac{\mathrm{FT}_\mathrm{pol-sub}^2}{k}}}{1-\sqrt{\dfrac{\mathrm{FT}_\mathrm{pol-sub}^2}{k}}} $$ (2) $$ k = \mathrm{FT_{mon-sub}^2}\left(\dfrac{n_\mathrm{mon}+n_\mathrm{sub}}{n_\mathrm{mon}-n_\mathrm{sub}}\right)^2 $$ (3) where
$ n_\mathrm{pol} $ ,$ n_\mathrm{mon} $ ,$ n_\mathrm{sub} $ are the refractive indices of the polymer, monomer, and substrate, respectively,$ \mathrm{FT}_\mathrm{pol-sub} $ and$ \mathrm{FT}_\mathrm{mon-sub} $ are the Fourier-transform OCT signals of the polymer-substrate and monomer-substrate interfaces, respectively. The resulting calibration curve for the recalculation of the measured OCT intensity with respect to the polymer refractive index is shown in Fig. 6b.Transfer-matrix calculations For the transfer-matrix calculations, we use code written by Shawn Divitt, which is available in the Matlab File Exchange49. In particular, we use a simulation range of
$ 5 $ μm, which we discretize into layers with a thickness of$ 2 $ nm. The refractive-index step, which is centred around$ x_0 = 2.5 $ μm, is implemented by$$ n(x) = \begin{cases} n_0 & \text{for } x < x_0-\frac{w}{2} \\ n_0 + \frac{n_1-n_0}{2} \times \left| \frac{x-(x_0-w/2)}{w/2} \right|^h & \text{for } x_0-\frac{w}{2} < x < x_0 \\ n_1 - \frac{n_1-n_0}{2} \times \left| \frac{x-(x_0+w/2)}{w/2} \right|^h & \text{for } x_0 < x < x_0+\frac{w}{2} \\ n_1 & \text{for } x > x_0+\frac{w}{2} \\ \end{cases} $$ (4) Herein, we assume real refractive indices
$ n_1 = 1.51 $ and$ n_2 = 1.545 $ with no losses. Calculations are performed for perpendicular incidence. To account for the broadband light source in the OCT, we perform calculations for different wavelengths centred around$ \lambda_0 = 845 $ nm in the range of$ 135 $ nm and in steps of$ 5 $ nm. The final$ R $ is obtained by averaging.