We demonstrate a compact, easy-to-build computational camera for single-shot three-dimensional (3D) imaging. Our lensless system consists solely of a diffuser placed in front of an image sensor. Every point within the volumetric field-of-view projects a unique pseudorandom pattern of caustics on the sensor. By using a physical approximation and simple calibration scheme, we solve the large-scale inverse problem in a computationally efficient way. The caustic patterns enable compressed sensing, which exploits sparsity in the sample to solve for more 3D voxels than pixels on the 2D sensor. Our 3D reconstruction grid is chosen to match the experimentally measured two-point optical resolution, resulting in 100 million voxels being reconstructed from a single 1.3 megapixel image. However, the effective resolution varies significantly with scene content. Because this effect is common to a wide range of computational cameras, we provide a new theory for analyzing resolution in such systems.

DiffuserCam: lensless single-exposure 3D imaging

Image data is processed to facilitate focusing and/or optical correction. According to an example embodiment of the present invention, an imaging arrangement collects light data corresponding to light passing through a particular focal plane. The light data is collected using an approach that facilitates the determination of the direction from which various portions of the light incident upon a portion of the focal plane emanate from. Using this directional information in connection with value of the light as detected by photosensors, an image represented by the light is selectively focused and/or corrected.

Imaging arrangements and methods therefor

A system for increasing the depth of field and decreasing the wavelength sensitivity and the effects of misfocus-producing aberrations of the lens of an incoherent optical system incorporates a special purpose optical mask into the incoherent system. The optical mask has been designed to cause the optical transfer function to remain essentially constant within some range from the in-focus position. Signal processing of the resulting intermediate image undoes the optical transfer modifying effects of the mask, resulting in an in-focus image over an increased depth of field. Generally the mask is placed at a principal plane or the image of a principal plane of the optical system. Preferably, the mask modifies only phase and not amplitude of light. The mask may be used to increase the useful range of passive ranging systems.

Extended depth of field optical systems

A method is performed to refocus a digital photographic image comprising a plurality of pixels. In the method, a set of images is computed corresponding to the digital photographic image and focused at different depths. Refocus depths for at least a subset of the pixels are identified and stored in a look-up table. At least a portion of the digital photographic image is refocused at a desired refocus depth determined from the look-up table.

Interactive refocusing of electronic images

Briefly stated, the operating depth of field for a bar code scanner, preferably a laser scanner, is increased by placing a cubic phase mask (CPM) in the scanning beam. The masked beam is then scanned and reflected off a bar code and received by a photodetector. The received signal is then processed to recover the original unperturbed representation of the bar code pattern. The processed signal has an increased depth of field over an unmasked scanner signal.

Method and apparatus for extending operating range of bar code scanner

Transmission functions are derived that are valid in the nonparaxial case for a class of lenses that will image a continuum of points along an optical axis to a single image point This lens, which we call a logarithmic asphere, is then used in a digital camera The resolution of the camera is limited by the pixel size of the CCD; ie, it is not diffraction limited Digital processing is used to recover the image, and image-plane processing is used for speed We find a tenfold increase in the depth of field over that for the diffraction-limited case

Electronic imaging using a logarithmic asphere.

A system for imaging with a circularly symmetric multifocal aspheric lens is provided for obtaining an extended depth of field. The system includes a camera for capturing an image of at least one object through a circularly symmetric multifocal aspheric lens to provide a blurred image, and a computer system for processing the captured blurred image to provide a recovered image of the object having an extended depth of field. The recovered image may be outputted to a display or other peripheral device. Processing of the blurred image utilizes one of inverse filtering, convolution matrix (e.g., edge sharpening matrix), or maximum entropy. The computer system performing image processing may be in the camera or represent a computer system external to the camera which receives the blurred image. The extended depth of field is characterized by the object being in focus over a range of distances in the recovered image.

Imaging using a multifocal aspheric lens to obtain extended depth of field

An extended depth of field is achieved by a computational imaging system that combines a multifocal imaging subsystem for producing a purposefully blurred intermediate image with a digital processing subsystem for producing a recovered image having an extended depth of field. The multifocal imaging system preferably exhibits spherical aberration as the dominant feature of the purposeful blur. A central obscuration of the multifocal imaging subsystem renders point-spread functions of object points more uniform over a range of object distances. An iterative digital deconvolution algorithm for converting the intermediate image into the recovered image contains a metric parameter that speeds convergence, avoids stagnations, and enhances image quality.

Extended Depth of Field Using a Multi-Focal Length Lens with a Controlled Range of Spherical Aberration and a Centrally Obscured Aperture

Imaging systems are described which use a logarithmic asphere and image processing in order to increase the depth of field substantially beyond classical limits. A nonparaxial form of the diffraction theory integral for an impulse response is derived and evaluated in order to establish a precise expression for the transmission function of this asphere. This nonparaxial physical optics formulation provides results of fractional wavelength accuracy that enable one immediately to complete the design and fabrication of the optical system. Circularly symmetric aspherical lenses, either for single-lens cameras or blurring phase filters for use with commercial photographic lenses, have been fabricated using advanced grinding and finishing machines. Computer simulation studies are presented to show that a logarithmic asphere is capable of diffraction-limited performance over an extended depth of field. Experimental imaging results including digital processing by an inverse filter show a tenfold increase in the depth of field.

https://iopscience.iop.org/article/10.1088/1464-4258/5/5/358/pdf

Extended depth of field using a logarithmic asphere

A theory for an integrated system is described that combines a logarithmic aspheric imaging lens with maximum-entropy digital processing to extend the depth of field ten times over that of a conventional lens and to provide near-diffraction-limited resolution. Two types of logarithmic aspheres are derived that are circularly symmetric lenses with controlled continuous radial variation of focal length. The details of an iterative maximum-entropy algorithm are also presented. The properties of convergence and speed of the algorithm are greatly improved by introducing a metric parameter to adjust the weight of different pixel values of the recovered picture in each loop properly.

Wanli Chi

Papers

Electronic imaging using a logarithmic asphere.

Imaging using a multifocal aspheric lens to obtain extended depth of field

Extended Depth of Field Using a Multi-Focal Length Lens with a Controlled Range of Spherical Aberration and a Centrally Obscured Aperture

Extended depth of field using a logarithmic asphere

Computational imaging with the logarithmic asphere: theory