Nonsymmetric Fourier transforming with an anamorphic system

Szoplik, Tomasz; Kosek, Wojciech; Ferreira, Carlos

doi:10.1364/ao.23.000905

Cited by 23 publications

(7 citation statements)

References 11 publications

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“…The two-dimensional anamorphic transformers [12,13], that is with different scale in two orthogonal directions, give rise to a redistribution of spatial frequencies in the Fourier plane . The simplest working under spherical wave illumination, is a two-crossed cylindrical lens set-up, as described in [13] .…”

Section: Features Of Anamorphic Transformersmentioning

confidence: 99%

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Anamorphic Multiple Matched Filter for Character Recognition, Performance with Signals of Equal Size

Ferreira

Vázquez

1990

Journal of Modern Optics

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The construction and performance of an anamorphic multiple matched filter for character recognition is presented, in the usual situation of characters of equal input size and having the same size in the target . So a simple anamorphic correlator can be employed to obtain the recognition of a given character. In order to avoid false alarms the characters in the target are rotated by different angles depending on the angular tolerance of the correlator, which is rotationally variant and smaller than in symmetrical systems within a certain angular region . Thus the number of signals to which the filter can be matched can be greater than with spherical optics correlators .

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Section: Features Of Anamorphic Transformersmentioning

confidence: 99%

“…Ferreira and C . Vazquez composed of anamorphic Fourier-spectrum analysers [12,13] in cascade, each of them with different magnifications in the x and y directions . In this way, we enhanced not only the discrimination between similar objects but we reduced the angular tolerance during the recognition process .…”

Section: Introductionmentioning

confidence: 99%

Anamorphic Multiple Matched Filter for Character Recognition, Performance with Signals of Equal Size

Ferreira

Vázquez

1990

Journal of Modern Optics

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“…In optical data processing, the so-called astigmatic processor [6] was employed as a device for one-dimensional (1D) Fourier transforming and imaging in two mutually perpendicular directions. But was Szoplik and co-workers who for the first time proposed an anamorphic twodimensional (2D) Fourier transformer composed of crossed cylindrical lenses of different focal lengths [7], working under parallel beam illumination. In their paper, Szoplik and coworkers proposed two systems.…”

Section: Introductionmentioning

confidence: 99%

“…The key elements in all these anamorphic systems are anamorphic lenses. Refractive [7] or diffractive [20] cylindrical lenses have been employed to build anamorphic optical processors.…”

Section: Introductionmentioning

confidence: 99%

Ray matrix analysis of anamorphic fractional Fourier systems

Moreno

Ferreira

2006

J. Opt. A: Pure Appl. Opt.

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In this work we extend the application of the ray matrix approach to analyse anamorphic fractional Fourier systems, i.e., fractional Fourier optical systems where the fractional power is different for two orthogonal directions. The application of the ray matrix approach allows for easily obtaining the properties of the optical system, and it is therefore a powerful tool to design and simplify complicated systems. For simplicity we consider fractional Fourier systems with real orders and systems without apertures. We start by presenting the analysis of some previously reported anamorphic Fourier and fractional Fourier systems, and we end by proposing a simple optical system with tunable anamorphic fractional orders that can be varied continuously without changing the input and output planes.

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“…1,2 Later, the idea of obtaining a nonsymmetrical Fourier transform with crossed cylindrical lenses of different focal lengths working under plane-wave illumination was presented. 3 Based on this idea, an anamorphic two-dimensional 12-D2 optical processor was designed. 4 In order to extend the performance of the nonsymmetrical Fourier transformer, Andres et al 5 proposed the use of spherical-wave illumination.…”

Section: Introductionmentioning

confidence: 99%

Anamorphic fractional Fourier transform: optical implementation and applications

et al. 1995

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An additional degree of freedom is introduced to fractional-Fourier-transform systems by use of anamorphic optics. A different fractional Fourier order along the orthogonal principal directions is performed. A laboratory experimental system shows preliminary results that demonstrate the proposed theory. Applications such as anamorphic fractional correlation and multiplexing in fractional domains are briefly suggested.

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Nonsymmetric Fourier transforming with an anamorphic system

Cited by 23 publications

References 11 publications

Anamorphic Multiple Matched Filter for Character Recognition, Performance with Signals of Equal Size

Anamorphic Multiple Matched Filter for Character Recognition, Performance with Signals of Equal Size

Ray matrix analysis of anamorphic fractional Fourier systems

Anamorphic fractional Fourier transform: optical implementation and applications

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