1. Introduction

The continued trend toward miniaturization of mobile cameras imposes significant constraints on the choice of their components [1]. Remarkable progress was achieved in the design (size, performance) and cost-reduction of fixed-focus mobile cameras as well as of autofocus (AF) cameras using voice coil motors (VCMs) [1]. However, VCMs remain very complex and costly to assemble and to control dynamically [1, 2]. Various alternatives have been considered [1–5], including electro-wetting liquid lenses, piezoelectric or shape memory materials, but without real commercial success. Gradient index (GRIN) type electrically tunable liquid crystal (LC) lenses (TLCLs) have been introduced to enable motion-free and deformation-free AF [3]. The operation principle of such lenses is based on the dynamic generation and control of the spatial profile of the effective refractive index n_GRIN (averaged along the thickness) of the LC material [1, 3–5]:

We think that TLCLs have significant potential to offer in such functions as motion-free AF, reducing the precision requirements for focus-free wafer scale camera assembly, dynamic aberration control and even optical image stabilization [1]. However, it is very challenging to introduce a new technology in consumer electronic products. A relatively easy approach for such introduction (here, of the TLCL) from the product engineering perspective might be the minimization of required modifications of existing solutions (here, the fixed-focus camera module’s architecture), for example, just by adding the TLCL on the top of an existing camera. This suggests that this camera, whose modulation transfer function (MTF) was already optimized, will “receive” an additional element (the TLCL) that may degrade its MTF. Obviously, it is highly desirable that this addition introduces as low as possible complementary root mean square (RMS) aberrations to keep the MTF of the camera as high as possible. Most importantly, the user experience shows that the long-distance performance of the camera (corresponding to low optical powers (OP) provided by the TLCL) should not be noticeably degraded to make this change acceptable. This imposes severe requirements on the optical quality of the TLCL.

The choice of the TLCL (see [1, 4, 5] and references therein) is defined also by other (than optical) performance parameters, the required driving voltage probably being the most important one since it defines the driver architecture (size and cost) as well as the overall power consumption (the battery charge duration in mobile phones being a key factor affecting the consumer choice). Indeed, there are different types of TLCLs using various electrode configurations and LC cell geometries [1]. Thanks to the massive use of LC materials [6, 7] in LC displays [8] and corresponding technological achievements, one of the most straightforward approaches (to build TLCLs) might be the use of multiple concentric electrodes [9]. This approach provides low voltage operation and, in some cases (when using up to ≈80 electrodes along with multiple inter-electrode floating layers), may provide very good performance [10]. However, high-precision manufacturing requirements and electrical driving complexity make such solutions less attractive for consumer electronic applications, where cost is an important factor.

In the quest for simpler and cost effective solutions, the number of control electrodes of the TLCL may be reduced in different ways. The corresponding approaches may be divided into several groups, but two of them would probably cover most of the lens designs (see, e.g., [1, 4, 5] and references therein): TLCLs with uniform and non-uniform LC gaps. TLCLs with non-uniform LC gap are more complex to manufacture in high quantities and generally suffer from relatively high aberrations when trying to change continuously the OP of the lens [11]. There are some rare examples of such lenses where aberrations may be quite acceptable for specific applications (e.g., in a blu-ray disc system [12]), but they suffer from several drawbacks, including the high voltages required to drive the lens (an order of magnitude higher compared to the case discussed here). Finally, the variation of the thickness of the LC layer from the periphery to the center of the lens must be very strong (estimated with the help of the formula OP = Δn/R, where Δn is the maximal effective birefringence of the LC and R is the curvature of the LC gap) to reach 10D of OP for a 2 mm clear aperture (CA) that is required for mobile phone cameras. This is not acceptable from light scattering and speed points of views [5].

Many examples of the first group (with uniform LC gap [1],) are also suffering from high voltages required [1, 4, 13–15] or are using undesirable (from the manufacturing point of view) curved electrodes [16, 17] or polymer stabilized LC networks, which suffer from light scattering or photo chemical instability [18, 19]. However, there is one approach within this group (the so called “modal control” lens [20, 21]) that is relatively simple to manufacture and that provides extremely low power consumption values. The basic concept of modal control was already described elsewhere [20–24]. This approach uses a uniform LC layer that is placed (see Fig. 1; note: the traditional approach does not include the floating transparent electrode, FTE) between one uniform transparent electrode (UTE, typically made of indium tin oxide or ITO) and one hole patterned electrode (HPE). In this way, the electric field E, generated inside the LC layer, is stronger in the periphery of the structure (x ≈ ± r, where r is the radius of the lens) compared to its center (x ≈0). Given the high aspect ratio (typically, the CA of the lens is 2 mm and the LC layer’s thickness is L ≈50 μm) there is a strong gradient dE/dx that is creating abruptly changing (along the x axis) orientation of the director n and correspondingly unacceptable optical aberrations. This is the reason why a high resistivity or weakly conductive layer (WCL) is added to the HPE (Fig. 1) to soften the spatial (along the x axis) variations of E and to limit the corresponding optical aberrations (note that the difficulty of manufacturing the WCL was the main practical limitation of this approach in the past; currently being resolved by a proprietary vacuum deposition procedure [25],). Namely, the fundamental mechanism of the electric field’s spatial shaping in those lenses is based on the combination of electrical capacitive and resistive properties of the LC cell. The presence of the HPE, covered with the WCL, that is facing the UTE (with the dielectric LC layer in between), creates an effective spatially distributed electrical RC circuit that can gradually attenuate the electric potential along the x axis (the potential being stronger in the areas of the lens that are closer to the HPE, i.e., x ≈ ± r). This design provides low driving voltages thanks to the close proximity of the UTE and the HPE. Those TLCLs can be considered as capacitive loads in an electronic circuit, the power consumption of which may be defined as

 

Fig. 1 Schematic presentation of the structure of the proposed TLCL. D_c – diameter of the controlling hole patterned electrode (HPE), D_f – diameter of the additional floating (non-connected) transparent electrode (FTE), WCL – weakly conductive layer, d – thickness of the top substrate, PI – polyimide alignment layer, L – thickness of the LC layer, UTE – uniform transparent electrode.

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Unfortunately, the spatial profile of the electric potential across the clear aperture (along the x axis) of this TLCL is not optimal. It may be represented with the help of Bessel functions (see the corresponding detailed theoretical analyses elsewhere, e.g., in [24]). As a result we usually obtain a relatively flat refractive index distribution in the close proximity of the peripheral zone (x ≈ ± r) and even flatter distribution in the center of the lens (x ≈0, Fig. 2), while, to have good optical aberrations, a spherically shaped refractive index n_GRIN modulation is often required (see Eq. (1)) over the entire clear aperture and for all values of OP (at least up to 10 D that is typically required for mobile phone cameras) [1].

 

Fig. 2 Theoretical simulation results for (a) the driving frequency dependence of the optical power (in Diopters) and (b) the influence of the distance of the FTE on the wavefront of output light for the TLCL with floating electrode. The black curve with squares corresponds to the modal control lens (no FTE); all the remaining curves correspond to the TLCL with FTE for d = 500 µm (blue circles), d = 100 µm (green diamonds), and d = 5 µm (red triangles).

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In addition, there is another problem related to the speed of traditional modal control lenses. Indeed, the fast start of this lens usually generates optical defects (related to so-called disclinations, representing abrupt spatial variations of molecular orientation). Those defects degrade the optical quality of the lens and slow down its operation. To resolve this problem, additional “active” (controlled) electrodes were proposed [26, 27] to enable a better control of aberrations as well as to avoid the formation of disclinations (see next section). However, this change introduces undesired additional complexity (fabrication cost and control).

In this work, we present the details of an alternative approach (recently briefly reported in [27]) that preserves all advantages of modal control lenses while improving significantly their optical quality (enabling extremely low aberrations) and speed. Namely, the proposed design is based on the addition of a floating (unpowered) transparent electrode (FTE, Fig. 1). The comparative theoretical and experimental analyses of the traditional modal control TLCL’s (without the floating electrode) performance versus the proposed here lens (using the FTE) is conducted in this work. It is shown that the appropriate choice of the driving electric signal’s voltage and frequency values improve significantly the performance of the lens. In addition, those lenses were mounted in front (on the top) of standard mobile phone cameras and a significant improvement of image quality was observed compared to the case without the FTE. Finally, some comparative dynamic autofocus experiments have also been performed by using commercial camera systems and the TLCL.

2. Proposed lens structure and driving technique

The proposed lens structure is schematically presented in the Fig. 1 [28, 29]. The main architectural difference with the previously described modal control lenses [20, 21] is the presence of the FTE. The addition of the FTE creates a parallel distributed capacitive layer that helps to modify (improve) the electric potential’s spatial attenuation profile (along the x axis) [27]. Namely, the addition of a conductive layer (that may be patterned at wish, e.g., by chemical etching or laser ablation) in the close proximity of the WCL allows the additional control over the local resonance value of the RC circuit by adding (where needed) more capacitance. While those changes remain rather subtle, the difference is quite noticeable since, as a result, we reduce the flatness of the field in the center of the TLCL (see theoretical and experimental results).

The uniform nematic LC (NLC) layer is sandwiched between two substrates (typically with LC molecules oriented almost parallel to the substrates’ surfaces with a small ground state tilt or “pretilt” angle [7]). The bottom substrate is covered by a UTE and by an alignment layer (made of polyimide, PI). The top substrate is covered by a WCL, by a control HPE (with internal diameter of D_c) and finally by an alignment layer PI. An additional highly conductive transparent layer (ITO with diameter D_f) is added at the external surface of the top substrate without connecting it (“floating electrode”, FTE, Fig. 1). The influence of this layer on the distribution of the electrical potential in the transverse plane of the cell is defined by the thickness d of the top substrate (distance from the WCL) and by its dielectric permittivity ε_g, see hereafter.

Another important difference of our approach is the simple (disclination-free) frequency driving technique developed to control the proposed lenses. Indeed, the OP of our lens can be controlled by applying various electric voltages as it was broadly discussed in the scientific literature. However, in general, the orientation of the electric field E(r) being tilted in opposite directions in two opposite corners of the lens (for x≤0 and x≥0 zones, Fig. 1) and the corresponding reorientation of the director n (in two opposed directions) will produce a disclination wall and corresponding optical defect line if we try to quickly start the operation of the lens (typical AF convergence times should preferably be of the order of 0.5 sec [1]). This will degrade lens quality (aberrations) and speed (those defects take time to be resorbed). As it was mentioned above, this problem was resolved by adding active electrodes (either two lateral linear electrodes [26] or a single disc-shaped electrode that is like the FTE, but connected and actively controlled). In the case of parallel linear electrodes, the operation starts with the application of a transient in-plane electric field. The disc-shaped approach allows starting the operation of the lens by first using this electrode (along with the HPE, activated at the same electric potential as the additional “active” electrode) to create a uniform electric field [27]. This allows generating director reorientations in the same direction in all zones of the lens (thus avoiding the formation of disclinations). This first step is then followed by a gradual introduction of the gradient of the E(x) and consequently of n(x). This is a very good solution, but it still requires the use of the WCL and adds a third active electrode and corresponding complexity and cost.

In contrast, we have developed a frequency control technique [25, 30] that does not require the third electrode being actively controlled. Namely, in our case, the driving signals’ frequency is first chosen to be very low, say ≈0.5 kHz. In this case, the electrical potential’s attenuation (from x ≈ ± r to x ≈0) is weak. Thus, the electric field’s transversal distribution is almost uniform, E(0)≈E(r) [30, 31], generating thus a relatively uniform reorientation of molecules (without disclinations) and correspondingly low OP since the effective optical path difference (OPD) in the center (x ≈0) and the periphery (x ≈ ± r) of the lens is almost zero:

Then, the driving frequency is gradually increased, say up to 13 kHz. In this case the drop of the electric field’s strength from the periphery to the center becomes significant (E(0)<E(r)), creating a non-uniform refractive index modulation and thus a high OP. No disclination appears during this transition.

It is important to emphasize that the frequency control [30, 31] described above is performed at fixed driving voltage and this technique is very different compared to the frequency control used in the so called “dual frequency liquid crystals” [32] since the Δε_LC of our LC material is very stable up to 100 kHz (the slope of variation of Δε_LC between 0.5 kHz and 13 kHz is ≈4·10⁻⁶/kHz). Namely, in our case, there is no change of the sign of Δε_LC and the driving frequency change only helps us to control the spatial shape of the refractive index n_GRIN(x) modulation (obtained thanks to the frequency dependence of the electrical potential’s attenuation by the distributed RC circuit) when moving from the periphery of the HPE towards the center of the lens (see [20] for details).

3. Theoretical modeling

The theoretical modeling of this lens is based on previously reported numerical modeling methods (see below). It describes the spatial shaping of the electric field E defined by the attenuation of the electric potential due to the effective RC circuit [20]. The floating electrode adds an additional parallel capacitive layer [28] and this modification is taken into account in our current simulations.

The method also uses the coupling between the E(r) and the NLC’s director n(r), see, e.g [14, 20]. It considers Frank’s free energy functional in the following form:

Considering the LC cell’s dimensions (width is much larger than thickness) we neglect the x component of the electric field and all x derivatives. Also one constant approximation (K₁₁ = K₃₃ = K) is used to simplify simulations. Minimization of the free energy [33] yields the Euler-Lagrange second order differential equation:

The electric field in Eq. (6) is derived by solving Maxwell’s equations in the LC and WCL layers of the lens. Assuming that no free charges are present in the LC layer and also that the control voltage is harmonic - the system of Maxwell’s equations leads to the equation for electric potential:

The bottom ITO electrode of the LC cell is grounded (V = 0); the electric potential is applied to the top electrode (V = V₀∙sin(ωt)); all other external boundaries of the system are electrically insulated (∂V/∂e = 0), where e is a unit vector normal to the considered surface.

The coupled system of partial differential equations with boundary conditions shown above is solved numerically using Comsol Multiphysics software:

As we have already mentioned, we introduce an additional distributed capacitance layer (parallel to the resistance layer, which is represented by the weakly conductive layer (Fig. 1)) when another glass substrate and a floating electrode are added. As a result, we have a change of the electric potential profile caused by the capacitive reactance of the glass substrate. In this case, the same system of differential equations can be solved in all layers, with slightly altered boundary conditions. Namely, the electrical potential on the floating electrode is not predetermined, but depends on currents in the system. The boundary condition that represents this situation is e×E = 0 (e is a unit vector normal to the floating electrode). The simulation parameters used are presented in Table 1.

Table 1. Parameters used for theoretical simulations of the TLCL’s performance.

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The OP was calculated using the standard expression for a GRIN lens with spherically shaped transversal distribution of n_GRIN (see Eq. (1)):

Using the described approach, the OP versus driving frequency curve has been simulated (see a typical example in Fig. 2(a); applied voltage is 4 V).

The influence of the distance d of the FTE from the WCL (Fig. 1) is also demonstrated (Fig. 2(b)) by using the shape of the wavefront of the exiting light. As it can be seen, in the absence of the FTE, there is a significant deviation from the parabolic form. The addition of the FTE starts altering its form, but this influence is weak for relatively large distances d = 500 µm (the typically used thickness of the glass substrate). However, the wavefront is much closer to the parabolic form for the d = 100 µm (Fig. 2(b)). Indeed, almost diffraction limited aberrations can be achieved for this distance (see details hereafter). The further reduction of the top substrate’s thickness d is not justified since it degrades the quality and complicates the manufacturing process.

The same simulations were done for various (fixed) driving voltages, for the given glass substrate thickness d (Fig. 1). From those data, the optimal driving voltage (providing minimum spherical aberrations when using only frequency control) has been identified (Fig. 3). This procedure has been repeated by varying the glass thickness (considering its dielectric permittivity ε_g at used driving frequencies). The optimal geometrical, dielectric and driving (frequency and voltage) conditions were identified and implemented in the experiment (see hereafter). Interestingly enough, we find that the achievable aberrations (here we consider only the square root of squared sum of 3rd, 5th and 7th spherical aberrations, see experimental section) can be twice lower for the lens with the FTE if the driving voltage is relatively low, around 3V (Fig. 3). Such an improvement may have important impact on the image quality. To verify this hypothesis, we have built corresponding camera assemblies (by using both lens models) and tested them, see hereafter.

 

Fig. 3 Theoretical simulation results for optimized RMS spherical aberrations at 10 Diopters of optical power with the TLCL using the floating electrode (orange squares, referred as “Floating”) and the traditional modal control TLCL (blue diamonds, referred as “Reference”).

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4. Experimental investigations of the lens

4.1 Experimental conditions and procedures

The experiment was conducted by using 100 μm thick glass substrates to build our TLCLs (Fig. 1). The bottom substrate was covered by a uniform ITO layer with the sheet resistance of ≈150 Ω/sq. and then by a 40 nm thick planar alignment polyimide (PI) layer. This substrate was positioned with the PI layer facing up and the PI was mechanically (unidirectional) rubbed. Then, liquid adhesive (monomer) reservoir walls were dispensed on the periphery of this substrate. Glass spacers (with 50 μm diameter) were mixed in advance with the adhesive to provide the desired thickness of the final sandwich (see hereafter). The droplet of a homemade NLC mixture (with optical birefringence of Δn = 0.2 and dielectric anisotropy of Δε_LC = 10.5) was injected in the central part of the reservoir.

The top glass substrate (with ε_g = 6.9) was covered by a thin uniform layer of the same ITO (from the external side) that was etched to produce the FTE (a disc of diameter D_f = 2.5 mm). The opposite (internal) side of the top substrate was covered by a metal oxide layer with the sheet resistance of ≈10 MΩ/sq. to produce the WCL. This WCL was then covered by a metal layer (made of Ag alloy) that was etched to produce the HPE of diameter D_c = 1.9 mm. The substrate was finally covered by a 40 nm thick planar alignment PI layer. The obtained substrate (with its PI layer facing down, after being rubbed in the opposite direction, compared to the first PI) was pressed on the bottom substrate containing the LC droplet within the reservoir walls and the latter were polymerized by using UV curing. The obtained “pretilt” angle was ≈3°. A similar sandwich (sometimes called “half” lens since it is focusing only the half of the natural light; only the extraordinary polarization) was fabricated and attached to the first sandwich with 90° rotation of the director n to obtain a “full” lens capable of focusing unpolarized light without the use of polarizers. In this way, the spectrally averaged (in the visible spectral range) transmission of our full lens is ≥90% [25].

The same assembly procedure was repeated without using a floating electrode (Fig. 1) to build a traditional modal control lens and to use it as reference. The initial optical tests were performed at room temperature (20°C) by using a Shack Hartmann wavefront sensor (from Imagine Optics, model HASO 3-42). The output plane of the TLCL was imaged on the input plane of the wavefront sensor by using a relay lens. The digital clear aperture of the sensor was defined as 1.74 mm. The voltage of the driving AC square shaped signal was chosen (fixed) between 3V and 4V (RMS values) and its frequency variation was used to control the OP of the lens. The frequency of the driving signal was changed from 0.5 kHz (where the electric field’s transversal distribution is uniform) up to 13 kHz (where the drop of the electric field’s strength from the periphery to the center becomes significant). The value of the residual OP (due to the mechanical deformation of substrates during the cell fabrication) was subtracted from the obtained OP to obtain the “clear” OP (COP).

4.2 Optical powers and aberrations

The dependence of COP versus the driving frequencies is presented in Fig. 4(a) (for the traditional modal control lens) and Fig. 5(a) (for the lens with FTE) for different (fixed) driving voltages. The corresponding RMS aberrations are presented in Figs. 4(b) and 5(b).

 

Fig. 4 Characterization of the traditional modal control TLCL (a) The clear optical power (COP) versus the frequency of the driving electric signal for various voltage values; (b) RMS spherical aberrations versus the COP.

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Fig. 5 Characterization of the proposed TLCL using the floating electrode (a) The OP versus the frequency of the driving electric signal for various voltage values; (b) RMS spherical aberrations versus the COP.

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As we can see from those figures, the achieved COP values are acceptable for both TLCLs’ designs (error bars are smaller than the size of symbols in the graph). Indeed, both of them allow achieving 10 D of OP that is required for close distance photography (bar code, check or other text scanning). However, the corresponding aberrations are quite different (Figs. 4(b) and 5(b)). Figure 4(b) shows the obtained total RMS aberrations versus the COPfor the traditional modal control lens. Here we consider only the spherical aberrations (square root of squared sum of 3rd, 5th and 7th spherical aberrations) to exclude the possible contributions of mechanical bend or deformation induced aberrations. It is important to note that reducing the spherical aberrations is indeed the main challenge in TLCLs. In our case, the total RMS aberrations of TLCLs, fabricated on large panels, was typically below 0.2 μm at 10D of OP.

The addition of the floating electrode is a relatively simple step in the manufacturing process (Fig. 1). However, the RMS aberrations of the lens are noticeably improved at all imaging distances, if the appropriate voltage is used for its driving. Spherical aberrations of such a lens are very low (below 0.01 μm) for low COP values (Fig. 5(b)). This should allow the recording of high quality images of distant objects. However, the reference lens without the floating electrode (Fig. 4(b)) also has good performance for distant objects. The difference (in performances of two lens designs) is more noticeable when the close distance photography is required (corresponding to higher OP values of the TLCL). The RMS aberrations of the new lens are almost twice lower than those for the traditional modal control lens. Thus, the RMS aberration value at 10D level of OP of the new lens is ≈0.04 μm versus the ≈0.085 μm for the traditional modal control lens. The corresponding summary (of experimental results) is presented in Fig. 6. We can see that there is a good qualitative agreement between our experimental and theoretical simulation results (Fig. 3).

 

Fig. 6 Comparative experimental results for optimized spherical aberrations at 10 Diopters of OP with the TLCL using the floating electrode (green circles, referred as “Floating”) and the traditional TLCL without the floating electrode (orange squares, referred as “Reference”).

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It is important to note that we have also tried to use more complicated driving techniques (by using specific pairs of voltage and frequency for each OP level) to minimize those aberrations for the traditional lens. However, the achievable level of aberrations for this lens was almost twice higher (for close distances) compared to the one obtained with the floating electrode. In addition, in this case (when using combined voltage-frequency control), the driver also would become more complex and expensive (requiring additional tables for different operation temperatures, etc.).

5. Experimental investigation of the camera performances

5.1 Image quality

Developed TLCLs were incorporated (including its miniature ASIC driver, see Fig. 7) in various camera kits to perform image quality (MTF, etc.) and autofocus convergence time (AFCT) measurements.

 

Fig. 7 Photography of the ASIC driver (left), the TLCL (center) and of a camera kit (right) with the TLCL incorporated on the top.

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A schematic presentation of the corresponding set-up is presented in Fig. 8.

 

Fig. 8 Schematics of the experimental set-up used for the characterization of the camera performance using different types of TLCLs

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This is the cross section of an autofocus camera lens incorporating a TLCL and a 4P injection molded base lens assembly with planar IR filter (IRF)/cover glass in front of the CMOS sensor [34]. The typical overall length of such a system may be approximately 3.7 mm, with an entrance pupil (stop) diameter of 1.2 mm. The distance d₀ between the position of the TLCL and the stop as well as the viewing angle define the minimum acceptable clear aperture of the TLCL.

As a target, we have used single frequency “plaid” chart targets (that we have designed ourselves, Fig. 9(a)) and also standard ISO12233 test charts [35] (Fig. 10(a)). As a base module, 5MP, 1/4-inch camera was used with 1.4 um pixel size, focal length = 2 to 3 mm, f/number = 2.2 to 2.4, field of view (full diagonal) = 60 to 80 degrees.

 

Fig. 9 Single spatial frequency plaid test target (a) used to study the MTF “map”; the typical experimental results (b) for the MTF “map” and the spatially averaged MTF (c) for both types of LC lenses (red squares: the lens with FTE; blue diamonds: the modal control lens) incorporated in a 5MP, 1/4 inch (1.4 um pixel). Ny/4 was used for measurements.

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Fig. 10 Resolution chart ISO12233 (a) and the intensity profile (b) along the vertical line (a) when using a traditional modal control lens (bottom b) and the developed lens with floating conductive layer (top b).

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The image of the plaid chart was used to calculate an approximation of MTF at the corresponding spatial frequency. A detailed map of MTF across the image was created (Fig. 9(b)). In the current work, the MTF calculation of plaid chart was done in 32x24 regions across the field. The typical MTF, calculated in plaid chart measurements (Ny/4 was used for these measurements) for the base module only (without the TLCL), was between 65% and 75% in the center and between 50% and 60% in the corners.

The addition of TLCLs and the calculation of the experimentally measured and spatially averaged MTF values (Fig. 9(c)) for both types of LC lenses incorporated in front of the above-mentioned camera showed the following features: in both cases, there was almost no degradation of the MTF at 100 cm distance (1D of OP); the MTF was practically the same as the base module and the quality of the obtained images was very high, Fig. 11. At 30 cm (~3D) of distance the center was still close to the baseline for the lens with FTE, but corner MTFs were reduced down to 35-40%. At 10 cm (10 D) of distance the MTF of the center had dropped to 45-60% and the corner to 25%.

 

Fig. 11 Long distance image quality obtained with the mobile camera including the TLCL with FTE.

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It is important to note that, despite this degradation, the AF of the lens with FTE provides quite acceptable performances for near field images. Indeed, as we have mentioned above, usually at least 10 cm distance is considered to be acceptable for scanning (short distance photography). We have used a book bar code (outlined by the yellow dotted-line rectangle, Fig. 12, left) to conduct comparative studies of the contrast. The image of the bar code was recorded (at normal office lighting conditions) with three mobile cameras, the first one without AF, then with a commercial AF (iPhone 6, 18 MP) and then the cell phone camera (LVAF, 5MP) using the TLCL.

 

Fig. 12 Study of the scanned image quality by using the image of a book’s bar code at 10 cm distance; left: the original image; right: the extracted bar code and the line of intensity profile analysis.

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The obtained bar code image (Fig. 12, right) was extracted without any additional processing and the intensity profile (along the yellow vertical line, Fig. 12, right) was analyzed by using ImageJ software. Figure 13 (bottom graph) shows the relative performances of three cameras. As expected, the fixed-focus camera has extremely poor performance (the contrast is ≈67 at the scale of 255 and the standard deviation is ≈21). The addition of the TLCL improves significantly the image quality (the contrast is ≈107 and the standard deviation is ≈9).

 

Fig. 13 Comparative demonstration of the near field image quality (contrast) obtained with various mobile cameras, including the TLCL, an iPhone 6 and a fix-focus camera (without AF). Top: contrast of the bar code at 5 cm; bottom: contrast of the bar code at 10 cm.

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This is more than enough to recognize the bar code. At this distance, the best result is obtained for the iPhone 6 (the contrast is ≈152 and the standard deviation is ≈4,5). However, at the distance of 10 cm, the image of the bar code for most mobile cameras is not filling completely the field of view for typical bar codes. As we can see (from Fig. 12, left), the bar code is occupying less than 15% of the image. To increase this ratio and to demonstrate also a “super-macro” focusing mode, we have approached the bar code to 5 cm (then the image of the bare code is approximately 50% of the field of view). The same procedure was repeated again and the obtained results are shown on the top of the Fig. 13. Again, as expected, the fixed-focus camera’s performance is further degraded (the contrast is ≈40 and the standard deviation is ≈6,5). However, the performance of the camera with TLCL (the contrast is ≈119 and the standard deviation is ≈11) is now noticeably better compared to the iPhone 6 (the contrast is ≈78 and the standard deviation is ≈12).

Coming back to the study of the camera’s MTF for two different types of TLCLs (with and without the FTE): the same analyses (of spatially averaged MTF values) for the traditional modal control lens confirms the important advantages of using the TLCL with the FTE. Indeed, the spatially averaged MTF value was almost 28% better in this case (Fig. 9(c)). In addition, as predicted theoretically, the optimization of MTF is reached at low voltages (≈3V) and the results are in good qualitative agreement with both our theoretical (Fig. 3) and experimental (Fig. 6) data concerning the lens alone.

The images of the camera resolution (ISO 12233) test chart (Fig. 10(a)) were acquired in the same conditions and an intensity plot was constructed along the vertical yellow line (Fig. 10(a)) for both cameras (with two TLCL models). As we can see (from Fig. 10(b)), the recording of ISO images confirms again the above-mentioned advantage of the lens using the FTE. Indeed, the intensity plot (Fig. 10(b)) along the vertical direction clearly shows the fast loss of resolution (modulation depth, see Fig. 10(b), bottom curve) in the case of the camera using the traditional modal control (noted as Reference) TLCL compared to the case of the TLCL with FTE (Fig. 10(b), top curve).

5.2 Autofocus algorithm and convergence time

The AFCT of TLCLs was the subject of many discussions since LCs are considered (for a reason) as electro-optic materials with slow response. In reality, the algorithm of the focus search appears to be key here. Indeed, the corresponding search algorithms can be split in two main groups: one is traditionally used for VCMs and the other one is specifically developed for TLCLs [30]. In the case of VCMs (Fig. 14(a)), the search is usually performed by multiple steps of moving the VCM (to focus different positions), recording of a small window in the scene(zone of interest) for each position and calculating the contrast of the image to generate the so-called “focus score” (for each step). The search is conducted with relatively large steps up to the change of the slope of the focus score curve (step n). However, to narrow the search, VCM systems must move completely back (step n + 1) to search in a narrower zone (dashed area centered at the maximum of the focus score curve, Fig. 14(a)). This is done to avoid the errors due to the hysteresis of VCMs. Thus, despite the rather fast single steps of the VCM [1], the number of steps needed to reach the optimal position is relatively high here. In addition, the AFCT (total duration of the search) depends upon the level of scene illumination since the search steps are correlated with the frame rate (to count, among others, the ringing effect of the VCM [1]), which is defined by the lighting level.

 

Fig. 14 Schematic presentation of the focus search algorithms for the case of (a) VCM and (b) TLCL.

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In contrast, TLCLs have no hysteresis and no ringing effect [1], and thus, it is easier to use a predictive algorithm of focus search (Fig. 14(b)). Indeed, just a couple of measurements (steps 1-2) are usually enough to predict the position of the maximum of the focus score curve and to move directly into this position (step 3). In the case of “overpassing” the optimal position (4*), there is no need to re-start the search process and a single step back (5*) is sufficient to reach the optimal position.

The corresponding experiments were conducted with several commercially available mobile cameras (Samsung Galaxy S3, iPhone 5 and Nokia Lumia 920) versus the TLCL (with 1.9 mm clear aperture) that was integrated into an Aptina SOC5140 demo system (here called LensVector Auto Focus or “LVAF Aptina” system). The AFCT data was collected using Sofica CamSpeed application (http://www.sofica.fi). Measurements have been done at the following target distances and illumination conditions:

Distances:

Obtained results are summarized in Fig. 15. As we can see (extreme right line, Fig. 15), at far distances (100 cm), the AFCT of the TLCL is the shortest one (compared to three other commercial cell phone cameras) in normal office lighting conditions (250 lux). For the closer positions (e.g., for bar code scanning applications) the AFCT is longer for the TLCL system, while still remaining at the same order of magnitude as other commercial systems. The advantage of the TLCL system is even more pronounced at low lighting conditions (since it is not affected by the frame rate reduction) and this advantage remains unbeaten at all distances (from 10 cm to 100 cm).

 

Fig. 15 Summary of AFCT measurements for 4 camera systems (in ms). Standard deviations are different for various lighting conditions and distances, but their approximate (for all distances) values are 48 ms, 65 ms, 78 ms and 228 ms (at 10 Lux) and 11 ms, 33 ms, 46 ms and 24 ms (at 250 Lux) for LVAF Aptina, Samsung SIII, Iphone 5 and Lumia 920, respectively.

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6. Discussions and conclusions

We have demonstrated that the addition of a simple floating electrode into a traditional modal control lens design allows a significant optimization of the electric potential’s spatial distribution. This in turn helps to improve (almost twice) the achievable spherical aberrations of the lens. In addition, the OP and RMS aberrations of the obtained lens were demonstrated in a very simple driving scheme (fixed voltage and variable frequency). The obtained values (OP > 10 D and RMS < 0.05μm) are quite acceptable for miniature camera applications with clear apertures of the order of 2 mm. While the results presented in this work were obtained by using 5MP cameras (with TLCL), we have also successfully incorporated those lenses into 8MP miniature cameras frequently used in cell phones. The MTF characterization of those cameras has been completed successfully showing a clear improvement in the case of using the lens with floating electrode (results will be reported elsewhere).

The performance of the system (camera and TLCL assembly) is particularly good when the distance d₀ between the TLCL and the camera stop is minimized. In this case, a smaller diameter TLCL can be used (e.g., 1.3 mm) and the overall requirements on the TLCL are then reduced significantly since the OP is inversely proportional to the clear aperture radius (Eq. (10)) and thus thinner LC layers and lower excitation regimes can be used to reach the required OP values. We have designed such a camera [36], incorporated our lens with FTE into this camera and tested it. The preliminary results are very good (significantly better than those reported in the present work; the corresponding results will be completed and reported elsewhere).

The cost aspect of TLCLs is also very important. Fabricated in the form of LCD panels (Fig. 16) and subsequently diced into thousands of single lens units, those lenses may have very low cost. In the high-volume manufacturing regime, this cost could be at the order of $0.05/lens. The cost of the ASIC driver (Fig. 7) may also be very low in high-volumes (of the order of $0.05 separately or 0.02$ if it is integrated into the CMOS). Thus, the liquid crystal lens technology offers an AF solution (performance and cost) that should enable almost all mobile cameras to benefit from it.

 

Fig. 16 TLCLs manufactured on a generation 2 LCD panel.

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Finally, given the significant improvement of the image quality and enhanced functionalities (such as depth mapping, growth of 3D print technologies, etc.) the above-mentioned advantages of TLCLs (low cost and power-consumption, absence of ringing and hysteresis, etc.) will be even more important when double-camera solutions would be more available, where the two cameras must work in tandem with one another since the obtained two images must be “fused”.