Radon–Wigner display: a compact optical implementation with a single varifocal lens

Granieri, Sergio; Furlan, Walter D.; Saavedra, Genaro; Andrés, Pedro

doi:10.1364/ao.36.008363

Cited by 26 publications

(28 citation statements)

References 10 publications

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“…mentally obtained [12], the method can be used to analyse the performance of di erent apodizing structures through their corresponding one-dimensional pupil versions. …”

Section: Discussionmentioning

confidence: 99%

Short Communication Analysis of the asymmetric apodization using the fractional Fourier transform

Granieri¹,

Zalvidea²,

Sicre³

1999

Journal of Modern Optics

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Abstract.The e ect of asymmetric apodization is analysed using the fractional Fourier transform. The focusing properties of an apodizing pupil mask are investigated by means of a simple display in a generalized phase-space (or x±p domain). Some comparative computer simulations are performed and curves displaying the Strehl ratio versus defocus are presented in order to illustrate the possibilities of our approach. IntroductionSeveral e orts to improve the quality of the point spread function (PSF) of an optical imaging system have been done by using apodizer apertures. The purpose of the apodization process is to produce the suppression of the secondary maxima, or side lobes, of a di raction pattern in order to enhance the resolving power of the optical system. It is a classical problem and it has been widely studied [1,2]. In the apodization method proposed by Cheng and Siu [3], the aperture is modi®ed in an asymmetric mode. This asymmetric aperture function produces the suppression of the secondary maxima at a side of the central peak of the di raction pattern at the cost of increasing the lobes at the opposite side [4].The fractional Fourier transform (FRT) was introduced in optical signal processing by Ozaktas and Mendlovic [5] and Lohmann [6]. Two di erent optical de®nitions of the FRT have been given. In the ®rst, the FRT was de®ned based on light propagation in quadratic graded index media. In the second de®nition, the FRT of fractional order p results from a phase-space rotation of the input Wigner distribution function by an angle of pº=2. The FRT is a generalization of the classical Fourier transform and the information content stored in the FRT changes from spatial to spectral as the fractional order varies from pˆ0 to pˆ1. The relation between a FRT of order p and the free-space di raction [7,8] allows the analysis of the tolerance of optical imaging systems to focus errors and/or aberrations. There are several criteria to analyse the performance of an optical imaging system based on the on-axis irradiance. The Strehl ratio (SR), de®ned as the intensity values on axis at the di raction focus conveniently normalized, is an important image quality parameter [9]. The purpose of this letter is to analyse the

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“…mentally obtained [12], the method can be used to analyse the performance of di erent apodizing structures through their corresponding one-dimensional pupil versions. …”

Section: Discussionmentioning

confidence: 99%

Short Communication Analysis of the asymmetric apodization using the fractional Fourier transform

Granieri¹,

Zalvidea²,

Sicre³

1999

Journal of Modern Optics

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“…However, for the case of fractional selfimaging (which is of interest due to its repetition rate multiplication capability), the gen eral relationships obtained here should be used for observ ing well conformed pulse trains. being ( The free space diffraction originated by an input object under spherical illumination is closely related to the FRT production, as it was demonstrated in [9]. In the FRT setup described above, the first lens generates the spherical wave being the only difference with free space diffraction the second lens action introducing a quadratic phase factor.…”

mentioning

confidence: 82%

Periodic pulse train conformation based on the temporal Radon–Wigner transform

Cuadrado-Laborde

Costanzo-Caso

Duchowicz

et al. 2007

Optics Communications

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By using the Radon-Wigner transform (RWT), we analyze the temporal selfimaging or Talbot effect for producing well-conformed pulse trains with variable repetition rates and duty-cycles. The relationships linking the selfimaging conditions with the fractional orders o f the RWT are first obtained for unchirped pulse trains. Then, we extend the analysis to chirped pulse sequences by deriving the con ditions to be fulfilled by an equivalent unchirped pulse train producing the same selfimage irradiances. This result becomes relevant for observing well-defined high order fractional selfimaging, which are o f interest due to their repetition rate multiplication. Besides, the effect of the finite extension of the pulse train on the selfimage quality is analyzed and a condition is found for relating the required min imum pulse number with the chirp parameter of the pulses. © 2007 Elsevier B.V. All rights reserved.The development of techniques for the analysis and synthesis of ultrashort optical pulses has become of most importance in the field of optical communications, pho tonic signal processing and ultrafast optics. The charac terization of the optical pulses can be performed from direct interferometric measurements in different domains such as time (t), frequency (v) or in a combined phase space domain (t, v)

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“…An optical implementation of a Radon-Wigner display using varifocal lens was discussed in [24]. The variety of integral transforms used in optics for analysis of optical signals demonstrates their importance and the necessity to discuss all the aspects of the methods of measuring amplitudes and phases of optical signals.…”

Section: F(t) ~-~ Ff(w)mentioning

confidence: 99%

Fractional Fourier transform in information processing, tomography of optical signal, and Green function of harmonic oscillator

Man’ko

1999

J Russ Laser Res

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A review of the properties of the fractional Fourier transform, which is used in information processing, is presented in connection with the symplectic tomography transform of optical signals. The relationship between the Green function of the quantum harmonic oscillator and the fractional Fourier transform is elucidated. An analysis of electromagnetic signals which uses an invertible map of analytic signal onto the tomographic probability distribution is made. The formal connection of the analysis with the tomography method of measuring quantum states is considered. The relation to other methods of time-frequency quasidistributions (for example, the Ville-Wigner quasidistribution) characterizing a signal is studied.

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Radon–Wigner display: a compact optical implementation with a single varifocal lens

Cited by 26 publications

References 10 publications

Short Communication Analysis of the asymmetric apodization using the fractional Fourier transform

Short Communication Analysis of the asymmetric apodization using the fractional Fourier transform

Periodic pulse train conformation based on the temporal Radon–Wigner transform

Fractional Fourier transform in information processing, tomography of optical signal, and Green function of harmonic oscillator

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