ABSTRACT
An optical implementation of the fractional Fourier transform (FRT) with broadband illumination is proposed by use of a single imaging element, namely, a blazed diffractive lens. The setup displays an achromatized version of the FRT of order P of any two-dimensional input function. This fractional order can be tuned continuously by shifting of the input along the optical axis. Our compact and flexible configuration is tested with a chirplike input signal, and the good experimental results obtained support the theory.
ABSTRACT
A method for obtaining phase-retardation functions, which give rise to an increase of the image focal depth, is proposed. To this end, the Wigner distribution function corresponding to a specific aperture that has an associated small depth of focus in image space is conveniently sheared in the phase-space domain to generate a new Wigner distribution function. From this new function a more uniform on-axis image irradiance can be accomplished. This approach is illustrated by comparison of the imaging performance of both the derived phase function and a previously reported logarithmic phase distribution.
ABSTRACT
Some properties of optical correlation based on the fractional Fourier transform are analyzed. For a particular set of fractional orders, a filter is obtained that becomes insensitive to scale variations of the object. An optical configuration is also proposed to carry out the fractional correlation in a flexible way, and some experimental results are shown.
ABSTRACT
A space-variant optical correlator is proposed on the basis of the fractional Fourier transform. The optical device uses as a recording medium for the holographic filter a photorefractive Bi(12)GeO(2) (BGO) crystal. The experimental results confirm the shift-variance properties. Some limitations that arise from the volume diffraction are also considered.
ABSTRACT
A temporally incoherent optical processor that combines diffractive and refractive components is proposed for performing two different operations simultaneously: an achromatic image along an axis and an achromatic one-dimensional Fourier transformation along the orthogonal axis. These properties are properly employed to achieve the achromatic white-light display of the Wigner-distribution function associated with a one-dimensional real signal, with high redundancy and variable scale.
ABSTRACT
A new technique is proposed to perform several image-processing operations with the same optical system. Each operation can easily be selected by properly loading a birefringent photoelastic plate, which acts as the spatial filter of the-system. Thus different pupil transmittance configurations can be achieved, each of which is associated with a certain image transformation.
ABSTRACT
An experiment similar to the Lau effect but employing the Walsh functions as diffracting apertures is performed. The equivalent resonance condition and the corresponding intensity light distribution are derived. This approach is used to implement a spatial-filtering optical device.
ABSTRACT
A method for displaying the complex degree of coherence (CDC) of a quasi-monochromatic spatially incoherent source is proposed. The phase of the CDC is encoded in a method similar to that used in interferometric imaging with incoherent light. The method is based on Fourier analysis of the speckle pattern that appears when a diffuser is illuminated with the partially coherent field whose CDC is to be displayed. In addition, an intensity pattern that resembles the spatial distribution of the incoherent source can also be obtained.
