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Abstract
Microbolometers are the dominant technology for uncooled thermal imaging; however, devices based on a direct retardation measurement of a liquid crystal (LC) transducer pixel have been shown to have comparable sensitivity. In this paper, an approach for increasing LC transducer sensitivity utilizing an etalon structure is considered. A detailed design for an LC resonant cavity between dielectric mirrors is proposed and the performance is evaluated numerically. The measured quantity is the transmission of a visible wavelength through the etalon, which requires no thermal contact with the IR sensor. Numerical and analytical calculations that consider a 470 nm thick LC pixel demonstrate that the change in transmitted intensity with temperature is 26 times greater in the device based on a resonant structure than in a device based on a direct retardation measurement. Finally, the paper discusses how the dielectric mirror materials, dimensions of the resonant cavity structure, and expected process tolerances affect the sensitivity of the device.
© 2018 Optical Society of America
1. INTRODUCTION
The resolution of uncooled thermal imagers for long-wave infrared (LWIR) detection has improved to the point where the sensors are being inserted into applications that had typically used cooled photodetectors. The dominant technology for uncooled thermal imagers is the microbolometer. Microbolometers utilize materials with a temperature-sensitive resistance, such as vanadium oxide, to construct an electronic image; they are typically capable of measuring changes in the scene temperature of the order of 20 mK [1]. However, the complexity of the readout integrated circuit results in difficulty scaling the device to larger formats [2]. Additionally, the thermal resistance of the isolation structure is limited by the requirement to be electrically conductive. Therefore, new methods should be considered which can result in simpler device design as well as increased sensitivity. One possibility is the use of liquid crystals (LCs) as the temperature-sensitive material in a thermal imager. LCs become less ordered when heated, which leads to a change in their ordinary and extraordinary indices of refraction; this allows changes in scene temperature to be probed optically rather than electronically.
Uncooled LC thermal imagers that utilize a direct measurement of the birefringence have already been shown to have sensitivity comparable to that of present microbolometers [3]. One challenge with this device design is achieving a fast thermal response time while maintaining high sensitivity. If the thermal capacitance of the pixel is considered, a straightforward way to reduce the thermal response time is to decrease pixel thickness. However, reduction in pixel thickness also leads to a decrease in the pixel retardation resulting in a less sensitive device. One possible solution to this problem is considering a device design based on the Fabry–Perot interferometer (etalon) rather than direct birefringence measurements. Etalons are known for their sharp spectral lines and can be designed with cavity thicknesses of the order of 100 nm for visible probe wavelengths. A thermal imager based on the Fabry–Perot structure has been proposed by RedShift Systems Corp., which uses silicon nitride and amorphous silicon as the thermally sensitive materials. The materials used in this device have been shown to have a refractive index that changes with temperature at the rate of [4]. In this paper it is shown that LCs can have a thermal response up to more sensitive; therefore, a dramatic increase in sensitivity can be expected.
First the sensitivity of an LC thermal imager based on a direct retardation measurement is investigated utilizing analytical expressions. Next, the theoretical background for the etalon is examined and used to show that a significant increase in device sensitivity can be expected relative to the retardation measurement. Finally, a design for a real device is proposed and the Berreman method is used to numerically predict the sensitivity of this device. Ultimately, it is shown that an order of magnitude increase in sensitivity is expected by utilizing an etalon design rather than a direct retardation measurement.
2. DEVICE ARCHITECTURE
A. Design Overview
The thermal imager operates by converting the IR illumination from the scene to a visible image detectable by a solid-state imager, such as a commercial off-the-shelf (COTS) CCD or CMOS active pixel sensor (APS). This device has previously been described and demonstrated by Clark et al., but a brief overview is given below [3]. First, IR illumination from the scene is focused onto an array of LC transducer pixels, which also include an IR absorbing layer. This causes a temperature change at the LC pixel and, in turn, a change in the pixel birefringence. The change in birefringence is detected by linearly polarized visible light transmitted through the LC pixel array; the transmitted light passes through a quarter-wave plate and a second polarizer and is focused on the solid-state imager. A simple schematic for the device architecture is shown in Fig. 1. One of the main advantages of this approach is the decoupling of the electronic readout from the transducer pixels. This allows for the individual components to be optimized separately and keeps the pixel design simple.
Fig. 1. Example of device architecture for an uncooled LC thermal imager which utilizes direct retardation measurement of the transducer array.
B. Fabrication of Microcavity Pixel Arrays
The process for fabrication of the LC transducer pixels has been demonstrated previously by Berry et al. [5]. Additionally, a process has been established for obtaining stable LC photoalignment in microcavities [6]. The process for LC pixel fabrication requires fewer than 10 photolithographic steps and results in highly uniform LC cavity thickness; over a 10 megapixel array cavity thickness was found to vary by 6 nm. The pixel consists of an LC cavity formed by silicon nitride, which is thermally isolated from the fused silica substrate by four silicon nitride legs. Figure 2 shows a scanning electron microscope image of an unfilled LC cavity and the thermal isolation structure.
Fig. 2. SEM image of an LC transducer cavity fabricated by Berry et al. A LC pixel is thermally isolated from the underlying substrate by four silicon nitride legs.
C. Thermal Response Time
A key parameter of the thermal imaging system is the thermal response time, which dictates the maximum frame rate the system can operate at. The thermal time constant, , is given by
where is the total heat capacity of the transducer pixel and is the thermal conductivity of the thermal isolation structure. The thermal conductivity of the isolation structure should be small to prevent heat flow from the thermal pixel to the substrate. Therefore, thermal response time is mainly controlled by limiting the heat capacity of the thermal pixel. The heat capacity of the pixel is determined by where 1, 2, 3 denote the different materials that the cavity structure is comprised of; and , , and represent the density, volume, and specific heat of the material, respectively. Figure 3 shows the cavity structure that is considered and Table 1 outlines the relevant material properties. For the thermal legs, a low thermal conductance of is assumed. Using the values from Table 1 it is found that the heat capacity of the pixel is . From Eq. (1), the response time of the thermal pixel is therefore estimated to be 7.75 ms. Given Eq. (2), the straightforward ways of decreasing the response time of the device are by reducing the pixel area or reducing the pixel thickness. Limiting pixel area reduces the fill factor of the pixel array and therefore limits the maximum signal that can pass through the device. Therefore, device designs that can achieve high sensitivity for a small pixel thickness are highly desirable.
Table 1. Various Material Layer Properties of LC Pixel Composition
3. PRINCIPLES OF LC THERMAL IMAGER DEVICES
A. Temperature Sensitivity of Indices of Refraction
The temperature dependence of the index of refraction of a nematic liquid crystal enables the LC pixels to be used as the transducer in a thermal imager. Lie et al. have proposed expressions for the temperature dependence of LCs which agree well with the experimental data for E7 [7]. The expressions for the ordinary and extraordinary indices are given by
where , , and are fitting parameters, is the nematic → isotropic transition temperature, and is the birefringence of the material as a crystal. Lie et al. have shown that the values for , , , and should be 1.75, , 0.24, and 0.377, respectively. is considered to be 333 K. These expressions are used to provide the temperature response of the optical constants throughout the paper. If the device is operated from the clearing temperature, then the extraordinary index will change with temperature at a rate of 0.015/K°.B. Direct Retardation Measurement
The retardation of an untwisted LC layer can be determined by measuring the transmitted intensity when the layer is between crossed polarizers with its alignment axis at 45° to the transmission axis of the polarizer and analyzer. The analytic expression for the transmitted intensity through this configuration is
where and is the retarder thickness, is the birefringence (), is the wavelength of the probe light, and represents a fixed retarder which may be included in the system. Equation (5) shows that the transmitted intensity will be most sensitive to changes in the birefringence when , where is an odd integer. If the LC pixel is too thin to have a quarter-wave retardation for the probe wavelength, a fixed retarder can be added to the system to bring the total retardation of the LC pixel and retarder to a quarter-wave.The temperature dependence of the birefringence was determined by Eqs. (3) and (4), and the transmitted intensity from Eq. (5) was plotted over a 200 mK temperature range from 331.9–332.1, which is near the nematic to isotropic transition temperature of E7 (Fig. 4). The probe wavelength was chosen to be 400 nm and the thickness of the retarder was considered to be 470 nm () or 1065 nm (). Additionally, the case was considered where a fixed retarder was added along with the 470 nm pixel to bring the total retardation to . In the case of a 470 nm pixel with a fixed retarder added, a 1.6% change in the transmission was predicted over a 200 mK temperature range. Over the same temperature range, for the 1065 nm pixel, a 3.6% change in the transmission was predicted. This increase in sensitivity corresponds exactly to the ratio of the pixel thicknesses. However, in a real device, there will be a trade-off in performance since thicker pixels will also lead to an increase in thermal response times. From Eqs. (1) and (2), increasing cavity thickness from 470 nm to 940 nm results in an increase in the thermal response time from 7.75 ms to 11.6 ms. In the case of a 470 nm thick pixel without a fixed retarder included, a 1% change in the transmission was predicted over the 200 mK temperature range. Therefore, the inclusion of the fixed retarder to bring the device to quarter-wave retardation resulted in a 1.6x increase in sensitivity. The magnitude of this sensitivity increase will depend on how far the LC pixel retardation is from quarter-wave.
Fig. 4. Modeled transmitted intensity for a thermal imager device based on direct measurement of retardation.
In the following section the performance of a 470 nm thick etalon device will be considered. The 1.6% change in transmitted intensity for the 470 nm thick LC pixel with a fixed retarder included will be used as a benchmark to compare the analytic and numerical calculations for the device based on a resonant structure.
C. Etalon Device
Etalons consist of a resonant cavity surrounded by highly reflective surfaces. The transmission through the etalon is given by [8]
where is given by is the index of refraction of the resonant cavity, is the thickness of the cavity, and is the probe wavelength. is called the coefficient of finesse and is given by where is the reflectivity of a single mirror; the etalon structure is composed of the resonant cavity and a highly reflective mirror on each side of the cavity. The derivative of the transmission with respect to the index of refraction of the LC is given by From Eqs. (8)–(11), it can be shown that the value of the derivative is maximum when . Additionally, Eq. (11) shows that the maximum value of the derivative can be increased by having high reflectivity at the surfaces of the resonant cavity, increasing the thickness of the resonant cavity, and using a short wavelength. In this paper the coefficient of finesse and the wavelength are considered constants. The value of was considered to be 4311 (corresponding to ). The probe wavelength was selected by plotting Eq. (8) and choosing a point at which . For the following calculations, the probe wavelength was selected to be 385 nm for both the case of a 470 nm thick and 940 nm thick LC cavity. Equations (3) and (4) were used to determine the temperature dependence of the extraordinary index over a 200 mK temperature range from 331.9–332.1 K. Then using the values of , , , and presented above, the transmission through the etalon was plotted versus temperature (Fig. 5). It is shown that a 20% change in transmission is expected over a 40 mK temperature range when the cavity thickness is 470 nm. This represents a increase in sensitivity when compared to the analogous result for a direct measurement retardation in Fig. 4. Additionally, Fig. 5 shows that when the cavity thickness is doubled, a increase in sensitivity is expected. This is a promising result, but it ignores the detailed structure of a real device. For example, the analytical expression does not consider the optical properties, such as absorption, of the materials used. In order to consider these losses a more rigorous calculation must be performed using the Berreman method.Fig. 5. Optical transmission through an etalon plotted versus temperature for resonant cavity thicknesses of 470 and 940 nm. The first number in the legend corresponds to the wavelength and the second corresponds to the cavity thickness.
4. NUMERICAL CALCULATIONS FOR TRANSMISSION THROUGH THE ETALON DEVICE
A. Cavity Structures
Following the treatment of Hodgkinson and Wu [9], software has been written implementing the Berreman method that allows the user to define a stack of materials of various thickness and index of refraction, and calculate the transmitted or reflected intensity of the stack [10]. A similar approach for analysis of an LC resonant cavity has been described by Isaacs et al. [11]. The materials for the bottom mirror were chosen to be compatible with VLSI processing. For the top mirror ZnS and KCl were chosen for their high transmission between 0.4–14 μm. The full list of materials considered is given below along with a cartoon depiction of the resonant cavity structure (Fig. 6). The optical properties of the materials were determined from [12–15] and are given in Table 2. The dielectric mirrors were designed to each have 97% reflectivity for a probe wavelength close to 400 nm to correspond to the analytical calculations from Sections 3.B and 3.C.
Fig. 6. Cartoon depiction of the stack of materials considered for a resonant cavity structure for thermal imaging. In order to achieve high reflectivity at the boundaries, the dielectric mirrors in the device considered are seven layers for the top mirror, and nine layers for the bottom mirror instead of the three-layer structure shown.
Table 2. Indices of Refraction and Extinction Coefficients for Materials Chosen for Resonant Cavity Structure in Fig. 4
B. Computational Results for Etalon-Based Thermal Imager
Utilizing the software mentioned in the previous section, plots of the transmitted intensity through the etalon as a function of wavelength were constructed (Fig. 7). Figure 7 shows the results for calculations which both include and ignore the extinction coefficients to confirm that losses are due only to absorption and not incorrect design choices for the dielectric mirrors and cavity structure. Following the discussion in Section 3.C, the probe wavelength was chosen by requiring the transmission to be equal to 0.5, which represents 75% of the maximum transmission. Then, utilizing the temperature dependence of the indices of refraction from Eqs. (3) and (4), the transmission through the device was plotted versus temperature (Fig. 8). This calculation was performed twice for light polarized such that it interacts with either the ordinary or extraordinary index. Over a 200 mK temperature range there was a 31% change in the transmission for and a 15% change in the transmission for ; the slope of the two curves have different signs because increases with increasing temperature while decreases. Respectively, this represents a and increase in sensitivity when compared to the device based on a direct birefringence measurement. However, the presence of distinct spectral peaks for both and make a differential measurement possible, which is a unique advantage of the etalon device. When a differential measurement is considered by subtracting the signal for from the signal for (Fig. 9), a 45% change in the signal is predicted over a 200 mK temperature range representing a increase in sensitivity when compared to the birefringence device.
Fig. 7. Transmission versus wavelength curves for the etalon device depicted in Fig. 6. Two distinct spectral peaks are present corresponding to light polarized such that it encounters the ordinary or extraordinary index. The darker curves correspond to calculations where the absorption of the materials was considered. The lighter curves correspond to calculations where the absorption was not considered.
Fig. 8. Transmission versus temperature curves for the etalon device depicted in Fig. 6 when light is polarized such that it encounters and . The probe wavelength for each measurement is given in parentheses in the legend.
Fig. 9. Transmission versus temperature for the etalon device pictured in Fig. 6 when a differential measurement is considered. The sensitivity of the device is enhanced by increasing the thickness of the resonant cavity.
The sensitivity of the device can be increased further by either increasing the reflectivity of the dielectric mirrors or increasing the thickness of the LC cavity. For a 470 nm thick cavity, Fig. 9 shows that a 45% change in the measured signal is expected over a 200 mK temperature range. In the case of a 940 nm cavity, Fig. 9 shows that a 45% change in the measured signal is expected over a 110 mK temperature range. Therefore, doubling the cavity thickness results in a increase in device sensitivity. This result agrees well with the analytical predictions in Section 3.C. Again, it is noted that doubling the thickness of the LC pixel increases the thermal response time from 7.75 ms to 11.6 ms.
C. Measuring Shift in Peak Wavelength
An alternative method for sensing the change in temperature of the LC pixel is to measure the shift in the peak wavelength of the transmitted light. Figure 10 shows the transmission spectrum for the etalon device at the extreme ends of a 200 mK temperature range. An advantage to this approach is that a broadband light source may be considered; measuring transmission requires a laser light source for narrow bandwidth. However, Fig. 10 shows that the shift in wavelength over this range is , which is approaching the resolution of commercially available spectrometers [16]. This approach for using a resonant device as a temperature sensor has been previously described; a similarly small shift in the peak wavelength of 0.373 nm/°C was determined [17]. Because of the increase in complexity and cost of the sensor required for this approach, only the transmission measurement is considered for further optimization.
Fig. 10. Transmission versus wavelength for the LC resonant cavity at each end of the 200 mK temperature range. The transmission peak is shifted by 0.116 nm for a 200 mK change in temperature.
D. Design Consideration—Probe Wavelength
Although 400 nm was chosen as the probe wavelength for the majority of calculations, the design can be easily generalized for other wavelengths by careful design of the dielectric mirrors. To demonstrate, the thickness of each layer in the dielectric mirrors was changed so that the optical path length was a quarter-wave for 550 nm (). Except for the thickness of each layer in the dielectric mirrors, nothing from the design in Fig. 6 was changed. The resulting device presented a transmission peak around 546 nm; at this wavelength the dielectric mirrors had a reflectivity greater than 0.98. The transmitted intensity versus temperature calculation in Fig. 11 shows that a 37% change in the transmission is expected over the 200 mK temperature range considered; this increase in sensitivity relative to the results in Fig. 8 can be attributed to the increased reflectivity of the dielectric mirrors. Therefore, the chosen probe wavelength of 400 nm is not inherent to the design and can be easily changed by appropriate design of the dielectric mirrors.
Fig. 11. Transmission versus temperature curve for a 470 nm thick cavity when the dielectric mirrors were designed to be highly reflective at 550 nm. The calculation was performed for light polarized such that it interacts with the extraordinary index of the LC; the wavelength for the calculation was 546.4 nm.
E. Design Consideration—Tolerance on Cavity Thickness
In Section 2.B, it was stated that over a 10 megapixel array of LC cavities, the variation in cavity thickness was found to be 6 nm. Therefore, in the worst case, the thickness of pixels near each other will vary by 6 nm. Using the probe wavelength of 400.8 nm defined in Fig. 8, transmission versus temperature curves were calculated for cavity thicknesses of 470, 469, and 464 nm to determine how different tolerances on the cavity thickness affect device performance. Figure 12 shows that cavities that vary from the designed thickness by 6 nm have lost almost all sensitivity; cavities that vary by 1 nm from the design thickness are half as sensitive.
Fig. 12. Transmission versus temperature curves for cavities of varying thickness when the top and bottom dielectric mirrors have seven and nine layers, respectively.
One way to ameliorate this problem is by decreasing the finesse of the device; this is accomplished by decreasing the reflectivity of the dielectric mirrors. This will result in broadened spectral peaks and relax the requirements on the tolerance for cavity thickness. Figure 13 shows transmission versus temperature curves when the number of layers in the top and bottom dielectric mirrors was reduced to three and five, respectively. Table 3 summarizes the results from Figs. 12 and 13. For lower reflectivity mirrors, cavities that vary by 1 nm exhibit a change in the absolute value of the transmission but little change in the overall sensitivity. The issue with the absolute value of the transmission should be easily solved through calibration of the device. With no LWIR radiation incident on the transducer array, the transmission through each pixel should be recorded. All measurements of transmission will then be made relative to this initial value. Unfortunately, the device with lower reflectivity mirrors offers an 8.6% change in transmission over the 200 mK temperature range compared to a 31% change in transmission for the higher reflectivity mirrors. However, this still represents a increase in sensitivity relative to the direct retardation measurement. Overall, process tolerances need to improve from current standards in order for this design to be applicable for a 10 megapixel array. Methods have been proposed for easing the requirements on device tolerances while maintaining an increase in device sensitivity compared to the ideal case for a device based on direct retardation measurement.
Fig. 13. Transmission versus temperature curves for cavities of varying thickness when the top and bottom dielectric mirrors have three and five layers, respectively.
Table 3. Summary of Results for %-Change in Transmission for Varying Reflectivity of Dielectric Mirrors and Cavity Thickness
F. Design Consideration—Air Gap Thickness
One way to simplify the fabrication of the device is to increase the thickness of the top air gap, eliminating the need to maintain the small 1 μm air gap between the dielectric mirror and cavity structure. Increasing the thickness of the air gaps to 5 μm results in a considerable sharpening of the spectral peaks, and a change in the device sensitivity might be expected. Including the air gaps, [Eq. (9)] can be rewritten as
Equation (12) represents a simplified analytical model of the device which ignores reflections at the interfaces between the air gaps, LC, and high-index materials. Plugging Eq. (12) into Eqs. (8) and (11) reveals that no change in the derivative with respect to the LC index of refraction is expected. Figure 14 shows that the numerical calculations for 1 and 5 μm air gaps confirm that no change in sensitivity is expected. This is an important result because it shows that this particular design parameter can be changed to ease fabrication without negatively impacting device performance.Fig. 14. Differential transmission measurement versus temperature for varying thickness of the top air gap. The first number in the legend refers to cavity thickness and the second to air gap thickness. The sensitivity is not affected by changing the thickness of the air gap.
5. SUMMARY AND CONCLUSION
Table 4 shows a summary of calculation results when the extraordinary index is considered for the birefringence device as well as the analytical and numerical calculations for the etalon device. It is shown that, when only the extraordinary peak is considered, a larger change is expected for the etalon device when compared to the birefringence device for the same pixel thickness. In Section 4.B it was demonstrated that an even larger gain can be achieved by utilizing a differential measurement. Table 4 also shows that discrepancies between the analytical and numerical calculations can be partly attributed to the absorptive losses of the system.
Table 4. Summary of Calculations Performed When Extraordinary Axis of the LC Material Is Considered
Importantly, Table 4 considers that there is no variation in cavity thickness across the transducer array. It was demonstrated that process tolerances can be relaxed by decreasing the reflectivity of the dielectric mirrors. Devices with the less reflective mirrors were demonstrated to be more sensitive than the analytical prediction for a direct retardation measurement.
Funding
Army Research Office (ARO) (W911NF-14-1-0650).
Acknowledgment
We thank ARO Program Manager Dr. Michael Gerhold.
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