Scattering by composite rough surfaces

Beckmann, P.

doi:10.1109/proc.1965.4081

Cited by 57 publications

(33 citation statements)

References 6 publications

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“…The term R i R * i represents the realization of the ensemble average between the scattered fields at two point positions −mx and −mx 1 [20] and is computed as an autocorrelation function. Moreover, the ensemble average may be substituted by a space average because the process is considered as statistically stationary [21].…”

Section: A the Dp Expressionmentioning

confidence: 99%

Response for light scattered in the ocular fundus from double-pass and Hartmann–Shack estimations

et al. 2016

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Double-pass (DP) and Hartmann-Shack (HS) are complementary techniques based on reflections of light in the ocular fundus that may be used to estimate the optical properties of the human eye. Under conventional data processing, both of these assessment modes provide information on aberrations. In addition, DP data contain the effects of scattering. In the ocular fundus, this phenomenon may arise from the interaction of light with not only the retina, but also deeper layers up to which certain wavelengths may penetrate. In this work, we estimate the response of the ocular fundus to incident light by fitting the deviations between DP and HS estimations using an exponential model. In measurements with negligible intraocular scattering, such differences may be related to the lateral spreading of light that occurs in the ocular fundus due to the diffusive properties of the media at the working wavelength. The proposed model was applied in young healthy eyes to evaluate the performance of scattering in such population. Besides giving a parameter with information on the ocular fundus, the model contributes to the understanding of the differences between DP and HS estimations.http://dx

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Section: A the Dp Expressionmentioning

confidence: 99%

Response for light scattered in the ocular fundus from double-pass and Hartmann–Shack estimations

et al. 2016

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“…The scalar value of the scattered field E2 at the point of observation P is given by the Helmholtz integral E2<p) =^t e-^)s as (5 ' where t = e*?T (6) and r' is the distance from P to a point r on the surface S.…”

Section: The Polarization Of E^shall Be Termed Vertical If E^liesmentioning

confidence: 99%

Backscatter of electromagnetic waves from a rough layer

Kumar

Koepsel²,

Durrani³

1966

Proc. IEEE

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“…For the above functions p(z) and B (7) one obtains [Beckmann, 1965a] P o( e) = ( cos 4 e + 1 ~:::!t sin 2 (J) -3/2 , with A the wavelength of the incident radiation.…”

Section: Theorymentioning

confidence: 99%

“…The first [Beckmann, 1965a] concerns an analysis of a rough surface generated by a superposition of several random processe.s: each with its own distribution and correlation function_ Let the distributions of the tj b e normal with mean zero and variances crJ , so that the scale roughness of the jth compone nt tj\X , y) is (7) and let the correlation fun ction of this component be (8) so that its "equivale nt " root-mean-square slope is 1 (9)…”

Section: (5)mentioning

confidence: 99%

Interpretation of angular dependence of backscattering from the Moon and Venus

Beckmann¹,

Klempere²

1965

J. RES. NATL. BUR. STAN. SECT. D. RAD. SCI.

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The small crater Heinsius A which exhibited th e radar e nhancem e nt is th e bri ght s pot indi cated by the arrow.Also, it is known that durin g a lun a r eclip se th e rayed crater s ex hibit a differen t coo lin g rat e than th e rest of th e lunar s urface. Th e mos t re ce nt measure· ments of a lunar eclipse in Dece mb er 1964, show that many other craters also s ho w thi s a nam olou s coo lin g behavior. On e of th e ne wly di scove red " th ermalanamolou s" cra ters ha s bee n te nt atively identified as He in siu s A, the c ra te r whi c h was bright under full moon and s howe d a radar e nhan ce me nt. The optical, thermal, and radar res ults can be explained by localized areas of bare, ex posed , and com pact roc k.In conclus ion , lunar radar ec hoes were examined in delay and frequ e ncy in a mann e r such that ret urns were reflected from localized areas on th e lunar surface. Th e ma ppin g of th ese re turn s s howe d that young and r aye d cra ters have e nh a nced radar sca tte rin g. Th e c raters which s how th ese rad a r e nh a nceme nts a lw ays a pp ear bri ght on th e full moon a nd from th e latest infrared res ult s, appear to be a namo lous in that regim e also. The resu lt s a t all wav ele ngth s ca n be exp lain ed if th ese are loca li zed a reas of bare, exposed, and co mpacted roc ks.Although this pape r concerned the radar behavior of young a nd rayed craters it should be noted that th e mountainou s regions we re s hown to re fle ct more power than th e maria regions. Th e e nhan ce ments we re mu c h less modes t th a n th ose for th e crate rs . For example, mountainous region s reR ected 11f2 to 2 times as much power as the maria region , while scattering e nhancements of craters s how th ey reflec ted up to 10 or 20 times as much power as o ther areas on the moon .Discussion Following Thompso n's Paper A previous ly de ri ved formula. ex press in g th e variation of the me an power bac kscatte red from the rough s urface of a planet with th e delay tim e or angle of inc id e nce by taking into account both th e co mpo site roughn ess of th e s urface a nd shadowing e ffec ts, is c hecked against ne w data from th e Moon and Venus a t fiv e diffe rent wav e length s. Th e a gree ment with the lunar data is very good and leads to ce rtain co nc lu s ions on th e nature of the lunar s urface. Th e data on Venu s are also in good agree ment and indi ca te that its s urface is smooth er than that of the Moon , but with an abundance of small s tru cture.

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Scattering by composite rough surfaces

Cited by 57 publications

References 6 publications

Response for light scattered in the ocular fundus from double-pass and Hartmann–Shack estimations

Response for light scattered in the ocular fundus from double-pass and Hartmann–Shack estimations

Backscatter of electromagnetic waves from a rough layer

Interpretation of angular dependence of backscattering from the Moon and Venus

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