Filter In Fourier Plane Research Articles

Analysis of the efficiency of a virtualoptical multiplexing method, by using theta modulation

We present an efficient virtual-optical multiplexing method for compressing information contained in gray level images. The efficiency is measured using three parameters: quality factors of recovered images, memory saving percentage achieved, and number of multiplexed images in the package. Theta modulation techniques are applied, to process an N number of gray level images, by using a virtual-optical 2f architecture, from which we obtain a complex package M, to be stored as two images, amplitude and phase, in commercial formats. We apply pixel optimization and Fourier plane filtering to amplitude and phase images, respectively, storing only a percentage of the Fourier plane with a pixel dynamic range optimization. The stored package spends much less memory than individual images. The recovered images after the demultiplexing process are compared with the original ones by using correlation coefficient, obtaining high quality factors for decompressed images. We perform simulations, showing the efficiency of the proposed process, and our results are compared to the same factors reported in recent publications, making our improvements evident.

Flexible contrast for low-coherence interference microscopy by Fourier-plane filtering with a spatial light modulator

We propose a full-field low-coherence interference (LCI) microscope that can provide different contrast modes using Fourier-plane filtering by means of a spatial light modulator. By altering the phase and spatial frequencies of the backreflected wavefront from the sample arm of the interferometer, we are able to change the contrast in the depth-resolved LCI images. We demonstrate that different types of contrast modes, such as, e.g., spiral phase contrast, can successfully be emulated to provide specific enhancement of internal structures and edges and to reveal complementary details within the samples under investigation.

Phase contrast enhancement in microscopy using spiral phase filtering

We demonstrate two methods based on Fourier plane filtering using (a) a fractional spiral phase plate (SPP) and (b) an off-axial SPP for phase contrast enhancement in optical microscopy. In comparison to previous works, a spatially incoherent LED is used in the Köhler illumination as the light source to illuminate the biological specimen. We demonstrate that both these methods can transform the phase specimen into a relief-like view even under such illumination. The degree and orientation of enhancement can be controlled by changing the phase structure of the filter. The SPP is displayed on a phase-only spatial light modulator, and can be integrated into the optical path of standard microscopes.

Reverse phase contrast: an experimental demonstration.

We present experimental results showing that the reverse phase contrast (RPC) technique is a viable method for the generation of a binary phase distribution from a spatially varying amplitude pattern using Fourier plane filtering techniques. Experimental results are shown for the generation of a binary 0-pi phase only distribution using either an amplitude mask or a spatial light modulator to provide the input and the results are shown to be in agreement with theoretical predictions for the RPC technique.

Introduction of the Impulse Response Function in Common-Path Interferometers with Fourier Plane Filters

In the present paper it will be shown how the introduction of a Fourier plane filter can create various types of common-path interferometers for measuring changes in surface tilt or curvature of an object surface. This is obtained by placing a holographic optical element in the Fourier plane of a 4-f optical system. The interferometers are analysed by using the paraxial approximation of the Huygens-Fresnel integral formalism, and the interferometer functions are given by a novel formalism using impulse response functions. Based on this technique, an interferometer for measuring dedicated changes in surface deflection is presented. This interferometer is insensitive to rigid surface rotations and displacements. The interferometer can be embedded in systems based on single point measurement of a time dependent deflection, i.e. vibrometers, as well as in full-field measurements such as electronic speckle interferometers.

Stabilization, manipulation and control of transverse optical patterns in a photorefractive feedback system

We present an experimental realization of an almost non-invasive stabilization and manipulation method of coexisting and unstable states of pattern forming systems. In a photorefractive single feedback system, a control path is used to realize amplitude and phase-sensitive Fourier-plane filtering, utilizing only a few per cent of the system's intensity. By that means, we were able to stabilize desired but not predominantly excited patterns in parameter space regions where several patterns are present as coexisting or underlying solutions. Changing the phase of the control signal allows one to switch between different pattern states.

Phase-change visualization in two-dimensional phase objects with a semiderivative real filter

A method of visualization of phase changes in two-dimensional pure-phase objects by use of two orthogonal Fourier plane filters that realize the half-order differentiation is presented. Real semiderivative filters used in two dimensions and in sequence yield output-image intensity signals proportional to the first derivatives of the input-object phase that appear on a constant background. This nonlinear filtration of spatial frequencies permits the alleviation of the consequences of square-law detection and makes phase changes visible. Phase changes in gradient-index phosphate glass are calculated experimentally. We discuss the accuracy of the proposed method.

Selection of Unstable Patterns and Control of Optical Turbulence by Fourier Plane Filtering

We report on selection and stabilization of transverse optical patterns in a feedback mirror experiment. Amplitude filtering in the Fourier plane is used to select otherwise unstable spatial patterns. Optical turbulence observed for nonlinearities far above the pattern formation threshold is stabilized by low-pass filtering of the optical power spectrum. Experimental observations obtained with a photorefractive nonlinearity are consistent with calculations based on a generic, cubic nonlinearity.

Intracavity spectral shaping in external cavity mode-locked semiconductor diode lasers

Intracavity spectral shaping techniques have been employed to artificially shape and broaden the optical spectrum of external cavity mode-locked semiconductor lasers. Using an intracavity spectrometer and intensity Fourier-plane filtering, active mode-locked output spectra with a multiplicity of independently tunable wavelengths have been generated, while an adjustable intracavity etalon has been employed to generate an 18-nm spectral width. Furthermore, hybrid mode-locking with a multiple-quantum-well (MQW) saturable absorber combined with the intracavity etalon, followed by dispersion compensation has led to the generation of optical pulses of 330 fs in duration.

Fractional derivative Fourier plane filter for phase-change visualization

Fractional derivatives of two-dimensional images have been discussed theoretically in terms of Fourier optics and computer simulated. Filters that realize the half-order differentiation can be either complex or real. We prove, in terms of fractional calculus, that the semiderivative filter is useful for the visualization of phase changes in a phase object in such a way that the output-image intensity is directly proportional to the first derivative of the input object. We give computer-simulated results of one-dimensional semidifferentiating.

Phase-object fractional differentiation using Fourier plane filters

This paper contains an analysis of fractional-order derivatives of two-dimensional (2D) phase objects. The expression for noninteger-order 2D derivatives is given in terms of the Fourier transform which suggests its optical implementation using Fourier optics techniques. We propose an oblique illumination geometry of a 4f correlator to achieve real Fourier plane differentiating filters. In computer simulations, we prove that only in the case of the semiderivative filter, the output intensity is directly proportional to the first derivative of an input phase object. Thus, the semiderivative filter allows exact visualization of phase changes. We show experimental results of differentiation with the first- and -order derivative real filters.

A femtosecond pulse-shaping apparatus containing microlens arrays for use with pixellated spatial light modulators

We discuss a modified femtosecond pulse shaper that uses microlens arrays to convert the continuous band of frequencies normally obtained at the mask plane of a pulse shaper to a series of discrete spots. Two possible modified pulse-shaping geometries are described and the optimum geometry is chosen. Our experiments demonstrate that this modification can improve pulse-shaping quality when modulator arrays with large interpixel gaps are used for Fourier-plane filtering.

Fringe visibility, irradiance, and accuracy in common path interferometers for visualization of phase disturbances

Common-path interferometers have been used to perform phase visualization for over 40 years. A number of techniques have been proposed, including dark central ground, phase contrast (π/2 and π), and field-absorption interferometers. The merits of the interferometers have been judged ad hoc by either tests with a small number of phase objects or by computer simulation. Three standardized criteria, which consolidate the work of others, are proposed to evaluate common-path interferometers: fringe visibility, fringe irradiance, and fringe accuracy. The interferometers can be described as one generic class of Fourier-plane filters and can be analyzed for all input conditions. Closed-form expressions are obtained for visibility and irradiance under the forced condition that little inaccuracy is tolerated. This analysis finds that the π-phase-contrast interferometer is a good choice if the optical phase disturbance is at least 2π; for smaller disturbances, the Π/2 filter selected by Zernike is near optimum. It is shown mathematically that the resulting fringe visibility is highly object dependent, and good results are not ensured. By allowing the optical beam to be 50% larger than the phase object, the interferometer performs well under all conditions. With this approach and a combination π-phase/field-absorption filter, interference fringe visibility is greater than 0.8 for all phase objects.

Crossed Bragg cell implementation of a Fourier-plane filter for optical image correlators

A two-dimensional optical image processor is described and demonstrated in which the point-spread function is generated by crossed acousto-opticells in the Fourier plane of a coherent optical correlator. Coherence effects and generation of nonseparable point-spread functions are considered.

Fourier-plane filtering by a thick grating: a space–bandwidth analysis: erratum

Fourier-plane filtering by a thick grating: a space–bandwidth analysis: erratum

Fourier-plane filtering by a thick grating: a space–bandwidth analysis

The space–bandwidth requirements of thick gratings in the Fourier plane of a coherent optical image processor are analyzed. Based on Kogelnik’s relationship for the diffraction efficiency, relations for the space–bandwidth products of the input image and the point-spread function are obtained in terms of grating parameters. It is concluded that thick gratings, such as photorefractive crystals, are not well suited for implementing shift-invariant operations through Fourier-plane filtering.

Nonlinear-optical processing by means of phase coding

A new look at nonlinear-optical processing that uses Fourier plane filtering is discussed. Traditional binary intensity-to-space recording (halftoning) is replaced by simple continuous phase coding. Some proof-of-principle experimental results demonstrate a superior 103:1 input dynamic range. The phase response of the photosensitive material can be measured as an addition to this proposed technique.

Coherent optical correlator using a deformable mirror device spatial light modulator in the Fourier plane

Attention is given to experimental results for a binary phase-only filter implementation's correlation operations, using the deformable mirror device (DMD) spatial light modulator as the Fourier plane filter. These results demonstrate the basic capabilities of the DMD in an image correlator system which, in combination with the potential 8-kHz frame rate for 128 x 128 DMDs, can constitute a very high speed pattern recognition system. The DMD has the further capability of operating in the analog mode.

Deblurring with a positive only filter after further blurring

A linear motion blurred object is deblurred using a purely attenuating Fourier plane filter after subjecting the blurred object to a further blur. The deblurring filter is generated as a photographic density variation and the experimental result is compared with that obtained from a complex filter.

Optical logic with variable-grating-mode liquid-crystal devices

A liquid-crystal device that performs a two-dimensional intensity-to-spatial-frequency conversion has been investigated for use as an optical transducer. When such a device is used as the input transducer in an optical filtering arrangement, image-intensity levels can be easily manipulated by using appropriate Fourier plane filters. The variable-grating-mode liquid-crystal device is well adapted to performing binary logic operations on images. Results demonstrating the implementation of common logic operations are presented.