Depth from diffracted rotation

Abstract

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...

Enhancing the performance of the light field microscope using wavefront coding

“…A phase mask that minimizes the Fisher information results in a PSF that is insensitive to defocus, thus granting the optical system extended depth of field. In contrast, in [21] the authors designed a phase-amplitude mask that results in a rotating PSF that yields a high Fisher information with respect to defocus. This allowed them to estimate the depth of a two-dimensional thin object from the rotation angle of the PSF via a deconvolution process.…”

Super-resolution photon-efficient imaging by nanometric double-helix point spread function localization of emitters (SPINDLE)

“…1(a) and 1(b), respectively. The DH-PSF enhances the Fisher information for axial localization and can be used for 3D imaging applications like localization based microscopy [22], particle tracking [22][23][24], super-resolution imaging [12], depth ranging [25], profilometry and imaging optical tweezers [26]. The DH-PSF allows 3D localization of multiple sparse particles in a single image with high localization precision and longer depthof-field than other 3D localization methods [18], making it attractive for tracking and superresolution imaging.…”

Three-dimensional, single-molecule fluorescence imaging beyond the diffraction limit by using a double-helix point spread function

“…1B Inset). This method is based on earlier work that showed that rotating intensity DH-PSF distributions could be formed by taking superpositions of G-Laguerre (GL) modes that form a cloud along a line in the GL modal plane (23)(24)(25). The DH-PSF has been used to localize photon-unlimited point scatterers inside the volume of a glass slide, and to track moving fluorescent microspheres (26).…”