1. Introduction

Mid-wave infrared (MWIR) focal plane arrays (FPAs) operating in a range of wavelengths (λ) from 3 to 5 µm are the main tools for thermal imaging [1]. The imaging systems based on MWIR FPAs benefit from the atmospheric transparency window and from reduced scattering compared to shorter wavelength systems. It should be noted that MWIR FPAs are the natural candidates for imaging in smog and turbid media. For example, firefighters use MWIR FPAs to see through smoke, find people and locate hotspots. Another important area of applications is connected with imaging and sensing the objects through the fog, mist, rain, snow, and sand in the marine and terrestrial environments. The cryogenically cooled thermal cameras provide the best quality MWIR imaging with sufficiently high signal-to-noise ratio [2]; however they are bulky, slow and expensive. In contrast, the uncooled thermal imagers are compact and inexpensive; however, they suffer from the thermal noise and other factors limiting the sensitivity, resolution, contrast, and angle-of-view (AOV) of MWIR cameras.

A natural way of increasing the resolution, decreasing the thermal noise, and, potentially, increasing the operation temperature of MWIR imagers is connected with the reduction of the diameter (d) of individual photodetector pixels [3]. This approach is currently limited at d~2λ~10 µm which is determined by the diffraction of light and small fractional area occupied by compact photodetector mesas on the FPA chip. At first sight, the photon collection efficiency can be regained by using the commercial microlens arrays which allow collection of light from the entire area of the array followed by focusing light into compact photodetector mesas in such a way that each microlens is optically coupled to an individual pixel. However, commercial microlens arrays contain lenses with long focal distances (f~200 µm) [4], so that a small change of angle of incidence causes the shift of the focused spot away from the compact photodetector mesa. This limits AOV = 2arctan(d/2f) at about 1-2 degrees, that is acceptable in astronomical imaging, but does not allow to develop other applications such as applications in surveillance cameras, motion trackers and many other imaging sensors.

It should be noted that in recent years the performance of FPAs was enhanced due to photon trap structures such as photonic crystals [5], textured surfaces with pyramidal relief features [6], and curved FPAs [7]. The spectral response of pixels was enhanced due to plasmonic gratings [8–12], nanoparticles [13], nanoantennas [14], subwavelength hole arrays [15], and microstructure surfaces [16, 17]. Although the absorptivity and spectral response of individual pixels can be enhanced by using these structures, the enhanced performance usually takes place in a relatively narrow range of wavelengths and AOV of such structures is also relatively narrow.

A promising way of increasing efficiency of MWIR FPAs is offered by photonic jets, the beams sharply focused by appropriately designed dielectric microspheres [18, 19]. Photonic jets produced by microspheres have narrow (down to ~λ/3) and elongated (length ~2λ) waists which allows efficient coupling of light incident on microspheres into photodetector mesas with subwavelength diameters (d<λ). Compared to the case of wide-field plane-wave illumination, integration with microspheres with diameter D>d can increase the sensitivity of individual photodetectors by a factor of ~(D/d)². The advantage of photonic jets for concentrating of electromagnetic power by ~10²-10³ times in very small excitation volumes was theoretically predicted for Ge photodiodes [20]. Experimentally, the sensitivity increase by up to 100 times was demonstrated for InAs/InAsSb type-II strained-layer superlattice (SLS) detectors at 80K [21, 22].

A combination of enhanced sensitivity with large AOVs makes integration with microspheres very attractive for developing next generation FPAs [23, 24], especially, taking into account that this technology can be used in uncooled thermal cameras. It requires, however, several conditions. First, a technology of massive-scale, defect-free assembly of microspheres needs to be developed. Second, the array of microspheres (assembled on a separate substrate) needs to be transferred at the FPA surface. The alignment of microspheres with individual pixels needs to be achieved with a micron-scale accuracy. Third, the methods of affixing the microspheres at the FPA surface need to be developed. Finally, the parameters of the FPA structures need to be optimized through numerical design to take into account the microsphere assembly and corresponding electromagnetic field focusing.

In this work, we address some of these issues. In Section 2, we discuss a technology which allows integrating a massive number of microspheres onto the individual pixels nearly defect-free. To this end, we propose to use air suction assembly by the vacuum chuck. Being an example of forced assembly, this technique allows obtaining structures with much smaller defect rates compared to any self-assembled structures [23]. After that, in Section 3 we present modeling results, including the design guidelines (Section 3.1), properties of commercial microlens arrays (Section 3.2), and properties of the back-illuminated (Sections 3.3 and 3.4) and front-illuminated (Section 3.5) FPAs integrated with microspheres. We optimized our designs for achieving collection of light with maximal AOV using microspheres with various index of refraction and diameters in the 30-60 μm range. We show that microspheres provide an order of magnitude higher AOVs compared to commercial microlens arrays.

2. Suction assembly and integration of microspherical arrays with FPAs

Each misaligned or missing microsphere creates a “broken” pixel, and only a small concentration of defects, typically less than ~0.1%, can be tolerated in these FPA structures. The high-quality thermographic cameras have the array-size of 1280 × 1024 pixels, while less expensive cameras with an array size of 160 × 120 or 320 × 240 pixels are still in use. This means that the self-assembly techniques cannot be used for such integration because their typical defect rates are several percent [25, 26]. Recently, we proposed assembly of microspheres in microhole arrays as a technique which can potentially reduce the defect rates [23, 24]. Microhole arrays with a small number of holes can be fabricated by the mechanical drilling [24]. The fabrication of larger-scale microhole arrays can be achieved by a laser ablation [27] or by photolithography followed by etching techniques [28]. The latter method was employed in this work which allowed us to study assembly of 53 𝜇𝑚 borosilicate microspheres on the surface of the FPA with a 60 𝜇𝑚 pitch size, as illustrated in Fig. 1.

 

Fig. 1 Schematic sketches illustrating steps of assembly microspheres by the suction forces: (a) lifting microspheres from the substrate by the suction force produces an ordered array of microspheres sitting in microholes, (b) blowing interstitial spheres away by a sideway air flux, and (c) perfectly ordered single monolayer of microspheres. Circular shape of micro-channels with 45 𝜇𝑚 diameters illustrated (d) from the front and (e) from the back surface of the wafer. Microscope image illustrating assembly of 53 µm borosilicate microspheres on (f) relatively small area of the array where there are no defects and (g) significantly larger area of the array with ~1% defect rate.

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The process begins with fabricating a sieve-like structure or micro-hole array with the geometrical parameters matching the properties of the array of pixels. The micro-hole array structure was fabricated at the Air Force Research Laboratory (AFRL) in a silicon wafer lapped down to have a 170 𝜇𝑚 thickness by etching a 256 × 256 array of holes. The circular shape of micro-channels with 45 𝜇𝑚 diameters in illustrated from the front surface in Fig. 1(d) and from the back surface of the wafer in Fig. 1(e). The comparison of these images shows that the micro-channels have straight sidewalls throughout the entire thickness of the silicon wafer. This wafer with the microhole array was then attached to an air suction system (Fig. 1(a)). The air suction through the holes lifts the individual microspheres from the substrate and sets them in the holes of the array. After the microspheres have been positioned, an additional air flux is applied parallel to the plate (with the main air suction still provided through the vacuum chuck) to remove interstitial microspheres (Fig. 1(b)). This allows for the removal of interstitial microspheres without the removal of the positioned microspheres, which yields a perfect array of microspheres, as schematically illustrated in Fig. 1(c).

Figure 1(f) illustrates the defect-free assembly in small areas. Our results show that in small arrays such as 10 × 10 or 20 × 20 the defect-free assembly can be obtained rather simply. For larger arrays, the local defects still present with a typical concentration ~1%, as illustrated in Fig. 1(g). The straight edges of the array clearly visible in Fig. 1(g) naturally appear as a result of suction assembly where the position of each sphere is determined by the underlying microhole. Obtaining such straight edges would be rather difficult in methods of directed self-assembly of microspheres. It is also seen that microspheres are assembled as a single monolayer and all interstitial spheres are removed due to additional sideway air blow. It should be noted that reduction of the defect rate below 0.1% might be possible by further advancing the proposed method. One of the resources is connected with shaking the structure by mechanical actuators in the course of filling the holes with microspheres which should facilitate filling the unoccupied holes. This, however, requires additional studies which will be a subject of our future work.

The proposed technology of forced assembly of microspheres has advantages and disadvantages compared to standard fabrication technologies. The advantage can be seen in a fact that once the array of microholes is fabricated, it can be multiply used for assembling and transferring arrays of microspheres from the suction chuck to the surface of FPA. In this sense, a single master microhole array can be used for fabricating hundreds of FPAs integrated with microspheres. Several problems, however, still need to be solved for developing this technology. First, the fabrication of microhole array is not a trivial process, especially, in the case of very large scale arrays. Second, several procedures following assembly of microspheres in the microholes need to be developed. These include alignment of microspheres positioned in microholes with pixels of FPAs. Such alignment can be achieved using fiducial markers. Alternatively, it can be achieved by commercial mask aligner using controlled observation. This task goes beyond the scope of the present work; however such alignment seems to be a feasible task since the microspheres need to be centered with the photodetector mesas (~10 𝜇𝑚 diameters) with a micron-scale accuracy which is achievable by using commercial mask aligner. An additional resource for controlling the quality of alignment is offered by imaging through microspheres which can be easily realized for front-illuminated FPAs [22]. The virtual image of photodetector mesa becomes visible through microsphere which allows checking that microspheres are centered with the pixels. Another problem is connected with fixing microspheres in these positions. It can be achieved by using a thin layer of glue or photoresist deposited over the semiconductor pixelated array. Once the microspheres are aligned and brought in contact with the pixels, the photoresist can be solidified by the UV exposure. Alternatively, the microspheres can be first embedded in a plastic coverslip [29] and then the whole coverslip can be attached to the FPA surface using optical methods for controlling alignment with the pixels.

3. Modeling results

3.1 Design guidelines

In the limit of large microspheres (D>>10λ) the focusing effects can be described in the paraxial approximation by the geometrical optics. In FPA structures, however, the spherical aberrations cannot be ignored. In addition, the optical properties need to be determined: i) assuming different microsphere sizes and indices of refraction, and specific thicknesses and indices of all the layers comprising the structure for both back- and front-illuminated structures and ii) assuming cases where the microspheres are partly immersed in a photoresist or truncated. For these reasons, we used the numerical modeling techniques.

FPA optimization is based on the following design guidelines: (i) The narrowest waist of the focused beam should be achieved at the photodetector’s mesa plane. The idea is that at normal incidence the focused beam should be coupled through the mesa with the minimal optical losses. (ii) The waist of the focused beam should be smaller than the mesa diameter. In the practical device structure, the photodetector mesa can be defined by the semi-circular metallic electrodes terminating the aperture of the incident focused beam [22]. (iii) The affixed microspheres with the diameters in the 30-60 µm range and the refractive indices in the 1.4-1.8 range have rather short focal distances that make it implausible to fabricate extremely thin substrates required for the back-illuminated structures. The solution comes from the fact that the refractive capability of microspheres can be reduced by partly-immersing them in a photoresist or by truncating them. Thus, by controlling the amount of immersion or truncation the structure satisfying guidelines (i-ii) can be designed. (iv) The limitation of AOV comes from the fact that increase of the angle of incidence causes the shift of the photonic jet away from the corresponding photodetector mesa. The amount of shift is proportional to the effective focal length of the microspheres. Thus, the way of increasing AOV is connected with reducing the focal distance of the microlens.

In our designs, we used the full wave FDTD modeling for microspheres with diameters in a 30‐60 µm range. Such microspheres can be assembled in close-packed arrays with the pitch and pattern matching that for photodetector arrays, so that the individual photodetectors are located just below each microsphere. We consider the period of arrays in the 30‐60 µm range since it is close to typical distance between the pixels in mid‐IR FPAs. To simplify calculations, we used a two-dimensional (2‐D) cylindrical geometry which has all essential features of 3‐D case. The numerical simulation was performed by finite difference time-domain (FDTD) method with the commercial software by Lumerical Solutions Inc. We selected photodetector mesa (pixel) diameter d = 10 µm which corresponds to minimal sizes used in practice in mid‐IR FPAs. For standard microlens array (Section 3.2), we considered dome-shaped microlenses fabricated at the top of the plastic layer with the refractive index n = 1.44 and the thickness 165 µm. This plastic layer is supposed to be mounted at the front surface of FPA. We show that this combination of parameters results in focusing of the incident plane waves at the plane of photodetector array; however the large focal distances result in AOV~1°. For back-illuminated structures enhanced with microspheres we considered two cases differing by parameters of microspheres and layer thicknesses. In Section 3.3, we consider microspheres with index, n = 1.46, and with diameter, D = 60 µm, partly immersed in a layer of photoresist and demonstrate AOV of 5°. In Section 3.4, we consider slightly truncated microspheres with higher index n = 1.56 (polystyrene) and diameter $D$ = 60 µm and show that it leads to AOV of 8°. For front‐illuminated structures (Section 3.5) the thickness of the semiconductor slab is not a relevant parameter. In the latter case, we consider high‐index (n = 1.8) microspheres with $D$ = 30 µm and show that it results in AOV of 20°. The illumination was provided by plane waves at $\lambda$ = 4.0 µm; however the investigated optical properties are not strongly wavelength dependent, and the results are generally applicable in the mid‐IR range 3‐5 µm. Thus, we demonstrate the increase of AOV by more than order of magnitude compared to commercial microlens arrays as a result of integration of FPAs with microspheres.

3.2 Standard microlens array

To show that conventional microlens arrays fabricated on a planar substrate inherently limit AOVs of FPAs, we consider a plastic moldable material with reasonable optical transmission properties in MWIR range. In our design we did not specify the material and simply assumed that it has the index of refraction 1.44 at λ = 4.0 µm. In practice, it can be polydimethylsiloxane (PDMS) or polymethyl methacrylate (PMMA) or other similar material. Silica can be also used, but it is absorptive in MWIR range. All these materials have the index of refraction which is sufficiently close to 1.44 which means that the conclusions of our consideration are generally applicable to all these materials. Alternatively, the MWIR FPAs can be fabricated from high index materials such as Si or Ge. It should be noted, however, that Si is fragile and hard to machine. In addition, the radius of curvature of Si lenses is usually large which results in sufficiently long focal distances [4] comparable to that obtained with plastic lenses which have larger curvature. Germanium has similar properties to Si, but is also much rarer. Since AOV is largely defined by the effective focal distances, all microlens arrays designs including low-index plastics and high-index semiconductor materials have very limited AOVs. Below we illustrate this problem for a low-index (n = 1.44) material.

As illustrated in Figs. 2(a) and 2(b), we assumed that the microlenses have the radius curvature of R_c = 72 µm. The lens has a dome shape with the base diameter of 57 µm, as shown in Fig. 2(a). It was assumed that such dome-shaped lenses are fabricated at the surface of a slab with the thickness of 165 µm in Figs. 2(a) and 2(b). The electric vector of input (from left to right) electromagnetic plane waves was linearly polarized in the xy plane. The incident beam had a Gaussian temporal modulation with 50 fs pulse duration and λ = 4.0 µm central wavelength. The location of microlens, substrate and detector are shown by dashed lines in the calculated EM maps in Fig. 2(c). The calculated EM map is for amplitude of electric field which contains all E-field components. The position of the optical components indicated by dashed lines in Fig. 2(c) corresponds to that in Fig. 2(a). We considered a back-illuminated structure with the 200 µm thick semiconductor substrate. The refractive index of the semiconductor substrate was 3.5. The mesh size in calculations was λ/(22n), where n is the index in the corresponding optical components. The plastic slab with microlenses is supposed to be attached to the front surface of a semiconductor slab. As shown in the lower image of Fig. 2(d), for the angle of incidence $\alpha$ = 1° the focused beam shifts away from the mesa’s center and reaches its edge. For angles of incidence beyond $\alpha$ = 1°, the beam is blocked by the edge of the mesa, which means that AOV is close to 1° in this case. It is seen that such array provides efficient collection of light only in extremely narrow cone around the normal direction which can be a limiting factor for some applications.

 

Fig. 2 (a,b) Schematics of the microlens array integrated with the back-illuminated optical detector FPA with 200 µm thickness of the substrate. (c) Electric field map calculated by FDTD simulation at λ = 4.0 µm. The position of microlens, substrate and detector are shown with dashed black lines. (d) Electric field map calculated at λ = 4.0 $\mu m$ for $\alpha$ = 0° (top image), and $\alpha$ = 1° (bottom image). In the latter case, it can be seen that the focused light beam hits the edge of the detector.

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3.3 Back-illuminated structure with microspheres partly immersed in a photoresist

The typical structure of FPA integrated with microspheres is illustrated in Fig. 3(a). The diameter of the microspheres is determined by the pitch of FPAs. In order to provide a surface coverage by microspheres with large areal fill factor required for efficient collection of light, the microsphere diameter should be close to the FPA pitch. In the example presented in Fig. 3(a), we considered microspheres with a 60 𝜇𝑚 diameter and 𝑛 = 1.46 refractive index (for soda-lime glass as an assigned material). As an example, such microspheres can be used in FPAs with 60 𝜇𝑚 pitch. Similar to the previous Section, the structure is back-illuminated, however, the completed microsphere has shorter focal distance which requires thinner substrate for focusing light at the photodetector mesa. We assumed that the microsphere was partly immersed in a 28 𝜇𝑚 photoresist layer with a refractive index of 1.57. The photoresist layer played a double function in our design. First, it can be solidified to permanently fix the microspheres. Second, it increases the effective focal distance of such lenses which means that the thicker substrates (compared to the case without the photoresist) can be used to provide sharp focusing at the plane of photodetector mesas. Our calculations showed that such structures require a substrate thickness around 47.2 𝜇𝑚. It can be realized in practice by polishing the semiconductor substrate. The alignment of microspheres with photodetectors can be achieved by using fiducial markers or by maximizing the optical signals from the detectors in the course of alignment. As it is shown in Fig. 3(c), such structure with reduced effective focal distance has AOV on the order of 𝛼 = 5°, which shows 5-times improvement compared to the standard microlens arrays.

 

Fig. 3 (a) Schematic of 60 $\mu m$ soda-lime glass microsphere immersed in a 28 $\mu m$ photoresist adhesive layer at the back-illuminated FPA structure. The thickness of the detector substrate is 47.2$\mu m$. (b,c) Electric field maps calculated at λ = 4.0 $\mu m$ for angles of incidence α = 0° and α = 5°, respectively.

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It should be noted that much smaller, subwavelength microspheres assembled as a monolayer can trap the incident light due to periodic diffraction effects leading to formation of 2-D photonic band structure [30, 31]. These effects should not be present in microspherical arrays with the characteristic spheres’ dimensions D>10λ considered in this work.

3.4 Back-illuminated structure with slightly truncated microspheres

The effective focal distance of dielectric microspheres can be further reduced by increasing their index of refraction. Another powerful resource for controlling the effective focal distance is offered by truncation of microspheres as opposed to its partial immersion in a photoresist. The FPA structure based on polystyrene or plastic microspheres with index n = 1.56 in mid-IR spectral range is illustrated in Fig. 4(a). This microsphere has the same diameter 60 µm as that illustrated in Fig. 3. It is known that the polystyrene of plastic microspheres can be slightly melted in a region where they contact the heated substrate [32–34]. This leads to a slightly truncated shape of microsphere illustrated in Fig. 4(a). It should be noted that such thermal treatment can be quite convenient in practice since it provides permanent attachment of the microsphere to the semiconductor substrate without using any kind of epoxy or photoresist. In Fig. 4(a) we assumed a truncation of microspheres by 5 µm due to removing of the corresponding polystyrene or plastic material. In practice the amount of truncation can be precisely controlled by the temperature of the substrate and duration of the thermal treatment. Controllable melting of the microspheres can lead to more complicated deformations of their shapes due to a material reflow. The truncation model illustrated in Fig. 4(a) can be considered only as a rough approximation to the real characteristic changes in the shape of the microsphere. As a result of this procedure, the microspheres can be permanently fixed in the optimal positions just above the photodetector mesas.

 

Fig. 4 (a) Schematic of 60 µm polystyrene microsphere truncated at a 5 µm depth in contact with a 20 µm substrate in the back-illuminated FPA. (b,c) Electric field maps calculated at λ = 4.0 μm for α = 0° and α = 8°, respectively.

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The combined effect of larger index of refraction and truncation leads to thinner substrates required for focusing incident plane waves at the back surface of the substrate. The results presented in Fig. 4 show that such focusing can be achieved with ~20 µm thickness of the polished substrate. In this case, comparison of the EM map in Fig. 4(b) calculated at normal incidence α = 0° with the corresponding map in Fig. 4(c) calculated at α = 8° shows that in the latter case the focused beam reaches the edge of the mesa indicating AOV = 8°. Such AOV exceeds that provided by a standard microlens array by almost an order of magnitude.

3.5 Front –Illuminated structure

The maximal increase of AOV can be achieved in the front-illuminated structure where the microspheres are positioned directly above the mesas of the photodetector array, as schematically illustrated in Fig. 5(a). Experimentally, this situation can be realized using barium-titanate glass (BTG) microspheres. According to a manufacturer, Mo-Sci Corporation, these microspheres have index ~1.9 in the red part of visible spectrum. The refractive index is not precisely defined for these microspheres. However, taking into account typical dispersion of the refractive index in high-index glasses, one can assume that their index should be close to ~1.8 in mid-IR spectral range. In addition, in our numerical design we assumed that these microspheres have smaller diameter D = 30 µm. Such microspheres focus plane waves close to their backside (not illuminated) surface and they can be used for enhancing front-illuminated FPAs. We assumed that fixing these microspheres can be achieved using a layer of photoresist with 10 µm thickness deposited by spin coating. After transferring the microspherical array and alignment of individual microspheres with the photodetector mesas, the photoresist layer can be solidified by the UV illumination. This combination of properties, refractive index, size of microspheres and their slight immersion in the photoresist, leads to formation of photonic jets at the plane of photodetector array.

 

Fig. 5 (a) Schematic of a front-illuminated FPA with a 30 µm barium titanate microsphere placed in contact with the 10 $\mu m$ detector mesa. (b,c) Electric field maps calculated at λ = 4.0 µm for incidence angles α = 0° and α = 20°, respectively.

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The case of front-illuminated FPAs is special because it maximizes the advantages of integration with microspheres. This is determined by the shortest focal distance which can be realized in FPAs integrated with microspheres which translates into maximal AOVs. The calculated EM map in Fig. 5(c) shows that for incident angle $\alpha$ = 20° the focused beam still hits the edge of the detector mesa, which means that AOV~20° in this case. Further increase of the refractive index of microspheres would result in focusing of light inside the microspheres which leads to the optical coupling losses in FPAs.

On the other hand, the case of front-illuminated structures is special also due to the fact that the same microspheres can be used for super-resolution imaging of the photodetector mesas located just below them [21, 22]. Such imaging termed microspherical nanoscopy attracted a significant interest in recent years due to the fact that it allows overcoming the standard far-field resolution limit, as it is described by the Abbe’s formula [35–43]. The resolution advantage of this method comes from the fact that the virtual image of the surface produced by microspheres is magnified by a factor between 2 and 5 and it is formed with participation of the object’s evanescent fields which carry high spatial frequencies containing more detailed information about the object. From the point of view of technology of integration of microspheres with FPAs, the imaging through microspheres opens a method of alignment of microspheres with the individual photodetector mesas based on direct visualization. If the microsphere is centered with the mesa, the latter appears with a non-distorted circular shape [22]. The fact that the optical imaging can be performed with an order of magnitude better resolution (at least ~λ_i/2 or better, where λ_i is the illumination wavelength used in the microscope system) than the typical MWIR wavelengths provides a sufficient accuracy for the alignment process.

4. Conclusion

To simultaneously increase the light collection efficiency, angle-of-view and signal-to-noise-ratio (SNR) for operation of MWIR FPAs at higher operating temperature, in our recent work we suggested using “photonic jets”, sharply focused beams with subwavelength transversal width produced by dielectric microspheres [22, 23]. Due to small waist of photonic nanojets, they can be efficiently coupled into photodetector mesas with ~10 μm diameters. In principle, even smaller mesa sizes can be realized which means that the thermal noise and SNR can be significantly reduced in FPAs integrated with microspheres.

In this work, it is shown that the microspheres can be assembled in ordered arrays by using air suction grippers through the microhole arrays. This technology can be used for synthesizing large-scale arrays with the concentration of defects below ~1%. Such concentrations are significantly smaller than the concentrations of defects which are achievable by self-assembly techniques. Further reduction of concentration of defects below ~0.1% will be investigated in our future work.

Using numerical modeling, we optimized our designs for achieving maximal AOVs for microspheres with different diameters in the 30-60 μm range, as well as various indices of refraction. It should be noted that the standard solution of the light collection efficiency problem is offered by the commercial microlens arrays. This solution, however, comes at a price of very narrow AOV~1-2° of the resulting mid-IR imaging system. We show that the microspheres allow combining high light collection efficiencies with larger AOVs.

We designed MWIR FPAs for different geometrical and structural parameters of spheres, substrates and additional layers. The designs are aimed at progressively larger AOVs which can be achieved by reducing the effective focal distance of the microspheres. The designs are developed for both back- and front-illuminated FPAs. We demonstrate that by increasing the refractive index of microspheres, the AOV can be increased from 5° and 8° in back-illuminated designs to 20° in front-illuminated structures. Different techniques of fixing microspheres such as their partial immersion in photoresist or their slight deliberate truncation due to temperature treatment are considered in our designs.