Improved superresolution in coherent optical systems

Objects that temporally vary slowly can be superresolved by the use of two synchronized moving masks such as pinholes or gratings. This approach to superresolution allows one to exceed Abbe's limit of resolution. Moreover, under coherent illumination, superresolution requires a certain approximation based on the time averaging of intensity rather than of field distribution. When extensive digital postprocessing can be incorporated into the optical system, a detector array and some postprocessing algorithms can replace the grating that is responsible for information decoding. In this way, no approximation is needed and the synchronization that is necessary when two gratings are used is simplified. Furthermore, we present two novel approaches for overcoming distortions when extensive digital postprocessing cannot be incorporated into the optical system. In the first approach, one of the gratings, in the input or at the output plane, is shifted at half the velocity of the other. In the second approach, various spectral regions are transmitted through the system's aperture to facilitate postprocessing. Experimental results are provided to demonstrate the properties of the proposed methods.     

Superresolution readout system with electrical equalization for optical disks

An electrical equalizer for a superresolution readout system with an optical apodizer is proposed and verified experimentally. This superresolution readout system uses a five-tap transversal filter as the electrical equalizer instead of additional optics to suppress enlarged sidelobes, and it achieves higher resolution than the diffraction-limited system. The transfer function of the electrical equalizer is also derived theoretically. This approach allows fabrication of a readout system with a good signal-to-noise ratio and a compact head.     

Superresolution optical system with two fixed generalized Damman gratings

We present a system that exceeds the Rayleigh limit of resolution, by placing two fixed gratings in predetermined positions. Lukosz suggested a setup that managed to exceed the Rayleigh limit of resolution [J. Opt. Soc. Am. 56, 1463 (1966); 57, 932 (1967)]. However, Lukosz's technique had some drawbacks that the new suggested system attempts to resolve. Similar to Lukosz's technique, the proposed system works without any moving elements and with no time- or wavelength-restricting conditions. It is suitable for coherent or incoherent two-dimensional imaging. However, the new system contains some important modifications. Although the system uses only two gratings, it is capable of producing superresolution without using an additional imaging lens at the output plane. The generalized Damman gratings allow for obtaining undistorted spectral restoration of information. To achieve superresolution, the input object is duplicated. The trade-off for higher resolution is a smaller field of view. Experimental results validate the theoretical analysis.     

One-dimensional superresolution optical system for temporally restricted objects

Objects that temporally vary slowly may be superresolved by use of moving gratings. A system of this kind had been proposed three decades ago. However, it provides some distortion of the spectral response of the resolved object. In this project, an enhanced method based on Dammann gratings instead of regular gratings is suggested. The modified approach achieves results with an undistorted output and relatively high light efficiency, and it is effective for both coherent and incoherent light. Experimental results are provided for demonstrating the ability of the new approach.     

Time multiplexing superresolution based on interference grating projection

In a previous work done by the authors, it was shown that the superresolution concept based on two moving gratings could be effected by a physical grating attached to the object and a virtual grating. This concept was shown to be very efficient and exhibited features that are helpful in removing some artifacts caused when coherent illumination is used. Furthermore, it simplifies the optical and mechanical modules of the super-resolving system by removing the need for mechanical movement of one grating. However, the system still required the need for moving the first (encoding) grating attached to the input. In this study the encoding grating is replaced by use of a projected grating. This approach simplifies the need for attaching the grating to the input object and thus new applications, such as remote sensing can be considered. The theoretical concept is demonstrated and experimental results are shown.     

Synthetic aperture superresolution with multiple off-axis holograms

An optical setup to achieve superresolution in microscopy using holographic recording is presented. The technique is based on off-axis illumination of the object and a simple optical image processing stage after the imaging system for the interferometric recording process. The superresolution effect can be obtained either in one step by combining a spatial multiplexing process and an incoherent addition of different holograms or it can be implemented sequentially. Each hologram holds the information of each different frequency bandpass of the object spectrum. We have optically implemented the approach for a low-numerical-aperture commercial microscope objective. The system is simple and robust because the holographic interferometric recording setup is done after the imaging lens.     

Axial superresolution of two-photon microfabrication

An axial superresolution diffraction theory is developed in a two-photon microfabrication system. This method can improve the axial superresolution of the two-photon microfabrication system. A theoretical analysis of the photosensitive resin is discussed based on the exciting power and the concentration of free radical theory. Simulated results of the two-photon microfabrication verify the method and show that it can provide insight into the microfabrication system.     

From the channel model of an InSb-based superresolution optical disc system to impulse response and resolution limits

The signal model of a superresolution optical channel can be an efficient tool for developing components of an associated high-density optical disc system. While the behavior of the laser diode, aperture, lens, and detector are properly described, a general mathematical model of the superresolution disc itself has not yet been available until recently. Different approaches have been made to describe the properties of a mask layer, mainly based on temperature- or power-dependent nonlinear effects. A complete signal-based or phenomenological optical channel model--from non-return-to-zero inverted input to disc readout signal--has recently been developed including the reflectivity of a superresolution disc with InSb used for the mask layer. In this contribution, the model is now extended and applied to a moving disc including a land-and-pit structure, and results are compared with data read from real superresolution discs. Both impulse response and resolution limits are derived and discussed. Thus the model provides a bridge from physical to readout signal properties, which count after all. The presented approach allows judging of the suitability of a mask layer material for storage density enhancement already based on static experiments, i.e., even before developing an associated disc drive.     

Mathematical extrapolation of image spectrum for constraint-set design and set-theoretic superresolution

Several powerful iterative algorithms are being developed for the restoration and superresolution of diffraction-limited imagery data by use of diverse mathematical techniques. Notwithstanding the mathematical sophistication of the approaches used in their development and the potential for resolution enhancement possible with their implementation, the spectrum extrapolation that is central to superresolution comes in these algorithms only as a by-product and needs to be checked only after the completion of the processing steps to ensure that an expansion of the image bandwidth has indeed occurred. To overcome this limitation, a new approach of mathematically extrapolating the image spectrum and employing it to design constraint sets for implementing set-theoretic estimation procedures is described. Performance evaluation of a specific projection-onto-convex-sets algorithm by using this approach for the restoration and superresolution of degraded images is outlined. The primary goal of the method presented is to expand the power spectrum of the input image beyond the range of the sensor that captured the image.     

Pseudospectral modal method for conical diffraction of gratings

For lamellar gratings and other layered periodic structures, the modal methods (including both analytic and numerical ones) are often the most efficient, since they avoid the discretization of one spatial variable. The pseudospectral modal method (PSMM) previously developed for in-plane diffraction problems of one-dimensional gratings achieves high accuracy for a small number of discretization points, and it outperforms most other modal methods. In this paper, an extension of the PSMM to conical diffraction problems is presented and implemented. Numerical examples are used to demonstrate the high accuracy and excellent convergence property of this method for both dielectric and metallic gratings.     

Thin infrared imaging systems through multichannel sampling

The size of infrared camera systems can be reduced by collecting low-resolution images in parallel with multiple narrow-aperture lenses rather than collecting a single high-resolution image with one wide-aperture lens. We describe an infrared imaging system that uses a three-by-three lenslet array with an optical system length of 2.3 mm and achieves Rayleigh criteria resolution comparable with a conventional single-lens system with an optical system length of 26 mm. The high-resolution final image generated by this system is reconstructed from the low-resolution images gathered by each lenslet. This is accomplished using superresolution reconstruction algorithms based on linear and nonlinear interpolation algorithms. Two implementations of the ultrathin camera are demonstrated and their performances are compared with that of a conventional infrared camera.     

Optical superresolution of focused partially spatially coherent laser beams

We report design theories of a diffractive superresolution element (DSE) to implement optical superresolution of focused partially spatially coherent laser beams. The design problem of the DSE can be transformed into a problem of linear programming to obtain a globally optimal solution. By using the design theories, some fundamental limits of optical superresolution of focused partially spatially coherent laser beams are proposed, and several design examples are provided. As expected, both the fundamental limits and the design examples show that worse spatial coherence will cause worse superresolution performance. The design theories provide a design approach with partially coherent beams and may be useful for other design problems under partially coherent illumination.     

Three-dimensional superresolution by three-zone complex pupil filters

Complex pupil filters are introduced to improve the three-dimensional resolving power of an optical imaging system. Through the design of the essential parameters of such filters, the transmittance and radius of the first zone, three-dimensional superresolution is realized. The Strehl ratio and the transverse and axial gains of such filters are analyzed in detail. A series of simulation examples of such filters are also presented that prove that three-dimensional superresolution can be realized. The advantage of such filters is that it is easy to realize three-dimensional superresolution, and the disadvantage is that the sidelobes of the axial intensity distribution are too high. But this can be overcome by the application of a confocal system.     

Transverse or axial superresolution with radial birefringent filter

The superresolution technique is well known for its ability to compress the central diffraction spot to a size that is smaller than the Airy diffraction spot. The radial birefringent filter, which consists of two parallel polarizers and a rotationally symmetric birefringent element, is introduced into the superresolution technology, and the pupil function of it is deduced. It is shown that such a filter can be adapted either for transverse superresolution or for axial superresolution simply by changing the angle between either of the two polarizers and the radial birefringent element. At the same time the superresolution parameters are discussed. The filter is relatively simple in construction as it requires no phase changes, and low-cost replication is possible.     

MAP fusion method for superresolution of images with locally varying pixel quality

Superresolution is a procedure that produces a high‐resolution image from a set of low‐resolution images. Many of superresolution techniques are designed for optical cameras, which produce pixel values of well‐defined uncertainty, while there are still various imaging modalities for which the uncertainty of the images is difficult to control. To construct a superresolution image from low‐resolution images with varying uncertainty, one needs to keep track of the uncertainty values in addition to the pixel values. In this paper, we develop a probabilistic approach to superresolution to address the problem of varying uncertainty. As direct computation of the analytic solution for the superresolution problem is difficult, we suggest a novel algorithm for computing the approximate solution. As this algorithm is a noniterative method based on Kalman filter‐like recursion relations, there is a potential for real‐time implementation of the algorithm. To show the efficiency of our method, we apply this algorithm to a video sequence acquired by a forward looking sonar system. © 2008 Wiley Periodicals, Inc. Int J Imaging Syst Technol, 18, 242–250, 2008; Published online in Wiley InterScience (www.interscience.wiley.com).     

Continuous radial superresolution filters with large focal depth

A new set of continuous superresolution filters is proposed which exhibits a radial superresolution performance with an extended depth of focus in an optical system by properly choosing the design parameters. Numerical simulation results of the performance parameters of the superresolution gain, the radial central core size, the Strehl ratio, the side-lobe factor and the depth of focus with different design parameters for the optimized patterns are displayed. We also give a design example for this kind of filter characterized by a birefringent element inserted between two parallel polarizers. This kind of filter would be useful in fields such as optical data storage systems.     

Simultaneous multiplane imaging with a distorted diffraction grating

We describe a simple technique for simultaneously imaging multiple layers within an object field onto a single camera. The approach uses a binary diffraction grating in which the lines are distorted such that a different level of defocus is associated with each diffraction order. The design of the gratings is discussed, and their ability to image multiple object planes is validated experimentally. Extension of the technique for spherical-aberration correction is described, and it is shown how the gratings can be used as part of a wave-front-sensing system.     

Second-harmonic generation in second-harmonic fiber Bragg gratings

We consider the production of second-harmonic light in gratings resonant with the generated field, through a Green's function approach. We recover some standard results and obtain new limits for the uniform grating case. With the extension to nonuniform gratings, we find the Green's function for the second harmonic in a grating with an arbitrary phase shift at some point. We then obtain closed form approximate expressions for the generated light for phase shifts close to π/2 and at the center of the grating. Finally, comparing the uniform and phase-shifted gratings with homogeneous materials, we discuss the enhancement in generated light and the bandwidth over which it occurs, and the consequences for second-harmonic generation in optical fiber Bragg gratings.     

Application of generalized grating imaging to pattern projection in three-dimensional profilometry

The theory of generalized grating imaging for a one-dimensional grating is applied to a pattern projection system in pattern projection profilometry. Contrast of the projected grating image is calculated under various conditions. The results help to determine the conditions suitable for obtaining high contrast grating images in a large space. Although the gratings required for the profilometry are hexagonal, the theory for two-dimensional gratings is prohibitively complex. Therefore, the projection system was designed using the one-dimensional theory. The projection system using two-dimensional hexagonal gratings was constructed and experiments were done with it. The result agrees approximately with the theoretical calculations for one-dimensional gratings. This suggests that the one-dimensional theory may be used for estimating the approximated behavior for hexagonal gratings for use in pattern projection profilometry. Some discussions are given for the application of the projection system for profiling the mannequin or human body.     

Prototype development and field-test results of an adaptive multiresolution PANOPTES imaging architecture

The design, development, and field-test results of a visible-band, folded, multiresolution, adaptive computational imaging system based on the Processing Arrays of Nyquist-limited Observations to Produce a Thin Electro-optic Sensor (PANOPTES) concept is presented. The architectural layout that enables this imager to be adaptive is described, and the control system that ensures reliable field-of-view steering for precision and accuracy in subpixel target registration is explained. A digital superresolution algorithm introduced to obtain high-resolution imagery from field tests conducted in both nighttime and daytime imaging conditions is discussed. The digital superresolution capability of this adaptive PANOPTES architecture is demonstrated via results in which resolution enhancement by a factor of 4 over the detector Nyquist limit is achieved.