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ER L-0325-TR AR -4-= SDEPARTMENT OF DEFENCE (I) DEFENCE SCIENCE AND TECHNOLOGY ORGANISATION '= ELECTRONICS RESEARCH LABORATORY I DEFENCE RESEARCH CENTRE SALISBURY SOUTH AUSTRALIA TECHNICAL REPORT ER L-0325-TR THE EFFECT OF VARYING THE INTERNAL ANGLE OF A DIHEDRAL CORNER REFLECTOR W.C. ANDERSON DTIC LCTE T hE* U N rM Eo TA T r- NA TIO N A L 0 r F - 1AUrH3F1SED To Ec~ EPHROUC AND SEL. s F,. - / 0 AIL C..) ut1L be $' blo m ( C omowat of Australia Appr vedrorwublc Reeas COPY No. " ' , 1 '1 1985

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Page 1: SDEPARTMENT OF DEFENCE - DTICat each point of the illuminated surface as though from an infinite tangent plane at that point. The physical optics surface current density for the conducting

ER L-0325-TR AR -4-=

SDEPARTMENT OF DEFENCE(I) DEFENCE SCIENCE AND TECHNOLOGY ORGANISATION

'= ELECTRONICS RESEARCH LABORATORY

I DEFENCE RESEARCH CENTRE SALISBURYSOUTH AUSTRALIA

TECHNICAL REPORT

ER L-0325-TR

THE EFFECT OF VARYING THE INTERNAL ANGLE

OF A DIHEDRAL CORNER REFLECTOR

W.C. ANDERSON DTICLCTE

T hE* U N rM Eo TA T r- N A TIO N A L 0 r F -1AUrH3F1SED To Ec~EPHROUC AND SEL. s F,. - /

0 AILC..) ut1L be $' blo m

( C omowat of AustraliaAppr vedrorwublc Reeas

COPY No. " ' , 1 '11985

Page 2: SDEPARTMENT OF DEFENCE - DTICat each point of the illuminated surface as though from an infinite tangent plane at that point. The physical optics surface current density for the conducting

UNCLASSIFIED

AR-004-IDEPARTMENT OF DEFENCE

DEFENCE SCIENCE AND TECHNOLOGY ORGANISATION

ELECTRONICS RESEARCH LABORATORY

TECHNICAL REPORT

ERL-0325-TR

THE EFFECT OF VARYING THE INTERNAL ANGLE OF A DIHEDRAL CORNER REFLECTOR

W.C. Anderson

SUMMARY

Small deviations from orthogonality can reduce drasticallythe backscattering radar cross section of dihedral cornerreflectors. In this paper this effect is studied usingthe method of physical optics with emphasis on thereductions of RCS achievable for modest departures fromorthogonality.

pc' Accesion For

NTIS CRA&* DTIC TAB 0

Unanrounced oJu;stficatonI-- .~~...... .. ...............

- -........... ................ .. '"" -". .." "By . .

Avaiiability Codes

t Avii;a;n/or

POSTAL ADDRESS: Director, Electronics Research Laboratory,Box 2151, GPO, Adelaide, South Australia, 5001.

UNCLASSIFIED

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ERL-0325-TR

TABLE OF CONTENTS

Page

1. INTRODUCTION 1

2. THEORY 1

2.1 The physical optics approach 1

2.2 Applications to the dihedral corner reflector 2

3. THEORETICAL RESULTS 5

4. EXPERIMENTAL MEASUREMENTS 7

4.1 The anechoic chamber 7

4.2 The dihedral reflectors 7

5. COMPARISON OF EXPERIMENTAL AND THEORETICAL RESULTS 8

6. CONCLUSIONS 8

7. ACKNOWLEDGEMENT 9

REFERENCES 10

LIST OF TABLES

1. EXPRESSIONS FOR THE CONTRIBUTIONS TO THE BACKSCATTERED FIELD 11

2. DEFINITIONS FOR a' AND b' AND THEIR ASSOCIATED DOMAINS OF VALIDITY 14

3. DEFINITIONS FOR a" AND THEIR ASSOCIATED DOMAINS OF VALIDITY 15

4. DEFINITIONS FOR b" AND THEIR ASSOCIATED DOMAINS OF VALIDITY 16

LIST OF FIGURES

1. Dihedral corner reflector

2. Comparison of RCS for 6 - 00 and e - 50

3. Elevation RCS for *

4. Comparison of RCS for reflector angles 80* and 1000

5. Reduction in RCS for 6 - -2*, -5*, -10* and -20*

(vertical polarisation)

6. Reduction in RCS for 6 - 2, 5", 10* and 20*(vertical polarisation)

7. Reduction in RCS for 6 - -2*, -5o, -10* and -20"

(horizontal polarisation)

8. Reduction in RCS for 6 - 2", 5*, 100 and 20"

(horizontal polarisation)

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ERL-0325-TR

9. RCS for 70° and 80* reflectors, a - b - 5A, c - I0A

10. RCS for 85" and 88* reflectors, a - b - c - 100A

11. RCS pattern for the special case, reflector angle - 60, compared withthe orthogonal reflector

12. Reduction in RCS for 6 - -2* and -5", (vertical polarisation).a - b - 20X

13. Reduction in RCS for 6 - 20 and 5, (vertical polarisation).

a - b - 20-

14. RCS reduction as a function of 6 at 0 w e a 00 for a - b -5

15. RCS reduction as a function of ' at 4 e - 0* for a - b - 10)

16. RCS reduction as a function of 6 at t - 0* for a - b - 20.

17. RCS reduction as a function of o at f - -= 00 for a - b - 40.

18. RCS reduction as a function of plate size at 0 - 6 - 00 for 6 - - *

19. RCS reduction as a function of plate size at 0 - 6 - 0* for 6 - V

20. RCS reduction as a function of plate size at * - e - 00 for 6 - -°

21. RCS reduction as a function of plate size at * - 0 - 0* for 6 -2*

22. RCS reduction as a function of plate size at * - 6 - 00 for 6 - -5*

23. RCS reduction as a function of plate size at p - e - 0* for o - 50

24. RCS reduction as a function of plate size at - C - 0* for 6 - -10

25. RCS reduction as a function of plate size at -= 00 for C - 100

26. RCS reduction as a function of plate size at = - 0* for F - -20*

27. RCS reduction as a function of plate size at -= 0* for e - 200

28. RCS reduction as a function of plate size at t - e- 0 for 6 - -30*

29. RCS reduction as a function of plate size at + - e - '0 for 6 - 30*

30. Reduction in RCS for 6 - -1*, -2* and -5° (vertical polarisation).a - b - 40X

31. Reduction in RCS for 6 - 1i, 2* and 50 (vertical polarisation).a - b - 40X

32. Reduction in RCS for 6 - -10, -2* and -5* (vertical polarisation).a - b - 100).

33. Reduction in RCS for 6 - 1., 2* and 5* (vertical polarisation).a - b - 100)

34. RCS for an asymmetric reflector with reflector angle 90*

35. RCS for asymmetric reflectors with reflector angles 850 and 920

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ERL-0325-TR

36. Reduction in RCS for asymmetric reflectors with 6 - -2", -5* and -10"

37. Reduction in RCS for asymmetric reflectors with e - 2*, 50 and 100

38. Comparison of theory with experiment for a/) - 2.5, e - 0, 2 - 85*(vertical polarisation)

39. Comparison of theory with experiment for a/A - 2.5, 6 - 0, 2Y - 90*(vertical polarisation)

40. Comparison of theory with experiment for a/X - 2.5, e - 0', 2) - 950(vertical polarisation)

41. Comparison of theory with experiment for a/, - 3.3, 6 - 0, 21 - 85(vertical polarisation)

42. Comparison of theory with experiment for a/X - 3.3, 6 - 00, 2y - 900(vertical polarisation)

43. Comparison of theory with experiment for a/A - 3.3, 6 - 00, 2y - 950(vertical polarisation)

44. Comparison of theory with experiment for a/X - 5.0, 6 - 0°, 2Y - 850(vertical polarisation)

45. Comparison of theory with experiment for a/X - 5.0, 6 - 0", 2Y - 900(vertical polarisation)

46. Comparison of theory with experiment for a/A - 5.0, 6 - 0, 2y - 95°

(vertical polarisation)

47. Comparison of theory with experiment for a/A - 2.5, 6 - 0, 2y - 850(horizontal polarisation)

48. Comparison of theory with experiment for a/,,, - 2.5, C - 00, 2 = 90(horizontal polarisation)

49. Comparison of theory with experiment for a/X - 2.5, e - 00, 2) - 950(horizontal polarisation)

50. Comparison of theory with experiment for a/, - 3.3, 6 - 0° , 2) - 85*(horizontal polarisation)

51. Comparison of theory with experiment for a/' - 3.3, P - 0', 2", - 900(horizontal polarisation)

52. Comparison of theory with experiment for a/) - 3.3, e - 0, 2Y - 950(horizontal polarisation)

53. Comparison of theory with experiment for a/ - 5.0, e - 0, 2Y - 850(horizontal polarisation)

54. Comparison of theory with experiment for a/A - 5.0, 0 - 0, 2Y - 900(horizontal polarisation)

55. Comparison of theory with experiment for a/A - 5.0, 8 - 0*, 2Y - 950(horizontal polarisation)

56. Predicted and reasured reduction in RCS for 6 -5*, a/A - 2.5 and

vertical polarisation

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ERL-0325-TR

57. Predicted and measured reduction in RCS for S - 50, a/X - 2.5 andvertical polarisation

58. Predicted and measured reduction in RCS for 6 - -5O, a/A = 3.3 andvertical polarisation

59. Predicted and measured reduction in RCS for 6 - 5*, a/A - 3.3 andvertical polarisation

60. Predicted and measured reduction in RCS for 6 = -5o, a/X - 5.0 andvertical polarisation

61. Predicted and measured reduction in RCS for 6 - 50, a/, - 5.0 andvertical polarisation

62. Predicted and measured reduction in RCS for e - -5*, a/, - 5.0 andhorizontal polarisation

63. Predicted and measured reduction in RCS for L, - 5*, a/ - 5.0 andhorizontal polarisation

64. Comparison of theory with experiment for a/A - 2.5, b - 5* and 21 - 95*(vertical polarisation)

65. RCS reduction as a function of plate size at 0 - 6 - 0 for 6 - 7.5*

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-1-- ERL-0325-TR

1. INTRODUCTION

Orthogonal corner reflectors are often used to effect a large backscatteringcross section over a substantial range of angles. The RCS of such reflectors Iare well known and well documented. In contrast, relatively little workappears to have been done on non-orthogonal reflectors despite the fact that

it is inevitable that deviations from orthogonality will result in the processof construction of such reflectors, particularly large ones. It would buseful to know what degradation in performance one can expect for a givendeviation from orthogonality. Alternatively one might be interested inknowing what angle of deviation from orthogonality is required to give aprescribed reduction in RCS.

This paper reports on an investigation of the effect of varying the internalangle of a dihedral corner reflector, using the method of physical optics.Singly, doubly and triply reflected contributions are considered so theresults obtained here are valid for all dihedral reflectors with reflectorangles greater than 600. This is an extension of Knott's results(ref.1) whichare valid only for obtuse and orthogonal reflectors as he failed to taketriply reflected rays into account. Moreover, Knott's results deal only withthe case of zero elevation angle whereas the results here allow for non-zeroelevation angles.

Three dihedral reflectors with included angles 850, 900 and 950 werefabricated and measurements were performed in the ERL anechoic chamber forexperimental validation of the theoretical results. Very good agreement wasobtained.

The results indicate that marked reductions in RCS are possible for quitemodest deviations from orthogonality for large reflectors. Interestingly forI symmetric reflectors very deep nulls can appear along the axis of symmetry, aninterference effect which is a function of the plate size and the deviationangle. This suggests that, contrary to common practice, the axis of symmetrymight not be a good choice for 'sighting' a dihedral reflector.

2. THEORY

2.1 The physical optics approach

The physical optics method(ref.2,3) approximates the electromagnetic fieldon the scatterer by the geometric optics field with scattering taking placeat each point of the illuminated surface as though from an infinite tangentplane at that point. The physical optics surface current density for theconducting body is therefore

A X--&xn H illuminated region(1

J -L- 0 shadow region

where n is the outward unit vector normal to the surf ace and Hi is theincident field on the surface. This approximation to the surface current .%density is only valid for scatterers whose dimension is not too small inrelation to the wavelength, A, of the incident field.

The magnetic field integral equation for scattering from a perfectlyconducting body whose surface current is knowil, together with theapproximation (1), yields for the scattered field H at any point in space

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ERL-0325-TR- 2-

1 s 2ikRH , po Is'R (2)

where k - 2w/X, and R is the distance between the field point and theintegration point on the illuminated surface S' of the scatterer.

When the field point, located by radius vector r from the origin, is at alarge distance from the scatterer, equation (2) is reduced to the far fieldapproximation

ikr i A -ikr.r'

4% r f

A rwhere r , , is the radius vector from the origin to the integration

point on the scatterer and f denotes the integral over the illuminated

surface. A time factor e is assumed and suppressed throughout.

2.2 Applications to the dihedral corner reflector

The geometry of the dihedral corner reflector with reflector angle 2y isshown in figure 1.

The reflector supports multiple reflections to an order which depends onthe reflector angle 2y. Only singly and doubly reflected rays contributeto the scattered field for 2y > 900 and only singly, doubly and triplyreflected rays contribute to the scattered field for 900 > 2y > 60. As 2ydecreases, higher and higher order reflections have to be taken intoaccount. In this investigation attention is confined to reflectors with2Y > 600.

Consider a Aplane electromagnetic wave incident on the reflector in thedirection k - (-cos+ cosO, -sin$ cosO, -sine). Suppressing the timefactor, the incident magnetic field with magnitude H and directionrepresented by the unit vector L is o

A ik. r'H L H e (4)

0

Ai here L - (sin#, -cos$, 0) for a vertically polarised incident field andA - (-cos sine, -sin# sine, cose) for a horizontally polarised incidentfield. Incident directions are confined to -y < + < y and 0* < e < 90.

Backscattered single bounce returns are then obtained from equation (3)__6 i -WI A A

with H - H and r - -k. Thus the single bounce backscattered magnetic

field H is

S A ikr A A A 21k (5)- - 2 H (n x ) x (-k) dS' (5)

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-3 ERL-0325-TR

where n n - (any, cosy, 0) for single bounce scattering from face I to-, SA A

give H, and n n a2 - (sinY,-cosy, 0) for single bounce scattering from

face 2 to give H2

AThe magnetic field incident on a face with normal n after reflection from a

1A iface with normal n is

r

A. A ik[k-2(k.n r)n ]l.r'

[t -2inr)n e r r (6)

Thus the double bounce backscattered magnetic field His

A A A A

ik ikr A A A A A kn r r dH 47r r 2 - 2 (i.nr)nr)] x ( f i)'

1 (7)

There are two double bounce contributionsH12 and 21, the former arisingfrom reflection off face 1 to face 2 and then back in the backscattering

A A A Adirection while the latter reflects first from face 2. n - nj, nr - 2 for

n D A A A A IrDH12 and n -h, fr n r for H2 1.

In the case of triply reflected rays, the magnetic field incident on a facewith normal n after reflection first from a face with normal and then

from a face with normal is

A oHT i * nR] H 0e r(8)

where

-~A A A )A= - E- 2(L.nr)nr]Ir It 21nr nr

and

A A Ak r [k- 2(k. nr)n r I

The triple bounce backscattered magnetic field is obtained fromequation (3) with equation (8) as the incident field

Wikr I A-.47 r r - r

A A A A '0 A ) -4W

21k k-(k .nr ) n (kr d S.r'x (-k) e rr rdS '

'~ (9)

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ERL-0325-TR -4-

Two triple bounce contributions are possible for y < 45*. H12 1 resultsfrom reflections off face 1 to face 2, back to face 1 and then back in the

A ^ A A A A "Tbackscattering direction with n - nl, n - n2 and nR - n1 . H2 12 results

from reflections off face 2 to face 1, back to face 2 and thence backA A A A A

in the backscatter direction with n = n2, n r n1 and nR - n2.

The contributions from the three mechanisms can be written concisely as

ikeikrH H P ,v - S, D, T (10)2w r o

whererA

PS e21k (k.r') S

f e dS'

A A A A A A

pD jS e2ik[k(knr)nr'rl~ r

SI

-(A XnA .X (_

s (x )x (-k)

D A A A AAAQ = x(I - 2(.nr)n r )] x (-k)

S[A x( - 2 .R)] x (-)

(,r R n

Only Q is polarisation dependent.

The illuminated areas for each of these mechanisms are worked out using raytracing and the integrals are then evaluated over these illuminated areas.Discontinuity can arise in the solution for horizontal polarisation whenfull ill,.mination of a plate by a multiply reflected ray drops abruptly tozero as the reflected ray moves through the tangent to that plate with asmall change in incident angle. In the case of vertical polarisation this

is compensated for by Q so that no discontinuity appears. The results for

equation (10) are tabulated io Tables 1, 2, 3 and 4.

The total backscattered magnetic field Hto t is then

--- -- WS -0 D -a. I'21 - T -*THto t H2 H12 + H12 1 + H2 12

and the radar cross section is given by

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-5 - ERL-0325-TR

lim 4rr2 tot 12" r H2 (12)

0

3. THEORETICAL RESULTS

A computer program has been written to evaluate the RCS patterns for varyingplate sizes and reflector angles down to 600. The RCS of the reflectors arecomputed in units of X2 ; RCS reduction (dB) values are the reduction in RCSof the non-orthogonal reflector from that of the orthogonal reflector at thecorresponding aspect angle. For the case 0 - 00 the reduction (in decibels)is independent of the reflector length c.

Figure 2 shows the azimuth RCS pattern of an orthogonal reflector witha-b-5X and c= 10 for e- 0 and e-50. It can be seen that thedihedral reflector has a very broad double bounce contribution over # with thesingle bounce contributions appearing as ripples. Specular single bouncereturns from the individual faces appear as peaks at f - t45 ° . There is avery dramatic drop in RCS as 0 departs from 0* as evidenced in the 6 - 50pattern and shown explicitly in figure 3 which gives the elevation RCS patternfor * - 00. Figure 4 shows the RCS patterns for two dihedral reflectors withthe same plate sizes as before but with reflector angles of 80' and 100. Thedouble bounce contributions are dramatically reduced but the single bouncespecular returns at - ±40* for the 100* reflector stay the same, asexpected.

Figure 5 shows the reduction in RCS for acute angled reflectors with angles ofdeviation from orthogonality 6 - -2*, -50, -10* and -20* while figure 6 showsthe reduction in RCS for obtuse angled reflectors with 6 - 2, 50, 100 and200. All the preceding results are for vertical polarisation of the incidentfield. Figures 7 and 8 show the reduction in RCS for horizontal polarisation.

In obtuse reflectors the dominant contribution to the backscattered field overmost of * comes from doubly reflected rays, the single bounce contributionbeing significantly lower except in the specular directions ie in directionsorthogonal to the individual plates. These individual flashes of the plates,observed at - ±(90 - y)0 for the obtuse reflectors are not reduced bydeviations from orthogonality. The average level of reduction in RCS achievedover a large # coverage increases with increasing deviation angle (figures 6and 8). In acute reflectors, the dominant contribution is still from doublyreflected rays for small angles of deviation. Triple bounce contributionsbecome increasingly important with increasing magnitude in deviation angles;in fact these contributions are non-zero for * - -y to -(y + 26) and 0 - y toY + 26. When 6 < -180, the coverage of triple bounce contributions is from* = -y to y. The triple bounce contributions can then dominate, instead ofdouble bounce contributions. Thus, in figures 5 and 7, the increasedsignificance of triple bounce contributions leads to a lower RCS reductionbeing achieved for 6 - -20* than for 6 = -10O which has non-zero triple bouncecontributions only for 1#1 > 200 compared to 11 < 350 for 6 - -200.

When e - 0, * ±(3y - 90) ° are the specular directions for the two triplyreflected rays. Depending on their magnitudes compared to those of the doublyreflected rays and the relative phases of all the rays, the triple bouncecontribution can reveal its presence as ripples in the RCS pattern (near

- ±30 ° for 2y - 80, figure 9 and near * - ±420 for 2y = 88° , figure 10),slight peaks (at 4 - ±15' for 2y - 70°, figure 9) or flashes as at * - ±37.50for 2y - 85° in figure 10. y - 30° is the special case when * - 0° is thespecular direction for both triply reflected rays which add coherently for the600 symmetric reflector to give a very large return centred at 00

(figure 11).

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ERL-0325-TR - 6-

The reduction in RCS achieved is dependent on the plate size. Figures 5, 6, 7and 8 corresponding to the case a - b - 5X show that a 2 deviation fromorthogonality produces a reduction in RCS of 1 dB over most of *. Figures 12and 13 show that when a - b - 20X a 2° deviation is sufficient to give verymarked reduction, up to 30 dB near - 00. Interestingly, figures 12 and 13reveal that while the overall RCS reduction is higher for i6 - 5* than for161 - 2, the RCS reduction along the line of symmetry, # - 0, isunexpectedly higher for 161 2 than for 161 5 5, particularly for theobtuse reflectors (figure 13). This is a significant result in that users ofsymmetric dihedral reflectors frequently 'sight' the reflector along the axisof symmetry as it is the direction in which a maximum return is expected foran orthogonal reflector. However, figures 12 and 13 indicate that a smallerror in the construction of the reflector can reduce this return drastically.In view of this, attention is focussed on the backscattered return along theaxis of symmetry. The level of this return is a function of o and the platesize.

Figures 14 to 17 show the reduction in RCS in the direction - - 0* as afunction of 6 for a given plate size. These figures show a symmetry about theorthogonal reflector (8 = 00) for small 6 when double bounce contributionsdominate for both acute and obtuse reflectors. The increasing importance oftriple bounce contributions becomes evident in the lower RCS reductionsachieved as 6 + -300.

Figures 18 to 29 show the reduction in RCS in the direction - 00 forsymmetric reflectors (a - b) as a function of a for a given 6. These figuresshow the typical interference lobe structures; thus for a given 6 there arenumerous plate sizes, in arithmetic progression, for which nulls are expectedin the backscattered RCS of the reflector at * = e = 0*. The peaks infigures 18 to 29 correspond to these nulls. Figures 20 to 23 show that thea - b - 20X reflectors are closer to these nulls for 6 = ±2° than for 6 - ±50.This explains the much higher reduction in RCS obtained for 6 - ±2° than for6 - ±50 in figures 12 and 13. The minima in figures 18 to 27 and 29 increasein magnitude as plate size increases over a large range in plate size exceptfor the special case of 6 - 30* (figure 28). In this special case, 0 - 0* isthe specular direction for triply reflected rays which add coherently to givea large return that is about 3 dB below the peak return for the correspondingorthogonal reflector over a large range of plate sizes.

Knott(ref.1) has derived an approximate expression for predicting thereduction, X, in the scattered field strength when 0 = 0* for dihedralreflectors with small deviations from orthogonality and plate sizes largerelative to wavelength, these conditions being necessary for his assumption

that double bounce contributions are the dominant contributions. The doublebounce contribution for the non-orthogonal reflector, DN, with small deviationangle 6 is (equation (14), reference 1)

2ikb sin 6 cos(0+7/4)) (D N _ cOl - e (13) ,(13

He then obtained X by dividing the maximum value of equation (13), ID Nimax , by

the maximum double bounce contribution of the orthogonal reflector, ID I awhere omax

I 2c (14(a))N max Xsin6

u V

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7 ERL-0325-TR

and

ID 2kbc cos(tan-1 b/a) (14(b))

Thus, the reduction in the backscattered field strength is

kb sin6 cos(tan -1 b/a) (15)

and the reduction in backscattered radar cross section is X2.

It will be shown here that X as given by equation (15) here and inKnott(ref.1) gives a very rough estimate of the reduction actually achieved.Equation (15), applied to the reflectors in figure 13, gives a reduction of9.8 dB for 6 - 20 and 17.8 dB for 6 = 5*. While the 17.8 dB reductionpredicted for 6 - 50 is a good description of the reduction level achievedover most of 6, the 9.8 dB reduction predicted for 6 - 2* falls very short ofthat achieved for a large region around - 00. This results from the factthat this reflector has a very deep null there which arises from cancellationbetween the two doubly reflected rays and thus equation (14(a)) Is anoverestimation of the scattered field in that region. If, instead ofequation (14), equation (13) is used to calculate X at 0 = 0', a reduction of37.7 dB is obtained and that agrees with figure 13. Thus equation (15) has tobe used with care.

Figures 30, 31, 32 and 33 show the reduction in RCS from reflectors witha - b - 40A and a = b - 100A respectively for 161 - I*, 20, 50. Here it isseen that even a 10 deviation from orthogonality yields very substantialreductions in RCS.

Figures 34, 35, 36 and 37 illustrate the asymmetry in the RCS patterns fordihedral reflectors with unequal plates. It is clear that large reductions inRCS are not conditional on the equal size plate geometry.

4. EXPERIMENTAL MEASUREMENTS

4.1 The anechoic chamber

The experimental observations carried out to check the theoreticalpredictions were performed in the ERL anechoic chamber. This facility hasa normal source-target separation of 12 m, a frequency range extending from2.5 GHz to 40 GHz, and analogue recording of measurements(ref.4).

4.2 The dihedral reflectors

Three dihedral reflectors with reflector angles 85*, 90* and 950,a - b - 10 cm and c - 20 cm, were fabricated of aluminium of thickness6 mm. Two plates of dimensions 10 cm by 20 cm were held together at therequired angle with polypropylene supports at the back. The long edges ofthe reflectors were chamfered back to approximate a thin edge.

Three frequencies were employed, viz 7.5, 10 and 15 GHz corresponding toa/X of 2.5, 3.3 and 5.0. Measurements of backscattered RCS were made overthe full azimuthal range but only results for -y < # I y were analysed.The analogue X-Y plotter output was sampled at 1* intervals.

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ERL-0325-TR - 8-

5. COMPARISON OF EXPERIMENTAL AND THEORETICAL RESULTS

The 6 - 0, vertical and horizontal polarisation RCS patterns in figures 38 to55 include the experimental data for reflectors with 6 - -5*, 0, 5o and platesizes of a/X - 2.5, 3.3 , 5.0. Agreement between theory and experiment is good- within ±2 dB for 1.1 < 30* in all cases except for figures 43 and 49 whereit is within ±3 dB. For 1.1 > 30, theory predicts much deeper nulls for the85* reflectors; apart from that agreement is still reasonable.

From these experimental data, the reduction in RCS has been calculated and isplotted against the predicted values in figures 56 to 63 for 6 - ±5%a/A - 2.5, 3.3, 5.0, vertical polarisation and 6 - ±5*, a/A - 5.0, horizontalpolarisation. These measured values confirm that the reduction in RCSachievable is dependent on the sizes of the reflectors relative to theincident wavelength.

Figure 64 verifies the RCS pattern for the 95° reflector with a/A - 2.5 viewedat O - 50 for vertical polarisation.

Figures 22 and 23 predict that the RCS patterns of the 85* and 950 reflectorsmade for experimental validation have nulls at *- e - 0* for a - b - 9A anda - b - 8.5X, ie at 26.9 GHz and 25.5 GHz respectively for verticalpolarisation. Unfortunately, attempts to collect reliable data at thesefrequencies failed because the available sources in the EL chamber are notsufficiently stable for the necessary nulling in the chamber to beaccomplished for frequencies over 21 GHz. In order to verify some of thepredicted nulls discussed in Section 3, new reflectors would have to be madeof a scale suited for measurement below 21 GHz. This is a task that may wellbe undertaken in the future.

Knott(ref.1) has an experimental validation of a reflector with 6 - 7.5* anda b - 5.6AX at 8 - 0*. Figure 65 shows that a fairly deep null can beexpected at 0 = e - 0* for this reflector and this is indeed shown to be thecase in reference 1, figure 5, with reasonable agreement with experiment.

6. CONCLUSIONS

This investigation has demonstrated the success of physical optics inpredicting the backscattering radar cross section of dihedral cornerreflectors with arbitrary included angle. Experimental measurements performedin the ERL anechoic chamber for reflectors with included angles of 85, 900and 950 are in excellent accord with theory over a wide range of incidentangles. Further, this agreement has been verified to hold for plates from 5Awidth down to 2.5X in width. The theory can be expected to yield even betterresutLa as plate sizes increase.

The reduction in RCS achievable for a given deviation from orthogonality isdependent on the size of the reflector, in terms of wavelength of the incidentradiation. For plate sizes in excess of a few wavelengths, very significantreductions in backscattered RCS can result from quite modest deviations fromorthogonality. As many practical dihedral scatterers are at least tenwavelengths wide, their RCS is extremely sensitive to such deviations. Inaddition non-orthogonality introduces deep interference nulls that are afunction of plate size and the deviation angle into the RCS patterns of thesereflectors. It has been shown here that a small deviation angle in areflector can meet the conditions for an interference null along the axis ofsymmetry. This somewhat unexpected result should be borne in mind whenemploying such reflectors.

Page 15: SDEPARTMENT OF DEFENCE - DTICat each point of the illuminated surface as though from an infinite tangent plane at that point. The physical optics surface current density for the conducting

9 ERL-0325-TR

7. ACKNOWLEDGEMENT

The anechoic chamber measurements incorporated in this paper were obtained byMr J. Crombie under the direction of Mr A. Tickner of Radar Division.Mr L. Nicholls of Weapon Systems Division, WSRL, made useful suggestions onpractical applications of the results.

19

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ERL-0325-TR - 10 -

REFERENCES

No. Author Title

1 Knott, E.F. "RCS Reduction of Dihedral Corners".IEEE Trans Antennas Propagat,Vol. AP-25, pp 406-409, 1977

2 Ruck, G.T., "Radar Cross Section HandbookBarrick, D.E., Volume 1".Stuart, W.D. and Plenum Press, New York, 1970Krichbaum, C.K.

3 Crispin, J.W. and "Methods of Radar Cross-SectionSiegel, K.M. Analysis".

Academic Press, New York, 1968

4 Tickner, A.T. and "The Electronics Research LaboratorySinnott, D.H. Anechoic Chamber and its Evaluation".

Seminar on Electromagnetic Antenna and

Scattering Measurements, Part II,CSIRO Division of Applied Physics,National Measurements Laboratory,November 1982

Page 17: SDEPARTMENT OF DEFENCE - DTICat each point of the illuminated surface as though from an infinite tangent plane at that point. The physical optics surface current density for the conducting

- 11 -ERL-0325-TR

-.- .,

i I .... V/

I-l. 1. 0I '@ 0 1I I .*

a 'A

-. -- *,.--- _ __ __ __ __ _ -A-l

0 -iE-4 0

DO A

i r

E4

CA0

' A 3446 ,-

Page 18: SDEPARTMENT OF DEFENCE - DTICat each point of the illuminated surface as though from an infinite tangent plane at that point. The physical optics surface current density for the conducting

U.L1;-0325-T"R - 12 -

v/ ,h

V .'I VV " 0 .•V

• -, ., 0

_ _ "_ _ _ -- _- _ _ -A

..

.II ,

Page 19: SDEPARTMENT OF DEFENCE - DTICat each point of the illuminated surface as though from an infinite tangent plane at that point. The physical optics surface current density for the conducting

- 13 - ERL-0325-TR

V

V w

i

0 0 0 P

tVI

.9g

tt

0 I A

Page 20: SDEPARTMENT OF DEFENCE - DTICat each point of the illuminated surface as though from an infinite tangent plane at that point. The physical optics surface current density for the conducting

ERL-0325-TR -14-

A V V A A V V A

C~ C. e- Cs C1 C

cu *%-4 co .14 co .4- c -4 m~ . I t C- r mI P

W o Iw CA "IA" t n 4 J

>1 .u 0 cu u uIZuV~

t" 2 W C tn *-C4 q0 *M 0 ."40 *.'400 .q 0* ~ - Mu t V)U th u

0 U A u n u A u ca . cd 0 0.0 c.0

A In ; An 'A 'll

?CA 0l tAf ?1; n ~0 C0 C 0 = 0

- ~ - 0 .0 4 0 .'f 0 .q 0 .04

Cu Cl l Cu 0u caCu

.10 4. 4.. ). 4. 4.5 4.a 4.

vI A A V/ A A

0041 +. ...4

z In 0 In.- _4

cd - 4

Page 21: SDEPARTMENT OF DEFENCE - DTICat each point of the illuminated surface as though from an infinite tangent plane at that point. The physical optics surface current density for the conducting

15 -ERL-0325-TR

InInIitoI~~.C A

.0 .0 41 I 1

In4 vi144 1

41.0 41 1.

v A

41 140 01 40 AU 40 40

414 414 414 14

Page 22: SDEPARTMENT OF DEFENCE - DTICat each point of the illuminated surface as though from an infinite tangent plane at that point. The physical optics surface current density for the conducting

EIL-0325-TR -16-

1% ciI

V V

m m! IiA v 'At -

315

Ix2 mm4 tom 2 0,I

9 at7

'A a i' c 0 In 0

\V A, A v A A \1 V\ A VA

U ~l~ amamph a

11 mu Lo w mu muAw

a a a el

a aa a 1- a a le

Page 23: SDEPARTMENT OF DEFENCE - DTICat each point of the illuminated surface as though from an infinite tangent plane at that point. The physical optics surface current density for the conducting

ERL-0325-TRFigure 1

z

FACE 2

FACE 1

C

k ICIDENTPLANE WAVE

, _y

x

Figure 1. Dihedral corner reflector

Figure

Page 24: SDEPARTMENT OF DEFENCE - DTICat each point of the illuminated surface as though from an infinite tangent plane at that point. The physical optics surface current density for the conducting

ERL-0325-TR ERL-0325-TRFigure 2 Figure 2

~0r

LIn

-= 0

z

i \;0o- -- =5

>N

~c = lox2y = 900

UN

vertical polarisation

-45.0 -30.0 -15.0 0.0 15.0 30.0 45.0

AZINRUIIlAL ANGLE (DEGREES) !

00

Figure 2. Comparison of RCS for "=0 ° and 0 5°

'.

Page 25: SDEPARTMENT OF DEFENCE - DTICat each point of the illuminated surface as though from an infinite tangent plane at that point. The physical optics surface current density for the conducting

ERL-0325-TRFigure 3

z

>

u

o A:_

N --

,C Vo iI

c lox

2y = 90'vertical polarisation \

0.0 15.0 30.0 45.0 6O.0 75.0 90.0

EIEVAT ION ANCI.i- (D;REES) ,

Figure 3. Elevation RCS for = 00

Page 26: SDEPARTMENT OF DEFENCE - DTICat each point of the illuminated surface as though from an infinite tangent plane at that point. The physical optics surface current density for the conducting

ERL-0325-TR ERL-0325-TRFigure 4 Figure 4

0

C00

0

4-

Cu

CNC

-<4 0

LW 0

000

0UO Z -)

0

C< -

z0

<U

0

C4

LI)

0,09 00OS 0*0 oi 0*07 0^01 O00

Page 27: SDEPARTMENT OF DEFENCE - DTICat each point of the illuminated surface as though from an infinite tangent plane at that point. The physical optics surface current density for the conducting

ERL-032S-TRFigure S

01-

C!

00

C 6= -20°

'. 0

006 -2

U

!-

a =b =SA

0 0000

-45.0 -30.0 -15.0 0.0 15.0 30.0 45.0

AZIOUllAL ANGLE (DEGREES)

Figure S. Reduction in RCS for 5 = -20, -50, -100 and -200 (vertical polarisation)

Page 28: SDEPARTMENT OF DEFENCE - DTICat each point of the illuminated surface as though from an infinite tangent plane at that point. The physical optics surface current density for the conducting

ERL-0325-TR ERL-0325-TRFigure 6 Figure 6

00

06 = 20

a6 = 1 0

z = 00

0O

0 =

u.0.

050

-.4.0 -30.0 -15.0 0.0 15.0 30.0 45.0

AZIMUTHAL ANGLE (DEGREES)

F . R 0Figure u. Reduction in RCS for 6 = 2, 5 , 10 and 20 (vertical polarisation)

Page 29: SDEPARTMENT OF DEFENCE - DTICat each point of the illuminated surface as though from an infinite tangent plane at that point. The physical optics surface current density for the conducting

ERL-0325-TRFigure 7

00

200

05

00

-- 2

0Z0

-45. -3 .0 -s.00.0 5.030.045.

0ZNMLAGL DGES

Fi u e 70 e u t o n R S f r6 = - , -5 1 n 2 h r z n a o a i a i n

Page 30: SDEPARTMENT OF DEFENCE - DTICat each point of the illuminated surface as though from an infinite tangent plane at that point. The physical optics surface current density for the conducting

ERL-0325-TRERL-0325-TR Figure 8Figure 8

200

0 1

00

00

on

00

0

0ZEn

-45.0 -30.0 -15.0 0.0 15.0 30.0 45.0

AZIMUTHAL ANGLE (DEGREES)

Figure 8. Reduction in RCS for 6 = 20. 50, 10 0 and 20 0 (horizontal polarisation)

Page 31: SDEPARTMENT OF DEFENCE - DTICat each point of the illuminated surface as though from an infinite tangent plane at that point. The physical optics surface current density for the conducting

ERL-0325-TRFigure 9

0

C!!

tn

02y 80

\...0J

0

0=0

vertical polarisation--

0 0

F 9 I Ii

-45.0 -30.0 -15.0 0.0 15.0 30.0 45.0 - ,

AZIrNIUTIIAL ANGLE (DEGREES)

Figure 9. RCS of 700 and 800 reflectors, a = b = S)X, c = 10O,

Page 32: SDEPARTMENT OF DEFENCE - DTICat each point of the illuminated surface as though from an infinite tangent plane at that point. The physical optics surface current density for the conducting

ERL-0325-TR ERL-0325-TRFigure 10 Figure 10

0

00

a--. ,2y =880

S ' 2y= 85 i

z 2

w go

'U IUz

vertical polarisationU

-.0 -30.0 -15.0 0.0 15.0 30.0 45.0

AZINITIAL ANGLE (DEGREES)

R0 a

Fiur 10'C f8 n 8rflcos :1

Page 33: SDEPARTMENT OF DEFENCE - DTICat each point of the illuminated surface as though from an infinite tangent plane at that point. The physical optics surface current density for the conducting

iiRL-0325-TRF-igure 1

0

00

o 2y 600

LU

0

a =b SA

c lox0 =00vertical polarisation

?45.0 -30.0 -15.0 0.0 15.0 30.0 45.0

AZINRJTIIAL ANGLE (DEGREES) P

Figre 1. CS attrn for the special case, reflector angle 60Ocompared with the orthogonal reflector

Page 34: SDEPARTMENT OF DEFENCE - DTICat each point of the illuminated surface as though from an infinite tangent plane at that point. The physical optics surface current density for the conducting

ERL-0325-TR ERL-0325-TRFigure 12 Figure 12

05

00o

i~i ' . 6 -S 0

U1A

\

0

0

= "

a = b = 20

o I p

-45.0 -30.0 -15.0 0.0 15.0 30.0 45.0

AZIMIUTHtAL ANGLE (DEGREES) iFigure 12. Reduction in RCS for 6 =-2 ° and -S° (vertical polarisation)

a = b =20)X

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ERL-0325-TR

Figure 13

00

6 2

I--

''

I ! I

- 0 =

M

-45.0 -30.0 -15.0 0.0 15.0 30.0 45.0

AZIUTHAL ANGLE (DEGREES)

Figure 13. Reduction in RCS for 6 = 20 and So (vertical polarisation)a - b = 20

Page 36: SDEPARTMENT OF DEFENCE - DTICat each point of the illuminated surface as though from an infinite tangent plane at that point. The physical optics surface current density for the conducting

ERL-0325-TR ERL-0325-TRFigure 14 Figure 14

10

jM

, z

U- 0"'f'! /

-LLI '/ /

-, /,,\/ 1//

V)/

vertical polarisation

-30.0 -20.0 -10.0 0.0 10.0 20.0 30.0

DEVIATION ANGLE (DEGREES)

Figure 14. RCS reduction as a function of 6 at = C =0for a = b = SX

Page 37: SDEPARTMENT OF DEFENCE - DTICat each point of the illuminated surface as though from an infinite tangent plane at that point. The physical optics surface current density for the conducting

ERL-0325-TRFigure 15

C!

0-0

s0

,PI

// vertical polarisation

-0 0-20.0 -10.0 0.0 10.0 20.0 30.0

DEVIATION ANGLE (DELGREES)

f-IgUre 15. RCS reduction ,,s ,function of at 0,: 0° 16for a =b = 101 .

Page 38: SDEPARTMENT OF DEFENCE - DTICat each point of the illuminated surface as though from an infinite tangent plane at that point. The physical optics surface current density for the conducting

ERL-0325-TR ERL-0325-TRFigure 16 Figure 16

-ZLn 0

D A

- I,

' ' II ":\

' , !I

\J

,, vrtical polarisation

DELVIATION ANGLE (DEGREES)

Figure 16. RCS reduction as a function of . at 0 . = 00for a b 20X

Page 39: SDEPARTMENT OF DEFENCE - DTICat each point of the illuminated surface as though from an infinite tangent plane at that point. The physical optics surface current density for the conducting

ERL-0325-TRFigure 17

C!0

L , vertical polarisation

Al I

-30.0 -20.0 -10.0 0.0 10.0 20.0 30.0

DEVIATION ANGLE (DEGREES)

Figure 17. RCS reduction as a function of 6 at

S=00 for a =b =40X

z IlI'I

ii

Page 40: SDEPARTMENT OF DEFENCE - DTICat each point of the illuminated surface as though from an infinite tangent plane at that point. The physical optics surface current density for the conducting

ERL-0325-TR ERL-0325-TR

Figure 18 Figure 18

o

S c

-l0

(9p) NoIIvi -

\ .K

- -

a...

-I

C -

0 SL O'(9 "55 '2 (PSI0 C

(AlP } NOI. V)flIIftht SJN

Page 41: SDEPARTMENT OF DEFENCE - DTICat each point of the illuminated surface as though from an infinite tangent plane at that point. The physical optics surface current density for the conducting

ERL-0325-TRFigure 19

0

00

0

0

'C -&

*Uj

> 0

o 05w

4U)

'4 -4

~4.

C!C

O*S- ,0 OSv OEO'l o0UIP) NH-ma- s:)-

Page 42: SDEPARTMENT OF DEFENCE - DTICat each point of the illuminated surface as though from an infinite tangent plane at that point. The physical optics surface current density for the conducting

ERL-0325-TR ERL-0325-TRFigure 20 Figure 20

0

o

0

C0 0$400

C 4

-4 00

> 0

0

* I,4.J

z C13

,

N

>- -4

0

04

-,-1

O'SL0"0 O'S 0"£ O'I 00 0

(SP)~~LL NOJ44(:I! :

~ 00

.C. ) C.

O*S4~~~ 0,9OS OEOS

(OP) O~nnam so

Page 43: SDEPARTMENT OF DEFENCE - DTICat each point of the illuminated surface as though from an infinite tangent plane at that point. The physical optics surface current density for the conducting

ERL-0325-TRFigure 21

0D

0

oI

00

.4If

4J0

0

.4-j

U 4on 0

r'j

CU I,

00

C.4

0D0j

-4

CCl

WSL *09 *StWOE 'sl '0

(OP)C, Wioaa a

Page 44: SDEPARTMENT OF DEFENCE - DTICat each point of the illuminated surface as though from an infinite tangent plane at that point. The physical optics surface current density for the conducting

ERL-0325-TR ERL-0325-TRFigure 22 Figure 22

C000

"-44j

w ~00Cd 0

~~L.0'

Cd

4j 0

> 0

0

0 -90

\0

LU 4

'A,

-40 W.

(UP)~U N~num

Page 45: SDEPARTMENT OF DEFENCE - DTICat each point of the illuminated surface as though from an infinite tangent plane at that point. The physical optics surface current density for the conducting

ERL-0325 -TRFigure 23

07

0

40

-4 G

0 0

00> 0

4.140N ol

* ~4.d0

0

'00

t4-I

o toLL.

O.S'l~~~L 0,9OS OE0S

(HP)~ ~ ~ ~ NO~ooisi

Page 46: SDEPARTMENT OF DEFENCE - DTICat each point of the illuminated surface as though from an infinite tangent plane at that point. The physical optics surface current density for the conducting

ERL-032S-TR ERL-0325-TRFigure 24 Figure 24

0

00

00

U

0

o 0o I!

o CCD

et.0

tno w 0"-U

00

0 SL 0,09 0'v C"0E 0"5I 0,0

(i-i

(8P) OIL rlfllll .".)

'.

Page 47: SDEPARTMENT OF DEFENCE - DTICat each point of the illuminated surface as though from an infinite tangent plane at that point. The physical optics surface current density for the conducting

ERL-0325-TRFigure 25

Ci

co

4j C

0 04>.0

C>

-Co

C;

0

0*0

C! 4J

Cl

C; 0

4j

oM

0,09~~~ Z*S WO s1(SP)L -O.ni ~

Page 48: SDEPARTMENT OF DEFENCE - DTICat each point of the illuminated surface as though from an infinite tangent plane at that point. The physical optics surface current density for the conducting

ERL-0325-TR ERL-0325-TRFigure 26 Figure 26

0

0

co

00

> 44

_ 0

0)

,-4-a

0C

00

C!!

00tn

4

- Qj

N

04

_ W 0 1

(8P) NaO01) som

Page 49: SDEPARTMENT OF DEFENCE - DTICat each point of the illuminated surface as though from an infinite tangent plane at that point. The physical optics surface current density for the conducting

ERL-0325-TRFigure 27

0

0-4.j 0

00

((D

0 0

oN%0

a €

-I -*

- -

C).

O'S' 0'O9 O'St 0,05: O'ST 0"0(HiP) NOL3 .I SD-

Page 50: SDEPARTMENT OF DEFENCE - DTICat each point of the illuminated surface as though from an infinite tangent plane at that point. The physical optics surface current density for the conducting

ERL-0325-TR ERL-0325-TRFigure 28 Figure 28

_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _C

0

0j -

co 0

04

000

00

4 4J

0

4400

0-4

44b

0

*0

o MG

O'SZ~~Lf Wo 0'T00 * *

(OP NNJna smi

Page 51: SDEPARTMENT OF DEFENCE - DTICat each point of the illuminated surface as though from an infinite tangent plane at that point. The physical optics surface current density for the conducting

ERL-0325-TRFigure 29

0

0 0

-r

-" $.- 0

0

0

------ ----- ,

.... . . ~ - -- --. . . . . ..-- --. L

0 -0

'00

-. __ z+4-.

O os I W W I 0 '[O 06 0 " O9 O " K 0 t0r

(H;:P) NOIJDnIOa:Im sm

Page 52: SDEPARTMENT OF DEFENCE - DTICat each point of the illuminated surface as though from an infinite tangent plane at that point. The physical optics surface current density for the conducting

ERL-0325-TR ERL -0325 -TRFigure 30 Figure 30

00

o )0

0 0

- 1 . 30, -1 . . 5. 0 04 .

- -

Fl~r 00 Reuto nRS o 1 2 ad-

(vria poaiain) 1 0

Page 53: SDEPARTMENT OF DEFENCE - DTICat each point of the illuminated surface as though from an infinite tangent plane at that point. The physical optics surface current density for the conducting

ERL-0325-TRFigure 31

VIVvvt44 -4..'

0O

01

LI~o

0

-

( v r i a p o a i a i n . a b = 0 °

"/"'.. P ,. 1

Figre 1. edutin i RC fo I 2 an S° ._,t0

(vetial olristin) a6=2b=,1

0, 0,#U

N • .- ,

Page 54: SDEPARTMENT OF DEFENCE - DTICat each point of the illuminated surface as though from an infinite tangent plane at that point. The physical optics surface current density for the conducting

ERL-0325-TR ERL-0325-TRFigure 32 Figure 32

0

Ln

0

--2

00

0

C

U

Fiur 32 Reuto inRSfr .10,-20ad-

(la

I' \

) 0=0°

- m !

-o .-. 3 .

1 .O0 0I

o 0 04

.

o MTIA'NGK(EGES

i gue3. Rduto nRC o ° 2 n

_ (ertial plarsatin) : = b=l0

Page 55: SDEPARTMENT OF DEFENCE - DTICat each point of the illuminated surface as though from an infinite tangent plane at that point. The physical optics surface current density for the conducting

ERL-0325-TRFigure 33

tn

0 0

6 2° 01

00

00o 6=5

Cir

o

0 0

-,45.0 =30.0 =15.0 0.0 15.0 30.0 45.0

AZIMUTHIAL, ANGLE (DEGREES)

Figure 33. Reduction in RCS for ,--1 ° 2° and S°p a

/vria polaisaton) b-10

Page 56: SDEPARTMENT OF DEFENCE - DTICat each point of the illuminated surface as though from an infinite tangent plane at that point. The physical optics surface current density for the conducting

ERL-0325-TR ERL-0325-TRFigure 34 Figure 34

0

00

0

z

N N

a = 20X

c = 20A,0 = 00

vertical polarisation i

-45.0 -30.0 -15.0 0.0 1S.O 30.0 4S.0

AZINIIlAL ANGLE (DEGREES)

Figure :,. RCS for an asymmetric reflector with reflector angle 90°0

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ERL-0325-TRFigure 35

0

0n

00

_ _ _ _ 00tn Lf$4 0)

00

040

4).

LW 44

-,j

4

00D 41 -

* ULnl C) 4

VOL ~ ~~ ~~ ~ 0*0 -4SOO Of ~ z -1

(HP)~~~LL z(I4-43VM/D

Page 58: SDEPARTMENT OF DEFENCE - DTICat each point of the illuminated surface as though from an infinite tangent plane at that point. The physical optics surface current density for the conducting

ERL-0325-TR ERL-0325-TRFigure 36 Figure 36

0 _ _ _ _ _ _ _ _ _

00

6 10

6=-

00

0

6 -

LnCd0

0C =- 00

-2 -1

Page 59: SDEPARTMENT OF DEFENCE - DTICat each point of the illuminated surface as though from an infinite tangent plane at that point. The physical optics surface current density for the conducting

ERL-0325-TRFigure 37

0 _ _ __ _ _

0Lfl

U

100

0

6=0o 2

cc;

4S.0 -30. -I. . s 004.

AZ2:nA ANL1(ERES

oiur 37 6u~o nRSfr smercrfetr o

o n 0

Page 60: SDEPARTMENT OF DEFENCE - DTICat each point of the illuminated surface as though from an infinite tangent plane at that point. The physical optics surface current density for the conducting

ERL-032S-TR ERL-0325-TR

Figure 38 Figure 38

- .-

z

-45.0 -30.0 .0 0,'0 15.0 30.0 45.0

AZINIUTIIAL ANGLI ;DUGREES) ,i

0080

.Y 8 vria plrsto'

Page 61: SDEPARTMENT OF DEFENCE - DTICat each point of the illuminated surface as though from an infinite tangent plane at that point. The physical optics surface current density for the conducting

ERL-0325-TRFigure 39

0

0M

C!

0 25

0 s

'5 . 3 . 1 . 0 01 . 0 04 .

AZNMA NL DGES

Fiue3 .Cmaio fterwt xeietfraX 250 00(etca oaiain

0%

01

Page 62: SDEPARTMENT OF DEFENCE - DTICat each point of the illuminated surface as though from an infinite tangent plane at that point. The physical optics surface current density for the conducting

ERL-0325-TR ERL-0325-TRFigure 40 Figure 40

Li0

0

co o

0

Ut 0

0.CCD U.

o 1t

It

Li 4 L) .4

00-4 L.*-

00~

C!

C) ~C~~~~oq~~ o4J ..-I'SO'Z0 10* ,

(90 (IL9349AM)/S4

Page 63: SDEPARTMENT OF DEFENCE - DTICat each point of the illuminated surface as though from an infinite tangent plane at that point. The physical optics surface current density for the conducting

ERL-0325-TRFigure 41

-' 0

W

LU t

0, a = b =3.3X

2 c = 6.7X

-45.0 -30.0 -15.0 0.0 15.0 30.0 45.0

AZINUTHAL ANGLE (DEGREES)

Figure 41. Gomparigon of theory with experiment for a/A 3.3, 0 =00

2y = 85 (vertical polarisation)

Page 64: SDEPARTMENT OF DEFENCE - DTICat each point of the illuminated surface as though from an infinite tangent plane at that point. The physical optics surface current density for the conducting

ERL-0325-TR ERL-0325-TR

Figure 42 Figure 42

C!0

00U 0

-oLU C

z

a = b =3.3A

c: = 6.7A

p I

-45.0 -30.0 -15.0 0.0 15.0 30. 0 45.0

AZIMUITHIAL ANGLE (DEGREES)

Figure 42. Comparison of theory with experiment for a/A 3.3, C=00,2y 90 0 (vertical polarisation)

Page 65: SDEPARTMENT OF DEFENCE - DTICat each point of the illuminated surface as though from an infinite tangent plane at that point. The physical optics surface current density for the conducting

ERL-0325-TRFigure 43

C.40

0S

If)

0

-< 0

0o A 0

Lf)U

o~~~~~~~4 O'4JO 'Eooz00 '

(SP)z(IU N919V.%I/S:0

Page 66: SDEPARTMENT OF DEFENCE - DTICat each point of the illuminated surface as though from an infinite tangent plane at that point. The physical optics surface current density for the conducting

ERL -0325S-TR ERL-0325-TRFigure 44 Figure 44

CD

z

Ln

U

>a =b =SA

c l ox

-o-30.0 -15.0 0.0 15.0 30.0 45.0

AZINMAL ANGLE (DEGREES)

Figure 44. Comparison of theory with experiment for a/A 5.0, 0 =00

2= 850 (vertical polarisation)U

Page 67: SDEPARTMENT OF DEFENCE - DTICat each point of the illuminated surface as though from an infinite tangent plane at that point. The physical optics surface current density for the conducting

ERL-0325-TRFigure 45

0~

00

2- 0 (etcl oaiain

zb

0,

Page 68: SDEPARTMENT OF DEFENCE - DTICat each point of the illuminated surface as though from an infinite tangent plane at that point. The physical optics surface current density for the conducting

ERL-0325-TR ERL-032S-TRFigure 46 Figure 46

LLA

> (D

0

* 0

0 gg

0

co

C; 0

10

Oa~

on U.o

0,09 ~ os "Ov 67 -

0.0s*. LAz ,0

NO (ILDN99AVM)/S:0

Page 69: SDEPARTMENT OF DEFENCE - DTICat each point of the illuminated surface as though from an infinite tangent plane at that point. The physical optics surface current density for the conducting

ERL-0325-TRFigure 47

0U "

W

00

Fiue4.CmarEno hoywiheprmn fraX 25

208 hrzna oaiain

Page 70: SDEPARTMENT OF DEFENCE - DTICat each point of the illuminated surface as though from an infinite tangent plane at that point. The physical optics surface current density for the conducting

ERL -0325-TR ERL- 0325 -TRFigure 48 Figure 48

0

01

U

Z

LO)

UL

a = 2S

a = b S 2X

4.0 -30.0 -15.0 0.0 15.0 30.0 45.0

AZINIUTHIAL ANGLE (DEGREES)

Figure *38. Comparison of theory with experiment for a/X 2.5, 0 0',M

2Y 90 (horizontal polarisation)U

Page 71: SDEPARTMENT OF DEFENCE - DTICat each point of the illuminated surface as though from an infinite tangent plane at that point. The physical optics surface current density for the conducting

ERL-0325-TRFigure 49

0!0

$0

Itt

.0 LnN LI;

- 0 0-

.940

o 1 .~4-4

M0

4.1 N.9.4

0 0

In 0

0

0.09 0 os ootV'io o~oz 0o0t 0*0s

CHP) (al9N3.1nAVAI) /SOH

Page 72: SDEPARTMENT OF DEFENCE - DTICat each point of the illuminated surface as though from an infinite tangent plane at that point. The physical optics surface current density for the conducting

ERL-0325-TR ERL-0325-TR

Figure S0 Figure 50

Z 0

o N

Uw

-~ 0

FiueS.Cmaio fter wtxeietfraX 33

2y 8 hrzna oaiain

Page 73: SDEPARTMENT OF DEFENCE - DTICat each point of the illuminated surface as though from an infinite tangent plane at that point. The physical optics surface current density for the conducting

ERL-0325-TRFigure 51

0;

9

U0

0,

0

~~0

Fiur 01 oprsno hoywt xeietfraX 33

2y=9 hoiotlpoaiain

Page 74: SDEPARTMENT OF DEFENCE - DTICat each point of the illuminated surface as though from an infinite tangent plane at that point. The physical optics surface current density for the conducting

ERL-032S-TR ERL-0325-TRFigure S2 Figure 52

0

-n " 0+

0 0

trI

LL

a-

0-19 ~o 000 0,T ~o 001 O~ li(HP) (Hl9NlgAVM/S:.

Page 75: SDEPARTMENT OF DEFENCE - DTICat each point of the illuminated surface as though from an infinite tangent plane at that point. The physical optics surface current density for the conducting

ERL-0325-TRFigure 53

C!E

Ln-

0

0

C!

cc LM~

a b

c l ox

-45 .0 -30.0 -15.0 0.0 15.0 .30.0 45.0

AZINqUTIAL ANGLE (DEGREES)

00

0iueS.Cmaio fter iheprmn o /.50

2y 8 hrzna oaiain

Page 76: SDEPARTMENT OF DEFENCE - DTICat each point of the illuminated surface as though from an infinite tangent plane at that point. The physical optics surface current density for the conducting

ERL-0325-TR ERL-0325-TRFigure 54 Figure S4

'0

0qt

1,

LU

0

o

* U

-LU> ~a = b 5X

c = lox

J50-30.0 -15.0 0.0 15.0 30.0 45.0

AZIMTHAL ANGLE (DEGREES)

Iigurc 54. Compari on of theory with experiment for a/X 6 .0, 0 0

2Y 90 (horizontal polarisation)

Page 77: SDEPARTMENT OF DEFENCE - DTICat each point of the illuminated surface as though from an infinite tangent plane at that point. The physical optics surface current density for the conducting

ERL-0325-TRFigure 55

.0 -4

0~-< 0I

In I

0U 0

0

0

0 $4- -cc 0

LU n

.n 0

-4 ..4$

S00

Ln

C' 0L

0*09 O~os 0ot 0(WT 0oz 0o 01 O'

Page 78: SDEPARTMENT OF DEFENCE - DTICat each point of the illuminated surface as though from an infinite tangent plane at that point. The physical optics surface current density for the conducting

ERL-0325-TR ERL-.0325-TRFigure 56 Figure 56

0LW

CA

U

0

0 O

00Fiue5.Peitd n esrdrdcio nRSfr6=-

a/ . n etclplrsto

Page 79: SDEPARTMENT OF DEFENCE - DTICat each point of the illuminated surface as though from an infinite tangent plane at that point. The physical optics surface current density for the conducting

ERL-0325-TRFigure 57

C .0

0

0

Ca

0

0

a =b =2.

c =5x

00

U= 0

Figure 57. Predicted and measured reduction in RCS for 6= °

a/X = 2.5 and vertical polarisation

Page 80: SDEPARTMENT OF DEFENCE - DTICat each point of the illuminated surface as though from an infinite tangent plane at that point. The physical optics surface current density for the conducting

ERL-025-TRERL-0325-TR

FgrS8Figure 58

0

0 0

00Fiue5.Peitdadmaue euto nRSfr6=-

0/ . n etclplrsto

Page 81: SDEPARTMENT OF DEFENCE - DTICat each point of the illuminated surface as though from an infinite tangent plane at that point. The physical optics surface current density for the conducting

ERL-0325-TRFigure 59

0

I-

0z

0 33

00Fiue5.Peice n esre euto n C o

a-, 20. n etclplrsto

Page 82: SDEPARTMENT OF DEFENCE - DTICat each point of the illuminated surface as though from an infinite tangent plane at that point. The physical optics surface current density for the conducting

ERL-0325-TR ERL-0325-TRFigure 60 Figure 60

0!

0

0 0

-4 . -30. -1 . . s 0 04 .00

-4oU

' 0

-45.0 -3. -S.0 and verica polarisatio

0ZNTA NL DGES

Fiue6 rdce admaue eutoni C o 4

a/* .0advetcl oaisto

Page 83: SDEPARTMENT OF DEFENCE - DTICat each point of the illuminated surface as though from an infinite tangent plane at that point. The physical optics surface current density for the conducting

ERL-0325-TRFigure 61

=00

00Fiue6.Peitda-maurdrdcini C o

a/ . n etclplrsto

Page 84: SDEPARTMENT OF DEFENCE - DTICat each point of the illuminated surface as though from an infinite tangent plane at that point. The physical optics surface current density for the conducting

ERL-0325-TR ERL-032S-TR

Figure 62 Figure 62

0g

0

00

Z -0-_U o

U Ca

0

u a = b 5XS

C = lox0=

6

-'45.0 -30.0 -15.0 0.0 15.0 30.0 45.0

AZIMRJMAL ANGLE (DEGREES)

Figure 6.2. Predicted and measured reduction in RCS for 6 =-aX= 5.0 and horizontal polarisation

Page 85: SDEPARTMENT OF DEFENCE - DTICat each point of the illuminated surface as though from an infinite tangent plane at that point. The physical optics surface current density for the conducting

ERL-0325-TRFigure 63

0>

0 !

0

0L

0>

0 0

00Fiue6.Peitdadmaurdrdcini C o

0/ . n oiotlplrsto

Page 86: SDEPARTMENT OF DEFENCE - DTICat each point of the illuminated surface as though from an infinite tangent plane at that point. The physical optics surface current density for the conducting

ERL-0325-TR ERL-0325-TRFigure 64 Figure 64

F0

00

It

(I;

It

W44

0 E

LJ a Ci 0

-3 r- .

UJ. x +..-; c

o < ~-

F 3-p 0

-0-

oD U

-4

t0., L/n

0

O~vWEO.0z 001 0.0 0*01h 00,

Page 87: SDEPARTMENT OF DEFENCE - DTICat each point of the illuminated surface as though from an infinite tangent plane at that point. The physical optics surface current density for the conducting

ERL-0325-TRFigure 65

0

to04.3n

00

U

4j'

4j

z 03C

00

43

U

w 0

43ON U

00

O'SL~~- 019 ltWO *TW

(OP)~~0 0~j:na o

Page 88: SDEPARTMENT OF DEFENCE - DTICat each point of the illuminated surface as though from an infinite tangent plane at that point. The physical optics surface current density for the conducting

ERL-0325-TR

DISTRIBUTION

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EXTERNAL

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ERL-0325-TR

Director General, Army Development (NSO), Russell Officesfor ABCA Standardisation Officers

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WITHIN DRCS

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DOCUMENT CONTROL DATA SHEET

Security classification of this page UNCLASSIFIED

I DOCUMENT NUMBERS 2 SECURITY CLASSIFICATION

AR 957 a. CompleteNumber: AR-004-W2r A-cut-" Document: Unclassified

Series b. Title inNumber: ERL-032S-TR Isolation: Unclassified

Other c. Summary inNumbers: Isolation: Unclassified

THE EFFECT OF VARYING THE INTERNAL ANGLEOF A DIHEDRAL CORNER REFLECTOR

4 rPERSONAL AUTHOR(S): 5FDOCUMENT DATE:

May 1985

W.C. Anderson 6 6.1TOTALNUMBER

:6.2 NUMBER OF

REFERENCES: 4

7 7.! CORPORATE AUTHOR(S): 8 REFERENCE NUMBERS

a. Task: DST 83/112Electronics Research Laboratory b. Sponsoring

Agency:

7.2 DOCUMENT SERIESAND NUMBER 9 [COST CODE:

Electronics Research Laboratory032S-TR 429002

10 IMPRINT (Publishing organisation) I I COMPUTER PROGRAM(S)

Defence Research Centre Salisbury

_ 12 RELEASE LIMITATIONS (of the document):

Approved for Public Release

Security classification of this page: UNCLASSIFIED

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Security classification of this page: UNCLASSIFIED

13 ANNOUNCEMENT UMITATIONS (of the information on these pages):

No Limitation

14FDESC-RIPTORS:7 15 COSATI CODES:

a. EJC Thesaurus Physical opticsTerms Corner reflectors

Electromagnetic scattering 20060Radar

b. Non-ThesaurusTerms

16 SUMMARY OR ABSTRACT:(if this is security classified, the announcement of this report will be similarly classified)

Small deviations from orthogonality can reduce drastically the back-scattering radar cross section of dihedral corner reflectors. In thispaper this effect is studied using the method of physical optics withemphasis on the reductions of RCS achievable for modest departures fromorthogonal ity.

Si n

S~cwiy chsifiatio of h~ pp: N- lE

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The official documents produced by the Laboratories of the Defence Research Centre Salisburyare issued in one of five categories: Reports, Technical Reports, Technical Memoranda, Manuals andSpecifications. The purpose of the latter two categories is self-evident, with the other three categoriesbeing used for the following purposes:

Reports documents prepared for managerial purposes.

Technical records of scientific and technical work of a permanent value intended for otherReports scientists and technologists working in the field.

Technical intended primarily for disseminating information within the DSTO. They are

Memoranda usually tentative in nature and reflect the personal views of the author.