The accuracy of depth estimation based on defocus effects has been essentially limited by the depth of field of the imaging system. We show that depth estimation can be improved significantly relative to classical methods by exploiting three-dimensional diffraction effects. We formulate the problem by using information theory analysis and present, to the best of our knowledge, a new paradigm for depth estimation based on spatially rotating point-spread functions (PSFs). Such PSFs are fundamentally more sensitive to defocus thanks to their first-order axial variation. Our system acquires a frame by using a rotating PSF and jointly processes it with an image acquired by using a standard PSF to recover depth information. Analytical, numerical, and experimental evidence suggest that the approach is suitable for applications such as microscopy and machine vision. © 2006 Optical Society of America OCIS codes: 110.6880, 110.4850, 100.6640, 150.5670. The human visual system uses defocus as a depth cue. 1 Optical images convey three-dimensional (3D) information by the amount of blur in each image region: the further the object is from the in-focus plane, the more blurred it appears. This principle is exploited in techniques known as depth from defocus (DFD) by jointly processing frames acquired in different focus or aperture settings. [1][2][3][4][5][6][7] Relative to stereovision, DFD is more robust to occlusion and correspondence problems. 8 Moreover, in applications that require a large numerical aperture (NA), particularly in high-magnification microscopy, DFD is more suitable than stereovision. Previous DFD work has concentrated on the implementation of signal processing algorithms based on a geometrical optical model. Typical systems have utilized a clear, circular aperture as is found in standard camera lenses. 1-7 However, the point-spread function (PSF) of such systems has not been optimized for depth estimation. Therefore in this Letter we engineer the PSF to achieve enhanced performance in this specific task. We exploit the freedom provided by diffractive optics to design unconventional optical responses. In particular, we investigate 3D PSFs whose transverse cross sections rotate with respect to each other as a result of diffraction in free space. 9-14 Rotating PSFs provide a faster rate of change with depth than PSFs of clear pupil systems having the same NA. 9 As a consequence, we show here that rotating PSFs present approximately an order of magnitude increase in Fisher information (FI) along the depth dimension, when compared with standard pupils. Finally, we demonstrate this principle in an experiment based on a two-channel system that encodes a rotating PSF.The more dissimilar the PSF is at different values of defocus, the easier it is to distinguish between depth planes in the presence of noise. Defocus is typically quantified by the defocus parameter , defined as 15where is the wavelength of light, and z obj focus and z obj Ј are the in-focus and actual object distances from the entrance pupil, re...

Accurate estimation of the three-dimensional (3D) position of particles is critical in applications like biological imaging, atom/particle-trapping, and nanomanufacturing. While it is well-known that localization accuracy better than the Rayleigh resolution limit is possible, it was recently shown that, for photon-limited cases, 3D point spread functions (PSFs) can be shaped to increase accuracies over a 3D volume [Pavani and Piestun, Opt. Express 16, 22048 (2008)]. Here, we show that in the detector-limited regime, the gain in accuracy occurs in all three dimensions throughout the axial range of interest. The PSF is shaped as a double helix, resulting in a system with fundamentally better 3D localization accuracies than standard PSF systems, capable of achieving single-image subnanometer accuracies.

Imaging systems using aspheric imaging lenses with complementary computation can deliver performance unobtainable in conventional imaging systems. These new imaging systems, termed Wavefront coded imaging systems, use specialized optics to capture a coded image of the scene. Decoding the intermediate image provides the "human-usable" image expected of an imaging system. Computation for the decoding step can be made completely transparent to the user with today's technology. Real-time Wavefront coded systems are feasible and cost-effective. This "computational imaging" technology can be adapted to solve a wide range of imaging problems. Solutions include the ability to provide focus-free imaging, to increase the field of view, to increase the depth of read, to correct for aberrations (even in single lens systems), and to account for assembly and temperature induced misalignment. Wavefront coded imaging has been demonstrated across a wide range of applications, including microscopy, miniature cameras, machine vision systems, infrared imaging systems and telescopes.

We present a method for passive ranging with incoherent light. The scheme uses a single optical channel and is particularly suitable for locating and ranging particles. Our aim is to create an optical system with increased discrimination among depth planes as compared to classical clear aperture solutions. We thus propose a criterion for evaluating a general point spread function for use in passive ranging. Then, we show that rotating point spread functions are good according to this criterion. An experimental realization of the point spread function by use of a computergenerated hologram is presented as well as a simulation of its depth discrimination.

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