Bispectral diffraction imagery I The bispectral optical transfer function

Barakat, Richard; Ebstein, Steven M.

doi:10.1364/josaa.4.001756

Cited by 12 publications

(7 citation statements)

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“…The main feature to point out here is the residual phase of the BTF close to important lines of symmetry, for the case of coma : these are the regions of high signal-to-noise ratio in the bispectrum used in object reconstruction algorithms . This sensitivity to coma was also reported by Barakat and Ebstein [13] .…”

Section: Bispectral Transfer Functions : Results and Discussionsupporting

confidence: 87%

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Effects of Aberrations on Transfer Functions Used in High Angular Resolution Astronomical Imaging

Zhang

Dainty

1992

Journal of Modern Optics

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. In this paper we present the results of the effect of aberrations on the transfer functions used in the high-angular resolution astronomical imaging techniques of speckle interferometry, Knox-Thompson and bispectral imaging . The analyses are based on a computer simulation of imaging through atmospheric turbulence . The results show that as the seeing becomes worse, its effect dominates the behaviour of the transfer functions which tend to be independent of (small) optical aberrations . However, if the wavefront variation due to fixed aberrations is significant over r o -sized regions in the pupil (where r o is the Fried parameter), the above transfer functions do depend on the aberration : in particular, the bispectral transfer function is relatively sensitive to odd aberrations, such as coma . . IntroductionThe effect of optical aberrations on transfer functions in high-resolution imaging in astronomy has been studied by many scientists since Labeyrie invented the technique of speckle interferometry in 1970 [1] . Speckle interferometry yields a diffraction-limited estimate of the Fourier modulus of the object (or equivalently, the autocorrelation of the object intensity), whereas extensions of it, in particular Knox-Thompson [2,3] and bispectrum imaging [4,5], provide an estimate of the Fourier phase as well . It is clearly important to know in all three cases the extent to which the aberrations (including defocus) affect the transfer function of the imaging process .Early investigations [6][7][8][9] showed that the speckle transfer function was much less sensitive to telescope aberrations than the normal transfer function applicable in the absence of turbulence . Telescope aberrations only begin to affect the speckle transfer function when the wavefront error is significant over a linear dimension comparable to the Fried parameter r o : this means that, as the seeing deteriorates (i .e . ro decreasing), the speckle transfer function becomes less sensitive to aberrations . Some experimental results on the effect of defocus were given by Karo et al . [10] and computational results, also on the effect of defocus, by Roddier et al . [11] .Two detailed studies of the effect of aberrations on the transfer functions in speckle interferometry [12], , and bispectrum imaging [13] have been made . In both cases, the atmospheric turbulence was modelled with a Gaussian correlation function . Publications of other authors who describe the effect of aberrations can be found in references [14][15][16] .If the fixed wavefront aberration is so severe that path length fluctuations greater than the coherence length of the light are introduced, then it may be necessary to reduce the bandwidth and thus increase the coherence length : this will clearly have an effect on the signal-to-noise ratio . This effect is unlikely to be encountered in practice and is not discussed here .

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Section: Bispectral Transfer Functions : Results and Discussionsupporting

confidence: 87%

“…[10] and computational results, also on the effect of defocus, by Roddier et al . [11] .Two detailed studies of the effect of aberrations on the transfer functions in speckle interferometry [12], , and bispectrum imaging [13] have been made . In both cases, the atmospheric turbulence was modelled with a Gaussian correlation function .…”

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confidence: 99%

Effects of Aberrations on Transfer Functions Used in High Angular Resolution Astronomical Imaging

Zhang

Dainty

1992

Journal of Modern Optics

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“…Making u 2 = , with r 0 /λ we can assume that F ( ) ≈ 1, and the term F (u 1 )F * (u 1 + ) of relation (9) appears. It has been shown [15] that it is enough to compute the bispectrum for the basic triangle OAB in figure 5; simple reasoning can show this. The total number of the transformations in the {u 1 , u 2 } plane that leave B(u 1 , u 2 ) unchanged are those that correspond to the six permutations of the three elements F (u 1 ), F (u 2 ) and F (−u 1 − u 2 ).…”

Section: Symmetries Of the Bispectrummentioning

confidence: 99%

Double-Layer Projection Display System Using Scattering Polarizer Film

Seo

Kim

2008

jjap

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This paper gives an introduction to speckle techniques developed for high angular-resolution imagery in astronomy. The presentation is focussed on fundamental aspects of the techniques of Labeyrie and Weigelt. The formalism used is that of Fourier optics and statistical optics, and corresponds to graduate level. Several new approaches of known results are presented. An operator formalism is used to identify similar regions of the bispectrum. The relationship between the bispectrum and the phase closure technique is presented in an original geometrical way. Effects of photodetection are treated using simple Poisson statistics. Realistic simulations of astronomical speckle patterns illustrate the presentation.

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“…It has been shown [15] that it is enough to compute the bispectrum for the basic triangle OAB in figure 5; simple reasoning can show this. The total number of the transformations in the {u 1 , u 2 } plane that leave B(u 1 , u 2 ) unchanged are those that correspond to the six permutations of the three elements F (u 1 ), F (u 2 ) and F (−u 1 − u 2 ).…”

Section: Symmetries Of the Bispectrummentioning

confidence: 99%