Extreme-depth-of-focus imaging with a flat lens: supplementary material

This document provides supplementary information to "Extreme-depth-of-focus imaging with a flat lens,” https://doi.org/10.1364/OPTICA.384164, including details on our literature survey as well as the EDOF MDL design, which were obtained using nonlinear optimization using a modified gradient-descent based search algorithm that maximized wavelength-averaged focusing efficiency. The PSF simulations were performed using commercially available FDTD software from Lumerical.


Measured Point Spread Function (PSF)
Some of the measured point spread functions (PSFs) for the designed MDLs are provided below: (5mm -1200 mm):

Fabrication
The MDL depicted was patterned in a photoresist (Microchem, S1813) film atop a glass wafer (thickness ∼ 0.6 mm) using grayscale laser patterning with a Heidelberg Instruments MicroPG101 tool [21][22][23]. In such conventional gray-scale lithography, the write head scans through the sample surface and the exposure dose at each point is modulated with different gray-scales [21,22] (see schematic illustration of Fig. S3). Most of these typical photoresists are characterized by a contrast curve. Different depths in accord with different exposure doses are achieved after development.
Greater dose leads to deeper feature. Before patterning structures, it is needed to calibrate this contrast curve. In this case, too, the exposure dose was varied with respect to position to achieve the multiple height levels dictated by the design.

Experiment details (focal spot characterization)
The flat lenses were illuminated with expanded and collimated beam from the SuperK VARIA filter (NKT Photonics). The wavelength and bandwidth can be changed using the VARIA filter [24]. The focal planes of the MDLs were magnified using an objective (RMS20X-PF, Thorlabs) and tube lens (ITL200, Thorlabs) and imaged onto monochrome sensor (DMM 27UP031-ML, Imaging Source).The gap between objective and tube lens was ~90 mm and that between the sensor and the backside of tube lens was about 148mm. The magnification of the objective-tube lens was 22.22X.

Image characterization
The flat lenses were used for imaging the object on to the sensor. The experimental setup is shown in Fig. S5 for both MDLs. The exposure time was adjusted to ensure that the images were not saturated. In each case, a dark frame was recorded and subtracted from the obtained images. For imaging, the objects were placed in front of the MDL. However, this time the objects were illuminated with both IR LEDs and IR floodlights to cover the entire range and the corresponding images were captured using a monochrome sensor (DMM 27UP031-ML, Imaging Source). The Field of View (FOV) for the MDL in both the vertical (Fig. S5 (a)) and horizontal direction ( Fig. S5 (b)) was calculated using trigonometry after noting down the appropriate distances. The distances were ascertained up to which the image was relatively sharp as seen with the naked eye. In addition, we measured the MTF as a function of incident angle as illustrated in Fig. S8. The following supplementary videos are also included: 1. EDOF_imaging_1: imaging stationary objects, keeping everything in focus. 2. EDOF_imaging_2: imaging stationary objects with 1 object in motion, keeping everything in focus.

Resolution from the USAF 1951 chart
Resolution test targets are typically used to measure the resolution of an imaging system. They consist of reference line patterns with well-defined thicknesses and spacing, which being designed to be kept in the same plane as the object being imaged. By identifying the largest set of non-distinguishable lines, one determines the resolving power of a given system. The R3L3S1N from Thorlabs (as used here) negative target uses chrome coating to cover the substrate, leaving the pattern itself clear, and works well in back-lit and highly illuminated applications. Because these targets feature sets of three lines, they reduce the occurrence of spurious resolution and thus help prevent inaccurate resolution measurements.

Modulation Transfer Function (MTF)
The average MTF at 10% contrast for the MDL is ~23 lp/mm over the entire range.

Comparison of EDOF MDL with conventional diffractive (Fresnel) lenses
To compare the EDOF MDL with regular diffractive lens, we have fabricated two Fresnel lens (FL) naming FL1 and FL2, having the same diameter as the EDOF MDL but each with a fixed focal length. The focal lengths of the FL1 and FL2 are 602.5mm and 100mm, respectively. The optical micrographs of the Fresnel lenses are shown in Fig .S13 The measured PSFs of FL1 and FL2 at their respective focal lengths and a few other exemplary distances are presented in Figure S14. The PSF of the EDOF MDL is also shown for reference. The XZ sections of the PSFs as a function of z is given in Figure  S15. We have also repeated Figure 3 and Figure 4 form the main text with the FL1 and FL2; the results are given in Fig. S16 and Fig. S17.

EDOF vs Reference aperture
We have also measured the diffraction pattern of a reference aperture having same diameter as the EDOF MDL. The cross section of the intensity patterns as a function of distance (z) is given in Fig. S18, the corresponding EDOF MDL values are also plotted for reference. Fig. S19: Measured intensity distribution at the YZ plane for the EDOF MDL and a reference aperture of same diameter.