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Abstract
The refractive index of commonly used 3D printing photosensitive resins were measured across the visible spectrum for s- and p-polarized light for the first time. Commercially available resins (Monoprice Clear and formlabs Clear) and a custom polyethylene glycol diacrylate photopolymer resin was characterized using a critical angle determination method with a Pulfrich-based refractometer setup. The refractive indices ranged between 1.505 − 1.533 across the visible spectrum (670 − 405 nm, respectively), while the Abbe number ranged between 44.4 − 67.8.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Three-dimensional printing (3DP), or additive manufacturing, of optical elements or devices has had increasing interest in the last few years [1–3]. Indeed, the flexibility afforded by custom optical elements, not possible with other fabrication methods, is of interest [4]. In particular, inexpensive and faster ways to fabricate lenses of optical quality using commercially available printers and resins have been explored [3,5–7]. Due to the finer resolutions possible with stereolithography (SLA) [8], SLA 3D printing has been investigated rather than fused deposition modelling (FDM) 3D printing or other methods [4]. However, the design of 3DP lenses critically depends on the refractive index (RI) which has not been sufficiently investigated. The characterization of a few commercial resins have been reported for particular wavelengths such as LUX Opticlear and formlabs Clear [5–7]. However, the wavelength dependence of 3DP resins have been limited (e.g. Nanoscribe IP-S, IP-Dip, IP-L, IP-G and OrmoComp, AutoDesk PR48 Clear) [3,6,9]. In addition, popular hydrogels such as poly(ethylene glycol) diacrylate (PEGDA) resins have been reported for various polymerization conditions, however only for a narrow wavelength range [10].
In this work, the refractive index of common commercially-available photosensitive resins (Monoprice Clear and formlabs Clear) are characterized across the entire visible spectrum (405-670 nm) for both s- and p- polarized light. Additionally, a custom resin consisting of PEGDA and Irgacure, is characterized across the same parameter space.
2. Method
In order to measure the refractive index of photopolymer resins, a modified Pulfrich refractometer optical setup was constructed (Fig. 1(a)) [9]. A Pulfrich refractometer setup was chosen due to the simplicity of operation and inexpensive components compared to other methods (e.g. ellipsometry or M-line) [11]. Linearly polarized light is directed from a laser diode (LD) onto the center of a prism (SF-11) via mirrors (M1-3), apertures (A1-2) and a linear polarizer (LP). Different laser diodes (LD) were used to measure the refractive index for different wavelengths (405, 515, 635, 670 nm) across the visible spectrum. The laser beam angle of incidence to the resin, $\theta$, was controlled by a rotation stage (ROT, Newport UTR120) with a mounted prism (SF-11) before the resulting output optical power was measured using an optical power meter (PM, Thorlabs PM100A) and rejecting scattered light using an aperture (A3). The beam input and output powers were measured and the critical angle was determined by finding the angle at which total internal reflection (TIR) was achieved.
Fig. 1. (a) The Pulfrich-based refractometer optical setup used to measure the refractive index of photopolymer resin used in 3DP. (b) Close-up sketch of prism (SF-11) with the photopolymer resin of interest attached to the prism hypotenuse.
The photopolymer resin of interest was cured onto the hypotenuse of a SF-11 prism (Fig. 1). The commercially-available photosensitive resins were measured directly as purchased. The custom PEGDA-based resin used 250 g/mol poly(ethylene glycol) diacrylate (Sigma-Aldrich) along with 2% by volume of Phynylbis(2,4,6-trimethylbenzoyl)phosphine oxide (Irgacure 819, Sigma-Aldrich) photo-initiator. The prism was placed in a cast where resin was poured onto the hypotenuse and exposed to a UVA lamp ($385-400$ nm) to polymerize (solidify) the resin. The UVA lamp was placed $4\ \textrm {cm}$ away from the prism (SF-11) and exposed for $5$ min with an irradiation intensity of $10mW/cm^2$. Once the photoresist solidified, the prism was mounted on a rotation stage (Newport UTR120), capable of an accuracy of 1 arc minute or 0.0167 $^{\circ }$ (Fig. 1(a)). The beam incident angle, $\phi$, the input optical power, $P_{in}$, and output optical power, $P_{out}$ was recorded. The measurement was repeated until the critical angle could be determined.
3. Theory
The reflectance, $R$, of an interface can be modeled by the Fresnel reflection coefficients for s-polarized, $r_s$, or p-polarized, $r_p$, light by $R=r_sr_s^*$ or $R=r_pr_p^*$, respectively, where $^*$ denotes the complex conjugate. Substituting Snell’s Law into the Fresnel reflection coefficients gives [12],
In order to model the system, the system power as a function of incident angle, $\phi$, is given by the product of the transmittance or reflectance of the three primary interfaces $T_1$, $R_2$ and $T_3$ (see Fig. 1(b)) by [12],
The fitting parameters for Eq. (3) are $\kappa$ and $n$ for a particular measured incident angle, $\phi$. Note the corresponding $n_i$ and $n_t$ must be used at each interface. For example, for $T_1$, $n_i = n_1$ (the surrounding medium, air in this case) and $n_t = n_2$ (the prism index) whereas for $R_2$, $n_i = n_2$ (the prism index) and $n_t = n$ (the resin index). Since $n_1$ and $n_2$ are known, those quantities are fixed for each corresponding interface and the unknown resin index, $n$ is fitted. The wavelength is fixed for each measurement and the wavelength dependent behavior of the index, $n(\lambda )$ is characterized for each wavelength. The $\alpha$ of the SF-11 prism is fixed for a particular wavelength given by previously reported measurements [13]. The length, $L$, of the prism is 10 mm.
The RI of the right angle SF-11 Prism (Edmund Optics, N-SF11, 45-950) was calibrated according to the previously known RI [13]. The prism RI of $n_2(405$ nm$) = 1.8421$ was used as a baseline measurement to characterize. The accuracy and precision of the method was determined by repeating the measurement with only the prism (no resin) ten times and indicated the measurement was within $\Delta n = 0.001$ of the known prism RI.
By way of example, Fig. 2 shows the angle dependent reflectance measurements for the custom resin (PEGDA) at a wavelength of $405$ nm for both s- and p- polarization.
Fig. 2. Reflectance angle dependence measurement of a PEGDA-based resin for s- and p- polarized light.
The measurements were fit to Eq. (3) and the RI, in this case (Fig. 2), was determined to be $1.533$ and $1.553$ for s- and p- polarized light, respectively. The RI values were determined by least squares fit to the model (see Eq. (3)). The model fitting parameters are $\kappa$ and $n$ for a particular incident angle, $\phi$. The wavelength is fixed for each measurement and the wavelength dependent behavior of the index, $n(\lambda )$ is characterized for each wavelength. The $\alpha$ of the SF-11 prism is fixed for a particular wavelength according to [13]. It can be seen at lower angles when the reflectance was significantly less for p-polarized light, the corresponding error was slightly higher. However, this did not effect the measurement significantly due to the location of where the critical angle (or where R is highest) was unaffected. Note the Brewster angle is not observed as it is outside the possible measured range of this particular optical setup.
4. Results and discussion
The refractive index wavelength dependence of several photosensitive resins were measured across the visible spectrum and for s-polarized (transverse electric, TE) and p-polarized (transverse magnetic, TM) light. Two commercially available resins were measured (Monoprice Clear and formlabs Clear) in addition to a custom poly(ethylene glycol) diacrylate (PEGDA) resin. The results are shown in Table 1 and Fig. 3 and indicate that resin RI ranges from $1.505$ to $1.533$ with increasing index as the wavelength decreases (as expected). The RI of each resin had differences of up to $\Delta n = 0.02$ enough to effect lens design. The polarization dependence showed index differences to within $\Delta n = 0.002$ indicating a polarization independent material with an amorphous structure. These results slightly differ from the supplier’s formlabs Clear reported index of 1.5403 [14], but is consistent with a more recent index characterization [6].
Table 1. Refractive index (RI) measurements of common 3D printing photosensitive resins for s- (TE) and p- (TM) polarized light.
The fit for PEGDA TE RI $n(587.56$ nm$) = 1.509$ was higher than in a previous report at $n(587.56$ nm$) = 1.4654$ with resin mixtures under similar conditions [10]. This may be due to the use of 2-hydroxy-2-methyl-propiophenone photo-initiator instead of Irgacure 819 (this work) [10]. A higher index is desirable to, for example, reduce the volume of lenses. The data points in Fig. 3 indicate the average RI whereas the error bars indicate the standard deviation of ten repeated measurements.
The index measurements were then used to determine Cauchy and Abbe parameters useful for lens design. The dispersion relationship was determined by fitting to the empirical Cauchy’s equation [12],
where $A$, $B$ and $C$ are the Cauchy parameters and $\lambda$ is the wavelength given in nanometers. The parameters for the best fit of the resin can be found in Table 2 and the plot of the fits are shown in Fig. 3.Table 2. Cauchy parameters for the RI measurements of the photoresists fitted to Eq. (4) and plots shown in Fig. 3.
The Cauchy parameters for formlabs Clear with TM (TE) polarized light were used to predict the RI using Eq. (4) for the measured RI in [6] and the index differences were 0.002, 0.001, 0.002 and 0.002 (0.001, 0.000, 0.001, and 0.003) for 486, 546, 589, and 656 nm, respectively. Therefore, the Cauchy parameters used to predict the index are highly consistent with independent index measurements [6]. The Cauchy parameters were then used to determine the Abbe number for each resin given by [12],
where $n_C$, $n_D$ and $n_F$ are the RI of the material at the Fraunhofer lines $C$, $D_1$ and $F$. These spectrum lines correspond to the wavelengths of $656.3$, $589.3$, and $486.1$ nm, respectively. The Abbe number, $v_d$, of Monoprice Clear was $49.72$ for s-polarized light whereas for p-polarized light was $51.94$. The formlabs Clear resin was $67.79$ and $57.29$ for s- and p- polarized light, respectively. Finally, the PEDGA resin Abbe number was $44.39$ and $49.33$ for s- and p- polarized light, respectively. The formlabs clear resin Abbe number calculated using the index values measured in [6] would give $\nu _d=56.44$ and hence is consistent with the data in this work using p-polarized light rather than s-polarized light.5. Conclusions
In conclusion, the refractive index was measured for three different 3D printing photoresins across the visible spectrum (405-670 nm) and s- and p-polarized light using a Pulfrich-refractometer with the critical angle determination method. Commercially available resins (Monoprice Clear and formlabs Clear) were measured as well as a common PEGDA-based resin. This is the first time Monoprice Clear refractive index has been reported. This work was consistent with previously investigated resins, such as formlabs Clear and the PEGDA-based resins, but extended the range of wavelengths and polarization dependence. The index values, on average, ranged from 1.505-1.533 and the Abbe numbers ranged from 44.4-67.8. These results contribute to a systematic optical characterization of photoresins in the visible spectrum useful for 3D printing optical components or devices. The measurements can be used to design lenses or other devices where the refractive index of the resin is a critical parameter. Future work would include characterization of critical polymerization conditions (e.g. temperature or curing wavelength).
Funding
Whitworth University.
Acknowledgments
The authors thank Taylor Burchard and Samartha Shrestha for help preparing the PEGDA resin.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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