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Evaluation of 3D printed optofluidic smart glass prototypes

Open Access Open Access

Abstract

Smart glass or smart windows are an innovative technology used for thermal management, energy efficiency, and privacy applications. Notable commercially available smart glass relies on an electric stimuli to modulate the glass from a transparent to a translucent mode of operation. However, the current market technologies, such as electrochromic, polymer dispersed liquid crystal, and suspended particle devices are expensive and suffer from solar absorption, poor transmittance modulation, and in some cases, continuous power consumption. The authors of this paper present a novel optofluidic smart glass prototype capable of modulating visible light transmittance from 8% to 85%.

© 2017 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

Until recently, most building envelope elements have been static and unresponsive to changes in season, solar radiation, and temperature. However, with the emerging market of energy efficient technologies, the push for kinetic and adaptive building envelopes has become increasingly important. Conventional windows in the United States account for approximately 30% of a building’s heating and cooling load, resulting in an annual impact of 4.1 Quads of primary energy [1]. A typical single pane window will transmit a large quantity of the solar spectrum and absorb a significant fraction of long wave radiation yielding an undesirable increase in air conditioning loading [2]. Smart windows are a relatively new form of energy efficient technology capable of generating energy savings above 30% by modulating solar energy transmittance [3]. Switchable glass or smart windows are devices capable of modulating light transmittance when voltage, light, or heat is applied. These devices allow for the state of the glass to switch from transparent to translucent, or vice versa. This transition can occur passively or actively depending upon the device technology. Currently, there are three types of technologies used in commercially available switchable glasses: chromic materials, liquid crystals, and electrophoretic or suspended particle devices. Chromic devices can be divided into four categories: electrochromic, gasochromic, photochromic, and thermochromic, with the latter two responding automatically to changes in light and temperature, respectively [4]. Despite a rise in market adoption, cost and intricate manufacturing processes still remain a challenge for the smart glass industry.

An electrochromic (EC) material is able to change its optical properties when a voltage is applied across it. A typical design for electrochromic windows consists of five thin film layers on a single glass pane or sandwiched between two glass substrates. In between two transparent conductive films is a counter electrode layer for ion storage, an electrolyte layer for conducting ions, and an electrochromic electrode [5]. As shown by Fig. 1(b), when ions are in the passive counter electrode, light is able to pass through the device. Applying a voltage across the five layers causes ions and associated electrons to transfer from the counter electrode to the electrochromic electrode, Fig. 1(a), resulting in decreased light transmittance [6]. Visible light transmission in commercially available electrochromic windows can vary from 3.5% to 62% depending on their operating state [2]. Drawbacks to electrochromic windows include high solar absorbance in devices using absorbing polymers, scalability issues in manufacturing, prolonged switching times as cycling increases, and high capital cost averaging $540 – $1,080/m2 [7–9].

 figure: Fig. 1

Fig. 1 Comparison of leading commercial smart glass technologies, (a) EC light blocking state, (b) EC light transmitting state, (c) SPD light blocking state, (d) SPD light transmitting state, (e) PDLC light scattering state, (f) PDLC light transmitting state.

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Suspended particle devices (SPD) consist of a suspension of fine particles that are strongly absorbing when no voltage is applied in the “off” state, Fig. 1(c), but align to an applied electric field in the “on” state leading to transparency, Fig. 1(d) [10]. Additionally, when operating in the transparent state, the device requires continuous application of an electric field with an associated power consumption of 5 Watts/m2 [11]. Light transmission values range from about 0.5 – 12% in the dark state to 64 – 80% in the clear state [12]. Development of suspended particle devices has been slowed due to a number of technological problems including long-term stability, cyclic durability, particle settling, agglomeration, and gap space control for larger glazing [3].

Polymer dispersed liquid crystal (PDLC) devices consist of micron-sized liquid crystalline (LC) droplets, dispersed uniformly in a polymer matrix. As shown by Fig. 1(e), when the crystals are randomly oriented, light is scattered. When the device is switched on by applying an electric field across the film, the molecular directors in the LC droplets are reoriented to match their ordinary refractive index with the refractive index of the polymer, Fig. 1(f), making the film transparent [13]. In the off state, PDLC devices rely on backscattering to reduce solar gain. However, as the wavelength of light increases, the backscattering effect is reduced, resulting in low transmittance modulation of 50 – 80% between the off / on states [14, 15]. Similar to SPDs, the transparent state requires a continuous electric field, with an average power consumption of 20 Watts/m2 [16]. Furthermore, the high cost of PDLC glazing, averaging $750 – $950/m2, and long term stability issues have continued to be a problem for market adoption.

Electrochromic, suspended particle devices, and polymer dispersed liquid crystal devices all rely on transparent conductors (TC) to alter their operating modes. The most commonly used TC is tin-doped indium oxide In2O3(Sn) (ITO), but the supply and rarity of indium is struggling to meet demand with the average cost around $1,000/kg [4]. In addition to high material cost, TC films are subject to hazing, and scattering losses which reduce the overall optical transmittance [17]. Large-area production and scalability are additional technological challenges for TC film manufacturing.

2. Optofluidic smart glass

Utilizing 3D printed geometric optics and the concept of refractive index matching, the optical transmission, reflection, and absorption can be tailored. The principle working mechanism of the proposed devices utilize total internal reflection between the material-air interfaces. Light incident upon a repeating pattern of corner cube reflectors reflects light back to the source (retroreflection). Filling the interstitial space with a fluid results in increased light transmittance. As the refractive index of the fluid increases to that of the surrounding material, refraction decreases, and specular transmittance increases. Thus, the device presented is capable of modulating reflectance and transmittance and offers the optimum solution to tailoring solar loads for increased heating, ventilation, and air conditioning efficiency. Additional applications of this type of optofluidic device presented include privacy panels, dynamic camouflage, and architecture.

A device capable of variable transmittance utilized the corner cube design by patterning it in the x and y directions. Fabrication of the device was done on an Objet30 Pro by Stratasys utilizing the photopolymer, VeroClear. VeroClear is a transparent 3D printed material having a refractive index of 1.52 at 589 nm and minimal absorption throughout the visible electromagnetic spectrum [18]. Figure 2 shows the device which measures approximately 54 mm × 55 mm. The corner cube reflector sheet measures 6.50 mm in height, with a 2 mm back plate for a total height of 8.50 mm. Prototyping the corner cube on the 3D printer indicated the optimum size was with a side wall of 4 mm. As the geometry reduces in size, printing defects increase and resolution decreases. Between the pattern and back plate is an interstitial space for fluid to be pumped. As shown by Fig. 3, this patterned design allows normally incident light rays to be reflected back at the source due to the refractive index difference at the material-air interface. Introducing a fluid into the cavity results in increased light transmittance.

 figure: Fig. 2

Fig. 2 Schematic view of variable transmittance prototype

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 figure: Fig. 3

Fig. 3 Operating modes of variable transmittance device, (left) air - reflective, (middle) water - diffuse transmittance, (right) index matched - specular transmittance.

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3. Spectral performance

Experimental testing to determine the spectral properties of the devices was carried out using the spectrophotometer setup at the University of Delaware Institute of Energy Conversion (IEC). The setup consisted of a PerkinElmer LAMBDA 750 UV/Vis/NIR spectrophotometer with a 60 mm integrating sphere accessory. This particular model has a tungsten-halogen and deuterium interface and an operating range of 190 – 3300 nm. Tests were performed over the wavelength range of 200 – 2500 nm, with 1 nm intervals at a scan speed of 284 nm/min. For transmittance measurements the prototyped device was placed on the light entrance port with the reflectance standard plate in place, Fig. 4(a). For reflectance measurements, the reflectance plate standard was removed and the prototyped device put in its place, Fig. 4(b).

 figure: Fig. 4

Fig. 4 Spectrophotometer setup/model for theoretical simulations and experimentation, (a) total transmittance measurement, (b) total reflectance measurement.

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3.1. Validation of theoretical model

To validate the theoretical model, ray tracing simulations in LightTools were benchmarked against spectrophotometer measurements. A 4.65 mm thick slab of VeroClear was tested using the spectrophotometer and integrating sphere accessory. Experimental transmittance (τ) and reflectance (ρ) measurements are shown in pink in Fig. 5. Data plotted in Fig. 5(a) and Fig. 5(b) indicates the theoretical model fits well with the experimental measurements. The percent difference between the theoretical and experimental transmittance is 8.3% for 200 – 2500 nm and 6.7% for 400 – 2500 nm. Percent difference for the theoretical and experimental transmittance data is 3.5% for 200 – 2500 nm. Here, it is assumed the spectrophotometer measurements are the accepted values for τ and ρ, with the theoretical simulations as the experimental value. Thus, the percent error is 7.7% and 2.9% for the ρ and τ data sets, respectively. We conclude this is low enough error to use the theoretical model as a template to develop more optimized prototypes.

 figure: Fig. 5

Fig. 5 Theoretical and experimental spectral properties of 4.65 mm thick VeroClear slab (a) transmittance, (b) reflectance.

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3.2. Device performance

Variable transmittance device prototypes were filled with air, water, and methyl salicylate. For these experimental tests, methyl salicylate was selected as the index matching fluid because of its low cost, low viscosity, and high refractive index similar to that of VeroClear. Each fluid filled device was tested experimentally on the spectrophotometer according to the test specifications previously outlined. Theoretical simulations were also executed and were compared to the experimental results. The device exhibits the physical phenomenon of retro-reflection, therefore, corrections to the theoretical model were made to make projections of the actual reflectance and transmittance. Additionally, the effects of surface roughness were also investigated.

Initially, the device was simulated with zero surface roughness and air in the interstitial space. This was considered the “ideal” or theoretical maximum device performance for the reflecting mode of operation. Light in the simulated model was normally incident upon the device using the modeled integrating sphere setup. As shown by Fig. 6, simulating the device with no light scattering effects results in no transmittance, with the reflectance of the device being driven by the material absorption. This high reflectance is due to total internal reflection taking place between the material-air interfaces. However, with the experimental setup, the device is angled at 8° for reflectance measurements. The off-axis placement for total reflectance measurements was a constraint of the integrating sphere accessory on the spectrophotometer. Thus, the theoretical model was adjusted so that the device was angled at 8°, Fig. 7(a). With this correction, we see that a significant amount of light exits the integrating sphere due to retroreflection, Fig. 7(b). In this case, the integrating sphere is only seeing the specular reflectance from the material surface, as indicated by the pink line. The cyan line represents the amount of light exiting the port (retroreflection) and not being measured by the integrating sphere. The black line represents the sum of these two quantities. Thus, we can infer that the maximum reflectance we will see in a reflectance measurement made on the spectrophotometer is given by the black line in Fig. 7(b).

 figure: Fig. 6

Fig. 6 Ideal reflectance and transmittance of variable transmittance device prototype.

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 figure: Fig. 7

Fig. 7 (a) Theoretical model setup of integrating sphere with device angled at 8° and no surface roughness, (b) simulated reflectance captured by the model integrating sphere (pink), exiting the integrating sphere port (cyan), and total reflectance (black).

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One of the main drawbacks to prototyping the devices on a 3D printer is surface roughness caused by the layer-by-layer deposition in the fabrication process. Surface roughness causes light scattering which can occur diffusely and specularly. Therefore, to accurately account for the effects of surface roughness, the theoretical model was adjusted using a customized scattering model in LightTools. In addition to the optical properties of a material, LightTools allows the user to specify surface properties. When a light ray strikes the surface, a percentage of the power carried by the ray can be absorbed or reflected. Surface absorption was assumed to be zero, with 100% of the power propagating. Light that is propagating at the material surface is then split fractionally according to the Fresnel equations. The reflected and transmitted power quantities can then be split into diffuse, P(θ)Diffuse, and specular, P(θ)Specular, components. Both are functions of angle, θ, from the normal axis. The breakdown of diffuse and near specular reflectance and transmittance was determined via experimentation. Diffuse and specular ρ and τ were measured for a slab consisting of a polished planar surface, and a glossy surface containing roughness. However, this only serves as an approximation as the surface roughness increases with print angle when 3D printing with VeroClear [19]. Experimental measurements yielded a 1% and 99% diffuse and near specular component for ρ, respectively. Transmittance measurements yielded a 6% and 94% diffuse and near specular component for τ, respectively. The power distribution and spread for each component is computed by Eq. (1) and Eq. (2), where θ is the angle from the normal axis, and σ represents the degree of power spread for the specular component. The diffuse component is modeled after Lambert’s cosine law. The Gaussian for the near specular components was adjusted until the model fit experimental data. A 5.25° σ was selected for the transmitted specular component and 10° spread for the reflected specular component.

P(θ)Diffuse=P0Diffusecos(θ)
P(θ)Specular=P0Speculare[(12)(θσ)]
Theoretical results from incorporating scattering effects can be seen in Fig. 8(a), where the pink line represents the light reflected into the model integrating sphere, cyan represents the light reflected out the port of the integrating sphere, and the black line represents the total reflectance or sum of these two quantities. This data represents the theoretical minimum and maximum, and a boundary that the experimental data should fit. As shown by Fig. 8(b), the measured reflectance of the device lies between the two reflectance curves. Thus, the theoretical model can be validated by the experimental data. Furthermore, a theoretical model containing a modified integrating sphere capable of capturing all scattered light could now be used to determine total reflectance at normal incidence. The projected reflectance at normal incidence is shown in Fig. 9. Although the testing apparatus is unavailable at university facilities, ASTM E1175-87(2015) or ASTM E1084-86(2015) could be used to more accurately determine reflectance at normal incidence. It is noted the only testing apparatus available involved the use of ASTM E903-12.

 figure: Fig. 8

Fig. 8 (a) Simulated reflectance captured by the model integrating sphere (pink), exiting the integrating sphere port (cyan), and total reflectance (black), (b) experimental reflectance of variable transmittance device plotted against theoretical maximum and minimum reflectance computed by the software.

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 figure: Fig. 9

Fig. 9 Experimental reflectance measured at 8° and theoretical reflectance adjusted for normal incidence.

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Transmittance simulations and experimentation were more straightforward because angular effects were not involved. As shown by Fig. 10(a), the device can be placed in front of the light entrance port of the simulated integrating sphere. Results plotted in Fig. 10(b) indicate the theoretical model fits well with experimental data taken with the spectrophotometer.

 figure: Fig. 10

Fig. 10 (a) Theoretical model setup of integrating sphere with device positioned for transmittance simulation, (b) experimental and theoretical data of normal transmittance for air filled variable transmittance device.

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The following plots were generated in the same manner as the air filled device. Figure 11(a) and Fig. 11(b) show the ρ and τ of the device when filled with water. Given the low Fresnel reflection between the material-water interfaces, it is expected that the device perform similarly to an index-matched device. The higher experimental transmission for water is most likely an artifact of the positioning of the photodetector in the integrating sphere. Light refracted by the water filled device surface results in a higher apparent reading. The theoretical model provides a more accurate depiction of the spectral properties of the water filled device. Figure 11(c) and Fig. 11(d) show the ρ and τ of the device when filled with methyl salicylate. As can be seen by the transmittance plots, Fig. 10(b) and Fig. 11(d), the device is capable of modulating visible light transmittance from 8% when filled with air to 85% when filled with methyl salicylate.

 figure: Fig. 11

Fig. 11 Theoretical and experimental ρ and τ plots of 3D printed device prototypes with different fluids, (a) ρ water filled, (b) τ water filled, (c) ρ methyl salicylate filled, (d) τ methyl salicylate filled

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4. Cycling performance

An important characteristic of a switchable glass is its ability to switch between states without degradation or deterioration of device performance [20]. To test the switching performance of optofluidic smart glass a small scale pumping station was constructed and operated for 1,000 cycles while the visible light transmittance was measured simultaneously. Two relay timers controlled two TCS Micropumps which enabled the device to be filled with an index-matching fluid, 2,2′-Thiodiethanol (TDE), for 35 seconds, and drained to an empty state for 20 seconds. Transition times between states took approximately 10 seconds for a steady state reading to be achieved. However, this is a function of pump flow rate and fluid properties and is subject to change. The pumps have a maximum flow rate of 1,150 ml/min with power consumption of 5.8 Watts. However, given the high viscosity of TDE, this flow rate was significantly reduced. As shown in Fig. 12 a black box enclosure was used to mount the light source, sensor, and block out unwanted ambient light that may have interfered with the intensity measurements. The light source used was a Dolan-Jenner (Model 180) illuminator, with a 150 Watt quartz halogen lamp emitting ample light over the visible electromagnetic spectrum. A Vernier light sensor, consisting of a silicon photodiode (400 – 700 nm) measured the intensity transmitted every 0.2 seconds for approximately 55,000 seconds (1,000 cycles).

 figure: Fig. 12

Fig. 12 Experimental setup for cycling.

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Figure 13 shows data from the cycling experiment and indicates the device performs well over time with only slight deviation in light transmittance. However, the device currently suffers from increased transmittance in the light blocking state due to residual fluid left between the corner cubes as the device is drained. A transparent, thin film oleophobic coating could help mitigate this issue. The sharp peaks that are prevalent at each transition are an artifact of the measurement that occurred as the device was filled or emptied of fluid, which caused spurious refraction into the photodetector. Prior to the device being filled with fluid, before cycle 1 begins, the transmittance averaged 10%. Surface roughness and defects brought about from 3D printing allow some scattered light to transmit through the device. In the light transmitting state, the device averaged 85% transmittance during cycle 1, and 86% during cycle 1,000. In the light blocking state, the device averaged 34% transmittance during cycle 1, and 38% transmittance at the end of cycle 1,000. The variation in transmittance between cycles is most likely attributed to residual fluid in the cavity and fluid absorption by the device material. Manufacturer data indicates that VeroClear has a 1 – 2% fluid absorption by weight after 24 hours, thus, some of the 2,2′-Thiodiethanol is most likely being absorbed by the material.

 figure: Fig. 13

Fig. 13 Visible light (400 – 700 nm) transmittance of optofluidic device as a function of cycling.

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 figure: Fig. 14

Fig. 14 Experimental setup for variable angle transmittance.

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 figure: Fig. 15

Fig. 15 Experimental and theoretical transmittance with respect to viewing angle, (a) device orientation, (b) integrating sphere illumination rotating about x-axis, (c) integrating sphere illumination rotating about y-axis, (d) transmittance rotating about x-axis, (e) transmittance rotating about y-axis.

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5. Variable angle transmittance

The reflecting mode of operation for this device is optimized at normal incidence. To characterize the performance with respect to viewing angle, the transmittance was measured over a range of angles with no fluid in the device. Figure 14 shows the experimental setup which consisted of a custom 3D printed integrating sphere, rotating stage, light sensor, and a focused light source. The integrating sphere was modeled after a standard 100 mm integrating sphere. The diameter of the integrating sphere was approximately 100 mm in diameter, with a 38 mm diameter light entrance port, and 15 mm diameter port for the light sensor. After printing the sphere components, the interior surfaces of the sphere were sanded and painted with a 1:1 ratio of flat white paint and barium sulfate. Ultra-fine grit sandpaper was used to ensure a smooth finish after painting was complete. The same Vernier light sensor described in the cycling experiment was also used in the integrating sphere. Using lenses, the same 150 Watt quartz halogen light source used in the cycling experiment was focused onto the light entrance port of the integrating sphere.

To determine the initial intensity in the sphere, the light source was focused on the back interior wall as the sphere was rotated. From −55° to 55°, the relative standard deviation was less than 1%. Intensity measurements were documented at 0°, 10°, 20°, 30°, 40°, 50°, and 55° with the device mounted to the front port. For each orientation, three trials of data were collected and averaged to determine the average transmittance with respect to angle of incidence. In addition to the experimental work, theoretical modeling was also conducted in LightTools. Transmission was simulated from −60° to 60°. A corner cube reflector array is asymmetric resulting in transmittance variation with respect to angle of incidence. It is noted here the theoretical simulations do not include surface roughness and assume the optical surface is perfectly smooth. Figure 15 shows the axes of rotation for the device as well as the recorded illumination and transmittance of the air filled device.Rotating the device about the x-axis results in transmittance peaks at −50° (0.53) and 55° (0.56). Rotating the device about the y-axis results in transmittance peaks at −40° (0.25) and 55° (0.63). For both axes of rotation, 0° represented the angle of incidence with the lowest transmittance. When operating in the index-matched state, the device does not show significant angular variation in transmittance. The incidence angle in this state does not impact transmittance, other than the minimal Fresnel reflectance at each interface.

6. Conclusion

The authors of this paper have presented theoretical and experimental data regarding the development of a new novel optofluidic smart glass that is capable of tailoring solar loading and light transmittance. Optofluidic smart glass exhibits superior transmittance in the light transmitting state compared to other commercially available smart glasses, such as, electrochromic, polymer dispersed liquid crystal, and suspended particle devices. At normal incidence, in the light blocking state, optofluidic smart glass exhibits only slightly higher transmittance than EC, while blocking significantly more light than liquid crystal and suspended particle devices. The corner cube variable transmittance device is capable of modulating visible light transmittance from 8% to 85% at normal incidence. Solar weighted energy transmittance modulation ranges from 22% when the device is filled with air to 79% when the device is filled with index matching fluid. A cycling experiment showed that optofluidic smart glass performs well over time with only slight deviation in light transmittance. Prior to cycle 1, the transmittance averaged 10% in the reflective mode. After cycle 1, the transmittance averaged 34%, indicating a 24% increase in transmittance when operating in the reflective mode. After 1,000 cycles, transmittance averaged 38% in the light blocking state, and 86% in the transmitting state. A variable angle transmittance experiment concluded that the device is optimized for normal incidence, with transmittance averaging 11% using a custom 3D printed integrating sphere. Rotating the device resulted in transmittance peaks at −50° (53%) and 55° (56%) when rotating about the x-axis. When rotating about the y-axis transmittance peaks were located at −40° (25%) and 55° (63%).

Funding

United States Department of Energy (DOE) (DE-EE0005544); Delaware Energy Office (13A01588).

Acknowledgments

Portions of this work were presented at Advanced Photonics 2016 (IPR, NOMA, Sensors, Networks, SPPCom, SOF) in 2016, JW4A.3 and Advanced Photonics 2017 (IPR, NOMA, Sensors, Networks, SPPCom, PS) in 2017, NoW1C.3. Additional sections were taken from the author’s doctoral dissertation titled “Low Cost Optofluidic Smart Glass for Energy Efficiency, Thermal Management, and Privacy Applications”.

References and links

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5. N. Sbar, M. Badding, R. Budziak, K. Cortez, L. Laby, L. Michalski, T. Ngo, S. Schulz, and K. Urbanik, “Progress toward durable, cost effective electrochromic window glazings,” Solar Energy Materials and Solar Cells 56, 321–341 (1999). [CrossRef]  

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Figures (15)

Fig. 1
Fig. 1 Comparison of leading commercial smart glass technologies, (a) EC light blocking state, (b) EC light transmitting state, (c) SPD light blocking state, (d) SPD light transmitting state, (e) PDLC light scattering state, (f) PDLC light transmitting state.
Fig. 2
Fig. 2 Schematic view of variable transmittance prototype
Fig. 3
Fig. 3 Operating modes of variable transmittance device, (left) air - reflective, (middle) water - diffuse transmittance, (right) index matched - specular transmittance.
Fig. 4
Fig. 4 Spectrophotometer setup/model for theoretical simulations and experimentation, (a) total transmittance measurement, (b) total reflectance measurement.
Fig. 5
Fig. 5 Theoretical and experimental spectral properties of 4.65 mm thick VeroClear slab (a) transmittance, (b) reflectance.
Fig. 6
Fig. 6 Ideal reflectance and transmittance of variable transmittance device prototype.
Fig. 7
Fig. 7 (a) Theoretical model setup of integrating sphere with device angled at 8° and no surface roughness, (b) simulated reflectance captured by the model integrating sphere (pink), exiting the integrating sphere port (cyan), and total reflectance (black).
Fig. 8
Fig. 8 (a) Simulated reflectance captured by the model integrating sphere (pink), exiting the integrating sphere port (cyan), and total reflectance (black), (b) experimental reflectance of variable transmittance device plotted against theoretical maximum and minimum reflectance computed by the software.
Fig. 9
Fig. 9 Experimental reflectance measured at 8° and theoretical reflectance adjusted for normal incidence.
Fig. 10
Fig. 10 (a) Theoretical model setup of integrating sphere with device positioned for transmittance simulation, (b) experimental and theoretical data of normal transmittance for air filled variable transmittance device.
Fig. 11
Fig. 11 Theoretical and experimental ρ and τ plots of 3D printed device prototypes with different fluids, (a) ρ water filled, (b) τ water filled, (c) ρ methyl salicylate filled, (d) τ methyl salicylate filled
Fig. 12
Fig. 12 Experimental setup for cycling.
Fig. 13
Fig. 13 Visible light (400 – 700 nm) transmittance of optofluidic device as a function of cycling.
Fig. 14
Fig. 14 Experimental setup for variable angle transmittance.
Fig. 15
Fig. 15 Experimental and theoretical transmittance with respect to viewing angle, (a) device orientation, (b) integrating sphere illumination rotating about x-axis, (c) integrating sphere illumination rotating about y-axis, (d) transmittance rotating about x-axis, (e) transmittance rotating about y-axis.

Equations (2)

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P ( θ ) D i f f u s e = P 0 D i f f u s e cos ( θ )
P ( θ ) S p e c u l a r = P 0 S p e c u l a r e [ ( 1 2 ) ( θ σ ) ]
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