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To obtain the Lena images through the lens arrays of Xenos peckii, insects were first anesthetized by cooling and were then decapitated, and the lens arrays of one of the eyes were removed. The inner surfaces of the arrays were gently cleaned from residual pigment and other cellular debris with a soft brush. Thereafter, it was placed on top of a small droplet of physiological saline solution that was placed on a microscopy cover slip25. Following the hanging-drop method, the cover-slip was inverted in such a way that the lens arrays, held by surface tension, floated to the bottom of the droplet5, 26. The arrays were placed on the stage of a compound microscope (Olympus BX 51) from which the condenser was removed. A printout of the Lena image (on photographic paper) was placed below the microscope stage, within the light path of the microscope's bottom illumination. In this way, the Lena print was in the light path of the lens arrays, which resulted in a series of small images (one for each Xenos lens) that could then be visualized through the microscope and imaged with a digital camera (Retiga 2000R, Qimaging).
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Black SU-8 was precisely dispensed on the edge of the microprism arrays by using a glass micropipette mounted on an xyz micromanipulator. The black SU-8 spreads through the interstitial gaps of the microprism post arrays due to capillary forces. The flow rate of the black SU-8 through the glass micropipette was precisely controlled with custom-made pumping system. After 3D filling, the black SU-8 was soft-baked at 95 ℃ on a hot plate. The top side of the device was then exposed to UV light, followed by post-exposure bake.
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Each microprism image was initially registered to the reference image by shifting images to seek the minimum normalized cross-correlation values between images. The registered multiple microprism images were then used to reconstruct a higher resolution image using a super-resolution approach27. We built a cost function to reconstruct a higher resolution image$X$ from multiple low-resolution input images$Y$:
$$ \mathop {\min }\limits_X \mathop {\sum }\limits_{k = 1}^N \left\| {F_kX - Y_k} \right\|_2^2 + {{\lambda \Gamma }}\left( X \right) $$ (1) where $F_k$ is a geometric motion operator between $X$ and the k-th image $Y_k$ and ${{\lambda }}$ is a regularization parameter. This optimization problem was solved with a bilateral-TVL1 regularizer ${{\Gamma }}(X)$:
$$ {{\Gamma }}\left( {{X}} \right) = \mathop {\sum }\limits_{l = 0}^P \mathop {\sum }\limits_{m = 0}^P \alpha ^{\left| m \right| + \left| l \right|}\left\| {X - S_x^lS_y^mX} \right\|_1^1 $$ (2) where $\alpha$ is a scale factor and $S_x^l\, {{and}}\, S_y^m$ are the shift operators along the horizontal and vertical axes, respectively. The objective function was solved using the conjugate gradient descent method with parameters λ = 2 and α = 0.6.