Input Plane Research Articles

Complex space source theory of partially coherent light wave

The complex space source theory is used to derive a general integral expression for the vector potential that generates the extended full Gaussian wave in terms of the input value of the vector potential of the corresponding paraxial beam. The vector potential and the fields are assumed to fluctuate on a time scale that is large compared to the wave period. The Poynting vector in the propagation direction averaged over a wave period is expressed in terms of the cross-spectral density of the fluctuating vector potential across the input plane. The Schell model is assumed for the cross-spectral density. The radiation intensity distribution and the power radiated are determined. The effect of spatial coherence on the radiation intensity distribution and the radiated power are investigated for different values of the physical parameters. Illustrative numerical results are provided to bring out the effect of spatial coherence on the propagation characteristics of the fluctuating light wave.

Differential Laser Doppler Velocimeter With Enhanced Range for Small Wavelength Sensitivity by Using Cascaded Mach–Zehnder Interferometers

A differential laser Doppler velocimeter (LDV) with enhanced wavelength range for small wavelength sensitivity is proposed by using cascaded Mach-Zehnder interferometers (MZIs) for shifting the position of the beam at the input plane according to the wavelength. The cascaded MZI structures are used to enhance the position shift of the beam at the input plane compared with the use of single-stage MZIs. The gradual shift in the incident angle of the beam to the object is brought about with the combination of cascaded MZI structures, lenses and apertures. The simulation results indicate that the wavelength range for small wavelength sensitivity can be successfully enhanced by using two-stage cascaded MZI structures.

Spatially efficient reference phase-encrypted joint transform correlator

A novel joint transform correlator (JTC) system is presented in which the stored reference image is phase encrypted prior to applying the JTC. The encryption disperses all the trivial correlation peaks in the correlator output. The reference image is encrypted electronically, which simplifies the need for a complex optical setup. The encryption removes the JTC requirement for spatial separation between the reference and the target images in the joint input plane. This efficient use of spatial light modulator space can be used to phase multiplex more reference images so that correlations with multiple reference images can be performed in a single JTC cycle.

Reactive power in the full Gaussian light wave

The electric current sources that are required for the excitation of the fundamental Gaussian beam and the corresponding full Gaussian light wave are determined. The current sources are situated on the secondary source plane that forms the boundary between the two half-spaces in which the waves are launched. The electromagnetic fields and the complex power generated by the current sources are evaluated. For the fundamental Gaussian beam, the reactive power vanishes, and the normalization is chosen such that the real power is 2 W. The various full Gaussian waves are identified by the length parameter b(t) that lies in the range 0 < or = b(t) < or = b, where b is the Rayleigh distance. The other parameters are the wavenumber k, the free-space wavelength lambda, and the beam waist w0 at the input plane. The dependence of the real power of the full Gaussian light wave on b(t)/b and w0/lambda is examined. For a specified w0/lambda, the reactive power, which can be positive or negative, increases as b(t)/b is increased from 0 to 1 and becomes infinite for b(t)/b=1. For a specified b(t)/b, the reactive power approaches zero as kw0 is increased and reaches the limiting value of zero of the paraxial beam.

Wavelength-insensitive laser Doppler velocimeter using beam position shift induced by Mach-Zehnder interferometers

A novel wavelength-insensitive differential laser Doppler velocimeter (LDV) without a grating has been proposed. The proposed LDV utilizes a position shift of the beam at the input plane according to wavelength change induced by Mach-Zehnder interferometers (MZIs). The gradual shift in the incident angle of the beam to the object is brought about with the combination of MZIs, lenses and apertures. The characteristics of the proposed structure are simulated using paraxial approximation of a lens system with an aperture. The simulation results indicate that almost wavelength-insensitive operation can be obtained by using the proposed structure without any grating element.

Encryption by using matrix-added, or matrix-multiplied input images placed in the input plane of a double random phase encoding geometry

In this paper, we describe image encryption by combining the images with several matrices made with letters/numerals and placed in the input plane of a double random phase encoding (DRPE) system. Addition or multiplication of several such matrices with an input image provides a modified image pattern which is encrypted in a DRPE system utilizing the 4-f geometry. For gray scale images, the results of encryption in case of addition of matrices are found more reliable and secure as compared to the results of multiplication. Simulation results are presented in support of the idea. Reliability of the technique has been established by evaluating the mean square-error (MSE) between the decrypted and the original image.

Optimal simulations of ultrasonic fields produced by large thermal therapy arrays using the angular spectrum approach.

The angular spectrum approach is evaluated for the simulation of focused ultrasound fields produced by large thermal therapy arrays. For an input pressure or normal particle velocity distribution in a plane, the angular spectrum approach rapidly computes the output pressure field in a three dimensional volume. To determine the optimal combination of simulation parameters for angular spectrum calculations, the effect of the size, location, and the numerical accuracy of the input plane on the computed output pressure is evaluated. Simulation results demonstrate that angular spectrum calculations performed with an input pressure plane are more accurate than calculations with an input velocity plane. Results also indicate that when the input pressure plane is slightly larger than the array aperture and is located approximately one wavelength from the array, angular spectrum simulations have very small numerical errors for two dimensional planar arrays. Furthermore, the root mean squared error from angular spectrum simulations asymptotically approaches a nonzero lower limit as the error in the input plane decreases. Overall, the angular spectrum approach is an accurate and robust method for thermal therapy simulations of large ultrasound phased arrays when the input pressure plane is computed with the fast nearfield method and an optimal combination of input parameters.

Semiderivative real filter for microoptical elements quality control

The article presents a proposal for a new method of automatic quality control of microlenses arrays, which is based on a semiderivative real filter. The use of the semiderivative filter for examining pure-phase objects involves modifying the spatial frequency. The basis of the proposed setup is a 4f correlator setup with coherent light. The phase object examined is placed in the input plane of the correlator. Next, the light passes through a filter located in the frequency plane, which gives an intensity signal. In the output plane a charge-coupled device (CCD) camera registers the light intensity, the range of which informs the shape of the phase object. The proposed method is shift invariant, so it allows for examination of single elements or a set of micro-optical elements simultaneously. Additionally, the same setup allows for measuring the phase of objects whose thickness is either considerably smaller or much bigger than 2π.

Reflection and Scattering of Electromagnetic Waves in Spatial Grids Consisting of Multiple Lossy Waveguides

Medical diagnosis technologies using X-ray and optical wave transmitted tomogra- phy have been rapidly developed with computer processing. X-ray and optical transmitted fleld characteristics in CT, that depend on biomedical absorption due to bio-molecules and atoms, yield biomedical information of human body tissues and cells. However, X-ray and optical trans- mitted fleld signals at receiving output of diagnosis CT sensors are disturbed by scattering waves in random bio-medical inhomogeneities around objects of body tissues and cells. Before sig- nal processing by computer, hardware tools of spatial flltering of disturbing scattering flelds for absorption characteristics in bio-medical tissues and cells are very useful system functions. Spatial flltering of scattered flelds by grid arrays consisting of transversely multiple lossy waveg- uides is one of excellent device function for spatial flltering in X-ray and optical diagnosis. Spa- tial fllter of grid arrays consisting of multiple lossy waveguides is waveguide array consisting of waveguides with transparent cores and lossy clads. Each waveguide has core size, clad size and waveguide length. Scattered flelds in random bio-medical media are incident on input plane of spatial fllter array, and coupled to lower modes of low losses for small scattering angles and higher modes of large losses for large scattering angles, in lossy waveguide array. Low angle scattered flelds couple to lower modes and large angle scattered flelds couple to lossy higher modes. Scattered flelds coupled to lossy higher modes are flltered in lossy grid arrays. Mode characteris- tics in lossy grid arrays excited by scattered fleld in random bio-medical media are discussed by mode expansion methods using boundary condition at input plane of lossy grid array, and flltered flelds at output plane of lossy grid array are shown by integral equations using Green's dyadics. Mode characteristics and flltered flelds are also investigated by the Wiener-Hopf method with spectral functions.

Multichanneled encryption via a joint transform correlator architecture

We propose a multichanneling encryption method by using multiple random-phase mask apertures in the input plane based on a joint transform correlation scheme. In the proposal, this multiple aperture arrangement is changed as different input objects are inserted and stored. Then, during the decryption step, the appropriate use of the random-phase mask apertures can ensure the retrieval of different information. This approach provides different access levels. Computer simulations show the potential of the technique and experimental results verify the feasibility of this method.

Image encryption based on gyrator transform and two-step phase-shifting interferometry

A novel optical image encryption method is proposed, based on gyrator transform and phase-shifting interferometry. The input two-dimensional image to be encrypted is gyrator transformed two times, and two random phase masks are placed at the input plane and the output plane of the first gyrator transform. Two-step phase-shifting interferometry is used to record the digital holograms of the input image encrypted by use of double-random phase encoding technique in gyrator transform domain. The rotation angles of gyrator transform, the random phase mask in the gyrator plane and the arbitrary phase shift used for recording form the keys for decryption of the input image. Numerical simulations are presented to verify its validity and efficiency.

Fundamental electromagnetic Gaussian beam beyond the paraxial approximation

The fundamental electromagnetic Gaussian beam is constructed from a single component of the electric vector potential oriented normal to the propagation direction. The potential is cylindrically symmetrical about the propagation direction. The paraxial beam and the first-order nonparaxial beam are obtained. In solving the inhomogeneous paraxial wave equation governing the evolution of the nonparaxial beam, both the particular integral and the complementary function are included. A procedure for deducing the proper asymptotic state of the nonparaxial beam is summarized. The amplitude coefficients of the cylindrically symmetric complex-argument Laguerre-Gauss beams, which constitute the complementary function are determined by requiring the potential to have the proper behavior asymptotically at infinity and near the input plane. From the potential function, the electromagnetic fields are developed and the electrodynamics of the fundamental electromagnetic Gaussian beam beyond the paraxial approximation is investigated. The role of the first-order nonparaxial beam in determining the average beam characteristics is examined.

Influence of incomplete weakening of metal on the yield point in continuous hot rolling of broad steel strip

In hot rolling, two processes occur at the same time over the length of the deformation source: hardening and softening (recrystallization). Hardening is due to reduction and the strain rate; softening is due to the temperature ( t = 800‐1200 ° C). From the input plane to the output plane, the relative reduction increases, while the strain rate declines to zero. Consequently, as we know, the minimum (natural) yield point σ 0 i corresponds to the input plane (as seen in the figure) [1]. The maximum yield point σ Y.m is at the midpoint of the contact arc, while the yield point σ Y1 of the metal in the output plane from the deformation source is somewhat higher than the yield point σ 0 i in the input plane. In the interval when the strip moves from cell n i to cell n j , the metal temperature t declines and the natural yield point of the metal increases to σ 0 j . As a result of recrystallization (softening), the yield point σ Y i (cell n i ) falls to σ 0 y in the time τ for the strip to move to cell n j ; σ 0 y is the initial value for the deformation source in cell n j . The difference between σ 0 y and σ 0 j determines the residual hardening of the metal ahead of the corresponding cell

On some properties of the Fabry-Perot etalon with negative permittivities of the medium

Specific features of the Fabry-Perot etalon with negative permittivities of the medium are analyzed. Inhomogeneous waves may exhibit, after passing through such an etalon, a giant amplitude enhancement. They remain inhomogeneous and do not transfer the field energy. Due to absorption and other losses, there may arise, in the inhomogeneous wave, running components and interference effects. The etalon cannot improve the diffraction-limited resolving power of the optical devices detecting traveling waves. The possibilities of application of the etalon in the near-field optics are noted. The giant enhancement of the inhomogeneous wave amplitude occurs due to resonance of the incident wave with eigen (surface) waves of the input and output planes of the etalon. It is shown that, with respect to inhomogeneous waves, the Fabry-Perot etalon with negative permittivities is a narrow-band filter with the peak transmission for the spatial frequency of the Fourier expansion of the boundary values on the order of the inverse wavelength. Under the resonance conditions, the running components, when passing through the etalon, experience aberrational distortions. Polarization properties of the resonance amplification are clarified.

Common-path phase-shifting digital holographic microscopy: A way to quantitative phase imaging and superresolution

We present an experimental setup useful for complex amplitude evaluation and phase image quantification of three-dimensional (3-D) samples in digital holographic microscopy (DHM). It is based on a common-path interferometric configuration performed by dividing the input plane in two contiguous regions and by placing a translation grating near to the Fourier plane. Then, complex amplitude distribution of the sample under test is recovered with phase-shifting standard method obtained by moving the grating using a linear motion stage. Some experimental results of an USAF resolution test are presented for different numerical aperture (NA) microscope lenses. In a second part, the proposed setup is tested under superresolution purposes. Based on the object’s spectrum shift produced by off-axis illumination, we use time multiplexing to generate a synthetic aperture enlargement that improves the final image resolution. Experimental results for the case of a biosample (human red blood cells) and a commercial low NA microscope lens validates the suggested superresolution approach.

One-shot phase-shifting phase-grating interferometry with modulation of polarization: case of four interferograms

An experimental setup for optical phase extraction from 2-D interferograms using a one-shot phase-shifting technique able to achieve four interferograms with 90 degrees phase shifts in between is presented. The system uses a common-path interferometer consisting of two windows in the input plane and a phase grating in Fourier plane as its pupil. Each window has a birefringent wave plate attached in order to achieve nearly circular polarization of opposite rotations one respect to the other after being illuminated with a 45 degrees linear polarized beam. In the output, interference of the fields associated with replicated windows (diffraction orders) is achieved by a proper choice of the windows spacing with respect to the grating period. The phase shifts to achieve four interferograms simultaneously to perform phase-shifting interferometry can be obtained by placing linear polarizers on each diffraction orders before detection at an appropriate angle. Some experimental results are shown.

Information security system based on iterative multiple-phase retrieval in gyrator domain

A novel information security system based on multiple-phase retrieval by an iterative gyrator transform algorithm is proposed. In this method, a series of phase masks are designed and located in the input plane and the gyrator planes, and the phase distributions of all the masks are adjusted simultaneously in each iteration. It can achieve fast convergence and high quality of the recovered image and can provide a higher degree of freedom in key space with more parameters as supplementary keys. Furthermore, the security level of this method is greatly improved by the sensitivity of recovered images with the angles of gyrator transform. Numerical simulations are presented to verify its validity and efficiency.

Elliptical Hermite-cosine-Gaussian beam and its propagation characteristics

A new kind of light beam named the elliptical Hermite-cosine-Gaussian beam (EHCosGB) is introduced in this paper by using a tensor method. An analytical propagation expression for an EHCosGB passing through an axially nonsymmetrical optical system is derived by using vector integration. By virtue of numerical simulations, the propagation properties of EHCosGBs through a free space and a focusing system are illustrated, respectively. The results indicate that an EHCosGB on the input plane can be regarded as the elliptical Hermite-Gaussian beam (EHGB) modulated by the cosine curves with certain oscillating frequency. Some of the neighboring lobes are combined and TEM-type Hermite-cosh-Gaussian beams are formed during the propagation.

Colour pattern recognition based on a multi-channel Mach–Zehnder joint transform correlator with multi-level quantized reference functions

Via the utilization of Stokes relations and a Mach–Zehnder interferometer we propose a novel structure of the optical correlator for colour pattern recognition. This system can directly remove the large zero order term, which decreases the recognition ability of the system, in only one step. We introduce the multi-level quantized reference functions for each colour channel since each colour can be separated into three channels. Simulation results show that this technique can be implemented at the input plane of liquid crystal spatial light modulator. In particular, each liquid crystal spatial light modulator using a reflective liquid crystal device is modulated along the real-valued axis.

A general approach to the analysis and description of partially polarized light in rigorous grating theory

Simple and intuitive principle is put forward to analyze the grating diffraction problem and to describe the polarization properties of diffraction orders. The method is applicable for any state of polarization of the input plane wave, including partially polarized or unpolarized fields.