Contrast enhancement of underwater images with coherent optical image processors

The use of coherent optical processors for improving the quality of degraded underwater images is discussed, and a holographic filter suitable for the enhancement of contrast in underwater images is described. The filter is a modified matched spatial filter, and it performs a nonlinear local contrast enhancement. The theory of the operation of the coherent optical image processor with this new filter is presented and experimentally verified. The removal of the backscattered light from underwater images is demonstrated under laboratory conditions. The results show an improvement in the overall image contrast.     

Describing functions for nonlinear optical systems

The concept of describing functions is useful for analyzing and designing nonlinear systems. A proposal for using the idea of describing functions for studying the behavior of a nonlinear optical processing system is given. The describing function can be used in the same way that a coherent transfer function or optical transfer function is used to characterize linear, shift-invariant optical processors. Two coherent optical systems for measuring the magnitude of the describing function of nonlinear optical processors are suggested.     

The Interferometer as an Optical Network

Abstract

We consider a generic interferometric set-up as a device to record interference fringes. The system is characterized by two variable transmission beam-splitters. A coherent signal is measured and its noise properties are manipulated by mixing in a squeezed vacuum through the second input port. The performance is optimized either by minimizing the noise at the dark and the light fringes, or alternatively by keeping it below the standard quantum limit for all phase angles observed. The analysis is carried out using a quantum optical network formalism generalizing the classical Jones calculus. The results obtained are interpreted and explained using the Wigner function for the output signals.     

Closed-form solution for the Wigner phase-space distribution function for diffuse reflection and small-angle scattering in a random medium

Within the paraxial approximation, a closed-form solution for the Wigner phase-space distribution function is derived for diffuse reflection and small-angle scattering in a random medium. This solution is based on the extended Huygens-Fresnel principle for the optical field, which is widely used in studies of wave propagation through random media. The results are general in that they apply to both an arbitrary small-angle volume scattering function, and arbitrary (real) ABCD optical systems. Furthermore, they are valid in both the single- and multiple-scattering regimes. Some general features of the Wigner phase-space distribution function are discussed, and analytic results are obtained for various types of scattering functions in the asymptotic limit s > 1, where s is the optical depth. In particular, explicit results are presented for optical coherence tomography (OCT) systems. On this basis, a novel way of creating OCT images based on measurements of the momentum width of the Wigner phase-space distribution is suggested, and the advantage over conventional OCT images is discussed. Because all previous published studies regarding the Wigner function are carried out in the transmission geometry, it is important to note that the extended Huygens-Fresnel principle and the ABCD matrix formalism may be used successfully to describe this geometry (within the paraxial approximation). Therefore for completeness we present in an appendix the general closed-form solution for the Wigner phase-space distribution function in ABCD paraxial optical systems for direct propagation through random media, and in a second appendix absorption effects are included.     

Achromatic White-light Self-imaging Phenomenon: An Approach Using the Wigner Distribution Function

Abstract

The propagation of polychromatic spatially coherent light through an optical system, developed for achromatizing Fresnel diffraction patterns, is discussed using the Wigner distribution function. This approach is applied for obtaining achromatic self-images. The residual chromatic aberration is analysed, and some experimental results are shown.     

Modal decomposition of partially coherent beams using the ambiguity function

Phase-space representations of optical beams such as the ambiguity function or the Wigner distribution function have recently gained considerable importance for the characterization of coherent and partially coherent beams. There is growing interest in beam properties such as the beam propagation factor and the coherence and phase information that can be extracted from these phase-space representations. A method is proposed to decompose a partially coherent beam into Hermite-Gaussian modes by using the ambiguity function. The modal weights and the possible phase relations of the Hermite-Gaussian modes are retrieved. The method can also be applied for the decomposition of the Wigner distribution function. Some examples are discussed in the scope of beam characterization.     

Phase mask for spatial and temporal control of ultrashort light pulses focused by lenses

The field amplitude associated with ultrashort light pulses was analyzed by using the phase-space formalism of the Wigner distribution function (WDF). The diffraction integral was properly modified to take into account the dispersion effects (up to second order). A two-dimensional WDF associated with a reduced pupil function was derived, from which the on-axis irradiance was obtained for varying times. A two-dimensional and rotationally symmetric quartic-phase mask to control the temporal stretching of femtosecond light pulses passing through optical systems was proposed and analyzed. A Gaussian spatial and temporal pulse passing through a single lens with and without the phase mask was investigated.     

Imaging detector of temporally coherent radiation

We present an optical architecture and image processor capable of detecting and locating temporally coherent radiation that may be dominated by incoherent background radiation. The optical architecture makes use of a coherent light modulator that modulates light of sufficient coherence length while it leaves light of short coherence length unmodulated. The design of the coherent light modulator offers a substantially wider field of view than did past designs, permitting its application within an imaging system. The image processor synchronously detects the modulation imposed on coherent light while it rejects incoherent light fluctuations. Results of a laboratory test are presented. The system tested in the laboratory had a 26 degrees field of view and was able to detect and locate coherent radiation >30 dB below the background incoherent light level.     

Particle image velocimetry analysis using an optically addressed spatial light modulator: effects of nonlinear transfer function

Optical processors for generating a two-dimensional squared autocorrelation function have been presented for postprocessing particle image velocimetry photographs of fluid flows. The incoherent-tocoherent conversion can be performed by an optically addressed spatial light modulator. The transfer function of these devices is far from linear and will influence the performance of the optical processor.

Two different transfer functions, characterizing the two main types of commercial optically addressed spatial light modulators as an analog and a binary transfer function, have been simulated digitally.

Results of numerical simulations on the influence of introducing these nonlinear transfer functions to the correlation function for particle image velocimetry analysis are presented.

     

Wigner Functions for Coherent and Squeezed States with Thermal Noise

Abstract

A generalized Wigner function W _T(α, ) including the thermal degrees of freedom is presented to calculate the ‘reduced’ Wigner functions for all kinds of coherent and squeezed states with thermal noise by the formalism of thermofield dynamics. The results show that the different definitions of coherent and squeezed state with the same corresponding density matrix give rise to the same reduced Wigner function. By our method, the reduced Wigner function can be calculated for an arbitrary vector in the thermal Fock space, of which the density matrix is too complicated to use.     

Multireference binary phase-only filter optimized by regions of support

A new formulation of a multiplex filter for filtering-based optical processors, based on the VanderLugt architecture, is presented. The multireference binary phase-only filter (MBPOF), optimized by regions of support (ROS), constitutes a formal rewriting of some multiplex or composite filters including optimization functions, such as the distribution function and the selection function. The first function optimizes the multiplexing of references into the multireference filter. The second function defines the ROS of an object's Fourier spectrum and can be independently used to optimize the conventional binary phase-only filter. Both functions result from a segmentation of the Fourier plane. The MBPOF with ROS can be optically implemented in a filtering-based optical processor owing to a binary-phase spatial light modulator. Simulation and optical results are given for different examples of the BPOF and the MBPOF, both with ROS optimizing different criteria of performance, such as peak-to-correlation energy, discrimination capability, and distortion sensitivity.     

Optical systems under broad-band illumination: Analysis based on a wigner distribution function approach

Abstract

The irradiance produced by an optical imaging system suffering from aberrations under broad-band illumination is analysed in the phase-space domain of the Wigner distribution function associated with a modified one-dimensional pupil aperture. To this end, a coordinate transformation is employed in such a way that the varying irradiance along different paths in the image space can be derived from different slices of the Wigner distribution function, which involve both the defocus distance and the dispersion properties of the optical system. The method is illustrated by comparing the axial irradiance distribution for different primary aberrations. Also, the irradiance along parabolic paths is obtained in order to analyse the coma effect.     

Wigner distribution and fractional Fourier transform for two-dimensional symmetric optical beams

A useful relationship between the fractional Fourier transform power spectra of a two-dimensional symmetric optical beam, on the one hand, and its Wigner distribution, on the other, is established. This relationship allows a significant simplification of the standard procedure for the reconstruction of the Wigner distribution from the field intensity distributions in the fractional Fourier domains. The Wigner distribution of a symmetric optical beam is analyzed, both in the coherent and in the partially coherent case.     

Properties of Output Signal Moments of Optical Processors

General results for the output signal moments are given for both linear and bilinear systems and both space-variant and space-invariant processing. As an example of a bilinear system, a partially coherent system is considered. The properties of intensity moments for a Fourier optical processor and an imaging system with partially coherent illumination are also investigated.     

Obtaining Any Given Intensity at Discrete Close Points at the Output of Band-limited Optical Systems

For general band-limited optical systems and coherent illumination, a procedure is presented for obtaining the functional form of at least one object amplitude that will generate any given intensity distribution at certain discrete close points at the output. The explicit form of the object is given as a function of the intensity data. Application to a simple imaging system is briefly discussed.     

The Wigner Distribution Function of Two-dimensional Signals Coherent-optical Generation and Display

We introduce the Wigner distribution function (WDF) as a self-windowed complex spectrogram and suggest some methods for the optical generation of the WDF of two-dimensional signals. The resulting WDFs, since they are four-dimensional functions, are represented as sectional images displayed either in parallel or as temporal sequences. We give some experimental results for real-valued input signals obtained from different coherent-optical WDF processors.     

Wigner functions for paraxial and nonparaxial fields

The Wigner function gives an intuitive representation of coherent and partially coherent wave fields in the frequency domain, which takes the form a ray weight distribution. However, this weight distribution is conserved along rays only for paraxial or significantly incoherent fields. Generalizations of the Wigner function have been defined for propagation through transparent homogeneous media that are exactly conserved along rays for any angular spread and state of coherence. A series expression is derived here for calculating these nonparaxial generalizations starting from the standard Wigner function.     

Phase properties of operator valued measures in phase space

Abstract

The Wigner phase operator (WPO) is identified as an operator valued measure (OVM) and its eigenstates are obtained. An operator satisfying the canonical commutation relation with the Wigner phase operator is also constructed and this establishes a Wigner distribution based operator formalism for the Wigner phase distribution. It is then argued that the WPO cannot represent a projective measurement of the phase; but is in fact to be interpreted as an operator valued measure for the phase. The non-positivity of the latter can be overcome by defining a positive operator valued measure (POVM) via a proper filter function, based on the view that phase measurements are coarse-grained in phase space, leading to the well known Q-distribution. The identification of the Q phase operator as a POVM is in good agreement with the earlier observation regarding the relation between operational phase measurement schemes and the Q-distribution. The Q phase POVM can be dilated in the sense of Gelfand–Naimark, to an operational setting of interference at a beam-splitter with another coherent state – this results in a von Neumann projector with well-defined phase in the expanded Hilbert space of the two modes.