Pub Date : 1998-09-01DOI: 10.1088/0963-9659/7/5/020
H. Yoshimura, T. Iwai
Effects of the aperture of a lens which is used to conduct an optical fractional Fourier transform on the fractional average intensity are analysed numerically using a computer. The fractional average intensity means the average intensity of the optical field produced from a partially coherent source in a fractional Fourier plane. In the present study, the fractional average intensities of a monochromatic Gaussian Schell model (GSM) source are evaluated using the root-mean square (RMS) difference between those with and without the effects of the lens aperture. It is clearly shown from our analysis that the aperture size of the lens should be twice as large as the GSM source size or greater in order to satisfy the condition of the RMS difference .
{"title":"Effects of lens aperture on the average intensity in a fractional Fourier plane","authors":"H. Yoshimura, T. Iwai","doi":"10.1088/0963-9659/7/5/020","DOIUrl":"https://doi.org/10.1088/0963-9659/7/5/020","url":null,"abstract":"Effects of the aperture of a lens which is used to conduct an optical fractional Fourier transform on the fractional average intensity are analysed numerically using a computer. The fractional average intensity means the average intensity of the optical field produced from a partially coherent source in a fractional Fourier plane. In the present study, the fractional average intensities of a monochromatic Gaussian Schell model (GSM) source are evaluated using the root-mean square (RMS) difference between those with and without the effects of the lens aperture. It is clearly shown from our analysis that the aperture size of the lens should be twice as large as the GSM source size or greater in order to satisfy the condition of the RMS difference .","PeriodicalId":20787,"journal":{"name":"Pure and Applied Optics: Journal of The European Optical Society Part A","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1998-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77755205","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1998-09-01DOI: 10.1088/0963-9659/7/5/014
R. Horák, C. Sibilia, M. Bertolotti
It is shown that the so-called paraxial approximation frequently used in nonlinear optics can break some conservation laws in the case of second harmonic generation.
结果表明，非线性光学中常用的所谓的近轴近似在二次谐波产生的情况下会破坏一些守恒定律。
{"title":"On conservation of momentum in ? interaction","authors":"R. Horák, C. Sibilia, M. Bertolotti","doi":"10.1088/0963-9659/7/5/014","DOIUrl":"https://doi.org/10.1088/0963-9659/7/5/014","url":null,"abstract":"It is shown that the so-called paraxial approximation frequently used in nonlinear optics can break some conservation laws in the case of second harmonic generation.","PeriodicalId":20787,"journal":{"name":"Pure and Applied Optics: Journal of The European Optical Society Part A","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1998-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78952853","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1998-09-01DOI: 10.1088/0963-9659/7/5/004
F. Gori, M. Santarsiero, S. Vicalvi, R. Borghi, G. Guattari
We present an approach for describing the properties of a quasi-monochromatic, beam-like field that is both partially polarized and partially coherent from the spatial standpoint. It is based on the use of a single matrix, called the beam coherence-polarization matrix, whose elements have the form of mutual intensities. This approach, which can be viewed as an approximate form of Wolf's general tensorial theory of coherence, appears to be very simple, yet it is able to cover significant aspects of the beam behaviour that would not be accounted for by a scalar theory or by a local polarization matrix approach. A peculiar interference law applying to mutual intensities is derived. We show through simple examples how this approach leads to distinguish fields that would appear identical in a scalar treatment or in a local polarization matrix description. Hints for extensions are given.
{"title":"Beam coherence-polarization matrix","authors":"F. Gori, M. Santarsiero, S. Vicalvi, R. Borghi, G. Guattari","doi":"10.1088/0963-9659/7/5/004","DOIUrl":"https://doi.org/10.1088/0963-9659/7/5/004","url":null,"abstract":"We present an approach for describing the properties of a quasi-monochromatic, beam-like field that is both partially polarized and partially coherent from the spatial standpoint. It is based on the use of a single matrix, called the beam coherence-polarization matrix, whose elements have the form of mutual intensities. This approach, which can be viewed as an approximate form of Wolf's general tensorial theory of coherence, appears to be very simple, yet it is able to cover significant aspects of the beam behaviour that would not be accounted for by a scalar theory or by a local polarization matrix approach. A peculiar interference law applying to mutual intensities is derived. We show through simple examples how this approach leads to distinguish fields that would appear identical in a scalar treatment or in a local polarization matrix description. Hints for extensions are given.","PeriodicalId":20787,"journal":{"name":"Pure and Applied Optics: Journal of The European Optical Society Part A","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1998-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75781322","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1998-09-01DOI: 10.1088/0963-9659/7/5/009
C. Aime
We show in this paper that the statistical properties of the speckle image formed at the focus of a large telescope can be fully described by a joint statistical analysis at N different spatial positions, where N is the number of resolution cells in the object's support. To obtain this result, the statistical properties are defined using multifold moment-generating functions (MGFs). Simplifying assumptions (discrete one-dimensional geometry, stationarity) are used to make the mathematical formalism simpler; they make the imaging process similar to a moving average process. General expressions are given for the twofold MGF and for MGFs of higher order. These relations are then used to show that an analysis of order N is exhaustive. It is shown that an MGF of order N + 1 can be written as the product of two MGFs of order N divided by an MGF of order N - 1. Alternatively, it is also shown that the cumulant of order N + 1 is equal to zero. A particular comment is made for the case of the double-star speckle pattern.
{"title":"On the order of analysis of speckle images in optical astronomy","authors":"C. Aime","doi":"10.1088/0963-9659/7/5/009","DOIUrl":"https://doi.org/10.1088/0963-9659/7/5/009","url":null,"abstract":"We show in this paper that the statistical properties of the speckle image formed at the focus of a large telescope can be fully described by a joint statistical analysis at N different spatial positions, where N is the number of resolution cells in the object's support. To obtain this result, the statistical properties are defined using multifold moment-generating functions (MGFs). Simplifying assumptions (discrete one-dimensional geometry, stationarity) are used to make the mathematical formalism simpler; they make the imaging process similar to a moving average process. General expressions are given for the twofold MGF and for MGFs of higher order. These relations are then used to show that an analysis of order N is exhaustive. It is shown that an MGF of order N + 1 can be written as the product of two MGFs of order N divided by an MGF of order N - 1. Alternatively, it is also shown that the cumulant of order N + 1 is equal to zero. A particular comment is made for the case of the double-star speckle pattern.","PeriodicalId":20787,"journal":{"name":"Pure and Applied Optics: Journal of The European Optical Society Part A","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1998-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90602484","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1998-09-01DOI: 10.1088/0963-9659/7/5/011
A. Consortini, F. Rigal
Use of moments of non-integer order (called fractional moments) in statistical optics is proposed for discriminating between candidates for probability density functions (PDFs) of the scintillation intensity to overcome the experimental problems encountered by using integer moments. Low-order (< 2) fractional moments allow comparison of experimental data with theoretical PDFs of the intensity in different scintillation regimes. A comparison procedure, based on two low-order measured fractional moments, is described and tested by utilizing Monte Carlo samples from three distributions commonly used in atmospheric propagation (Ln, LnME and K). The bin width required to discriminate between different distributions and the effect of noise are investigated. Examples of application to experimental data are presented.
{"title":"Fractional moments and their usefulness in atmospheric laser scintillation","authors":"A. Consortini, F. Rigal","doi":"10.1088/0963-9659/7/5/011","DOIUrl":"https://doi.org/10.1088/0963-9659/7/5/011","url":null,"abstract":"Use of moments of non-integer order (called fractional moments) in statistical optics is proposed for discriminating between candidates for probability density functions (PDFs) of the scintillation intensity to overcome the experimental problems encountered by using integer moments. Low-order (< 2) fractional moments allow comparison of experimental data with theoretical PDFs of the intensity in different scintillation regimes. A comparison procedure, based on two low-order measured fractional moments, is described and tested by utilizing Monte Carlo samples from three distributions commonly used in atmospheric propagation (Ln, LnME and K). The bin width required to discriminate between different distributions and the effect of noise are investigated. Examples of application to experimental data are presented.","PeriodicalId":20787,"journal":{"name":"Pure and Applied Optics: Journal of The European Optical Society Part A","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1998-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77686367","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1998-09-01DOI: 10.1088/0963-9659/7/5/025
B. Hoenders, H. A. Ferwerda
We separate the field generated by a spherically symmetric bounded scalar monochromatic source into a radiative and non-radiative part. The non-radiative part is obtained by projecting the total field on the space spanned by the non-radiating inhomogeneous modes, i.e. the modes which satisfy the inhomogeneous wave equation. Using residue techniques, introduced by Cauchy, we obtain an explicit analytical expression for the non-radiating component. We also identify the part of the source distribution which corresponds to this non-radiating part. The analysis is based on the scalar wave equation.
{"title":"THE NON-RADIATING COMPONENT OF THE FIELD GENERATED BY A FINITE MONOCHROMATIC SCALAR SOURCE DISTRIBUTION","authors":"B. Hoenders, H. A. Ferwerda","doi":"10.1088/0963-9659/7/5/025","DOIUrl":"https://doi.org/10.1088/0963-9659/7/5/025","url":null,"abstract":"We separate the field generated by a spherically symmetric bounded scalar monochromatic source into a radiative and non-radiative part. The non-radiative part is obtained by projecting the total field on the space spanned by the non-radiating inhomogeneous modes, i.e. the modes which satisfy the inhomogeneous wave equation. Using residue techniques, introduced by Cauchy, we obtain an explicit analytical expression for the non-radiating component. We also identify the part of the source distribution which corresponds to this non-radiating part. The analysis is based on the scalar wave equation.","PeriodicalId":20787,"journal":{"name":"Pure and Applied Optics: Journal of The European Optical Society Part A","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1998-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81702077","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1998-09-01DOI: 10.1088/0963-9659/7/5/007
H. Arimoto, Y. Ohtsuka
The theoretical foundation is described not only of how to determine the angular separation of two point spectral sources, but also on how to recover each spectral profile from the measured complex degree of spectral coherence. It is shown that the so-called space-frequency equivalence law is not always required. A simple simulation experiment is done by incorporating paired superluminescent diodes as the two point sources with different broadband spectra. The experimental results verify the validity of the theoretical prediction.
{"title":"Angular separation and spectra of two point sources determined from measured spectral coherence","authors":"H. Arimoto, Y. Ohtsuka","doi":"10.1088/0963-9659/7/5/007","DOIUrl":"https://doi.org/10.1088/0963-9659/7/5/007","url":null,"abstract":"The theoretical foundation is described not only of how to determine the angular separation of two point spectral sources, but also on how to recover each spectral profile from the measured complex degree of spectral coherence. It is shown that the so-called space-frequency equivalence law is not always required. A simple simulation experiment is done by incorporating paired superluminescent diodes as the two point sources with different broadband spectra. The experimental results verify the validity of the theoretical prediction.","PeriodicalId":20787,"journal":{"name":"Pure and Applied Optics: Journal of The European Optical Society Part A","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1998-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90484150","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1998-09-01DOI: 10.1088/0963-9659/7/5/022
D. Fischer
The theory of diffraction tomography is generalized to random media. A relationship between the two-point spatial correlation function of the dielectric susceptibility and the cross-spectral density of the scattered field is derived, and the reconstruction of the two-point spatial correlation function from measurements of the cross-spectral density in two planes, on different sides and at finite distances from the medium, is investigated. It is shown that the two-point spatial correlation function cannot be determined uniquely, in general, from scattered field measurements, except for a class of random media known as quasi-homogeneous random media.
{"title":"Generalized theory of diffraction tomography for random media","authors":"D. Fischer","doi":"10.1088/0963-9659/7/5/022","DOIUrl":"https://doi.org/10.1088/0963-9659/7/5/022","url":null,"abstract":"The theory of diffraction tomography is generalized to random media. A relationship between the two-point spatial correlation function of the dielectric susceptibility and the cross-spectral density of the scattered field is derived, and the reconstruction of the two-point spatial correlation function from measurements of the cross-spectral density in two planes, on different sides and at finite distances from the medium, is investigated. It is shown that the two-point spatial correlation function cannot be determined uniquely, in general, from scattered field measurements, except for a class of random media known as quasi-homogeneous random media.","PeriodicalId":20787,"journal":{"name":"Pure and Applied Optics: Journal of The European Optical Society Part A","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1998-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83195196","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1998-09-01DOI: 10.1088/0963-9659/7/5/013
Z. Bouchal, J. Peřina
The polarization properties of the phase-conjugate wave generated by means of degenerate four-wave mixing in isotropic Kerr-like media are analysed for monochromatic plane waves of arbitrary polarizations using the Laplace transformation to solve the coupled wave equations. The model presented enables us to find the reflection and transmission matrices defined for the electric and magnetic strength vectors and to discuss the efficiency and fidelity of the phase conjugation.
{"title":"Vectorial electromagnetic theory of degenerate four-wave mixing in isotropic Kerr-like media","authors":"Z. Bouchal, J. Peřina","doi":"10.1088/0963-9659/7/5/013","DOIUrl":"https://doi.org/10.1088/0963-9659/7/5/013","url":null,"abstract":"The polarization properties of the phase-conjugate wave generated by means of degenerate four-wave mixing in isotropic Kerr-like media are analysed for monochromatic plane waves of arbitrary polarizations using the Laplace transformation to solve the coupled wave equations. The model presented enables us to find the reflection and transmission matrices defined for the electric and magnetic strength vectors and to discuss the efficiency and fidelity of the phase conjugation.","PeriodicalId":20787,"journal":{"name":"Pure and Applied Optics: Journal of The European Optical Society Part A","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1998-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84122410","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1998-09-01DOI: 10.1088/0963-9659/7/5/019
A. A. Khan, M. Zubairy
We present an optical algorithm for parallel multiplication of vectors and matrices using simple grating structures. The proposed scheme has the advantage that it does not require optical elements. Light while passing through the spatial light modulators, consisting of grating structures, gets multiplied and summed at the output plane. The scheme has the flexibility to perform matrix operations without changing the hardware.
{"title":"Optical computing without using optical elements","authors":"A. A. Khan, M. Zubairy","doi":"10.1088/0963-9659/7/5/019","DOIUrl":"https://doi.org/10.1088/0963-9659/7/5/019","url":null,"abstract":"We present an optical algorithm for parallel multiplication of vectors and matrices using simple grating structures. The proposed scheme has the advantage that it does not require optical elements. Light while passing through the spatial light modulators, consisting of grating structures, gets multiplied and summed at the output plane. The scheme has the flexibility to perform matrix operations without changing the hardware.","PeriodicalId":20787,"journal":{"name":"Pure and Applied Optics: Journal of The European Optical Society Part A","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1998-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73762887","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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