## 5 Experimental Achromatic Diffractive Lens Implemented in an LCoS Display  
In this section, we show the potential of multiorder lenses displayed on an LCoS-SLM with a large phase dynamic range to design achromatic diffractive lenses. In the exemplary study of this section, we considered a diffractive lens of 150 mm focal length under polychromatic illumination. The described Holoeye LCoS display permits a maximum phase modulation range of 8\(\pi\) (Figures 4 and 6f) for a wavelength in the green region of the visible spectrum (514, 520 nm), attaining a larger phase modulation depth in the blue region (476 nm) and approaching 6\(\pi\) in the red region (647 nm). By using the response curves of Figure 6f, we designed a four-order diffractive lens for a design wavelength \(\lambda_{0}=470\) nm and \(f=600\) mm focal length that operates with maximum efficiency in its fourth diffraction order at \(f\)/m = 600/4 = 150 mm. This four-order diffractive lens under blue illumination has a phase profile that behaves, under illumination with \(\lambda_{\mathrm{R}}=625\) nm, as a third-order diffractive lens of \(f=450\) mm that shows its maximum diffraction efficiency at \(f\)/m = 430/3 = 150 mm from the lens plane (Equations (2) and (3)). In other words, such a phase profile achromatizes the multiorder diffractive lens with a common plane of maximum efficiency for both the blue and red wavelengths. We compared the performance of this multiorder lens, designed to be ideally achromatic, with a conventional modulo 2\(\pi\) lens, designed for \(\lambda_{0}=530\) nm with a focal length \(f_{0}=150\) mm, when both were illuminated under polychromatic light. These lenses were implemented on the LCoS display using either the calibration curve for a linear 8\(\pi\) phase modulation (Figure 6f) (achromatic multiorder lens) or the calibration curve for a linear 2\(\pi\) phase modulation (Figure 6b) (conventional modulo 2\(\pi\) lens). The setup depicted in Figure 7 was used in this experiment. We sequentially illuminated both lenses with three different LED sources whose featured wavelengths covered the visible spectrum (\(\lambda_{\mathrm{B}}=470\) nm, \(\lambda_{\mathrm{G}}=530\) nm, and \(\lambda_{\mathrm{R}}=625\) nm) and acquired the focal spots at the planes of higher diffraction efficiency. Distance from the LCoS screen was measured in each case. Figure 10 shows the experimental results. Figure 10a shows the focalization planes obtained for the conventional modulo 2\(\pi\) diffractive lens. At the location of the design focal plane (\(f_{0}=150\) mm) the focal spot for the green LED (\(\lambda_{\mathrm{G}}=530\) nm) was obtained. When the first-order diffractive lens was illuminated with either the red or blue LEDs, the focal plane moved in opposite direction with respect to the green wavelength. Both red and blue focal plane positions are indicated in Figure 10a. These results evidence the remarkable chromatic aberration of a diffractive lens, for which focal planes for the three R, G, and B testing wavelengths are located some distance apart from each other. In our experiment, the focal planes of the extreme wavelengths of the visible spectrum (625 and 470 nm) are separated around 41 mm. Figure 10b provides the experimental results for the achromatic multiorder lens. It consists of a fourth-order diffractive lens with a \(f\) = 600 mm focal length for a design wavelength of \(\lambda_{0}=\lambda_{\text{B}}\) = 470 nm. The lens was sequentially illuminated by the three LED sources in the red, green, and blue regions of the visible spectrum. Focalization planes with the highest diffraction efficiencies were acquired, and their positions from the LCoS screen were measured. As a fourth-order diffractive lens (\(m=4\)) for the blue light, the focalization plane with maximum efficiency for blue was located at \(f\)/m = 600/4 = 150 mm from the SLM display. Since this lens was, at the same time, a third-order diffractive lens for red light (\(\lambda_{\text{R}}\) = 625 nm), both bright blue and red spots appeared at the same position.