Optimized logarithmic phase masks used to generate defocus invariant modulation transfer function for wavefront coding system

In a previous Letter [Opt. Lett. 33, 1171 (2008)], we proposed an improved logarithmic phase mask by making modifications to the original one designed by Sherif. However, further studies in another paper [Appl. Opt. 49, 229 (2010)] show that even when the Sherif mask and the improved one are optimized, their corresponding defocused modulation transfer functions (MTFs) are still not stable with respect to focus errors. So, by further modifying their phase profiles, we design another two logarithmic phase masks that exhibit more stable defocused MTF. However, with the defocus-induced phase effect considered, we find that the performance of the two masks proposed in this Letter is better than the Sherif mask, but worse than our previously proposed phase mask, according to the Hilbert space angle. (C) 2010 Optical Society of America

The structure and function of neurons with variable nonlinear transfer function

One novel neuron with variable nonlinear transfer function is firstly proposed, It could also be called as subsection transfer function neuron. With different transfer function components, by virtue of multi-thresholded, the variable transfer function neuron switch on among different nonlinear excitated state. And the comparison of output's transfer characteristics between it and single-thresholded neuron will be illustrated, with some practical application experiments on Bi-level logic operation, at last the simple comparison with conventional BP, RBF, and even DBF NN is taken to expect the development foreground on the variable neuron.. The novel nonlinear transfer function neuron could implement the random nonlinear mapping relationship between input layer and output layer, which could make variable transfer function neuron have one much wider applications on lots of reseach realm such as function approximation pattern recognition data compress and so on.

Approximate analytical optical transfer function for a wavefront-coded imaging system with two-dimensional rectangularly separable phase masks

Wavefront coding can be used to extend the depth of field of incoherent imaging systems and is a powerful system-level technique. In order to assess the performance of a wavefront-coded imaging system, defocused optical transfer function (OTF) is the metric frequently used. Unfortunately, to the best of our knowledge, among all types of phase masks, it is usually difficult to obtain the analytical OTF except the cubic one. Although numerical computation seems good enough for performance evaluation, the approximate analytical OTF is still indispensable because it can reflect the relationship between mask parameters and system frequency response in a clearer way. Thus, a method is proposed to derive the approximate analytical OTF for two-dimensional rectangularly separable phase masks. The analytical results are well consistent with the direct numerical computations, but the proposed method can be accepted only from engineering point of view and needs rigorous proof in future. (c) 2010 Society of Photo-Optical Instrumentation Engineers. [DOI: 10.1117/1.3485759]

Performance of an improved logarithmic phase mask with optimized parameters in a wavefront-coding system

In two papers [Proc. SPIE 4471, 272-280 (2001) and Appl. Opt. 43, 2709-2721 (2004)], a logarithmic phase mask was proposed and proved to be effective in extending the depth of field; however, according to our research, this mask is not that perfect because the corresponding defocused modulation transfer function has large oscillations in the low-frequency region, even when the mask is optimized. So, in a previously published paper [Opt. Lett. 33, 1171-1173 (2008)], we proposed an improved logarithmic phase mask by making a small modification. The new mask can not only eliminate the drawbacks to a certain extent but can also be even less sensitive to focus errors according to Fisher information criteria. However, the performance comparison was carried out with the modified mask not being optimized, which was not reasonable. In this manuscript, we optimize the modified logarithmic phase mask first before analyzing its performance and more convincing results have been obtained based on the analysis of several frequently used metrics. (C) 2010 Optical Society of America

Remote sensing of ocean waves by along-track interferometric synthetic aperture radar

A new wave retrieval method for the Along-Track Interferometric Synthetic Aperture Radar (AT-InSAR) phase image is presented. The new algorithm, named parametric retrieval algorithm (PRA), uses the full nonlinear mapping relations. It differs from previous retrieval algorithms in that it does not require a priori information about the sea state or the wind vector from scatterometer data. Instead, it combines the observed AT-InSAR phase spectrum and assumed wind vector to estimate the wind sea spectrum. The method has been validated using several C-band and X-band HH-polarized AT-InSAR observations collocated with spectral buoy measurements. In this paper, X-band and C-band HH-polarized AT-InSAR phase images of ocean waves are first used to study AT-InSAR wave imaging fidelity. The resulting phase spectra are quantitatively compared with forward-mapped in situ directional wave spectra collocated with the AT-InSAR observations. Subsequently, we combine the parametric retrieval algorithm (PRA) with X-band and C-band HH-polarized AT-InSAR phase images to retrieve ocean wave spectra. The results show that the ocean wavelengths, wave directions, and significant wave heights estimated from the retrieved ocean wave spectra are in agreement with the buoy measurements.

Validation of RADARSAT-2 fully polarimetric SAR measurements of ocean surface waves

C band RADARSAT-2 fully polarimetric (fine quad-polarization mode, HH+VV+HV+VH) synthetic aperture radar (SAR) images are used to validate ocean surface waves measurements using the polarimetric SAR wave retrieval algorithm, without estimating the complex hydrodynamic modulation transfer function, even under large radar incidence angles. The linearly polarized radar backscatter cross sections (RBCS) are first calculated with the copolarization (HH, VV) and cross-polarization (HV, VH) RBCS and the polarization orientation angle. Subsequently, in the azimuth direction, the vertically and linearly polarized RBCS are used to measure the wave slopes. In the range direction, we combine horizontally and vertically polarized RBCS to estimate wave slopes. Taken together, wave slope spectra can be derived using estimated wave slopes in azimuth and range directions. Wave parameters extracted from the resultant wave slope spectra are validated with colocated National Data Buoy Center (NDBC) buoy measurements (wave periods, wavelengths, wave directions, and significant wave heights) and are shown to be in good agreement.

Remote sensing of ocean waves by polarimetric SAR

A new method to measure ocean wave slope spectra using fully polarimetric synthetic aperture radar (POLSAR) data was developed without the need for a complex hydrodynamic modulation transform function. There is no explicit use of a hydrodynamic modulation transfer function. This function is not clearly known and is based on hydrodynamic assumptions. The method is different from those developed by Schuler and colleagues or Pottier but complements their methods. The results estimated from NASA Jet Propulsion Laboratory (JPL) Airborne Synthetic Aperture Radar (AIRSAR) C-band polarimetric SAR data show that the ocean wavelength, wave direction, and significant wave height are in agreement with buoy measurements. The proposed method can be employed by future satellite missions such as RADARSAT-2.

Computation of the ambiguity function for circularly symmetric pupils

A method of computing the ambiguity function (AF) for a circularly symmetric pupil function is presented. The AFs of a clear aperture and two shaded apertures are considered in detail and an explicit expression for the first of these AFs is given. We explain these results in the context of the well-known optical transfer function theory and show a primary application of these computations. A good analytic approximation is also introduced, providing an alternative method for calculating the AF, in a simpler way.

On the nonlinear integral transform of an ocean wave spectrum into an along-track interferometric synthetic aperture radar image spectrum

We present a new nonlinear integral transform relating the ocean wave spectrum to the along-track interferometric synthetic aperture radar (AT-INSAR) image spectrum. The AT-INSAR, which is a synthetic aperture radar (SAR) employing two antennas displaced along the platform's flight direction, is considered to be a better instrument for imaging ocean waves than the SAR. This is because the AT-INSAR yields the phase spectrum and not only the amplitude spectrum as with the conventional SAR. While the SAR and AT-INSAR amplitude spectra depend strongly on the modulation of the normalized radar cross section (NRCS) by the long ocean waves, which is poorly known, the phase spectrum depends only weakly on this modulation. By measuring the phase difference between the signals received by both antennas, AT-INSAR measures the radial component of the orbital velocity associated with the ocean waves, which is related to the ocean wave height field by a well-known transfer function. The nonlinear integral transform derived in this paper differs from the one previously derived by Bao et al. [1999] by an additional term containing the derivative of the radial component of the orbital velocity associated with the long ocean waves. By carrying out numerical simulations, we show that, in general, this additional term cannot be neglected. Furthermore, we present two new quasi-linear approximations to the nonlinear integral transform relating the ocean wave spectrum to the AT-INSAR phase spectrum.

Phase-space analysis of wavefront coding imaging systems

We explore the use of the Radon-Wigner transform, which is associated with the fractional Fourier transform of the pupil function, for determining the point spread function (PSF) of an incoherant defocused optical system. Then we introduce these phase-space tools to analyse the wavefront coding imaging system. It is shown that the shape of the PSF for such a system is highly invarient to the defocous-related aberrations except for a lateral shift. The optical transfer function of this system is also investigated briefly from a new understanding of ambiguity function.

The origin of the super-resolution via a nonlinear thin film

In laser applications, resolutions beyond the diffraction limit can be obtained with a thin film of strong optical nonlinear effect. The optical index of the silicon thin film is modified with the incident laser beam as a function of the local field intensity n(r) similar to E-2(r). For ultrathin films of thickness d << lambda the transmitted light through the film forms a profile of annular rings. Therefore, the device can be related to the realization of super-resolution with annular pupils. Theoretical analysis shows that the focused light spot appears significantly reduced in comparison with the diffraction limit that is determined by the laser wavelength and the numerical aperture of the converging lens. Analysis on the additional optical transfer function due to the thin film confirms that the resolving power is improved in the high spatial frequency region. (C) 2007 Published by Elsevier B.V.