Open Access
Add to BibSonomy
Abstract
We describe the use of stacked electrically tunable liquid crystal lenses (TLCLs), along with rod gradient index (GRIN) fixed focus lenses, for endoscopic applications. Architectural and driving conditions are found for the optimization of total aberrations of the assembly. Particular attention is devoted to the coma and polarization aberrations. The coma aberration is reduced by stacking two TLCLs with “opposed” pre-tilt angles (all molecules are in the same plane), and then two such doublets are used with cross oriented molecules (in perpendicular planes) to reduce the polarization dependence. The obtained adaptive rod-GRIN lens enables a focus scan over 80μm (with exceptionally low RMS aberrations ≤0.16μm), making possible the high-quality observation of neurons at various depths.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Electrically tunable liquid crystal (LC) lenses (TLCLs) [1–3] have been considered for various applications, including aberration control [4–6], imaging [7] and vision [8–15]. Thanks to their high sensitivity to electric fields [16,17], those devices can operate at very low current and voltage values (requiring μW electrical power consumption) being thus “user friendly” for mobile applications. Namely, one of the growing needs in TLCLs is the focus tuning in miniature endoscopic probes [18–21] designed to study brain activities in freely behaving small animals (typically mice) [21,22]. This application imposes very specific additional requirements on the TLCL. First of all, the majority of TLCLs are using nematic LC (NLC) materials, which are inherently polarization sensitive and can focus only one linear (extraordinary) polarization of light in the transmission geometry (we call them “half-lenses”). Neural fluorescence images being recorded in non-polarized light, a combination of at least two TLCLs is needed (with ground state optical axis rotated at 90° with respect to each other) to handle two orthogonal polarizations of light [7,23]. Thus the mismatch of optical power (OP) values between those TLCLs and the corresponding mismatch of focal points (at the origin of “polarization aberrations”) must be reduced to avoid the degradation of images.
In addition, the typical clear aperture (CA) of the optical system in general (and of the TLCL in particular) must be reduced (sometimes down to 0.5mm) to minimize the damage to the brain tissue. In this case, coma aberration become very important [6,24].
Finally, to reach deep zones of the brain, rather long (several mm long) gradient index (GRIN) rod lenses must be used with huge (fixed) OP values, often at the order of 2000 Diopters (D). This last requirement imposes two additional constrains: increased aberrations of the system because of the low quality of commercially available GRIN lenses and the need to have very high OP variation range (provided by the TLCL) to insure a noticeable shift of the image plane (see hereafter).
One possible solution for the coma problem of the Rod-GRIN/TLCL assembly was already described in [24]. The current work aims addressing differently this problem as well as the polarization aberration problems in above-mentioned assemblies (the GRIN aberrations alone were partially analyzed in [6]). Thus, we shall start by briefly reminding the coma aberration problem and by describing an alternative approach to reduce it. We shall then describe our experimental results in the framework of an imaging system with multiple GRIN/TLCL assembly and will analyze the corresponding polarization aberrations’ problem. We shall present both numerical simulations and experimental observations. We shall then discuss the obtained results and conclude.
2. Coma aberration
For this application we have used the well-known “modal-control” lens design [25,26]. The basic unit of this TLCL is a single layer of NLC [16] that is sandwiched between two substrates of thickness = 0.1mm. The optical birefringence of the NLC was Δn ≡n||-n⊥≈0.18, were n⊥ and n|| are ordinary and extraordinary refractive indices. The dielectric anisotropy of the NLC used was Δε≡ε||-ε⊥≈10. The electric field profile (inside the cell) was generated with the help of a uniform indium tin oxide (ITO) layer (on the first substrate) and a combination of a hole shaped electrode (with an internal diameter of CA = 0.55mm) and a weakly conductive layer of ≈40MΩ/sq sheet resistance (on the second substrate). Both substrates were further covered by planar alignment layers (Polyimide), which were rubbed in “anti-parallel” directions to obtain a mono domain cell with approximately α≈3° of pretilt angle (the angle between the local averaged molecular orientation, the so-called director [16], and the cell substrates). The details of cell fabrication can be found elsewhere [24,27,28]. The thickness of the NLC layer was maintained at L = 40μm by means of spacers (inserted in advance in the peripheral adhesive walls).
The control of the OP of this lens was performed for fixed voltage values (see hereafter) by changing the frequency of the electrical signal (square shaped AC), see, e.g [27]. The OP and aberration values were detected by means of a Shack-Hartmann wave front sensor. Obtained results are summarized in Fig. 1.
Fig. 1 a) Optical power (in diopters) versus control frequency (in kHz) and b) circles - total RMS aberrations (in μm) and triangle - separated coma aberrations versus the optical power for the TLCL.
Since the TLCL is a flat electrically variable GRIN lens, its OP variation range scales quadratically with the inverse of its radius r = CA/2 (see, e.g [24].):
Large L (40μm) and small r (0.275mm) values explain the relatively large OPs observed experimentally (Fig. 1(a)). Indeed, the corresponding theoretical estimation (using the Eq. (1)) shows that the maximum possible OPmax≈190D. However, the LC orientation is also non uniform along the light propagation direction (in the non-saturated mode, the LC reorientation could be described by a half sinusoid: zero at boundaries and maximal in the center of the cell since we have strong boundary alignment conditions on cell substrates) that reduces the effective modulation depth of the refractive index. Typically, we can use a factor of ≈0.85 (for the “efficiency” of use of Δn) to obtain the experimentally achievable values. This would bring us down to ≈161D, which matches perfectly with our experimental data (Fig. 1(a)).Most importantly, we can see the significant contribution of the systematic coma aberration (triangles, Fig. 1(b)) in total RMS aberrations of the TLCL. One possible solution to this problem (based on the stack of NLC layers) was discussed by S. Sato and associates [29]. Another solution (based on the segmentation of the hole patterned electrode) was discussed in [24]. The aimed-here endoscopic application would favor the first approach due to the desire to study the calcium activity in the brain [30], which requires relatively fast scans of image planes. The stacked solution may be preferred here since it allows the use of thin NLC layers and the reorientation (and thus focus scanning) time is proportional to L2. This will be certainly more expensive approach, but the price is not a critical factor for this application. We shall thus further explore the stacked solution.
Figure 2 demonstrates the single and stacked solutions as well as the corresponding experimental results (all experiments were conducted by applying a square shaped AC signal with an amplitude ranging between 3.5 and 4.5 volts). Figure 2a demonstrates the observed strong coma in the case of a TLCL with single NLC layer (see the cell schematics, top left column). Traditional polarimetric set-up was used (the TLCL was placed between two crossed polarizers, with the ground state director of NLC along the diagonal) to visualize the coma by fringe spacing (Fig. 2(a), the photo at the bottom left column; each bright fringe representing 2π shifts on the transmitted phase front, see, e.g [24].). The right column of Fig. 2(a) shows its compensation by the combination (stack) of two TLCLs with “opposed’ pretilt angles (see the cell schematics, top right column). Figure 2b shows the OP versus the control frequency for 2individual TLCLs with single NLC layer (squares and triangles) and for their combination TLCL (double NLC layer with two “antiparallel” pretilt angles, circles [29]). As we can see (from Fig. 1(a)), the contrast of fringes is slightly degraded for the double cell. We think that this is related to the increased light scattering and to the imperfect alignment of two cells. It is interesting also to notice that the maximum achievable OP (circles, Fig. 2(b)) for the double cell TLCL is less than the addition of OP values of two individual TLCLs. This might be related to the imperfect alignment of those cells as well as due to the fact that the focusing phenomenon is more efficient (stronger) for collimated beams while the use of the second TLCL becomes less efficient due to the wavefront curvature created by the previous TLCL.
Fig. 2 a) Demonstration of the strong coma in the case of a TLCL with single NLC layer (left column) and its compensation by the combination of two TLCLs with “opposed” pretilt angles (right column). b) Optical power (in diopters) versus control frequency (in kHz) for 2 TLCLs with single NLC layers (squares and triangles) and for one combined TLCL (double NLC stack, circles). c) Total RMS aberrations, d) Coma aberrations.
Corresponding RMS and coma aberrations are demonstrated in Fig. 2(c) and Fig. 2(d), respectively.
As we can see, total and coma aberrations of the combined (double) cell are significantly better (lower) than the corresponding aberrations of two TLCLs with single NLC cells. This allows extending significantly the OP’s variability range (Fig. 2).
3. Polarization aberration
We have seen that the obtained TLCL (with double NLC layers) can be used to focus (Fig. 2(b)) a linearly polarized light with good optical quality (Fig. 2(c) and Fig. 2(d)). However, as we have mentioned above, the fluorescence light is not polarized. There have been several studies addressing this issue. The use of TLCLs with so called blue-phase materials [31,32] would not have such “polarization sensitivity” problem, but it would require much higher voltages, which is not compatible with mobile applications targeted here. The use of a specific scanning procedure and image processing algorithm might be another solution [33], but it will delay the scanning process and will complicate the video recording. We could change the imaging arm to use a lens with a single NLC layer in reflection geometry [34], but this would be a rather important design change. Binary (on-off) focus switching [35] also cannot be accepted here since we need a continuous scan. Those are the reasons why we shall further proceed with a straightforward solution [28], where we use two “double” TLCLs (rotated at 90°) to record images with an unpolarized (fluorescence) light.
In combination with a GRIN lens assembly (a first GRIN of diameter ∅ = 0.5mm, pitch = 0.5, NA = 0.2 combined with a second GRIN of ∅ = 0.5mm, pitch 0.23, NA = 0.5; from GoFoton) the final stack (with the TLCL having a total of 4 layers) has demonstrated between 80μm and 90μm spatial shift. With a typical neuron size of 10μm-20μm, this would be an excellent tool to study their behavior at several depths.
However, there are many ways how different individual TLCLs (with single NLC layers) may be assembled together to form the above-mentioned “polarization independent” stack. For example, if we consider the worst-case scenario where the stronger TLCL #1 (Fig. 2(b), squares) is placed (as shown in the Fig. 3(a)) before the weaker TLCL #2 (Fig. 2(b), triangles), followed by a rod-GRIN (OP = 2174D), and both TLCLs are controlled with the same electrical excitation signal (which is simpler and cost effective), then two orthogonal polarized images will be created at different distances (triangles). At the maximum of OP (triangles, Fig. 3(b)), this mismatch may be more than 10μm, which will degrade the image of the neuron.
Fig. 3 a) Schematic demonstration of one possible TLCL stacking option (to demonstrate the polarization mismatch problem, triangles). b) Mismatch values (in μm) versus the control frequency (defining the OP of the lens) for two slightly different TLCLs (with different OP values, Table 1) and extreme cases: triangles: wrong positioning; squares: the right positioning, circles: individual control (see text for details).
In contrast, if we invert the positions of those TLCLs, the mismatch will not be completely eliminated, but the situation will be noticeably improved (squares, Fig. 3(b)). Obviously, the best scenario would be to drive those lenses individually (circles, Fig. 3(b)) if it is acceptable from cost and complexity points of view (in this particular case, it is). Using our experimental data (OP versus driving frequency F, Fig. 2(b)) and Zemax simulations, we can find the drive parameters (Table 1) enabling the complete elimination of this polarization mismatch (circles, Fig. 3(b)).
Table 1. Values of drive parameters used for obtaining minimal polarization mismatch.
To provide a quantitative tool that may be used for TLCLs’ stacking strategy, it is important to evaluate the impact of the focus mismatch (polarization aberrations) on the image quality recorded. Surprisingly enough, despite the growing popularity of TLCLs, articles describing this problem are rather rare [36]. We have thus decided to characterize those polarization aberrations by using a simple stack of two TLCLs with cross oriented ground state directors (a total of two NLC layers). Figure 4(a) describes the experimental set-up used for this purpose.
Fig. 4 a) Experimental set-up used to characterize the impact of polarization mismatch on the quality of recorded images. b) micro photography of obtained images, c) intensity slope versus driving frequency of one TLCL (see the main text for details).
Periodic black and white (10μm width) colored stripes where used as object 1 to be imaged. The imaging system was composed of an imaging rod-GRIN lens 2 (OP = 2174D, ∅ = 0.5mm, pitch = 0.23, NA = 0.5; from GoFoton), followed by the TLCL 3 and by a relay rod-GRIN lens 4 (OP = 328D, ∅ = 0.5mm, pitch = 0.25, NA = 0.2; from GoFoton). Light from GRIN-TLCL-GRIN assembly was when collimated using a microscope objective 5 (6.3X Neofluar, Zeiss) and transmitted to infinity-corrected tube lens 6 (ITL200, Thorlabs) specially designed for use with plan visible imaging to minimize chromatic aberrations across the field of view. Images were captured using a CMOS camera 7 (DCC1645C, Thorlabs).
To estimate the quality of imaging, we have used the slope of pixel intensity variation σ = ΔI/Δx (where ΔI is the difference of pixel intensity and Δx is the difference of positions of pixels) between the black and white zones of obtained images. The reason for this choice is the non-uniform intensity distribution within the white zone of images (Fig. 4(a)) that makes difficult the identification of the contrast between black and white zones. At the same time, the degradation of image quality is clearly seen in the slope of transition between those zones when we change the polarization mismatch. To simulate a controllable polarizationmismatch, we have started by choosing the driving frequency of 15kHz for both cross oriented half lenses (in the optimal order, see squares in Fig. 3(b), and driven together). In this case, the image recorded had the best quality (middle photography, Fig. 4(b)) since two half lenses are providing similar OP values (and they are positioned in the right sequence). Then, one of the half lenses was kept in the same excitation state, while the other one (with perpendicular ground state optical axis) was driven with different frequency (below and above 15kHz), generating thus different OP values. Images were recorded and the slope of the intensity (pixel value) change along the direction perpendicular to stripes was measured (Fig. 4(c)) for transition zones (between the white and black areas).
4. Discussions and conclusions
We have shown that RMS aberrations in general and the coma aberration in particular have been significantly improved by the cell stacking approach (Figs. 2(c) and 2(d)). However, that has created the problem of polarization aberrations. We have also demonstrated that we can reduce the degradation of image quality because of the polarization mismatch by an appropriate choice of the stacking sequence, TLCL characteristics and the driving technique.
Indeed, we have used this opportunity to study the resulting polarization aberrations of the endoscopic imaging system (TLCL and rod-GRIN assembly). Thus, as we can see from Figs. 4(b) and 4(c), the best transition slope (affecting the image quality) is obtained when two TLCLs are well synchronized and focus approximately at the same plane (driven at 15kHz, corresponding to ≈105D of OP, chosen deliberately to be in the strongest OP variation zone). However, the slope drops (≈twice) when the mismatch of OP values for cross oriented TLCLs is ΔOP≈44D (at 30kHz).
It is important to emphasize that the polarization aberration problem must be considered within the framework of the optical assembly and target application. Thus, in combination with the above mentioned GRIN assembly; with a TLCL #1 driven at 105D (15kHz) and the TLCL #2 being tuned from 64D (at 11kHz) to 146D (at 23kHz), we obtain a spatial mismatch that changes from – 8.3μm to + 8.7μm (relatively “limited” thanks to the presence of high power GRIN lens with OP = 2174D). This mismatch indeed may appear to be limited, but we must keep in mind the typical sizes of neurons and their spines (at the order of 1μm) that we are trying to image. In another context, the same driving conditions would generate a focus change ranging from – 5.8mm to + 2.8 mm if the TLCLs are considered alone (without the GRIN lens).
In conclusion, we think that the proposed here solution (stacking TLCLs in the same and in perpendicular planes) will enable the construction of high quality miniature endoscopic systems for “mobile” imaging. We are currently building such endoscopes and our preliminary results confirm the above-mentioned statement. Corresponding results will be reported soon elsewhere.
Acknowledgments
First of all, we would like to thank our collaborators in the field of ophthalmology. We would like also to thank LensVector inc. for the material and financial support of this work. We would like to thank FRQNT for the scholarship supporting AB. Finally, we would like to acknowledge the Canada Research Chair in Liquid Crystals and Behavioral Biophotonics 230212 (hold by TG) as well as NSERC (05888) and FRQNT for their continuous financial support.
References
1. S. Sato, “Liquid-crystal lens-cells with variable focal length,” Jpn. J. Appl. Phys. 18(9), 1679–1684 (1979). [CrossRef]
2. L. Guoqiang, “Adaptive Lens,” Prog. Opt. 55, 199–283 (2010). [CrossRef]
3. Y.-H. Lin, Y.-J. Wang, and V. Reshetnyak, “Liquid crystal lenses with tunable focal length,” Liq. Cryst. Rev. 5(2), 111–143 (2017). [CrossRef]
4. J. Knittel, M. Hain, H. Richter, T. Tschudi, and S. Somalingam, “Liquid crystal lens for spherical aberration compensation in a Blu-ray disc system,” IEE Proc. Sci. Meas. Technol. 152(1), 15–18 (2005). [CrossRef]
5. A. Tanabe, T. Hibi, S. Ipponjima, K. Matsumoto, M. Yokoyama, M. Kurihara, N. Hashimoto, and T. Nemoto, “Correcting spherical aberrations in a biospecimen using a transmissive liquid crystal device in two-photon excitation laser scanning microscopy,” J. Biomed. Opt. 20(10), 101204 (2015). [CrossRef] [PubMed]
6. L. Begel and T. Galstian, “Dynamic compensation of gradient index rod lens aberrations by using liquid crystals,” Appl. Opt. 57(26), 7618–7621 (2018). [CrossRef] [PubMed]
7. T. Galstian, O. Sova, K. Asatryan, V. Presniakov, A. Zohrabyan, and M. Evensen, “Optical camera with liquid crystal autofocus lens,” Opt. Express 25(24), 29945–29964 (2017). [CrossRef] [PubMed]
8. G. Li, P. Valley, P. Äyräs, D. L. Mathine, S. Honkanen, and N. Peyghambarian, “High-efficiency switchable flat diffractive ophthalmic lens with three-layer electrode pattern and two-layer via structures,” Appl. Phys. Lett. 90(11), 111105 (2007). [CrossRef]
9. G. Li, D. L. Mathine, P. Valley, P. Ayräs, J. N. Haddock, M. S. Giridhar, G. Williby, J. Schwiegerling, G. R. Meredith, B. Kippelen, S. Honkanen, and N. Peyghambarian, “Switchable electro-optic diffractive lens with high efficiency for ophthalmic applications,” Proc. Natl. Acad. Sci. U.S.A. 103(16), 6100–6104 (2006). [CrossRef] [PubMed]
10. Y.-H. Lin and H.-S. Chen, “Electrically tunable-focusing and polarizer-free liquid crystal lenses for ophthalmic applications,” Opt. Express 21(8), 9428–9436 (2013). [CrossRef] [PubMed]
11. H. E. Milton, P. B. Morgan, J. H. Clamp, and H. F. Gleeson, “Electronic liquid crystal contact lenses for the correction of presbyopia,” Opt. Express 22(7), 8035–8040 (2014). [CrossRef] [PubMed]
12. T. Galstian, “Tuneable liquid crystal lens intraocular implant and methods therefor,” 2018, US Patent App. 13/369,806.
13. T. Galstian and H. Earhart, “Reprogrammable tuneable liquid crystal lens intraocular implant and methods therefor,” 2016, US14924950.
14. H.-S. Chen, Y.-J. Wang, P.-J. Chen, and Y.-H. Lin, “Electrically adjustable location of a projected image in augmented reality via a liquid-crystal lens,” Opt. Express 23(22), 28154–28162 (2015). [CrossRef] [PubMed]
15. Y.-H. Lee, G. Tan, T. Zhan, Y. Weng, G. Liu, F. Gou, F. Peng, N. V. Tabiryan, S. Gauza, and S.-T. Wu, “Recent progress in Pancharatnam–Berry phase optical elements and the applications for virtual/augmented realities,” Opt. Data Process. Storage 3(1), 79–88 (2017). [CrossRef]
16. P.-G. de Gennes and J. Prost, The Physics of Liquid Crystals, Second Edition, International Series of Monographs on Physics (Oxford University, 1995).
17. L. M. Blinov and V. Chigrinov, “Electrooptic Effects in Liquid Crystal Materials”, Partially Ordered Systems (Springer-Verlag, 1994).
18. H.-S. Chen and Y.-H. Lin, “An endoscopic system adopting a liquid crystal lens with an electrically tunable depth-of-field,” Opt. Express 21(15), 18079–18088 (2013). [CrossRef] [PubMed]
19. C.-W. Chen, M. Cho, Y.-P. Huang, and B. Javidi, “Three-dimensional imaging with axially distributed sensing using electronically controlled liquid crystal lens,” Opt. Lett. 37(19), 4125–4127 (2012). [CrossRef] [PubMed]
20. T. Galstian, A. Saghatelyan, and A. Bagramyan, “Tunable Optical Device, Tunable Liquid Crystal Lens Assembly and Imaging System Using Same,” U.S. patent WO/2016/187715 (December 2, 2016).
21. A. Bagramyan, T. Galstian, and A. Saghatelyan, “Motion-free endoscopic system for brain imaging at variable focal depth using liquid crystal lenses,” J. Biophotonics 10(6-7), 762–774 (2017). [CrossRef] [PubMed]
22. R. P. J. Barretto and M. J. Schnitzer, “In vivo optical microendoscopy for imaging cells lying deep within live tissue,” Cold Spring Harb. Protoc. 2012(10), 071464 (2012). [CrossRef] [PubMed]
23. T. V. Galstian, Smart Mini-Cameras (CRC, 2013).
24. L. Begel and T. Galstian, “Liquid crystal lens with corrected wavefront asymmetry,” Appl. Opt. 57(18), 5072–5078 (2018). [CrossRef] [PubMed]
25. A. F. Naumov, M. Y. Loktev, I. R. Guralnik, and G. Vdovin, “Liquid-crystal adaptive lenses with modal control,” Opt. Lett. 23(13), 992–994 (1998). [CrossRef] [PubMed]
26. A. Naumov, G. Love, M. Y. Loktev, and F. Vladimirov, “Control optimization of spherical modal liquid crystal lenses,” Opt. Express 4(9), 344–352 (1999). [CrossRef] [PubMed]
27. T. Galstian, K. Asatryan, V. Presniakov, A. Zohrabyan, A. Tork, A. Bagramyan, S. Careau, M. Thiboutot, and M. Cotovanu, “High optical quality electrically variable liquid crystal lens using an additional floating electrode,” Express, OE 25(24), 29945–29964 (2016). [CrossRef] [PubMed]
28. T. Galstian, O. Sova, K. Asatryan, V. Presniakov, A. Zohrabyan, and M. Evensen, “Optical camera with liquid crystal autofocus lens,” Opt. Express 25(24), 29945–29964 (2017). [CrossRef] [PubMed]
29. B. Wang, M. Ye, and S. Sato, “Liquid crystal lens with stacked structure of liquid-crystal layers,” Opt. Commun. 250(4-6), 266–273 (2005). [CrossRef]
30. K. K. Ghosh, L. D. Burns, E. D. Cocker, A. Nimmerjahn, Y. Ziv, A. E. Gamal, and M. J. Schnitzer, “Miniaturized integration of a fluorescence microscope,” Nat. Methods 8(10), 871–878 (2011). [CrossRef] [PubMed]
31. C.-T. Lee, Y. Li, H.-Y. Lin, and S.-T. Wu, “Design of polarization-insensitive multi-electrode GRIN lens with a blue-phase liquid crystal,” Opt. Express 19(18), 17402–17407 (2011). [CrossRef] [PubMed]
32. Y. Li and S.-T. Wu, “Polarization independent adaptive microlens with a blue-phase liquid crystal,” Opt. Express 19(9), 8045–8050 (2011). [CrossRef] [PubMed]
33. R. Bao, C. Cui, S. Yu, H. Mai, X. Gong, and M. Ye, “Polarizer-free imaging of liquid crystal lens,” Opt. Express 22(16), 19824–19830 (2014). [CrossRef] [PubMed]
34. T. Galstian and K. Allahverdyan, “Focusing unpolarized light with a single-nematic liquid crystal layer,” OE 54(2), 025104 (2015).
35. M. Wahle, B. Snow, J. Sargent, and J. C. Jones, “Embossing reactive mesogens: a facile approach to polarization-independent liquid crystal devices,” Adv. Opt. Mater. 7(2), 1801261 (2019). [CrossRef]
36. H. Chen, Y. Wang, C. Chang, and Y. Lin, “A polarizer-free liquid crystal lens exploiting an embedded-multilayered structure,” IEEE Photonics Technol. Lett. 27(8), 899–902 (2015). [CrossRef]
