1. Introduction

Over the last decades, devices such as optical shutters, variable optical attenuators and optical modulator technologies have seen an expansion with regards to optical communications networks, fiber optics and integrated circuit fabrication technologies [1–6]. Several technologies and designs for optical shutters range from micro shutter/cantilever arrays or matrices that block incoming light [7–9], thermally switched reflective mirror plates [10], to liquid crystal or dye based shutters [11,12]. Most of these optical shutter designs can be adapted to different systems such as spectrometers [13], reconnaissance cameras [14], high precision experimental instruments [15], sensor protection [16,17] and systems where optical fiber protection is required [18,19].

Different shutters are used for different applications and technologies. Mechanical shutters are commonly integrated in laser systems to control aperture or display systems [20,21]. They can also be adapted into bigger designs for temperature control purposes and thermal energy storage [22,23]. Electro-optical shutters can be substantially faster than their mechanical counterpart, with switching speeds in the range of $\mu$s’s [15,24]. Typically these shutters are integrated into systems for optical modulation of transmittance and reflectance [25,26], and frequency modulation [27]. Different materials, specifically phase change materials can be incorporated into the design of electro-optical shutters to further enhance the modulation capabilities of the device. Phase change materials such as germanium telluride (GeTe) have shown a transmittance modulation of around 70 % when integrated into an array of sub-wavelength gold slits filled with GeTe for a wavelength of 1550 nm [24,28,29]. Chalcogenide phase change materials with large changes in their optical constants have also successfully been shown capable of adaptive thermal control in the infrared region [30]. Naturally, phase change materials with a low transition temperature, ease of fabrication and low power consumption are desirable for smart material fabrication.

Vanadium dioxide (VO$_2$) phase transition was first observed by Morin more than 50 years ago. The material changes from insulator to metal due to a temperature change above 68$^oC$ [31]. This increase in temperature can be achieved either by direct heating (Joule heating, conductive heating) or light induced. The crystal structure of the material undergoes a monoclinic to tetragonal change [32,33] and several properties of the material such as mechanical [34], optical and electrical [35–37] change as well. This makes VO$_2$ an excellent candidate for different applications varying from infrared camouflage, smart coatings [38–41], smart windows [42], MEMS micromirrors [43] and electrical switches [44]. Due to VO$_2$’s intrinsic phase transition, modulation of optical transmittance is achievable and a considerable change in the optical properties is seen in the IR region [35,45,46]. Furthermore, the lower power input required for actuation due to its small temperature window, low phase transition temperature (68$^0C$) closest to room temperature (in comparison to GeTe that requires a temperature change above 200$^0C$) [24,47], memory capabilities and hysteresis, makes VO$_2$ a more practical material for applications with low-power operational requirements.

We have previously reported on the implementation of VO$_2$-based smart windows for programming of emissivity states, emissivity modulation and shape converting capabilities [38,39]. This work reports on the development of micrometer sized VO$_2$-based optical tunable shutters. The micrometer size devices are made of two structures. A VO$_2$-based cantilever with integrated resisitive heaters for actuation is fused to a VO$_2$-based optical window that can also be actuated via resistive heaters. By actuation of the cantilever, modulation of the transmitted power can be achieved like a normal mechanical shutter. Furthermore, actuating the optical window allows for modulation of the transmittance within the boundaries of the hysteresis. This in turn creates a tunable mechanical-optical shutter, no longer being a binary (0 or 1) shutter. To the best of our knowledge, this work is the first to successfully implement a mechanical and optical structure based on VO$_2$ to fully demonstrate its intrinsic optical tuning capabilities.

2. Results and discussion

Figure 1 shows the optical setup used for measurements and is explained in detail in the Experimental Section of this paper. Figure 2(a-d) shows the fabrication flow process and SEM images of the VO$_2$-based shutter and it is further explained in the Experimental Setup section. Thermal distribution images and thermal distribution simulation results are further discussed in Supplement 1 along with actuation videos. A table comparing the transmittance maximum and minimum, along with transmittance ratio, power consumption and switching time for various shutters and modulation devices is presented in Supplement 1.

 

Fig. 1. (a) VO$_2$-based optical shutter experimental setup. Blue, solid line represents the actuation current for the window. Red, dashed line represents the actuation current for the cantilever (tilt control). Black arrow represents direction of actuation upon Joule heating (figure is not to scale) . (b) Top close up view for the cantilever/window structure. Squares represent release holes for ease of etch. Orange, red and yellow spots represents where the beam is focused on the window as seen on (a).

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Fig. 2. (a) Fabrication flow process for the VO$_2$-based optical shutter. Cross-section views correspond to the dotted blue line shown in Fig. 2-d. (1) 500 $\mu$m Si wafer. (2) Deposition of a 1 $\mu$m layer of SiO$_2$ by PECVD. (3) Deposition of VO$_2$ layer by PLD. (4) Patterning and etching of VO$_2$ layer. (5) Deposition of a 300 nm layer of SiO$_2$ by PECVD. (6) Patterning and etching of second SiO$_2$ layer. (7) Evaporation and metal lift-off of Au/Cr layer. (8) Deposition, patterning, and etching of a 200 nm layer of SiO$_2$. (9) Structure release by XeF$_2$ etching. (b) Cross-section of the VO$_2$ based cantilever showing the top and bottom SiO$_2$ layer thickness and VO$_2$ layer thickness. (c) Side angle view for a released VO$_2$ based shutter (d) Top view SEM image for an un-released shutter. Dotted lines represent cross-section cuts.

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2.1 Performance of VO$_2$-based tunable optical shutters

Figure 3(a) shows the transmittance of the VO$_2$ window as a function of the actuation current of the window (bottom x-axis) and cantilever current (top x-axis). Actuating the resistive heater trace around the window results in a single hysteretic loop with a transmittance drop of 23% across the phase transition. This is achieved by focusing a beam spot with a diameter of $\sim$ 80 $\mu$m around one of the quadrants of the window, between two release squares. The purpose of this is to avoid the beam spot shining into one of the release squares of the window (see orange spot in Fig. 1(b)), which will cause the beam (or part of it) to travel through free-space and not provide a measurement of the transmittance through the window. A transmittance drop of 23 $\%$ ( or greater) for VO$_2$ at a wavelength of 1550 nm is on par with previous reported results as seen in [38,39,48]. Actuation of the metal traces of the window will result in some curving of the window structure, due to structural changes in VO$_2$ films during its phase transition [49,50]. As a result of this, the beam spot was placed either on the left or right side of the center of the window (shown as an orange spot in Fig. 1(b)) so that the position of the beam stays inside the window during actuation. Throughout the window-heating experiments, the beam spot moved along the window surface, avoiding the release holes (refer to Visualization 1 for a visual guide). This was validated through preliminary experiments, and was done to obtain reliable measurements of the transmittance changes across the window only (and not through free-space outside the window or release holes). If the beam spot is located close to the edge of the window, then during the experiments, the only action that would remove the window from the beam path is the actuation of the cantilever structure. When the actuation current signal is sent to the cantilever metal trace, the structure bends, creating an actuation mechanism that resembles that of a mechanical shutter (tilt control mechanism). Upon enough cantilever actuation, the window is driven away from the beam path, causing the transmittance to increase, since the beam travels through free-space at this point. A current below 6.7 mA for the cantilever was selected to avoid any damage to the metal traces and window structure. For an actuation current of 6.7 mA, an increase of 21 % was observed (see Fig. 3(a)). During the cantilever actuation, the increase on transmittance is purely from the change in position of the window with respect to the beam spot and is not affected by any effects that the input current might have on the window structure. Since the heat distribution from the cantilever is not enough to reach the top edge of the window, this cantilever actuation will not induce a change of phase in the window (refer to thermal images in Supplement 1). It should be noted that the measured transmittance that corresponds to free-space is about 92 %. This 8% loss is attributed to a small portion of the beam profile still being blocked by the window, even after full cantilever actuation. For the cantilever actuation experiments, the beam spot is placed around the top edge of the window (red spot in Fig. 1(b)), in order to maximize the free-space beam path upon cantilever actuation. As the current input signal is sent, the cantilever structure moves downward. While this actuation is active, the beam spot will start to move upward with some part of the beam being in free space and the other part being blocked by the structure. However, even after full cantilever actuation, the edges of the beam spot could still be in contact with the edge of the window, resulting in some power loss as seen from the detector (refer to Visualization 2). The power measured by the photo-detector in free-space without the focusing lens was around 0.232 mW, and the power measured just before the shutter was 0.163 mW. The transmittance ($T$) is calculated as the ratio of the power measured before the window ($P_0$) and after passing through the window ($P$) (i.e. $T$=$P/P_0$). For measurements where both the window and cantilever are actuated, the beam spot is lower in order to accommodate space for the beam spot to stay over the window’s surface during the actuation of the window traces. This in turn resulted in a lower initial value for the transmittance. Figure 3(b) shows the transmittance drop of the window due to the actuation of the window traces with a transmittance drop of 28 %. Once the hysteresis reaches around 0.32 of transmittance, the cantilever heater is actuated with a current step of 6 mA. This actuation causes a deflection of the device, which in turn takes the beam spot out of the window. A transmittance increase of 37 % is followed by a similar drop once the actuation current step is no longer supplied to the cantilever traces. The transmittance then follows the cooling hysteretic loop and comes back to the initial 0.61 value (refer to Visualization 3 for actuation video). Since the hysteresis of the window is being measured, the beam spot must be placed around the sides of the middle release square of the window or higher (yellow spot in Fig. 1(b)). The beam spot will be driven to the edge of the window by the actuation of the window traces. Once the heating curve for the window is recorded (reaches a value of 31%), the cantilever is actuated (tilt control) with the current step ($i$= 6 mA), resulting in an increase of transmittance. Since the window moves downward upon actuation of the window traces, and the beam spot moves upward, the beam might experience some blockage by the window’s top edge when the cantilever is actuated. This results in an increase of transmittance, but not one as high in comparison to the one where only the cantilever traces are actuated. Another factor that could lead to some variance on the initial values of transmittance is due to the curvature of the window, due to the intrinsic stress of the structure, the VO$_2$ window is not a flat surface and possess some curvature. Other factors include the variance of the VO$_2$ material across the window structure.

 

Fig. 3. Transmittance Measurements upon actuation of window and/or cantilever: (a) Steady-state transmittance results for separate actuation; i.e. actuation of resistive heaters for window or cantilever (tilt control). (b) Results for window actuation, followed by cantilever actuation with a current step of 6 mA. Insert shows the current actuation step supplied to the cantilever traces. (c) Transmittance minor loops due to actuation of the window heater. Insert shows the voltage input used to trace the minor loops. (d) Results for cantilever actuation (with a current step of 6 mA) after partial actuation of the window (x-axis). Dashed lines represent the transition points where the cantilever was actuated. Solid lines represent overall transmittance change. Legend shows the voltage/current point during the window hysteresis where the current step was applied.

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By taking advantage of VO$_2$’s intrinsic phase transition, programming of transmittance states can be achieved. Figure 3(c) shows the hysteretic minor loops for the VO$_2$ while the window heater is actuated. A current pulse (not the same pulse used for the modulation section.) is programmed with not enough amplitude to completely transition across the hysteresis loop. This will cause the phase transition to return through one of the minor loops inside the hysteresis. The minor hysteretic loops cover a transmittance range from 51% to 29%, thus allowing for the programming of any transmittance state as long as it is within the bounds of hysteresis. Figure 3(d) shows transmittance of the VO$_2$ window while both heaters are independently actuated. First, the window heater is actuated up to a certain point during the transition (e.g. 7.6 mA, red curve on Fig. 3(d), marked by red dashed line), which marks the trigger point for the actuation of the cantilever (tilt control) with a current step of 6 mA (same one shown in Fig. 3(b) insert). Once the cantilever current step is applied at the trigger point, a sudden increase in transmittance is measured (13% for the case of the 7.6 mA –see Fig. 3(d)). This is done for several points across the phase transition (actuation step for tilt control is marked by dashed lines on Fig. 3(d) and overall transmittance change is marked by full lines), with transmittance changes due to the actuation of the cantilever ranging from 13% to 45%. This successfully demonstrates the tunable capabilities of the optical shutter.

2.2 VO$_2$-based electro-optical tunable modulator

Since VO$_2$ intrinsic phase transition allows to program optical states within the hysteresis, then modulation of the optical signal is viable within the boundaries of the phase transition. Optical modulation usually involves a light beam that can be modulated by varying the current that is used to driving it, or a material that will act as a light modulator to either manipulate the phase, amplitude or frequency of the input beam [51]. Applications for such modulators range from power modulation for high speed communications to pulse laser generation [52]. Figure 4(a) insert shows the input current (sinusoidal wave) required for optical modulation of transmittance for the VO$_2$ window (no current input was sent to the cantilever traces). A pre-heating current of i$_{ph}$= 10.5 mA is sent to the window heater. This value of current is specifically chosen to be at the onset of the phase transition. This in turn will allow a better monitoring of the transmittance drop (T$_{ph}$= 0.52) when the pulse is sent. The pulse used for modulation has an amplitude of V$_{Amp}$= 1 V (i=2.7 mA) and a frequency of f$_{el}$= 0.28 Hz. These values where chosen to facilitate data acquisition and to avoid any damage that higher frequencies could do to the window/cantilever structure. Figure 4(a) shows the modulated transmittance for the VO$_2$ window as a consequence of the sinusoidal electrical input sent via resistive heaters. Once the input is sent, an initial drop of 22% is seen, followed by the transmittance being modulated between 0.43 and 0.31. It can be noted that due to the sinusoidal input, the transmittance will follow a behavior that can be described as T$_{Modulated}$ = T$_{Amp}$ sin($\omega$t), with a transmittance modulation of 14 % and a transmittance ratio of 1.38. Figure 4(a) shows the minor hysteretic loops for the VO$_2$ window with the marked values for preheating current and limits of modulation. Once the initial pulse is sent, the transmittance will follow through out the main heating loop and return through the cooling main loop. While the modulation continues, the transmittance will follow one of the minor heating loops from 0.43, and return through one of the cooling loops to 0.31 respectively. Since VO$_2$ is a phase transition material and possess an intrinsic hysteresis with a change in its optical and electrical properties [36], the frequency response of the system will follow a non-linear response. By taking the average output power from the optical window due to the input current,and taking a Fast Fourier Transform, a more in-depth analysis of the output frequency can be accomplished. Figure 4(c) shows the FFT for the input current (Fig. 4(a) insert) and the FFT for the output power from the optical window as measured by the optical detector within the range of 0 Hz to 2.5 Hz. An initial peak at f$_{Tr}$=0.28 Hz can be observed on both plots, which corresponds to the input frequency used for modulation (f$_{el}$= 0.28 Hz). Second peak and third transmittance frequency peaks are found at two and three times the initial frequency, respectively – i.e. 2 $\times$ f$_{Tr}$= 0.56 Hz and 3 $\times$ f$_{Tr}$= 0.84 Hz for the output power. In order to verify the effects of VO$_2$’s non-linearity on the input signal, the total harmonic distortion (THD) was obtained from the amplitude FFT for both the input and output signal (refer to Supplement 1 for FFT plot). A total THD of 4.07% (-27.7 dB) was calculated for the input current signal and a THD of 14.10% (-17.01 dB) was obtained for the output signal. A total 10 % distortion is attributed to VO$_2$’s intrinsic phase change (refer to Supplement 1 for the calculation of THD).

 

Fig. 4. (a) Transmittance minor loops due to actuation of the window heater. Red lines represents limits of voltage values used for modulation. Green line represents the current value used at the onset of the phase transition. Insert shows the input current for modulation. A preheated current of 10.5 mA (4.2 V) is hold on the device (onset of phase transition), then a sine wave with an amplitude of 1 V and frequency of 0.28 Hz is sent. (b) Modulated transmittance of the optical window due to the current input. (c) FFT for input current and output power for the VO$_2$ optical window.

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A similar modulation along the phase transition is shown for the VO$_2$ based optical window ($i_{Cantilever}$= 0 mA). This is done to demonstrate the higher change of transmittance and modulation within the hysteresis minor loops. Figure 5(a) shows the current input while the amplitude and frequency are kept fixed and the DC offset is modulated. For the purpose of this experiment, the DC offset is started at the onset of the phase transition (4.2 V, 10.5 mA) and its modulated by steps of 0.2 V (0.6 mA) until reaching the end of the transition at 5.6V (14.7 mA). The DC offset is then swept along the minor loops (Fig. 3(c)) driving it across the phase transition. Once the maximum DC offset is reached, it is swept back to the initial value and it follows the cooling hysteretic minor loops. Figure 5(b) shows such response due to the modulation of the DC offset effect on the transmittance of the device. As the DC offset is increased, a greater change in the modulation of the optical signal is observed, A change that can be noted by the slope and width of the minor loops hysteresis curve in Fig. 3(c).

 

Fig. 5. (a) Input current with modulated DC offset and constant voltage amplitude with an input frequency of 1 Hz. Modulation is done for both heating and cooling cycles with an increment on the DC offset of 0.2 V (0.6 mA). (b) Transmittance with modulated DC offset and constant voltage amplitude (0.7 V) with an input frequency of 1 Hz. Transmittance is modulated for both heating and cooling cycles and it starts at the onset of the PT at 4.5 V or 10.5 mA.

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3. Conclusion

VO$_2$-based MEMS optical shutters with continuous (or analog) transmittance tunability have been demonstrated. The optical shutters are based on the design of VO$_2$ cantilevers and VO$_2$ based optical windows with integrated resisitive heaters for independent actuation. Using a wavelength of $\lambda$= 1550 nm, a transmittance drop of 23% along the hysteresis is shown while actuation of the optical window occurs. Furthermore, by actuating the VO$_2$ based cantilever, a shuttering effect is achieved with a transmittance increase of 32%. While actuating both the window and cantilever traces, the transmittance change is no longer limited to the constraints of the hysteresis of the optical window and can be further tuned with the incorporation of the cantilever actuation. This modulated shuttering effect makes it tunable and no longer a binary shutter (0 or 1 outcome). A modulation of around 37% of transmittance is achieved for a wavelength of 1550 nm. Previous shutter technologies such as cellulose-based nano and microfiber thin films and cholesteric liquid crystal films [53,54], have successfully shown and on/off state of transmittance. Since no phase-change material is used, then this type of optical shutter is limited to either a 1 or 0 state. In comparison to a VO$_2$-based shutter, that introduces an intrinsic phase change thus providing tuning capabilities at a transition temperature ($T_{PT}$= 68 $^oC$) close to room temperature. Transmittance modulation of the optical window was demonstrated by using a sinusoidal current input with a frequency of 0.28 Hz. By using a preheating current to drive the transmittance until the onset of the phase transition, a modulation of 14% is achieved. Likewise, a modulation along the whole of the phase transition hysteresis loop of the VO$_2$ window is shown with a modulated input with fixed amplitude and frequency. By modulating the DC-offset in steps of 0.2 V (0.6 mA), the transmittance was modulated for both heating and cooling cycles. As the DC offset was increased, an increase on the change of the transmittance modulation was obtained with an overall change in transmittance of 21%.

4. Experimental

4.1 Device fabrication

The electro-mechanical-optical shutter device design consists of a combination of VO$_2$ optical windows [38,39] and VO$_2$-based MEMS actuators [49], where the window was added to the end of the cantilever structure. Separate resistive heaters allowed for individual actuation of the cantilever structure and the optical window; i.e., a resistive heater along the cantilever was used for controlling the mechanical position of the shutter device (Fig. 1(a), red, dashed line); while a separate heater around the window was used for controlling the optical properties of the window (Fig. 1(a), blue, dashed line). The fabrication process of the MEMS VO$_2$-based optical shutter devices is shown in Fig. 2(a), and discussed next. The cross-section 2D diagrams corresponds to the dotted, blue line shown on Fig. 2(d). A 1 $\mu$m layer of SiO$_2$ was deposited via PECVD at a temperature of 250 $^oC$ on a 500 $\mu$m thick Si wafer. This was followed by approximately 160 nm of VO$_2$ (confirmed by SEM pictures) by PLD (Pulsed Laser Deposition) using a KrF laser which operated at 10 Hz and a fluence of $\sim$ 2 J/cm$^2$ for 25 minutes and a $O_{2}$ pressure of 20 sccm. During deposition, the substrate was heated by a ceramic heater located behind the substrate, kept at a temperature of 595 $^oC$ during the 25 minute deposition, and a 30-minute post annealing step at the same deposition conditions. Patterning and etching of the VO$_2$ layer was performed and followed by a 300 nm layer deposition of SiO$_2$ (done in 3 steps of 100 nm at 225 $^oC$, each to reduce the amount of voids in the layer). After patterning and etching the SiO$_2$ layer, metallization and lift off of a Au/Cr film (180 nm/ 20 nm) was completed. A final encapsulating layer of SiO$_2$ (200 nm) was deposited at a temperature of 225 $^oC$. This was followed by dicing of the wafer into individual dies that contained two identical optical shutter devices. After dicing, the devices are released via isotropic etching of the silicon substrate using XeF$_2$ gas. The final device consisted of cantilevers with length and widths of 750 $\mu$m x 80 $\mu$m, respectively; and square (650 $\mu$m$^2$) optical windows. The cantilever heater length and width are 700 $\mu$m x 4 $\mu$m, with the window heater that runs along the length of the cantilever and start of the window being 800 $\mu$m x 16 $\mu$m respectively. Similarly the circular heater inside the window has a diameter of 600 $\mu$m and a width of 16 $\mu$m. For ease of release during the XeF$_2$ etch, each window a total of nine release squares with dimensions of 80 $\mu$m x 80 $\mu$m. Figure 2(b-c) and d shows SEM images (JEOL 7500F) of the VO$_2$-based optical shutter (before and after release), coated with a thin layer of osmium (10 nm) using a NEOC-AT osmium CVD coater (Meiwafosis Co., Ltd.), this conductive coating is necessary to avoid charging and to improve the secondary electron signal for the SEM furthering improving the image [55]. Figure 1(b) shows a magnification of the cantilever structure, where two pairs of traces are identified: the wider pair runs to the window and is used to heat the window square; while the other one corresponds to the cantilever heater, used to heat and actuate the cantilever structure. A VO$_2$ gap of 15 $\mu$m between the cantilever structure and window was also implemented on the design. This is done to minimize the heat distribution between the cantilever and window upon actuation of the metal traces. The SEM cross-section image is taken after cutting a single unreleased die perpendicular to the cantilever (dotted red line on Fig. 2(d)). From the cross-section, the measured thickness for the bottom SiO$_2$, middle VO$_2$ and top SiO$_2$ are 1.33 $\mu$m, 160 nm and 200 nm, respectively.

4.2 Experimental setup

The electro-optical setup used to test the VO$_2$-based optical shutter is similar to the one used for experimentation in [38,39] and is shown in Fig. 1(a). A die containing the device is wire-bonded to a IC package which is then mounted on a solderless breadboard with the required electrical connections for actuation of both heaters. A 980 nm laser diode (Thorlabs, L980P010) with a focused diameter of approximately 80 $\mu$m, an operating current of 30 mA and coupled into an optical fiber is used to align the beam spot in the area of interest in the VO$_2$ window and photo-detector (S144C, Thorlabs) which is connected to a power meter (PM100D, Thorlabs) with a sampling rate of 100 Hz. In order to align the beam spot, a ccd camera (Sony CCD-IRIS Hyepr HAD B&W CCTV) is used. Once the beam spot is aligned, a 1550 nm laser diode (Thorlabs, ML925B4SF) operated with a current of 15 mA and coupled into the optical fiber is used for measurements. Actuation of the device is done via Joule heating by passing a current through the heaters (represented by dashed red and solid blue lines in Fig. 1(a)), which was computer-controlled and -monitored via a virtual instrument and data acquisition (NI USB-6001) tool. A limiting resistance ($R_{L}$ = 325 $\Omega$) connected in series with the heaters of the device is used to prevent overheating on the thin metal resistive heaters, due to voltage spikes in the applied signal. For experiments where both heaters need to be actuated at the same time, the window heater current was computer controlled (NI USB-6001, data acquisition tool) and the cantilever heater was manually controlled with a step input provided by a power supply. For window actuation only, the voltage input signal will go from 0 to 7 volts (0 mA to 15.7 mA) in steps of 0.1 V with a holding time of 500 ms. For the cantilever transmittance measurements, the voltage input signal was programmed to go from 0 to 3.5 volts in steps of 0.1 V and a holding time of 500 ms. For measurements where both the window and cantilever are actuated, the voltage input signal was programmed from 0 to 7.5 volts (0 mA to 16.5 mA) in steps of 0.1 V and a holding time of 500 ms. The extra voltage steps where used to accommodate the actuation of the cantilever with the supplied current step (6 mA). This is followed by the voltage returning to 0 volts following the same rate for all cases. While the input voltage is applied, the computer software will convert the input to current and each current point will be associated with a power value that comes from the photo-detector. In order to calculate the transmittance value, the power before the window is measured and is inputted into the computer software. The calculated transmittance is then plotted as a function current.