1. Introduction

Conventional refractive optics are bulky due to their nature. Planar optics are possible either by metasurfaces [1–4] or via diffractive optics [5,6]. As we have pointed out previously, metasurfaces and metalenses (“meta-optics”) are uniquely suited for manipulating the vector properties of the electromagnetic field (such as polarization). However, compared to diffractive optics, meta-optics require drastically more complex fabrication including sub-wavelength minimum feature widths and extremely large aspect ratios. These fabrication challenges make it very difficult to fabricate millimeter-scale meta-optics that also operate over the full visible spectrum. Relatively large metalenses have been demonstrated, but only at a single operating wavelength in the near infrared [7]. On the other hand, diffractive optics, when appropriately designed, can operate over a broad spectral regime and are drastically simpler to fabricate and manufacture at volume via embossing [8].

Previously, we have demonstrated flat diffractive lenses that can operate over the full visible spectrum at high efficiency and high numerical apertures [6]. However, for realistic imaging systems such as those used in photography, one needs the ability to change the focus and magnification in a flexible manner. Concatenating at least two lenses as illustrated in Fig. 1(a) enables this capability. By moving one lens relative to the other (g) and adjusting the image sensor (v), it is possible to adjust the working distance of the object (u) as well as the magnification of the image. Here, we demonstrate this capability with two flat broadband diffractive lenses. It is important to note that multiple lenses are also required to match the acceptance angle of the pixels of the image sensor to that of the optical system [9], an aspect we do not explore in this study.

 

Fig. 1 (a) Schematic using two flat lenses for imaging. Optical micrographs of the two flat lenses made with S1813 (a) and with AZ9260 (b). The focal length and NA of both lenses are 25mm and 0.05, respectively.

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2. Design and fabrication

The design methodology for flat lenses has been described previously [5]. Briefly, we used nonlinear optimization based on the modified direct-binary-search algorithm to select the heights of the circular pixels (zones) so as to maximize the focusing efficiency averaged over the bandwidth of interest. The focusing efficiency is defined as the ratio of the power inside a circle of diameter equal to 3 times that of the corresponding diffraction limited spot to the power incident on the lens. The simulations were performed using the scalar diffraction theory. Although the detailed trade-offs between the bandwidth and achromaticity of the lens is outside the scope of this report, we can generally point out that larger the maximum height of the zones and smaller the width of the zones, the better the focusing efficiency will be.

Using the methods described previously, we designed and fabricated two flat lenses, whose optical micrographs are shown in Figs. 2(b) and 2(c), respectively. The two lenses were fabricated in Shipley 1813 and AZ9260 photoresist, respectively. The design parameters of the two lenses are summarized in Table 1 below. The two different photoresists allow for not only different dispersion properties, but more importantly, different aspect ratios. The maximum feature heights achievable using S1813 and AZ9260 were 2.6μm and 8μm, respectively. Our previous studies have indicated that larger maximum feature heights should translate directly into higher lens efficiencies [10]. This is qualitatively borne out by the experiments as described later. We note that the two different photoresists are not essential for the achromaticity of our two-flat-lens experiments. Instead, we just wanted to explore the potential of the higher aspect ratio offered by the AZ9260 photoresist.

 

Fig. 2 Characterization of each lens separately. (a)-(d) The measured and simulated point-spread function as a function of illumination wavelength (bandwidth = 10nm) is shown for the two lenses, respectively. (e)-(f) The images of a resolution test chart as a function of illumination wavelength is shown for the two lenses, respectively. The image of the resolution test chart taken under broadband illumination (430nm to 660nm, bandwidth = 230nm) is shown in the rightmost column. The size of the resolution-test image is ~2mm.

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Table 1. Design parameters for the two lenses

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3. Characterization of individual lenses

First, we verified the performance of each lens separately. This was done by capturing the point-spread function (PSF) of each lens as a function of wavelength. A collimated beam, whose wavelength can be tuned, first illuminates each lens. The experimental setup has been described previously [6]. The PSF is magnified via an objective-tube-lens system by 22.22X, and the magnified image is captured using a monochrome CMOS sensor (DMM 27UP031-ML, Imaging Source). The experimental and simulation results are shown in Figs. 2(a)-2(d) for the two lenses. It was noted that the Flat lens 2 produced images with exposure times that are approximately 1.5 times lower than those for the Flat lens 1. This qualitatively confirms that the Flat lens 2 has higher efficiency than Flat lens 1 as expected from simulations. Significant sidelobes were noticed in the PSFs for Flat lens 2, which we attribute to the enhanced fabrication errors resulting from the more complex, higher-aspect ratio process. Nevertheless, both flat lenses focus across the full visible range and exhibit excellent achromatic behavior.

Figures 2(e) and 2(f) showcase images of the standard resolution test chart (Model R3L3S1N, Thorlabs) when illuminated by different wavelengths. In this experiment, the test chart was transmissive and illuminated by collimated light from behind. This setup and procedure is identical to what we have described previously [6]. Relatively sharp images of the test charts confirm the achromatic behavior of both lenses. Finally, the two rightmost images in Fig. 2 show the test chart when illuminated by the visible spectrum using the same light source (430nm to 660nm).

Finally, we assembled each lens separately with a color CMOS image sensor (DFM 72BUC02-ML, The Imaging Source). Images of test objects were taken under 3 different illumination conditions: Indoor with a halogen lamp, Indoor with a white LED and Outdoor under sunlight. The captured raw images are displayed in Fig. 3. Chromatic aberrations are minimized in these images. Some errors in color rendering (for example under the halogen lamp) are attributed to the internal image-sensor software, which we did not have access to. As in conventional cameras, white balancing can be applied to correct such errors, which we have not pursued here. We have included captured raw video files, one for each of the flat lenses, which illustrate video imaging (Visualization 1 and Visualization 2).

 

Fig. 3 Characterization of color imaging of each individual lens under different illumination conditions. Visualization 1 and Visualization 2 showcase raw video images captured using Flat lens 1 and Flat lens 2, respectively.

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4. Characterization of two-lens camera

Finally, following the schematic in Fig. 1(a), we assembled the two flat lenses with the monochrome image sensor and characterized the camera performance as a function of illumination wavelength. The images taken of the resolution test chart are summarized in Fig. 4(a). The geometric parameters (u,v) used in each case are summarized in Fig. 4(b). Subsequently, the two flat lenses were assembled with the color CMOS sensor and the resulting images are shown in Fig. 4(c) with gap, g between the two flat lenses equal to 2mm. Chromatic aberrations are minimized under all conditions. Note that these images are not post-processed in any fashion. Visualization 3 contains the raw video file of the camera at a fixed focus (magnification). Visualization 4 shows that by changing the gap g between the flat lenses, we can readily change the magnification. An overview of the camera itself is also included in Visualization 4.

 

Fig. 4 Imaging using the 2-flat-lens system under different illumination conditions. (a) Resolution test chart under narrowband and broadband illumination. (b) Object (u) and image distance (v) and magnification (M) for the images in (a). (c) Color images taken with two flat lenses and the color CMOS image sensor under different illumination conditions. Visualization 3 and Visualization 4 are raw video files at fixed magnification and varying magnification, respectively. (d) Two frames from Visualization 4 are shown with different magnifications.

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5. Impact of fabrication errors

We numerically analyzed the effect of fabrication errors on the performance of the flat lenses. There are primarily two types of fabrication errors: (a) error in the heights of the rings (pixels) due non-uniform spin-coating and development of photoresist or due to slight variation in resist exposure doses, and (b) error in the widths of the rings (pixels) due to variation in resist exposure dose. Figure 5(a) summarizes the simulated average focusing efficiency vs standard deviation of height-error. The average focusing efficiency is defined as the focusing efficiency averaged over the bandwidth of interest. The focusing efficiency is defined as the ratio of the power inside a circle of diameter equal to 3 times that of the corresponding diffraction limited spot to the power incident on the lens. Since the heights can be controlled to within several tens of nanometers in our process, we believe that performance close to 90% of the ideal case can be achieved. Figure 5(b) shows the same result as a function of the pixel size error. The efficiency seems to be more sensitive to this error. Improved fabrication processes available in commercial facilities will improve the performance of our flat lenses.

 

Fig. 5 Numerical analysis of fabrication errors. Average focusing efficiencies of the two flat lenses as (a) function of standard deviation of pixel-height error and (b) function of pixel size error.

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6. Conclusions

We experimentally demonstrate the use of two concatenated millimeter-scale flat lenses to achieve varying focal length and magnification in full-color video imaging. By improving the fabrication process, it is readily possible to increase the numerical aperture as well as size of the lenses. Since these lenses are significantly simpler to manufacture than metalenses and even conventional refractive lenses, we expect such lenses to enable lightweight high quality video imaging for many applications.