Nojan Motamedi

Fiber-coupled monocentric lens imaging

Monocentric lenses have proven exceptionally capable of high numerical aperture wide-field imaging - provided the overall system can accommodate a spherically curved image surface. We will present a summary of recent work on the design optimization and experimental demonstrations of monocentric wide-field imaging, including systems based on waveguide coupling of the image to conventional focal plane sensor(s).

Analysis and compensation of moiré effects in fiber-coupled image sensors

Imaging fiber bundles can relay a curved image surface to a conventional at focal plane, effectively providing the curved image sensor needed for some high performance lenses. If the fiber bundle period or image sensor pitch are very different, the system resolution is determined by the oversampled fiber or sensor feature. But crosstalk imposes an approximately 2µm minimum waveguide pitch, and light collection and fabrication constraints impose a lower limit of 1-2µm for the sensor pitch. Maximizing image information leads to some degree of aliasing, which appears in the form of moiré pattern on the raw image sensed. For example, a 30 Mpixel 120° field of view imager using a 1.75µm Bayer filtered CMOS focal plane with 2.5µm pitch fiber bundle yielded images with visible moiré. Here we present a study of moiré effects in fiber-coupled image sensors, including a method for quantitative analysis of moiré, and experimental characterization of the sensors with 1.1µm pixel pitch, the highest spatial resolution in commercially available focal plane arrays. We investigate the effect of exposure time of the sensor, angle of incidence of collimated light, and imaging lens F/# on the raw moiré pattern strength. This study provides guidelines for optimization and operation of high resolution fiber-coupled imagers.

Efficient analysis of deep high-index-contrast gratings under arbitrary illumination

An efficient method for computing the problem of an electromagnetic beam transmission through deep periodic dielectric gratings is presented. In this method the beam is decomposed into a spectrum of plane waves, transmission coefficients corresponding to each such plane wave are found via Rigorous Coupled Wave Analysis, and the transmitted beam is calculated via inverse Fourier integral. To make the approach efficient for deep gratings the fast variations of the transmission coefficients versus spatial frequency are accounted for analytically by casting the summations and integrals in a form that has explicit rapidly varying exponential terms. The resulting formulation allows computing the transmitted beam with a small number of samples independent of the grating depth.

Quantitative analysis and temperature-induced variations of moiré pattern in fiber-coupled imaging sensors.

Imaging fiber bundles can map the curved image surface formed by some high-performance lenses onto flat focal plane detectors. The relative alignment between the focal plane array pixels and the quasi-periodic fiber-bundle cores can impose an undesirable space variant moiré pattern, but this effect may be greatly reduced by flat-field calibration, provided that the local responsivity is known. Here we demonstrate a stable metric for spatial analysis of the moiré pattern strength, and use it to quantify the effect of relative sensor and fiber-bundle pitch, and that of the Bayer color filter. We measure the thermal dependence of the moiré pattern, and the achievable improvement by flat-field calibration at different operating temperatures. We show that a flat-field calibration image at a desired operating temperature can be generated using linear interpolation between white images at several fixed temperatures, comparing the final image quality with an experimentally acquired image at the same temperature.

Digital image processing for wide-angle highly spatially variant imagers

High resolution, wide field-of-view and large depth-of-focus imaging systems are greatly desired and have received much attention from researchers who seek to extend the capabilities of cameras. Monocentric lenses are superior in performance over other wide field-of-view lenses with the drawback that they form a hemispheric image plane which is incompatible with current sensor technology. Fiber optic bundles can be used to relay the image the lens produces to the sensors planar surface. This requires image processing to correct for artifacts inherent to fiber bundle image transfer. Using a prototype fiber coupled monocentric lens imager we capture single exposure focal swept images from which we seek to produce extended depth-of-focus images. Point spread functions (PSF) were measured in lab and found to be both angle and depth dependent. This spatial variance enforces the requirement that the inverse problem be treated as such. This synthesis of information allowed us to establish a framework upon which to mitigate fiber bundle artifacts and extend the depth-of-focus of the imaging system.

Enhanced Field of View Fiber Coupled Image Sensing

Fiber-coupled sensors allow detection of spherical image surfaces. We investigate the field of view possible with a single straight fiber bundle, demonstrating how the field can be extended by annular microprisms near the image surface.

Image restoration in fiber-coupled imagers using space-variant impulse response characterization

Fiber-coupled image sensors have attracted interest in recent years for high-resolution conformal image transfer, including mapping of the spherical image surface of a monocentric wide-angle lens to one or more flat focal plane sensors. However, image resolution is lost due to fiber bundle defects, moiré from lateral fiber-sensor misalignment, and blur due to the nonzero gap between fiber bundle and the image sensor. Here we investigate whether subpixel impulse response characterization of the strongly shift-variant impulse response can be used with existing image-processing techniques to recover the resolution otherwise lost in image transfer. We show that the submicrometer impulse response is experimentally repeatable, and can be used to recover image data and reveal fine features of the input surface structure of a 2.5 μm pitch fiber bundle.

Curved fiber bundles for monocentric lens imaging

Monocentric lenses allow high resolution panoramic cameras, where imaging fiber bundles transport the hemispherical image surface to conventional focal planes. Refraction at the curved image surface limits the field of view coupled through a single bundle of straight fibers to less than ±34°, even for NA 1 fibers. Previously we have demonstrated a nearly continuous 128° field of view using a single lens and multiple adjacent straight fiber-coupled image sensors, but this imposes mechanical complexity of fiber bundle shaping and integration. However, a 3D waveguide structure with internally curved optical fiber pathways can couple the full continuous field of view onto a single focal plane. Here, we demonstrate wide-field imaging using a monocentric lens and a single curved fiber bundle, showing that the 3D bundle formed from a tapered fiber bundle can be used for relaying a 128° field of view from a curved input to the planar output face. We numerically show the coupling efficiency of light to the tapered bundle for different field of views depends on the taper ratio of the bundle as well as center of the curvature chosen for polishing of the fiber bundle facet. We characterize a tapered fiber bundle by measuring the angle dependent impulse response, transmission efficiency and the divergence angle of the light propagating from the output end of the fiber.

Panoramic full-frame imaging with monocentric lenses and curved fiber bundles

Panoramic imaging is important for many different applications, including content for immersive virtual reality. Although compact 360 cameras can be made from an array of small-aperture ‘smartphone’ imagers, their small (typically 1.1 m) pixels provide low dynamic range. Moreover, digital single-lens-reflex and cinematographic imagers have 4–8 m pixels, but require correspondingly longer focal length lenses. Conventional ‘fisheye’ lenses are also problematic because they are bulky and have low light collection (typically F/2.8 to F/4, where F is the focal length divided by the lens aperture). An alternative path to panoramic imaging is ‘monocentric’ optics, where all surfaces—including the image surface—are concentric hemispheres.1 The symmetry of these lenses means that lateral color and off-axis aberrations (astigmatism and coma) are eliminated. In addition, the simple lens structures can be used to correct for spherical and axial color aberrations to yield extraordinarily wide angle resolution and light collection.2 The image that is produced can be coupled to a conventional focal plane, via a fiber bundle faceplate (with a curved input and flat output face).3 Fiber faceplates are solid glass elements made of small, high-index optical fibers separated by a thin, low-index cladding, used for nonimaging transfer of light between the input and output faces. From our research, within the Defense Advanced Research Projects Agency (DARPA) SCENICC (Soldier Centric Imaging via Computational Cameras) program, we have shown that fiber bundles can reach a spatial resolution of 2 m.4 We have also Figure 1. Geometry of a monocentric lens (left) and the spherical image surface it forms (right) can be coupled to CMOS focal plane(s) by an array of straight fiber bundles (top) or a single curved fiber bundle (bottom). The F-number is the focal length (f) divided by the lens aperture.