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Journal ArticleDOI

Extended depth of field through wave-front coding

10 Apr 1995-Applied Optics (Optical Society of America)-Vol. 34, Iss: 11, pp 1859-1866
TL;DR: An optical-digital system that delivers near-diffraction-limited imaging performance with a large depth of field that is the standard incoherent optical system modified by a phase mask with digital processing of the resulting intermediate image.
Abstract: We designed an optical‐digital system that delivers near-diffraction-limited imaging performance with a large depth of field. This system is the standard incoherent optical system modified by a phase mask with digital processing of the resulting intermediate image. The phase mask alters or codes the received incoherent wave front in such a way that the point-spread function and the optical transfer function do not change appreciably as a function of misfocus. Focus-independent digital filtering of the intermediate image is used to produce a combined optical‐digital system that has a nearly diffraction limited point-spread function. This high-resolution extended depth of field is obtained through the expense of an increased dynamic range of the incoherent system. We use both the ambiguity function and the stationary-phase method to design these phase masks.

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Citations
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Journal ArticleDOI
TL;DR: In this article, a single high-resolution image of the scattered light, captured with a standard camera, encodes sufficient information to image through visually opaque layers and around corners with diffraction-limited resolution.
Abstract: Optical imaging through and inside complex samples is a difficult challenge with important applications in many fields. The fundamental problem is that inhomogeneous samples such as biological tissue randomly scatter and diffuse light, preventing the formation of diffraction-limited images. Despite many recent advances, no current method can perform non-invasive imaging in real-time using diffused light. Here, we show that, owing to the ‘memory-effect’ for speckle correlations, a single high-resolution image of the scattered light, captured with a standard camera, encodes sufficient information to image through visually opaque layers and around corners with diffraction-limited resolution. We experimentally demonstrate single-shot imaging through scattering media and around corners using spatially incoherent light and various samples, from white paint to dynamic biological samples. Our single-shot lensless technique is simple, does not require wavefront-shaping nor time-gated or interferometric detection, and is realized here using a camera-phone. It has the potential to enable imaging in currently inaccessible scenarios. Diffraction-limited imaging in a variety of complex media is realized based on analysis of speckle correlations in light captured using a camera phone.

899 citations

Journal Article
TL;DR: Methods for learning dictionaries that are appropriate for the representation of given classes of signals and multisensor data are described and dimensionality reduction based on dictionary representation can be extended to address specific tasks such as data analy sis or classification.
Abstract: We describe methods for learning dictionaries that are appropriate for the representation of given classes of signals and multisensor data. We further show that dimensionality reduction based on dictionary representation can be extended to address specific tasks such as data analy sis or classification when the learning includes a class separability criteria in the objective function. The benefits of dictionary learning clearly show that a proper understanding of causes underlying the sensed world is key to task-specific representation of relevant information in high-dimensional data sets.

705 citations

Proceedings ArticleDOI
29 Jul 2007
TL;DR: A novel design to reconstruct the 4D light field from a 2D camera image without any additional refractive elements as required by previous light field cameras is presented.
Abstract: We describe a theoretical framework for reversibly modulating 4D light fields using an attenuating mask in the optical path of a lens based camera. Based on this framework, we present a novel design to reconstruct the 4D light field from a 2D camera image without any additional refractive elements as required by previous light field cameras. The patterned mask attenuates light rays inside the camera instead of bending them, and the attenuation recoverably encodes the rays on the 2D sensor. Our mask-equipped camera focuses just as a traditional camera to capture conventional 2D photos at full sensor resolution, but the raw pixel values also hold a modulated 4D light field. The light field can be recovered by rearranging the tiles of the 2D Fourier transform of sensor values into 4D planes, and computing the inverse Fourier transform. In addition, one can also recover the full resolution image information for the in-focus parts of the scene. We also show how a broadband mask placed at the lens enables us to compute refocused images at full sensor resolution for layered Lambertian scenes. This partial encoding of 4D ray-space data enables editing of image contents by depth, yet does not require computational recovery of the complete 4D light field.

660 citations


Cites methods from "Extended depth of field through wav..."

  • ...Wavefront Coding [Dowski and Cathey 1995; Dowski and Johnson 1999; van der Gracht et al. 1996] is another technique to achieve extended Depth of Field (DOF) that use aspheric lenses to produce images with a depth-independent blur....

    [...]

Journal ArticleDOI
TL;DR: Freeform optics is the next generation of modern optics, bringing advantages of excellent optical performance and system integration as mentioned in this paper, and finds wide applications in various fields, such as new energy, illumination, aerospace and biomedical engineering.

638 citations

Journal ArticleDOI
TL;DR: In this article, a review of high-resolution miniature spatial light modulators (SLMs) in optical microscopy has been presented, which can be used to control and shape the sample illumination, or they can act as spatial Fourier filters in the imaging path.
Abstract: With the availability of high-resolution miniature spatial light modulators (SLMs) new methods in optical microscopy have become feasible. The SLMs discussed in this review consist of miniature liquid crystal displays with micron-sized pixels that can modulate the phase and/or amplitude of an optical wavefront. In microscopy they can be used to control and shape the sample illumination, or they can act as spatial Fourier filters in the imaging path. Some of these applications are reviewed in this article. One of them, called spiral phase contrast, generates isotropic edge enhancement of thin phase samples or spiral-shaped interference fringes for thicker phase samples, which can be used to reconstruct the phase topography from a single on-axis interferogram. If SLMs are used for both illumination control and spatial Fourier filtering, this combination for instance allows for the generalization of the Zernike phase contrast principle. The new SLM-based approach improves the effective resolution and avoids some shortcomings and artifacts of the traditional method. The main advantage of SLMs in microscopy is their flexibility, as one can realize various operation modes in the same setup, without the need for changing any hardware components, simply by electronically switching the phase pattern displayed on the SLMs.

409 citations


Cites methods from "Extended depth of field through wav..."

  • ...The so-called wavefront coding technique [46], which uses a combination of aspherical elements with numerical post-processing, can also extend the focal depth....

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References
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Book
01 Jan 1969
TL;DR: In this paper, a re-lease of the classic 1969 text examines step-by-step the development of radar resolution theory, including the capabilities and limits of radar and the details of radar design.
Abstract: This re-lease of the classic 1969 text examines step-by-step the development of radar resolution theory. Key topics include the capabilities and limits of radar and the details of radar design.

787 citations

Journal ArticleDOI
TL;DR: The method to obtain an increased depth of field consists of producing a modified incoherent image of the three dimensional object which, though degraded, has the same degradation for all object planes.

207 citations

Journal ArticleDOI
TL;DR: To improve the imaging properties of a defocused optical system, the use of shaded apertures is studied theoretically and experimentally and shows that near focus the OTF for T(A) has higher values in the low frequency region than has either T(B) or T(c).
Abstract: To improve the imaging properties of a defocused optical system, the use of shaded apertures is studied theoretically and experimentally. The study is based on the optical transfer function (OTF). The two shaded apertures studied are the type in which the amplitude transmittance decreases gradually from the center of the pupil toward its rim, T(A), and the type in which the amplitude transmittance decreases from its rim toward the center, T(B). For comparison, the effects achieved with a clear aperture, T(C), are included. The results of the calculations show that near focus the OTF for T(A) has higher values in the low frequency region than has either T(B) or T(c). When the system is defocused, the shaded aperture of the type T(A) yields an improved defocused image that is faithful to the outline of the object. The quality of the defocused image obtained with T(B) is worsened. When the OTF is used as a means for judging the quality of the defocused image, the two necessary conditions on the functions appear to be that the OTF (1) must be a monotonically decreasing function and (2) must be nonnegative. These conditions are confirmed by experiment. Since the transmittance variation of the shaded apertures is achieved by absorption, the effects due to the resultant decreases in light level are also considered.

171 citations

Book
10 Apr 1974

145 citations

Journal ArticleDOI
TL;DR: In this article, it was shown that the Ambiguity function of the generalized pupil function of an optical system is a polar display of the optical transfer function with the focus error as variable.

141 citations