nn Carles Santacana, G., Muyo, G., Bustin, N., Wood, A., and Harvey, A. R. (2015) Compact multi-aperture imaging with high-angular- resolution. Journal of the Optical Society of America A: Optics Image Science and Vision, 32(3). pp. 411-419. Copyright © 2015 Optical Society of America. A copy can be downloaded for personal non-commercial research or study, without prior permission or charge Content must not be changed in any way or reproduced in any format or medium without the formal permission of the copyright holder(s) http://eprints.gla.ac.uk/101672/ Deposited on: 03 March 2015 Enlighten – Research publications by members of the University of Glasgow http://eprints.gla.ac.uk Compact multi-aperture imaging with high-angular-resolution Guillem Carles, 1 Gonzalo Muyo, 2 Nicholas Bustin, 3 Andrew Wood, 3 and Andrew R. Harvey1 ,* 1 School of Physics and Astronomy, University of Glasgow, United Kingdom 2 School of Engineering and Physical Sciences, Heriot-Watt University, United Kingdom 3 Qioptiq Ltd, St Asaph, United Kingdom *Corresponding author: [email protected] Received Month X, XXXX; revised Month X, XXXX; accepted Month X, XXXX; posted Month X, XXXX (Doc. ID XXXXX); published Month X, XXXX Previous reports have demonstrated that it is possible to emulate the imaging function of a single conventional lens with an NxN array of identical lenslets to provide an N-fold reduction in imaging-system track length. This approach limits the application to low-resolution imaging. We highlight how using an array of dissimilar lenslets, with an array width that can be much wider than the detector array, high-resolution super-resolved imaging is possible. We illustrate this approach with a ray-traced design and optimization of a long-wave infrared system employing a 3x3 array of free-form lenslets to provide a four-fold reduction in track length compared to a baseline system. Simulations of image recovery show that recovered image quality is comparable to that of the baseline system. © 2012 Optical Society of America OCIS codes: (100.3020) Image reconstruction-restoration; (100.6640) Superresolution; (110.1758) Computational imaging. http://dx.doi/org/10.1364/AO.99.099999 1. Introduction track-length. Focal-length reduction decreases the object-space angular sampling frequency of the detector array (that is, the The physical dimensions of conventional imaging systems are detector sampling frequency projected onto the scene), but since dominated by the interplay between fundamental parameters N×N images are recorded with, in general, dissimilar sampling such as field-of-view, angular resolution and detector size, and in phases, super-resolution techniques may be used to effectively particular by the focal length of the lens. Multi-aperture (MA) maintain the higher sampling frequency of the single-aperture imaging [1] involves the replacement of the function of a single imaging system [7]. This is true only if (1) sampling is non- conventional lens by an array of lenses of shorter focal length to redundant between image channels and (2) if the reduced record an array of images onto a single detector array that are diffraction-limited angular resolution of the smaller image combined using super-resolution algorithms to yield a single channels is not too low. On the first issue; MA imaging relies on high-resolution image. When the angular resolution is limited by aliasing to encode angular-frequency information lying above the the size of the detector pixels, this can enable a significant Nyquist frequency within the baseband of recorded images, and reduction in imaging-system track length without sacrificing on non-redundancy between images to enable super-resolution to angular resolution. The use of a single detector array with an recover the angular-frequency components between the Nyquist array of nominally identical lenses, as previously reported [2-6], frequency and the optical cut-off from baseband images. The limits the maximum aperture of the lens array to the width of sampling phase and redundancy varies with range and at certain the detector array and hence the benefit for MA imaging has ranges there could, for a perfectly manufactured system, be previously been restricted to low-angular-resolution systems. We significant redundancy between channels and super-resolution describe how the use of arrays of dissimilar lenses, some would be ineffective. In practice however, typical manufacturing operating off-axis, but with an overall width wider than the tolerances tend to randomize sampling phase, maintaining the detector array, enables the length-reduction benefit of MA effectiveness of super-resolution with range [8]. On the second imaging to be attained for high-resolution imaging. We issue; the N-fold reduction in width of a lens aperture also demonstrate the concept with an example design and simulation reduces the diffraction-limited angular resolution by a factor N of imaging performance in the long-wavelength infrared (LWIR) and thus MA imaging can maintain the angular resolution of a band in which the length of the lens is reduced by a factor of four single-aperture imaging system only for small N. MA imaging whilst maintaining imaging performance. have previously been used to improve compactness, but its In general, substitution of a single full-aperture lens by a MA application has been restricted to low-angular resolution imaging system consisting of N×N smaller-aperture imaging channels [2-6]. This restriction is associated with the use of arrays of allows an N-fold reduction in focal length and hence in the lens identical lenslets, whereas we describe here how use of arrays of which enables high-resolution MA imaging for common practical systems for the first time. This requires that the outer lenses of the lens array operate off-axis and generally introduces dissimilar distortions between channels that provide, in principle, the benefit of breaking the redundancy to provide consistent super-resolution performance [8]. The arrangement of this article is as follows: section 2 offers a physical insight into the fundamental design trade-offs; section 3 presents an example optimized and ray-traced design for a LWIR imaging system employing a 3x3 array of lenses with an aperture 4.5 times wider than the detector, and shows simulated imaging performance compared with a conventional baseline system; we conclude in section 4. 2. Multi-aperture design The salient aim in the design of a MA imaging system is reduction of physical length while maintaining imaging performance. We consider here the replacement of a single lens of focal length f and diameter D by an N×N array of lenslets of focal length f/N and diameter D/N. We will consider first the configuration reported in [1] and termed Thin Observation Module by Bound Optics (TOMBO) where the lens-array width D is limited to be equal to the detector width. This restriction limits application of this concept to low-angular-resolution imaging. We will then consider how the use of a larger aperture DD' = α allows higher angular resolutions to be achieved. Traditional TOMBO-like designs thus correspond to MA systems with N ≥ 2 and α ≤ 1 . The focal length of each subsystem is reduced by a factor N for a MA system and the aim is hence to maximally increase N Fig. 1. Variation of normalized system cutoff frequency sys with ν c without degrading angular resolution. The width of the point- N for representative MA systems, for (a) f=33mm with α=1 and (b) spread function (PSF) at the detector is the same regardless of N f=100mm with α=1 (grey line) and α=4.5 (black line). The because focal ratio is preserved, but since the magnification is drawings depict the gain in compactness. Pixel pitch is p=25µm increased by a factor N, the angular-resolution limit due to and λ=10µm. diffraction is reduced by N. We describe resolution in angular larger, but necessarily dissimilar lenslets, offers the potential of frequencies to allow comparison for different N. We thus now reduced track-length for high-angular-resolution imaging. A quid consider how the angular resolution varies in terms of the system pro quo for this advantage is the increased complexity of image angular cutoff frequency of the imaging system. For the baseline recovery associated with spatial variations in imaging N=1 imager, the angular optical-cutoff frequency is ναλo = D / , characteristics. where λ is the wavelength, but for detector-limited imaging, the Use of MA architectures is also found in the so-called system cutoff frequency is the Nyquist angular frequency, compound-eye cameras, for example using prisms or dissimilar ν Ny = fp/2 , where p is pixel pitch. For a MA system, the lenslets to steer light beams to extend the field-of-view by Nyquist angular frequency of each channel is reduced to stitching the acquired subimages [9-12]. These approaches ch / N but the effective Nyquist frequency of the super- include use of dissimilar lenses to increase non-redundancy [6] or ννNy= Ny lenslet arrays exceeding detector width [11, 12]; however, none of resolved image is identical to that of the baseline imager, these demonstrate reduced track length for arbitrarily high provided the sampling is non redundant. Throughout this paper angular resolution. MA imaging is also a feature of light-field we refer to νNy as the Nyquist angular frequency of the baseline imaging, such as is found in plenoptic cameras [13, 14] where a imaging system. The optical cutoff frequency for each lenslet is lenslet array is placed close to the image plane. By reimaging the ch sys ναλo = DN/( ) and the system cutoff frequency, ν c , is differing parts of the pupil, these techniques have similarities ch therefore the lesser of νNy and ν ; that is, with MA imaging, including the ability to digitally simulate o reduced depth of field, but improved compactness has not been ⎧ααDDp2 reported.