# First Earth-Imaging CubeSat with Harmonic Diffractive Lens
## 3 Remote Sensing Camera with a Harmonic Diffractive Lens  
The diffractive lens has been fairly well studied as an optical imaging element [31; 32; 33; 34; 35; 36; 37; 38; 39]. The majority of the publications consider the diffractive lens either as an auxiliary element to compensate for chromatic aberration of the refractive imaging system [31; 32; 33; 34; 35; 36] or as a focusing element, with an on-axis intensity distribution from a focused coherent light beam discussed in [37; 38]. The focusing of a plane wave with a Fresnel lens was studied in [39]. For a diffractive lens used for image acquisition, a variety of lens fabrication techniques have been proposed [40; 41; 42], which, among others, may include the use of a limited spectral range [43]. Chromatic aberrations can also be reduced by synthesizing a microrelief with higher features, typically referred to as harmonic lenses [5]. Unlike a diffractive lens, a harmonic lens generates a sharp image for a set of wavelengths (harmonics) in the focal plane, enabling the highly effective use of neural networks for digital processing to enhance the image quality. The harmonic lens relief can approximate aspheric lenses, thus reducing geometric aberrations [44]. Our harmonic diffractive lens for the CubeSat optical system had to satisfy two major constraints. The first constraint was imposed by the CubeSat cubic 100 mm payload dimensions. After accounting for electronic components, only 72 mm remained available for the optics from 100 mm of the CubeSat cubic payload dimension, and we settled on a 70 mm focal length harmonic lens design. Second, our diffractive microrelief synthesis technique forced us to select the lens speed (the ratio of the focal length to the output aperture diameter) to be no less than 5 to accurately fabricate the outermost diffractive lens zones. Based on these considerations, we settled on a 10 mm lens diameter. The diffractive lens for the CubeSat optical system was synthesized on a direct laser writing station CLWS-2014 [45]. The microrelief was recorded in a 6 \(\upmu\)m thick layer of a positive photoresist FP-3535, coated onto a 25 mm quartz substrate by centrifuging. Two identical harmonic lenses were synthesized for the CubeSat lens assembly. Figure 3a shows an optical microscope image of one of the fabricated harmonic lenses. Figure 3b shows a profilogram measured along the lens radius. We developed our own diffractive lens simulation software that we called Harmony (described in more detail in [46]), capable of simulating both individual harmonic diffractive lenses and whole optical systems that contain these diffractive lenses. To describe the resulting chromatic aberrations, we plotted the principal focus shift against the light wavelength, as shown in Figure 3c. The microrelief geometry approximates a fairly complex aspheric surface designed with a technique proposed in [44], which produces an optimal microrelief to minimize on-axis geometric aberrations. The resulting lens has a concave shape when looking at the microrelief peak heights, per [44], with the synthesis algorithm generating the required lens shape from the edges to the center. The concave shape turned out to be useful in the manufacturing process as well, where the laser engraving also starts from the edges of the lens and the etching increases as the laser approaches the center, the most challenging area to produce. As seen in Figure 3c, the principal focus of the harmonic lens varies in a fairly wide range from 64.5 mm to 75.5 mm, leading to a blurred image. However, unlike a purely diffractive lens, the harmonic diffractive lens can still produce a sharp image at several wavelengths. In the fabricated lens shown in Figure 3c, these wavelengths are located at the intersections of each sawtooth segment with the horizontal line at \(\Delta\)f = 5 mm (so, these wavelengths are 428 nm, 476 nm, 535 nm, and 612 nm). By delivering this additional