アンテナアレイファクターによる電波画像処理とその応用

アンテナアレイファクターによる電波画像処理とその応用

小 林 弘 一

• • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • •

(2020 年 7 月 31

_{• • • • • • • • • •}

Imaging Technology of Electromagnetic Wave by Using Antenna Array-Factor and

its Application

Hirokazu Kobayashi

Electromagnetic Information System Laboratory,

Department of Electronics and Information Systems Engineering

Abstract

• •

The array factor (AF) describes the electromagnetic radiation characteristic of an array of numerous small antenna

elements; the antenna composed of these plural elements is called an array antenna. The AF concept can be applied not

only to antenna characteristic theory but also to the image processing method discussed in this paper. Synthetic aperture

radar (SAR) is a typical imaging method for microwaves. In this method, the transmitting and receiving antennae are

moved in a wide area to generate an equivalent large antenna, and the reflected signal is processed to obtain an image

with high resolution based on the beam with higher sharpness. In general, SAR systems tend to be large and have

advantages for distant targets such as satellite SAR and earth mapping.

On the other hand, AF theory superposes the signals received from each element in consideration of the path

difference, which is the phase variation between the transmitting and receiving elements via the target scatterer.

Therefore, unlike SAR, a focal point of the array can be obtained, allowing short-range targets to be imaged with high

resolution. However, both methods are equivalent for image processing through Fourier theory. In this paper, the authors

will review previously published articles and discuss various applications and future prospects, such as equivalent

complex-permittivity measurements, wall-through radar, and near-field to far-field transformation methods.

キ ー ワ ー ド ;

ア レ イ フ ァ ク タ ー

_{, レ ー ダ 画 像 , ア レ イ ア ン テ ナ , 合 成 開 口 レ ー ダ , 誘 電 率 計 測 ,}

壁透過レーダ

, 近傍電磁界遠方変換, 幾何光学解説理論, MIMO レーダ

Keyword;

Array-factor, radar imaging, array antenna, synthetic aperture radar, focusing, permittivity measurement,

wall-through radar, near-field to far-field transformation, geometrical theory of diffraction (GTD), MIMO

radar.

アンテナアレイファクターによる電波画像処理とその応用

小 林 弘 一

• • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • •

(2020 年 7 月 31

• • • • • • • • • •

Imaging Technology of Electromagnetic Wave by Using Antenna Array-Factor and

its Application

Hirokazu Kobayashi

Electromagnetic Information System Laboratory,

Department of Electronics and Information Systems Engineering

Abstract

• •

The array factor (AF) describes the electromagnetic radiation characteristic of an array of numerous small antenna

elements; the antenna composed of these plural elements is called an array antenna. The AF concept can be applied not

only to antenna characteristic theory but also to the image processing method discussed in this paper. Synthetic aperture

radar (SAR) is a typical imaging method for microwaves. In this method, the transmitting and receiving antennae are

moved in a wide area to generate an equivalent large antenna, and the reflected signal is processed to obtain an image

with high resolution based on the beam with higher sharpness. In general, SAR systems tend to be large and have

advantages for distant targets such as satellite SAR and earth mapping.

On the other hand, AF theory superposes the signals received from each element in consideration of the path

difference, which is the phase variation between the transmitting and receiving elements via the target scatterer.

Therefore, unlike SAR, a focal point of the array can be obtained, allowing short-range targets to be imaged with high

resolution. However, both methods are equivalent for image processing through Fourier theory. In this paper, the authors

will review previously published articles and discuss various applications and future prospects, such as equivalent

complex-permittivity measurements, wall-through radar, and near-field to far-field transformation methods.

キ ー ワ ー ド ;

ア レ イ フ ァ ク タ ー

_{, レ ー ダ 画 像 , ア レ イ ア ン テ ナ , 合 成 開 口 レ ー ダ , 誘 電 率 計 測 ,}

壁透過レーダ

, 近傍電磁界遠方変換, 幾何光学解説理論, MIMO レーダ

Keyword;

Array-factor, radar imaging, array antenna, synthetic aperture radar, focusing, permittivity measurement,

wall-through radar, near-field to far-field transformation, geometrical theory of diffraction (GTD), MIMO

radar.

電子情報システム工学科，波動情報システム研究室

（2020 年 7 月 31 日受理）

Osaka Institute of Technology Vol. 65, No. 1（2020）pp. 21〜42

1.·͕͖͑ ΞϨΠϑΝΫλʔ(Array-Factor:AF)ͱ͸ɺిؾతʹ খ͞ͳΞϯςφ(ૉࢠΞϯςφͱݺΜͰ͍Δ)Λෳ਺ݸ഑ ྻͨ͠ͱ͖ͷΞϯςφશମ͕࡞Δ์ࣹಛੑΛࢦ͢ɻ࣮ࡍ ͸͜ͷAFʹ֤ૉࢠͷࢦ޲ੑΛॏ৞ͤͨ͞΋ͷ͕ΞϨΠΞ ϯςφͷ࠷ऴ์ࣹύλʔϯͱͳΔɻ͜ͷΞϨΠΞϯςφ ͷ֤ૉࢠͷҐ૬ࠩΛ͋ΔΞϧΰϦζϜͰੜ੒͢ΔͱɺAF ͸ίϯϑΥʔϚϧΞϨΠΛؚΉిࢠ૸ࠪͷϏʔϜϑΥʔ Ϛʔͱͯ͠ݟΔ͜ͱ͕Ͱ͖Δ͠[1]ɺ֤ૉࢠʹॏΈΛ෇͚ Δ͜ͱͰΞμϓςΟϒͳॲཧ΋ՄೳͱͳΔɻ·ͨɺۙ๣ ೾ݯͱͯ͠AFΛଊ͑Δͱԕํม׵ͷΞϧΰϦζϜʹ΋Ԡ ༻Ͱ͖Δ[2]ɻAF͸֤ૉࢠͷ஗ԆҐ૬ͷ࿨ͱͳΔͷͰɺ ͜͜Ͱओʹٞ࿦͢Δి೾ը૾ॲཧͷՄೳੑ΋͋Δ[3,4]ɻ ຊ࿦Ͱ͸ɺಋମฏ൘ͳͲͷ୯७ͳλʔήοτʹΑΔ൓ࣹ ࢄཚ೾ʹର͠ɺۙ๣քΛؚΉͦͷཧ࿦ܭࢉ஋Λ༻͍ͨը ૾ॲཧ͓Αͼ࣮ଌ֬ೝʹ͍ͭͯɺࠓ·Ͱͷஶऀͷจݙ౳ Λ·ͱΊΔܗͰٞ࿦͠ɺࠓޙͷݚڀൃలͷࢿͱ͍ͨ͠ɻ ͳ͓ɺ࣮ଌσʔλʹΑΔը૾͚ͩͰ͸ͳ͘ܭࢉཧ࿦Ͱγ ϛϡϨʔγϣϯ͕Ͱ͖Δͱ͍͏͜ͱ͸ɺص্Ͱ΋֬ೝ࡞ ۀ͕Ͱ͖Δͱ͍͏͜ͱΛҙຯ͠ɺ༷ʑͳύϥϝʔλͷ࠷ దԽΛਤΔ͜ͱ͕ՄೳͱͳΔɻ લड़ͷΞϨΠΞϯςφʹΑΔϨʔμը૾ͷߟ͑ํ͸ɺ ૹ৴Ξϯςφɺ໨ඪ෺ମɺͦͯ͠ड৴ΞϯςφؒͷҐ૬ ৘ใͱরࣹྖҬ಺ͷ໨ඪ෺͔Βͷཧ࿦తͳΤίʔ৴߸ͷ Ґ૬৘ใͷ૬ؔੑΛΈΔํ๏Ͱ͋Δɻ͜ͷ૬ؔੑ͸؆୯ ͳҐ૬ͷڃ਺ܭࢉͰߦ͏͜ͱ͕Ͱ͖ɺ݁Ռ͕෼ղೳͷ޲ ্ʹͭͳ͕ΔҰछͷ߹੒։ޱॲཧͱΈͳ͢͜ͱ͕Ͱ͖Δɻ ి೾Λૹ৴͠ɺͦͷΤίʔΛड৴͢ΔͨΊʹ͸ɺΞϨΠ ͷ֤ૉࢠΛશͯ༻ҙ͢Δඞཁ͸ͳ͍ɻλʔήοτͱϨʔ μͷҐஔؔ܎͕૬ରతʹݻఆ͞Ε͍ͯΔɺ͋Δ͍͸ॲཧ Ϩʔτ಺Ͱ΄΅Ҡಈ͍ͯ͠ͳ͍ɺͳͲ͕ԾఆͰ͖Δͱɺ1 ݸͷΞϯςφΛػցతʹ૸ࠪͯ͠΋Α͍ɻ·ͨɺૹड৴ Ξϯςφ͸ճ࿏ͷෳࡶ͞Λආ͚ΔͨΊɺผʑʹ༻ҙ͢Δ ํ͕ଌఆܥ΋؆୯ʹͳΔɻྫ͑͹ɺ൚༻ͷωοτϫʔΫ ΞφϥΠβͳͲΛૹ৴ݯ͓Αͼड৴ܥʹ༻͍Δ৔߹ɺૹ ड৴ͷΞΠιϨʔγϣϯΛऔΔͨΊʹૹ৴ͱड৴ͷΞϯ ςφΛۭؒతʹ཭͢ߏ੒΋ՄೳͰ͋Δɻ·ͨҠಈ͢Δૹ ৴ͷҐஔ࠲ඪ਺ͱड৴ͷͦΕ͸ҧ͍ͬͯͯ΋Α͘ɺૹ৴ϙ Πϯτͷํ͕ड৴ΑΓ΋গͳ͍ߏ੒͸ίετޮ཰͕ߴ͍ ͱࢥΘΕΔɻ͜ͷΑ͏ʹߟ͑ΔͱɺAFʹΑΔը૾ॲཧ͸ ݱࡏप஌ͱͳ͍ͬͯΔMIMO(Multiple-input multiple output)Ϩʔμͱجຊతʹ౳ՁͰ͋Δ͜ͱ͕෼͔Δɻ ຊ࿦ͷ಺༰͸ҎԼͷΑ͏ʹͳ͍ͬͯΔɻઌ߲ͣ࣍Ͱ AFͷఆࣜΛߦ͍ɺΞϯςφϏʔϜΛిࢠతʹ૸ࠪ͢Δ ϑΣʔζυΞϨΠΞϯςφΛྫʹͱͬͯɺAFͷجຊతͳ ߟ͑ํΛड़΂Δɻଓ͘3.߲Ͱɺۙڑ཭λʔήοτΛҙ ࣝͯ͠ΞϨΠͷয఺ԽΛߦ͍ɺ4.߲Ͱɺ͜ͷয఺ԽAF Λ࢖ͬͨϨʔμը૾ʹ͍ͭͯٞ࿦͢Δɻ5.߲Ͱ͸ɺը૾ ͷཧ࿦ݕ౼Λߦ͏ͨΊɺλʔήοτ͕ಋମετϦοϓͷ ͱ͖ͷUniform Asymptotic Theory(UAT)ͱPhysical

Optics(PO)ʹΑΔఆࣜԽߦ͍ɺ6.߲Ͱ2ຕͷετϦο ϓΛ௚ަͤͨ͞ίʔφʔϦϑϨΫλʔϞσϧͷ࣮ଌͱܭ ࢉͷൺֱݕ౼Λߦ͏ɻଓ͚ͯɺ7.߲ͰΞϯςφϏʔϜΛ ߟྀͨ͠ͱ͖ͷը૾ධՁɺ8.߲Ͱ༠ిମฏ൘͕͋Δ৔ ߹ͷը૾ݕ౼Λٞ࿦͢Δɻ༠ిମฏ൘͸นಁաϨʔμͱ ͯ͠ݟͳ͢͜ͱ͕Ͱ͖Δɻͦͯ͠ɺ༠ిମฏ൘ͷ༗ແʹ Αͬͯը૾ͷੜ੒Ґஔ͕มԽ͢Δ͜ͱΛԠ༻͢Δͱɺฏ ൘ͷ౳Ձ༠ి཰ΛධՁ͢Δ͜ͱ͕Ͱ͖Δɻ͜ͷٞ࿦Λ9. ߲ͱ10.߲Ͱߦ͏ɻ·ͨ෇࿥1.Ͱ͸ɺجຊύϥϝʔλͷ มԽʹΑΔը૾γϛϡϨʔγϣϯ݁ՌΛఏࣔͯ͠Δɻ 2.ΞϨΠϑΝΫλʔͷఆࣜͱϏʔϜ૸ࠪ ࠓɺෳ਺ͷ೾ݯ͕ܗ੒͢Δి࣓քʹରͯ͠ɺͦͷ೾ݯΛ ఺ͱͯ͠ଊ͑౳ํੑͷ์ࣹύλʔϯΛԾఆ͢Δɻͦͯ͠ɺ ֤೾ݯʢΞϯςφʣ͸ͦͷҐஔͰڅిͷҐ૬͸ಉ͡Ͱ͋ Δͱͯ͠ɺԕํͰͷి࣓քΛ֤Ξϯςφͷ࠲ඪʹΑΔҐ ૬ࠩҟΛߟྀͨ͠೾ಈͷ୯७ͳॏͶ߹ͤͰදݱ͢Δɻ೾ ݯ഑ྻ࠲ඪ͕ฏ໘ͷ৔߹ɺAF͸Fourierڃ਺ͱಉ͡ܗͱ ͳΔɻ࣮ࡍͷ֤Ξϯςφ͸ࢦ޲ੑ͕͋ΔͷͰɺ͜ΕΛAF ʹॏ৞ͤ͞ΔͱɺΞϨΠશମͷ߹੒์ࣹύλʔϯ͕ܭࢉ Ͱ͖ΔɻͨͩɺΞϯςφؒͷۭؒ૬ޓ݁߹Λແࢹ͍ͯ͠ ΔͷͰɺ৚݅ʹΑͬͯ͸࣮ࡍͱ߹Θͳ͍৔߹΋ൃੜ͢Δɻ ্ͯ͞ड़ͷΑ͏ʹɺۭؒ಺ͷ೚ҙ࠲ඪʹ఺೾ݯ͕ݽཱ ͯ͠഑ྻ͞Ε͍ͯΔͱ͖ͷAF͸ɺ೾ݯͷҐ૬͸ͦͷҐஔ ࠲ඪʹґଘ͍ͯ͠ΔͷͰɺٿ࠲ඪͷ֯౓ม਺Λ(θ, ϕ)ͱ ͯ͠ɺ୯७ʹ f (θ, ϕ) =∑anexp{jk(xnu + ynv + zncos θ)} (1) Ͱ༩͑Δ͜ͱ͕Ͱ͖Δɻ͜͜Ͱɺ(xn, yn, zn)͸n൪ૉ

ࢠͷ3࣍ݩۭؒ࠲ඪ(u = sin θ cos ϕ, v = sin θ sin ϕ)Ͱ͋

Γɺk = 2π/λ͸೾਺Λࢦ͢ɻ·ͨɺan͸֤ૉࢠͷෳૉৼ ෯Ͱ͋Δɻ͜ͷ؆ܿͳجຊࣜ͸఺ঢ়ͷ์ࣹݯͷू߹͕ԕ ํͰͭ͘Δ์ࣹքΛද͍ͯ͠Δ͕ɺ࣮ࡍଘࡏ͍ͯ͠Δͱ ࢥΘΕΔ֤Ξϯςφૉࢠؒͷి࣓քతͳ૬ޓ݁߹͸ແࢹ ͍ͯ͠Δɻਤ1͸1࣍ݩͷ౳ִؒϦχΞΞϨΠʹฏ໘೾ ͕ೖࣹͨ͠ͱ͖ɺ֤ૉࢠʹྭى͞ΕΔҐ૬ࠩΛࣔͨ͠΋

1.·͕͖͑ ΞϨΠϑΝΫλʔ(Array-Factor:AF)ͱ͸ɺిؾతʹ খ͞ͳΞϯςφ(ૉࢠΞϯςφͱݺΜͰ͍Δ)Λෳ਺ݸ഑ ྻͨ͠ͱ͖ͷΞϯςφશମ͕࡞Δ์ࣹಛੑΛࢦ͢ɻ࣮ࡍ ͸͜ͷAFʹ֤ૉࢠͷࢦ޲ੑΛॏ৞ͤͨ͞΋ͷ͕ΞϨΠΞ ϯςφͷ࠷ऴ์ࣹύλʔϯͱͳΔɻ͜ͷΞϨΠΞϯςφ ͷ֤ૉࢠͷҐ૬ࠩΛ͋ΔΞϧΰϦζϜͰੜ੒͢ΔͱɺAF ͸ίϯϑΥʔϚϧΞϨΠΛؚΉిࢠ૸ࠪͷϏʔϜϑΥʔ Ϛʔͱͯ͠ݟΔ͜ͱ͕Ͱ͖Δ͠[1]ɺ֤ૉࢠʹॏΈΛ෇͚ Δ͜ͱͰΞμϓςΟϒͳॲཧ΋ՄೳͱͳΔɻ·ͨɺۙ๣ ೾ݯͱͯ͠AFΛଊ͑Δͱԕํม׵ͷΞϧΰϦζϜʹ΋Ԡ ༻Ͱ͖Δ[2]ɻAF͸֤ૉࢠͷ஗ԆҐ૬ͷ࿨ͱͳΔͷͰɺ ͜͜Ͱओʹٞ࿦͢Δి೾ը૾ॲཧͷՄೳੑ΋͋Δ[3,4]ɻ ຊ࿦Ͱ͸ɺಋମฏ൘ͳͲͷ୯७ͳλʔήοτʹΑΔ൓ࣹ ࢄཚ೾ʹର͠ɺۙ๣քΛؚΉͦͷཧ࿦ܭࢉ஋Λ༻͍ͨը ૾ॲཧ͓Αͼ࣮ଌ֬ೝʹ͍ͭͯɺࠓ·Ͱͷஶऀͷจݙ౳ Λ·ͱΊΔܗͰٞ࿦͠ɺࠓޙͷݚڀൃలͷࢿͱ͍ͨ͠ɻ ͳ͓ɺ࣮ଌσʔλʹΑΔը૾͚ͩͰ͸ͳ͘ܭࢉཧ࿦Ͱγ ϛϡϨʔγϣϯ͕Ͱ͖Δͱ͍͏͜ͱ͸ɺص্Ͱ΋֬ೝ࡞ ۀ͕Ͱ͖Δͱ͍͏͜ͱΛҙຯ͠ɺ༷ʑͳύϥϝʔλͷ࠷ దԽΛਤΔ͜ͱ͕ՄೳͱͳΔɻ લड़ͷΞϨΠΞϯςφʹΑΔϨʔμը૾ͷߟ͑ํ͸ɺ ૹ৴Ξϯςφɺ໨ඪ෺ମɺͦͯ͠ड৴ΞϯςφؒͷҐ૬ ৘ใͱরࣹྖҬ಺ͷ໨ඪ෺͔Βͷཧ࿦తͳΤίʔ৴߸ͷ Ґ૬৘ใͷ૬ؔੑΛΈΔํ๏Ͱ͋Δɻ͜ͷ૬ؔੑ͸؆୯ ͳҐ૬ͷڃ਺ܭࢉͰߦ͏͜ͱ͕Ͱ͖ɺ݁Ռ͕෼ղೳͷ޲ ্ʹͭͳ͕ΔҰछͷ߹੒։ޱॲཧͱΈͳ͢͜ͱ͕Ͱ͖Δɻ ి೾Λૹ৴͠ɺͦͷΤίʔΛड৴͢ΔͨΊʹ͸ɺΞϨΠ ͷ֤ૉࢠΛશͯ༻ҙ͢Δඞཁ͸ͳ͍ɻλʔήοτͱϨʔ μͷҐஔؔ܎͕૬ରతʹݻఆ͞Ε͍ͯΔɺ͋Δ͍͸ॲཧ Ϩʔτ಺Ͱ΄΅Ҡಈ͍ͯ͠ͳ͍ɺͳͲ͕ԾఆͰ͖Δͱɺ1 ݸͷΞϯςφΛػցతʹ૸ࠪͯ͠΋Α͍ɻ·ͨɺૹड৴ Ξϯςφ͸ճ࿏ͷෳࡶ͞Λආ͚ΔͨΊɺผʑʹ༻ҙ͢Δ ํ͕ଌఆܥ΋؆୯ʹͳΔɻྫ͑͹ɺ൚༻ͷωοτϫʔΫ ΞφϥΠβͳͲΛૹ৴ݯ͓Αͼड৴ܥʹ༻͍Δ৔߹ɺૹ ड৴ͷΞΠιϨʔγϣϯΛऔΔͨΊʹૹ৴ͱड৴ͷΞϯ ςφΛۭؒతʹ཭͢ߏ੒΋ՄೳͰ͋Δɻ·ͨҠಈ͢Δૹ ৴ͷҐஔ࠲ඪ਺ͱड৴ͷͦΕ͸ҧ͍ͬͯͯ΋Α͘ɺૹ৴ϙ Πϯτͷํ͕ड৴ΑΓ΋গͳ͍ߏ੒͸ίετޮ཰͕ߴ͍ ͱࢥΘΕΔɻ͜ͷΑ͏ʹߟ͑ΔͱɺAFʹΑΔը૾ॲཧ͸ ݱࡏप஌ͱͳ͍ͬͯΔMIMO(Multiple-input multiple output)Ϩʔμͱجຊతʹ౳ՁͰ͋Δ͜ͱ͕෼͔Δɻ ຊ࿦ͷ಺༰͸ҎԼͷΑ͏ʹͳ͍ͬͯΔɻઌ߲ͣ࣍Ͱ AFͷఆࣜΛߦ͍ɺΞϯςφϏʔϜΛిࢠతʹ૸ࠪ͢Δ ϑΣʔζυΞϨΠΞϯςφΛྫʹͱͬͯɺAFͷجຊతͳ ߟ͑ํΛड़΂Δɻଓ͘3.߲Ͱɺۙڑ཭λʔήοτΛҙ ࣝͯ͠ΞϨΠͷয఺ԽΛߦ͍ɺ4.߲Ͱɺ͜ͷয఺ԽAF Λ࢖ͬͨϨʔμը૾ʹ͍ͭͯٞ࿦͢Δɻ5.߲Ͱ͸ɺը૾ ͷཧ࿦ݕ౼Λߦ͏ͨΊɺλʔήοτ͕ಋମετϦοϓͷ ͱ͖ͷUniform Asymptotic Theory(UAT)ͱPhysical

Optics(PO)ʹΑΔఆࣜԽߦ͍ɺ6.߲Ͱ2ຕͷετϦο ϓΛ௚ަͤͨ͞ίʔφʔϦϑϨΫλʔϞσϧͷ࣮ଌͱܭ ࢉͷൺֱݕ౼Λߦ͏ɻଓ͚ͯɺ7.߲ͰΞϯςφϏʔϜΛ ߟྀͨ͠ͱ͖ͷը૾ධՁɺ8.߲Ͱ༠ిମฏ൘͕͋Δ৔ ߹ͷը૾ݕ౼Λٞ࿦͢Δɻ༠ిମฏ൘͸นಁաϨʔμͱ ͯ͠ݟͳ͢͜ͱ͕Ͱ͖Δɻͦͯ͠ɺ༠ిମฏ൘ͷ༗ແʹ Αͬͯը૾ͷੜ੒Ґஔ͕มԽ͢Δ͜ͱΛԠ༻͢Δͱɺฏ ൘ͷ౳Ձ༠ి཰ΛධՁ͢Δ͜ͱ͕Ͱ͖Δɻ͜ͷٞ࿦Λ9. ߲ͱ10.߲Ͱߦ͏ɻ·ͨ෇࿥1.Ͱ͸ɺجຊύϥϝʔλͷ มԽʹΑΔը૾γϛϡϨʔγϣϯ݁ՌΛఏࣔͯ͠Δɻ 2.ΞϨΠϑΝΫλʔͷఆࣜͱϏʔϜ૸ࠪ ࠓɺෳ਺ͷ೾ݯ͕ܗ੒͢Δి࣓քʹରͯ͠ɺͦͷ೾ݯΛ ఺ͱͯ͠ଊ͑౳ํੑͷ์ࣹύλʔϯΛԾఆ͢Δɻͦͯ͠ɺ ֤೾ݯʢΞϯςφʣ͸ͦͷҐஔͰڅిͷҐ૬͸ಉ͡Ͱ͋ Δͱͯ͠ɺԕํͰͷి࣓քΛ֤Ξϯςφͷ࠲ඪʹΑΔҐ ૬ࠩҟΛߟྀͨ͠೾ಈͷ୯७ͳॏͶ߹ͤͰදݱ͢Δɻ೾ ݯ഑ྻ࠲ඪ͕ฏ໘ͷ৔߹ɺAF͸Fourierڃ਺ͱಉ͡ܗͱ ͳΔɻ࣮ࡍͷ֤Ξϯςφ͸ࢦ޲ੑ͕͋ΔͷͰɺ͜ΕΛAF ʹॏ৞ͤ͞ΔͱɺΞϨΠશମͷ߹੒์ࣹύλʔϯ͕ܭࢉ Ͱ͖ΔɻͨͩɺΞϯςφؒͷۭؒ૬ޓ݁߹Λແࢹ͍ͯ͠ ΔͷͰɺ৚݅ʹΑͬͯ͸࣮ࡍͱ߹Θͳ͍৔߹΋ൃੜ͢Δɻ ্ͯ͞ड़ͷΑ͏ʹɺۭؒ಺ͷ೚ҙ࠲ඪʹ఺೾ݯ͕ݽཱ ͯ͠഑ྻ͞Ε͍ͯΔͱ͖ͷAF͸ɺ೾ݯͷҐ૬͸ͦͷҐஔ ࠲ඪʹґଘ͍ͯ͠ΔͷͰɺٿ࠲ඪͷ֯౓ม਺Λ(θ, ϕ)ͱ ͯ͠ɺ୯७ʹ f (θ, ϕ) =∑anexp{jk(xnu + ynv + zncos θ)} (1) Ͱ༩͑Δ͜ͱ͕Ͱ͖Δɻ͜͜Ͱɺ(xn, yn, zn)͸n൪ૉ

ࢠͷ3࣍ݩۭؒ࠲ඪ(u = sin θ cos ϕ, v = sin θ sin ϕ)Ͱ͋

Γɺk = 2π/λ͸೾਺Λࢦ͢ɻ·ͨɺan͸֤ૉࢠͷෳૉৼ ෯Ͱ͋Δɻ͜ͷ؆ܿͳجຊࣜ͸఺ঢ়ͷ์ࣹݯͷू߹͕ԕ ํͰͭ͘Δ์ࣹքΛද͍ͯ͠Δ͕ɺ࣮ࡍଘࡏ͍ͯ͠Δͱ ࢥΘΕΔ֤Ξϯςφૉࢠؒͷి࣓քతͳ૬ޓ݁߹͸ແࢹ ͍ͯ͠Δɻਤ1͸1࣍ݩͷ౳ִؒϦχΞΞϨΠʹฏ໘೾ ͕ೖࣹͨ͠ͱ͖ɺ֤ૉࢠʹྭى͞ΕΔҐ૬ࠩΛࣔͨ͠΋ ਤ-1 ฏ໘೾রࣹ࣌ͷ౳ִؒΞϨΠૉࢠʹ༠ى͞ ΕΔҐ૬ࠩ

Fig.1 Phase differences induced in equi-pitched array elements as plane wave incident.

ͷͰ͋Γɺ͜ΕΒͷड৴ʑ߸ͷ࿨ΛͱͬͯΞϨΠΞϯςφ ͷड৴ʑ߸ग़ྗͱ͢Δɻҩྍը૾෼໺Ͱ͸ɺ͜ͷߟ͑Λ ʮ஗Ԇͨ͠ෳ਺৴߸ͷҐ૬࿨ʯͱ͍͏ҙຯͰɺDelay and Sum Beamforming(DAS)ͱݺΜͰ͍Δ[5]ɻͳ͓ɺ্ड़ ͸์ࣹքͱ͍͏ૹ৴ܥͰఆࣜԽ͍ͯ͠Δ͕ɺฏ໘೾͕Ξ ϨΠ໘ʹࣼΊʹೖࣹ͢Δͱͯ͠ٻΊͯ΋ಉ݁͡ՌͱͳΔɻ ୈ(1) ࣜͷෳૉৼ෯ an ʹ஫໨͢Δͱɺ͜ΕΛॏΈ ؔ਺ͱ֤ͯ͠ૉࢠͷड৴ʑ߸ʹಠཱͯ͠ࢪ͢͜ͱʹΑ Γɺ֤छͷదԠܕΞϨΠॲཧ͕ՄೳͱͳΔɻͦͷॲཧΞ ϧΰϦζϜͷ୅ද͕֨MUSIC(MUltiple SIgnal

Clas-sification) ๏Ͱ͋Γɺి೾౸དྷํ޲ͷධՁ͋Δ͍͸

ׯ ব ೾ ํ ޲ ΁ ͷ ψ ϧ ܗ ੒ ͳ Ͳ ͕ ظ ଴ Ͱ ͖ Δ ख ๏ Ͱ ͋ Δɻ͜ͷΞμϓςΟϒΞϯςφॲཧͱ௚ަप೾਺ଟॏ෼ ׂ:OFDM(Orthogonal Frequency Division Multiplex-ing)ͳͲͷมௐٕज़Λ૊Έ߹ͤͯɺۙ೥MIMOγεςϜ ͕੝Μʹݚڀ͞Ε͍ͯΔͷ͸प஌ͷ௨ΓͰ͋Δɻ͜Ε͸ ૹड৴ͰΞϨΠΞϯςφΛߏ੒͠ɺ௨৴඼࣭Λ޲্ͤ͞ Δ͜ͱΛ໨తͱ͍ͯ͠ΔεϚʔτΞϯςφٕज़ͷҰͭͱ ݴΘΕ͍ͯΔ[6,7] ɻૹ৴ిྗ͓ΑͼଳҬ෯͚ͩʹґଘ ͠ͳ͍Ͱɺෳ਺ͷ఻ൖ࿏ΛؚΊͯ৘ใྔ͋Δ͍͸௨৴ڑ ཭Λվળ͢ΔํࣜͰ͋ΓɺݪཧతʹϨʔμγεςϜʹ΋ Ԡ༻͕ظ଴Ͱ͖Δɻ·ͨୈ(1)ࣜͷҐ૬߲ʹ஫໨͢Δͱɺ ݶఆ͞Εۭͨؒ಺ͰϏʔϜͷࢦ޲ํ޲Λ೚ҙʹมԽͤ͞ Δ͜ͱ͕Ͱ͖ΔɻϚΠΫϩ೾ଳ(RF)Ͱ͜ΕΛߦ͏ʹ͸ɺ ઢ࿏௕Λ੾Γସ͑ΔҠ૬σόΠε͕ඞཁͱͳΔɻલड़ͷ ΞμϓςΟϒॲཧͰ͸ɺϕʔεόϯυۙลͰσδλϧత ʹॏΈͷෳૉॲཧ΋ՄೳͰ͋Δɻ ͞Βʹจݙ[2] Ͱ΋ใࠂ͞Ε͍ͯΔΑ͏ʹɺAFͷ఺೾ ݯΛۙ๣քͰͷి࣓քσʔλͱ͢Δͱɺ͜Ε͕ͦͷ·· ԕํքʹม׵͞ΕΔɻલड़ͨ͠AFΛٻΊΔߟ͑ํ͔Β͠ ͯ౰વͷؼ݁Ͱ͋Δɻۙ๣ి࣓քΛԕํʹม׵͢Δʹ͸ɺ ਤ-2 ࡾ֯഑ྻͷฏ໘ΞϨΠ

Fig.2 Planar array in triangular placed elements.

ฏ໘೾εϖΫτϥϜల։๏ͱ͍͏ݫີͳཧ࿦ʹج͖ͮม ׵ࣜΛఆࣜԽ͍ͯͨ͠ɻಛʹฏ໘ঢ়ʹऔಘͨۙ͠๣ք͸ ݁ՌతʹFourierม׵ͷܗͰԕํք͕ٻΊΒΕΔͷͰɺ औಘͨۙ͠๣σʔλΛ୯ʹFFT͢Ε͹ԕํք͕ಘΒΕΔ ͜ͱ͸ྑ͘஌ΒΕ͍ͯΔɻҰํɺԁ౵૸ࠪ͋Δ͍͸ٿ໘ ૸ࠪͰ͸Besselؔ਺ͳͲͷಛघؔ਺͕ඞཁͰ͋Γɺԕํ քʹม׵͢Δʹ͸ॏ͍࡞ۀͱͳ͍ͬͯͨɻ͔͠͠ɺࣜ(1) ͚ͩʹجͮ͘AFͷํ๏Ͱ΋ɺΞϯςφͷԕํք͋Δ͍͸ ৚݅෇͖ͰϨʔμஅ໘ੵͷԕํք͕༰қʹٻΊΒΕΔɻ Ҏ্ͷΑ͏ʹΞϯςφܥΛ཭ࢄԽͯ͠औΓѻ͏ͱɺ্ ه(1)ࣜͷ֤ύϥϝʔλΛॴ๬ͷྔʹಠཱͯ͠ૢ࡞Ͱ͖ ΔͷͰɺ໨తʹԠ༷ͯ͡ʑͳԠ༻͕ߟ͑ΒΕΔɻຊ࿦Ͱ ͸ɺ͜ͷ಺ɺAFʹΑΔฏқͳը૾ॲཧʹ͍ͭͯɺλʔήο τϞσϧͷۙ๣քΛجʹجຊతͳݕ౼Λߦ͏ɻ͜ͷը૾ ॲཧ͸ɺ௒Ի೾ྖҬͰͷΞμϓςΟϒͳॲཧΛ൐Θͤͨ ҩྍؔ࿈Ͱͷ෼໺[8]ɺ͋Δ͍͸ϚΠΫϩ೾ྖҬͰͷ஍ දۙลͷۚଐ෺ମͷϨʔμը૾ʹΑΔࣝผ[9] ͳͲʹ΋ ΄΅ಉ͡ߟ͑ํͰԠ༻͞Ε͍ͯΔɻ ͳ͓MUSIC๏ͳͲͰ͸ɺݻ༗஋ΛѻͬͨΓαϒΞϨΠ Խͯͦ͠ͷͱ͖ͷ౷ܭ஋Λ༻͍ͨΓ͢ΔͷͰɺߦྻʹΑ ΔϕΫτϧද͕ࣔศརͰ͋ΓɺࢀߟॻΛؚΉଟ͘ͷจݙ Ͱ΋ߦྻදࣔͱͳ͍ͬͯΔɻ͔͠͠ຊ࿦Ͱ͸ͦ͜·Ͱཱ ͪೖΒͳ͍ͷͰɺ෼͔Γқ͍εΧϥʔදࣔͷ··ٞ࿦͢ Δ͜ͱʹ͢Δɻ ্ͯ͞هAFΛཧղ͢ΔͨΊʹɺϑΣʔζυΞϨΠΞϯ ςφ(Ґ૬ܕిࢠ૸ࠪΞϯςφ)Λ೦಄ʹAFͷ۩ମతͳ දࣔʹ͍ͭͯٞ࿦͓ͯ͘͠ɻલड़ͷϦχΞΞϨΠΛ2࣍

ݩʹ֦ுͨ͠ϓϥφΞϨΠΛਤ2ʹࣔ͢ɻૉࢠ഑ྻ͸Ұ ൠੑΛ࣋ͨͨ͢Ίɺx࣠ํ޲ʹִஈ͕δx͚ͩͣΕͨࡾ֯ ഑ྻͱ͢Δɻ͜ͷૉࢠ࠲ඪΛͦͷ··ୈ(1)ࣜʹ୅ೖ͢ Ε͹ɺΞϨΠͷ์ࣹಛੑ(AF)͕ٻΊΒΕΔɻిࢠతͳ ϏʔϜ૸ࠪΛҙࣝ͢Δͱɺ֤ૉࢠʹڅి͢ΔྭৼҐ૬͸ ಠ੍ཱͯ͠ޚͰ͖ΔΑ͏ʹ͓ͯ͘͠ඞཁ͕͋Δɻ͜ͷΑ ͏ͳిࢠϏʔϜ૸ࠪํࣜͷΞϯςφΛϑΣʔζυΞϨΠ ͱݺΜͰ͓ΓɺຆͲͷγεςϜ͸Ґ૬ΛՄมͤ͞Δσό ΠεͰ͋ΔҠ૬ثΛ࠾༻͍ͯ͠Δɻ֤ૉࢠͷ͜ͷҐ૬Λ Ͳ͏ͷΑ͏ʹઃఆ͢Ε͹Α͍͔ɺ͜Ε͸Huygensͷݪཧ ΑΓ௚ͪʹ༠ಋͰ͖ΔɻϏʔϜΛ޲͚͍ͨํ޲ʹ֤ૉࢠ ͔Βͷ์ࣹքͷҐ૬ΛͣΒͤ͹Α͍ɻ͜ͷج४͸ΞϨΠ ์ࣹքͷ౳Ґ૬໘͕ϏʔϜํ޲ͱਨ௚ʹͳΔΑ͏ʹҠ૬ ثΛۦಈ͢Δ͜ͱͰ͋Δ[1]ɻࠓɺΞϨΠ։ޱ͕(x, y) ໘ʹଘࡏ͠ɺzํ޲ΛϏʔϜࢦ޲ํ޲ͱ͢Δɻ֤ૉࢠ͸ɺ ਤ2ʹࣔ͢Α͏ʹm, n = 1, 2,· · · ͱͯ͠ɺنଇతʹࡾ֯ ഑ྻ͞Ε͍ͯΔɻ͜ͷͱ͖ɺૉࢠͷ࠲ඪ͸ xm= dx{m−1}+δx· mod(n, 2), yn={n − 1} dy (2) Ͱද͞ΕΔɻ্ࣜͰmod(a, b)͸a/b ͷ༨ΓΛද͓ͯ͠ Γɺmod(n, 2)͸0͔1ʹͳΔɻૉࢠִؒ͸xͱyํ޲ Ͱ֤ʑdx, dyͱ͍ͯ͠Δɻ૬ޓ݁߹Λߟ͑ͳ͍৔߹ɺ(1) ࣜͷ ∑ ͸ ∑_m·∑_n ͱ෼཭Ͱ͖ΔͷͰɺ࣍ࣜͷΑ͏ʹ มܗͰ͖Δɻ f (θ, ϕ) = M ∑ m=1 N ∑ n=1 amnexp(jψmn), ψmn= k{dx(m−1)+δx·mod(n, 2)} u+kdy(n−1)v. (3)

͜͜Ͱɺ(u, v) = (sin θ cos ϕ, sin θ sin ϕ)͸ٿ࠲ඪͱ௚֯ ࠲ඪͷม׵ҼࢠͰ͋ΓɺM, N ͸֤ʑm, nͷ࠷େ஋Ͱ ͋ΔɻϏʔϜΛ_(u0, v0)ʹ޲͚͍ͨ৔߹ɺͭ·ΓϑΣʔ ζυΞϨΠγεςϜ౳ͰͷϏʔϜ૸ࠪͰ͸ɺ(u, v) Λ (u_{− u}0, v− v0) Ͱஔ͖׵͑Ε͹Α͍ɻ͜Ε͸AF͕։ޱ ෼෍ͷFourierม׵ͱͳ͍ͬͯΔ͜ͱʹؾ෇͚͹ɺ༰қ ʹཧղͰ͖Δઢܗܥͷجຊੑ࣭Ͱ͋Δɻ૬ޓ݁߹ͷӨڹ Λແࢹ͍ͯ͠ΔͷͰҐ૬΋෼཭Ͱ͖ɺamn͸amn= aman ͱͰ͖Δɻैͬͯɺ(3)ࣜ͸ f (u, v) = M ∑ m=1 amexp{j(αm+βm)}· N ∑ n=1 anexp{(jαn+βn)} , αm= k{dx(m− 1) + δx· mod(n, 2)} u, αn= kdy(n− 1)v, βm=−k {dx(m− 1) + δx· mod(n, 2)} u0, βn=−kdy(n− 1)v0 (4) ͱ੔ཧ͞ΕΔɻ͜Ε͕ϏʔϜ૸ࠪ(u0, v0)ΛؚΊ֤ͨૉ ࢠͷྭৼ͢΂͖Ґ૬෼෍Ͱ͋Γɺݱଘ͢Δେܕ͔Βখܕ ʹࢸΔଟ͘ͷϑΣʔζυΞϨΠγεςϜ͸ɺ͜ͷ୯७ͳ ͔ࣜΒۦಈ͢΂͖Ґ૬ྔΛܭࢉ͍ͯ͠Δɻ ֤ૉࢠ͔Βͷ೾໘ͷแབྷઢʹ૬౰͢Δ౳Ґ૬໘ʹର͠ ͯɺϏʔϜ͸ਨ௚ʹࢦ޲͢Δɻ͜Ε͸Huygensͷݪཧ͔ Βࣔࠦ͞ΕΔɻ֤ૉࢠͷҐ૬ΛԿΒ͔ͷΞϧΰϦζϜͰ ੍ޚ͢Δͱɺ์ࣹύλʔϯʹψϧ΋ੜ੒Ͱ͖ɺϏʔϜͱψ ϧΛಠཱͯ͠૸ࠪ͢Δ͜ͱ΋ߟ͑ΒΕΔɻ·ͨɺϏʔϜ ͷిྗ൒஋෯͋Δ͍͸αΠυϩʔϒ΋ঢ়گʹԠͯ͡ม͑ Δ͜ͱ͕Ͱ͖Δɻ͜ͷΑ͏ͳ์ࣹύλʔϯ੍ޚΛҰׅ͠ ͯߦͳ͏ٕज़ΛϏʔϜϑΥʔϛϯάͱ͍͏͕ɺRF৴߸Λ ϕʔεόϯυ৴߸ʹม׵ͯ͠σδλϧσʔλͱͯ͠ѻ͏ ͜ͱͰɺ৴߸ॲཧͱͷ੔߹ੑ͕࣮ݱͰ͖Δɻ͜ΕΛσδ λϧϏʔϜϑΥʔϛϯά(DBF)ͱݺΜͰ͍ΔɻDBFʹड ৴ʑ߸ͷS/Nൺͷ৘ใΛՃ͑ΔͱɺΞϯςφ͕ࣗ཯తʹ ׯব೾Λආ͚ΔΑ͏ͳΞϧΰϦζϜ͕ߟ͑ΒΕΔɻ͜Ε ͕લड़ͷΞμϓςΟϒΞϯςφͰ͋Γɺۙ೥ɺA/Dม׵ث (Analogue-digital converter)ͱίϯϐϡʔλͷߴ଎ ԽΛഎܠʹ࣮༻Խ͞Εͭͭ͋Δॲཧٕज़Ͱ͋Δɻ ԁܗ(Ϧϯά)ΞϨΠɺ͋Δ͍͸ͦΕΛଟஈʹॏͶͨԁ ౵ΞϨΠʹରͯ͠͸ɺ(1)ࣜͷجຊ͔ࣜΒAFͷผͷදࣔ ͕ࣜ༠ಋͰ͖Δɻಛʹۙ๣քͷԕํม׵Ͱ͸ɺଌఆਫ਼౓ ΛߴΊΔͨΊฏ໘૸ࠪΑΓ΋ดۭͨؒ͡Λͭ͘Δԁ౵૸ ࠪͷํ͕๬·͍͜͠ͱ͕ଟ͍ɻ͜ͷͱ͖ͷม׵ΞϧΰϦ ζϜʹAFΛ༻͍ɺϓϩʔϏϯά༻ͷΞϯςφࢦ޲ੑΛߟ ྀͨ͠ܭࢉޮ཰ͷྑ͍ද͕ࣔࣜٻΊΒΕΔ[2]ɻҩྍ޲ ͚ͷը૾ॲཧ෼໺Ͱ͸ɺ௒Ի೾ଳͰͷϦϯάΞϨΠํࣜ ΋ଟ͘࠾༻͞Ε͍ͯΔΑ͏Ͱ͋Δɻ ۙ೥ɺϨʔμը૾ͷ෼ੳʹภ೾৘ใΛԠ༻ͨ͠ཧ࿦͕Ϧ Ϟʔτηϯγϯά෼໺Ͱਫ਼ྗతʹݚڀ͞Ε͍ͯΔ[10]ɻ ͜Ε͸ϨʔμʹΑͬͯੜ੒͞Εͨը૾ͷதʹࢄཚମʹԠ ͍ͯ͡Ζ͍Ζͷภ೾੒෼ؚ͕·Ε͓ͯΓɺ໨ඪࣝผΛ໨ తͱͯ͠ɺಘΒΕͨϨʔμը૾͔Βภ೾৘ใʹԠͯ͡࠶ ෼ղ͢Δٕज़Ͱ͋Δɻྫ͑͹ɺւ໘͋Δ͍͸஍໘ͳͲฏ ໘ঢ়ͷλʔήοτ͔Β͸1ճͷද໘൓ࣹɺϏϧσΟϯά ͳͲͷίʔφʔঢ়ͷ෺ମ͔Β͸2ճͷμϒϧ൓ࣹɺ৿ྛ ͳͲ͸Ԟߦ͖·Ͱߟྀͨ͠ମੵࢄཚ͕ओମͱͳΔ͜ͱ͕ ෼͔͍ͬͯΔɻैͬͯɺͦΕʹԠͯ͡ಘΒΕͨը૾ͷࢄ ཚߦྻΛ࠶෼ղ͢Δ͜ͱͰɺ෼ྨࣝผ͕ՄೳͱͳΔɻຊ ॻͷΑ͏ͳܭࢉཧ࿦Ͱ͸λʔήοτͱภ೾ํ޲Λ೚ҙʹ ઃఆͰ͖ΔͷͰɺશภ೾৘ใΛؚΜͩը૾ͷγϛϡϨʔ γϣϯ΋ՄೳͰ͋Δɻ

ݩʹ֦ுͨ͠ϓϥφΞϨΠΛਤ2ʹࣔ͢ɻૉࢠ഑ྻ͸Ұ ൠੑΛ࣋ͨͨ͢Ίɺx࣠ํ޲ʹִஈ͕δx͚ͩͣΕͨࡾ֯ ഑ྻͱ͢Δɻ͜ͷૉࢠ࠲ඪΛͦͷ··ୈ(1)ࣜʹ୅ೖ͢ Ε͹ɺΞϨΠͷ์ࣹಛੑ(AF)͕ٻΊΒΕΔɻిࢠతͳ ϏʔϜ૸ࠪΛҙࣝ͢Δͱɺ֤ૉࢠʹڅి͢ΔྭৼҐ૬͸ ಠ੍ཱͯ͠ޚͰ͖ΔΑ͏ʹ͓ͯ͘͠ඞཁ͕͋Δɻ͜ͷΑ ͏ͳిࢠϏʔϜ૸ࠪํࣜͷΞϯςφΛϑΣʔζυΞϨΠ ͱݺΜͰ͓ΓɺຆͲͷγεςϜ͸Ґ૬ΛՄมͤ͞Δσό ΠεͰ͋ΔҠ૬ثΛ࠾༻͍ͯ͠Δɻ֤ૉࢠͷ͜ͷҐ૬Λ Ͳ͏ͷΑ͏ʹઃఆ͢Ε͹Α͍͔ɺ͜Ε͸Huygensͷݪཧ ΑΓ௚ͪʹ༠ಋͰ͖ΔɻϏʔϜΛ޲͚͍ͨํ޲ʹ֤ૉࢠ ͔Βͷ์ࣹքͷҐ૬ΛͣΒͤ͹Α͍ɻ͜ͷج४͸ΞϨΠ ์ࣹքͷ౳Ґ૬໘͕ϏʔϜํ޲ͱਨ௚ʹͳΔΑ͏ʹҠ૬ ثΛۦಈ͢Δ͜ͱͰ͋Δ[1]ɻࠓɺΞϨΠ։ޱ͕(x, y) ໘ʹଘࡏ͠ɺzํ޲ΛϏʔϜࢦ޲ํ޲ͱ͢Δɻ֤ૉࢠ͸ɺ ਤ2ʹࣔ͢Α͏ʹm, n = 1, 2,· · · ͱͯ͠ɺنଇతʹࡾ֯ ഑ྻ͞Ε͍ͯΔɻ͜ͷͱ͖ɺૉࢠͷ࠲ඪ͸ xm= dx{m−1}+δx· mod(n, 2), yn={n − 1} dy (2) Ͱද͞ΕΔɻ্ࣜͰmod(a, b)͸a/b ͷ༨ΓΛද͓ͯ͠ Γɺmod(n, 2)͸0͔1ʹͳΔɻૉࢠִؒ͸xͱyํ޲ Ͱ֤ʑdx, dyͱ͍ͯ͠Δɻ૬ޓ݁߹Λߟ͑ͳ͍৔߹ɺ(1) ࣜͷ ∑ ͸ ∑_m·∑_n ͱ෼཭Ͱ͖ΔͷͰɺ࣍ࣜͷΑ͏ʹ มܗͰ͖Δɻ f (θ, ϕ) = M ∑ m=1 N ∑ n=1 amnexp(jψmn), ψmn= k{dx(m−1)+δx·mod(n, 2)} u+kdy(n−1)v. (3)

͜͜Ͱɺ(u, v) = (sin θ cos ϕ, sin θ sin ϕ)͸ٿ࠲ඪͱ௚֯ ࠲ඪͷม׵ҼࢠͰ͋ΓɺM, N ͸֤ʑm, nͷ࠷େ஋Ͱ ͋ΔɻϏʔϜΛ_(u0, v0)ʹ޲͚͍ͨ৔߹ɺͭ·ΓϑΣʔ ζυΞϨΠγεςϜ౳ͰͷϏʔϜ૸ࠪͰ͸ɺ(u, v) Λ (u_{− u}0, v− v0) Ͱஔ͖׵͑Ε͹Α͍ɻ͜Ε͸AF͕։ޱ ෼෍ͷFourierม׵ͱͳ͍ͬͯΔ͜ͱʹؾ෇͚͹ɺ༰қ ʹཧղͰ͖Δઢܗܥͷجຊੑ࣭Ͱ͋Δɻ૬ޓ݁߹ͷӨڹ Λແࢹ͍ͯ͠ΔͷͰҐ૬΋෼཭Ͱ͖ɺamn͸amn= aman ͱͰ͖Δɻैͬͯɺ(3)ࣜ͸ f (u, v) = M ∑ m=1 amexp{j(αm+βm)}· N ∑ n=1 anexp{(jαn+βn)} , αm= k{dx(m− 1) + δx· mod(n, 2)} u, αn= kdy(n− 1)v, βm=−k {dx(m− 1) + δx· mod(n, 2)} u0, βn=−kdy(n− 1)v0 (4) ͱ੔ཧ͞ΕΔɻ͜Ε͕ϏʔϜ૸ࠪ(u0, v0)ΛؚΊ֤ͨૉ ࢠͷྭৼ͢΂͖Ґ૬෼෍Ͱ͋Γɺݱଘ͢Δେܕ͔Βখܕ ʹࢸΔଟ͘ͷϑΣʔζυΞϨΠγεςϜ͸ɺ͜ͷ୯७ͳ ͔ࣜΒۦಈ͢΂͖Ґ૬ྔΛܭࢉ͍ͯ͠Δɻ ֤ૉࢠ͔Βͷ೾໘ͷแབྷઢʹ૬౰͢Δ౳Ґ૬໘ʹର͠ ͯɺϏʔϜ͸ਨ௚ʹࢦ޲͢Δɻ͜Ε͸Huygensͷݪཧ͔ Βࣔࠦ͞ΕΔɻ֤ૉࢠͷҐ૬ΛԿΒ͔ͷΞϧΰϦζϜͰ ੍ޚ͢Δͱɺ์ࣹύλʔϯʹψϧ΋ੜ੒Ͱ͖ɺϏʔϜͱψ ϧΛಠཱͯ͠૸ࠪ͢Δ͜ͱ΋ߟ͑ΒΕΔɻ·ͨɺϏʔϜ ͷిྗ൒஋෯͋Δ͍͸αΠυϩʔϒ΋ঢ়گʹԠͯ͡ม͑ Δ͜ͱ͕Ͱ͖Δɻ͜ͷΑ͏ͳ์ࣹύλʔϯ੍ޚΛҰׅ͠ ͯߦͳ͏ٕज़ΛϏʔϜϑΥʔϛϯάͱ͍͏͕ɺRF৴߸Λ ϕʔεόϯυ৴߸ʹม׵ͯ͠σδλϧσʔλͱͯ͠ѻ͏ ͜ͱͰɺ৴߸ॲཧͱͷ੔߹ੑ͕࣮ݱͰ͖Δɻ͜ΕΛσδ λϧϏʔϜϑΥʔϛϯά(DBF)ͱݺΜͰ͍ΔɻDBFʹड ৴ʑ߸ͷS/Nൺͷ৘ใΛՃ͑ΔͱɺΞϯςφ͕ࣗ཯తʹ ׯব೾Λආ͚ΔΑ͏ͳΞϧΰϦζϜ͕ߟ͑ΒΕΔɻ͜Ε ͕લड़ͷΞμϓςΟϒΞϯςφͰ͋Γɺۙ೥ɺA/Dม׵ث (Analogue-digital converter)ͱίϯϐϡʔλͷߴ଎ ԽΛഎܠʹ࣮༻Խ͞Εͭͭ͋Δॲཧٕज़Ͱ͋Δɻ ԁܗ(Ϧϯά)ΞϨΠɺ͋Δ͍͸ͦΕΛଟஈʹॏͶͨԁ ౵ΞϨΠʹରͯ͠͸ɺ(1)ࣜͷجຊ͔ࣜΒAFͷผͷදࣔ ͕ࣜ༠ಋͰ͖Δɻಛʹۙ๣քͷԕํม׵Ͱ͸ɺଌఆਫ਼౓ ΛߴΊΔͨΊฏ໘૸ࠪΑΓ΋ดۭͨؒ͡Λͭ͘Δԁ౵૸ ࠪͷํ͕๬·͍͜͠ͱ͕ଟ͍ɻ͜ͷͱ͖ͷม׵ΞϧΰϦ ζϜʹAFΛ༻͍ɺϓϩʔϏϯά༻ͷΞϯςφࢦ޲ੑΛߟ ྀͨ͠ܭࢉޮ཰ͷྑ͍ද͕ࣔࣜٻΊΒΕΔ[2]ɻҩྍ޲ ͚ͷը૾ॲཧ෼໺Ͱ͸ɺ௒Ի೾ଳͰͷϦϯάΞϨΠํࣜ ΋ଟ͘࠾༻͞Ε͍ͯΔΑ͏Ͱ͋Δɻ ۙ೥ɺϨʔμը૾ͷ෼ੳʹภ೾৘ใΛԠ༻ͨ͠ཧ࿦͕Ϧ Ϟʔτηϯγϯά෼໺Ͱਫ਼ྗతʹݚڀ͞Ε͍ͯΔ[10]ɻ ͜Ε͸ϨʔμʹΑͬͯੜ੒͞Εͨը૾ͷதʹࢄཚମʹԠ ͍ͯ͡Ζ͍Ζͷภ೾੒෼ؚ͕·Ε͓ͯΓɺ໨ඪࣝผΛ໨ తͱͯ͠ɺಘΒΕͨϨʔμը૾͔Βภ೾৘ใʹԠͯ͡࠶ ෼ղ͢Δٕज़Ͱ͋Δɻྫ͑͹ɺւ໘͋Δ͍͸஍໘ͳͲฏ ໘ঢ়ͷλʔήοτ͔Β͸1ճͷද໘൓ࣹɺϏϧσΟϯά ͳͲͷίʔφʔঢ়ͷ෺ମ͔Β͸2ճͷμϒϧ൓ࣹɺ৿ྛ ͳͲ͸Ԟߦ͖·Ͱߟྀͨ͠ମੵࢄཚ͕ओମͱͳΔ͜ͱ͕ ෼͔͍ͬͯΔɻैͬͯɺͦΕʹԠͯ͡ಘΒΕͨը૾ͷࢄ ཚߦྻΛ࠶෼ղ͢Δ͜ͱͰɺ෼ྨࣝผ͕ՄೳͱͳΔɻຊ ॻͷΑ͏ͳܭࢉཧ࿦Ͱ͸λʔήοτͱภ೾ํ޲Λ೚ҙʹ ઃఆͰ͖ΔͷͰɺશภ೾৘ใΛؚΜͩը૾ͷγϛϡϨʔ γϣϯ΋ՄೳͰ͋Δɻ 3.ΞϨΠͷয఺ԽʹΑΔϨʔμը૾ ਫಓ؅ɺ஍ཕͳͲͷ஍தຒઃ෺ͷ୳ࠪʹ͸ɺλʔήο τͷը૾σʔλ͕ਖ਼֬Ͱ͋Ε͹ࣝผ൑ఆͷ֬౓͸େ͖͘ ޲্͢Δɻ೾ಈʹΑΔը૾Խॲཧͷ෼໺Ͱ͸ɺখதن໛ ͷݻఆΞϯςφ͸෼ղೳ͕௿͍͜ͱ΋͋ΓɺۭؒతʹҠ ಈͤ͞౳Ձతʹେ͖ͳ։ޱΛಘͯ෼ղೳΛ͋͛Δ߹੒։ ޱॲཧ(SAR)Λجʹͨ͠ํ๏͕޿͘ීٴ͍ͯ͠Δɻ͜͜ Ͱ͸ɺຊ֨తͳSARͰߦ͏ΞδϚεѹॖ͓ΑͼϨϯδѹ ॖ(ύϧεѹॖ) ͷΑ͏ͳϋʔυͱιϑτ΢ΣΞʹؔΘ ΔॲཧͰ͸ͳ͘ɺ؆қͳϋʔυͱલड़ͷAFཧ࿦ʹΑΔॲ ཧ๏ʹ͍ͭͯٞ࿦͢Δɻ೾ಈͷը૾ॲཧʹຊ֨తͳSAR ॲཧΛ࠾༻͢ΔͱɺϨʔμͷϋʔυ΢ΣΞ΋ͦͷॲཧʹ ߹Θͤͯઃܭ͠ͳ͚Ε͹ͳΒͳ͍ɻҰํɺAFΛૹड৴Խ ͠ɺ૝ఆͨ͠λʔήοτͷ࠲ඪΛݩʹλʔήοτΤίʔ ͷҐ૬ͱൺֱ͢Δ͜ͱͰ΋ɺλʔήοτ࠲ඪͷۙลͰͷ ૬ؔੑ͕ධՁͰ͖Δɻ͜ͷ୯७ͳ֓೦ʹΑΔͱɺϨʔμ ͷϋʔυ͓Αͼιϑτ΢ΣΞ͸ඇৗʹγϯϓϧͳߏ੒ͱ ͳΔɻͨͩ͠রࣹྖҬશൠΛը૾ॲཧ͢Δ৔߹ɺԾఆ͠ ͨ໨ඪ෺ͷ࠲ඪ͸શҬͰܭࢉ͢Δඞཁ͕͋ΔͷͰܭࢉ࣌ ؒίετͷ໰୊͕͋Δɻ͔͠͠ɺ࠷ۙͷPCͰ͸େ͖ͳ ໰୊ͱ͸ͳΒͳ͍ͱ༧૝͍ͯ͠Δɻͨͩ͜ͷཧ༝ͷͨΊɺ

AFʹΑΔয఺Խը૾(Array-Factor Focusing: AFF)

ͷԠ༻ൣғ͸ɺൺֱతۙڑ཭ͷখྖҬͷը૾ॲཧʹ࠷ద Ͱ͋ΔͱࢥΘΕΔɻ લड़ͷ೗͘ΞϨΠʹΑΔϨʔμը૾ͷߟ͑ํ͸ɺ࣮ଌ ৴߸ͷҐ૬৘ใͱরࣹྖҬ಺ͷ໨ඪ෺͔Βͷཧ࿦తͳΤ ίʔ৴߸ͷҐ૬৘ใͷ૬ؔੑΛΈΔํ๏Ͱ͋Δɻ͜ͷ૬ ؔੑ͸؆୯ͳҐ૬ͷڃ਺ܭࢉͰߦ͏͜ͱ͕Ͱ͖ɺ݁Ռ͕ ෼ղೳͷ޲্ʹͭͳ͕ΔҰछͷ߹੒։ޱॲཧͱΈͳ͢͜ ͱ͕Ͱ͖Δɻి೾Λૹ৴͠ɺͦͷΤίʔΛड৴͢ΔͨΊ ʹ͸ɺΞϨΠͷ֤ૉࢠΛશͯ༻ҙ͢Δඞཁ͸ͳ͍ɻλʔ ήοτͱϨʔμͷҐஔؔ܎͕૬ରతʹݻఆ͞Ε͍ͯΔɺ͋ Δ͍͸ॲཧϨʔτ಺Ͱ΄΅Ҡಈ͍ͯ͠ͳ͍ɺͳͲ͕Ծఆ Ͱ͖Δͱɺ1ݸͷΞϯςφΛػցతʹ૸ࠪͯ͠΋Α͍ɻ· ͨɺૹड৴Ξϯςφ͸ճ࿏ͷෳࡶ͞Λආ͚ΔͨΊɺผʑʹ ༻ҙ͢Δํ͕ଌఆܥ΋؆୯ʹͳΔɻྫ͑͹ɺ൚༻ͷωο τϫʔΫΞφϥΠβͳͲΛૹ৴ݯ͓Αͼड৴ܥʹ༻͍Δ ৔߹ɺૹड৴ͷΞΠιϨʔγϣϯΛऔΔͨΊʹૹ৴ͱड ৴ͷΞϯςφΛۭؒతʹ཭͢ߏ੒΋ՄೳͰ͋Δɻ·ͨҠ ಈ͢Δૹ৴ͷҐஔ࠲ඪ਺ͱड৴ͷͦΕ͸ҧ͍ͬͯͯ΋Α ͘ɺૹ৴ϙΠϯτͷํ͕ड৴ΑΓ΋গͳ͍ߏ੒͸ίετ ޮ཰͕ߴ͍ͱࢥΘΕΔɻ ͯ͞ɺΞϨΠͷجຊࣜ(1)Λ΋͏গ͠ৄ͘͠ݟΔͨΊ ʹɺը૾σʔλΛҙࣝͨ͠Ґஔ࠲ඪม਺ͷࢄཚքϞσϧ Λ࣍ࣜͰ༩͑Δɻ es(x, z) = M ∑ m=1 Am· δ(r − rm). (5) ͜͜Ͱɺr, rm͸֤ʑ೾ݯͱ؍ଌ఺ͷҐஔϕΫτϧͰ͋ ΓɺDiracͷDeltaؔ਺δ(r_{− r}m)͕͍ΘΏΔը૾ͷϐ Ϋηϧ࠲ඪʹରԠ͍ͯ͠Δͱߟ͑ΒΕΔɻδ(r− rm)͸ Fourierม׵ཧ࿦ΑΓ δ(r−rm) = ∫ ∞ −∞ exp{−j(k·rm}·exp{j(k·r)}dk (6) ͱۙࣅͰ͖Δ[11]ɻͭ·Γ೾਺ϕΫτϧۭؒkͰͷࢄཚ քΛEs_{(k)ͱ͢Δͱɺ͜ΕΛٯFourierม׵ͨ͠΋ͷ͕} ্ࣜʹͳΔɻैͬͯɺ͜ΕΛ͞ΒʹFourierม׵͢Δͱɺ Es(k) = M ∑ m=1 Amexp{−j(k · rm)} (7) ͕ಘΒΕΔɻ্ࣜͰྫ͑͹ɺx_{− z}໘Ͱͷը૾(z ͸Ϩ ϯδํ޲)͸rm= (xm, zm), r = (x, z), k = (kx, kz)ͱͳ Δɻୈ(7)ࣜ͸ϨʔμͰಘΒΕΔड৴σʔλͷܗͱͳͬ ͓ͯΓɺୈ(1)ࣜͷAFͱྨࣅͨ͠දࣔࣜͱͳ͍ͬͯΔɻ ͭ·Γɺୈ(1)ࣜ͋Δ͍͸(7)ࣜΛجʹۙ๣λʔήοτ ͷয఺Խͱૹड৴Խૢ࡞Λߦ͑͹ɺλʔήοτ࠲ඪͷը ૾σʔλ͕ಘΒΕΔ͜ͱʹͳΔɻ্ड़ͷࢄཚମΛෳ਺ͷ ఺ঢ়෺ମͱͯ͠ѻ͏ํ๏͸ɺ఺෼෍ؔ਺(point spread function)ͱͯ͠޿͘༻͍ΒΕ͍ͯΔۙࣅղ๏Ͱ͋Δɻ ఺ঢ়෺ମʹΑΔࢄཚ೾ಈ͸؆୯ʹදݱͰ͖ΔͷͰɺߟ͑ ͍ͯΔର৅෺ମͷද໘࠲ඪΛෳ਺ͷ఺ͰͳͧΒ͑ɺ͜Ε Βͷ఺͔ΒͷҐ૬ࠩΛߟྀ͢Δ͚ͩͰ߹੒ࢄཚ೾Λ༰қ ʹධՁͰ͖Δ͜ͱʹͳΔɻ ΞϨΠ֤ૉࢠͰͷ஗ԆҐ૬Λߟ࡯͢ΔͨΊʹɺਫฏ ໘಺ͷ֯౓ํ޲ɺํҐͱڑ཭͓Αͼߴ͞ํ޲ͷ࠲ඪΛ ௚֯࠲ඪܥ(x, y, z)Ͱද͢͜ͱΛߟ͑Δɻਤ3ʹࣔ͢ Α͏ʹɺm ൪໨ʹ͓͚Δૹ৴Ξϯςφͷ࠲ඪΛrt m= (xt m, ymt , zmt) ͱ͠ɺn൪໨ʹ͓͚Δड৴Ξϯςφͷ ࠲ඪΛrr n= (xrn, ynr, znr) ͱ͢ΔɻҰํɺը૾σʔλ ͷม਺ͱͳΔ໨ඪࢄཚ෺ͷ࠲ඪΛrp= (xp, yp, zp) ͱ ද͢ɻ͜͜Ͱr͸ҐஔϕΫτϧΛද͍ͯ͠Δɻm൪໨ ͷૹ৴Ξϯςφ͔Βͷ৴߸͸ɺয఺ͱԾఆ͢Δ໨ඪ෺ ͷ࠲ඪ(xp, yp, zp)Ͱ൓ࣹࢄཚͨ͠ޙɺn൪໨ͷड৴Ξ ϯςφʹ໭Δɻ͜ͷͱ͖ͷޫֶతͳܦ࿏௕͸ɺ͜ΕΛ rmn(xp, yp, zp)ͱ͢Δͱɺ rmn(xp, yp, zp)=|rp− rtm| + |rrn− rp|

ਤ-3 AFয఺ԽʹΑΔϨʔμߏ੒(஫ҙ: ਤ2

ͷ൪߸m, nͱऔΓํ͕ҟͳΔ)

Fig.3 Radar configuration in AF focusing. Note the different m, n from Fig.2.

={(xtm− xp)2+ (ymt − yp)2+ (ztm− zp)2} 1 2 +{(xrn− xp)2+ (ynr− yp)2+ (znr− zp)2} 1 2 ₍₈₎ ͱܭࢉ͞ΕΔɻ೾਺kΛߟྀ͢ΔͱɺҐ૬ܦ࿏͸krmn ʹ׵ࢉ͞ΕΔɻฏ໘೾Λ৚݅ͱͯ͠ఆࣜԽ͞ΕͨAFୈ (1)ࣜʹର͠ɺ(8)ࣜ͸ۙ๣ྖҬΛҙࣝͨ͠য఺Խૢ࡞ (focusing)ʹ૬౰͢Δɻ 4.AFFʹΑΔը૾Խͷఆࣜ લ߲Ͱ͸ΞϨΠͷয఺Խʹର͢Δߟ͑ํ(AF Focus-ing:AFF)ʹ͍ͭͯٞ࿦ͨ͠ɻ͜͜Ͱ͸ɺϨʔμͷप೾਺ ಛੑΛߟྀͯ͠ը૾ΛಘΔͨΊͷ۩ମతͳॲཧ๏ʹ͍ͭ ͯɺਤ3Λࢀর͠ͳ͕Βٞ࿦͢Δɻ Ϩʔμͷૹ৴प೾਺ʹ͸࿈ଓ೾ܗ(CW)Λ૝ఆ͠ɺप೾ ਺Λεςοϓঢ়ʹ૟Ҿͤ͞Δɻεςοϓঢ়ʹ૟Ҿ͢Δͷ ͸ɺଌఆثͷಛੑΛߟྀͯ͠ͷ͜ͱͰ͋Γɺͦͷεςο ϓ෯ɺप೾਺౳ͷύϥϝʔλʹΑΓ୯ௐ૿Ճؔ਺ʹ͍ۙ ܗͰ૟Ҿͯ͠΋ྑ͍ɻΞϨΠͷm൪໨ͷૹ৴Ξϯςφ ͔Βૹ৴ͯ͠n൪໨ͷड৴ΞϯςφͰܭଌ͞Εͨℓ൪໨ ͷεςοϓप೾਺ fℓ Ͱͷड৴ڧ౓ΛPℓmn(fℓ, rmn)ͱ ͢Δɻ͜ͷͱ͖ɺλʔήοτ࠲ඪrpΛը૾ྖҬͰͷม ਺r(x, y, z)ʹஔ͖׵͑Δͱɺલ߲(7)ࣜͰݟͨΑ͏ʹɺ Ϩʔμલํͷి࣓քڧ౓ɺ͢ͳΘͪϨʔμը૾͸ Q0(r)= 1 LM N L ∑ ℓ=1 M ∑ m=1 N ∑ n=1 Pℓmn(fℓ, rmn) · exp {jkℓrmn(xp, yp, zp)} = 1 LM N L ∑ ℓ=1 M ∑ m=1 N ∑ n=1 Pℓmn(fℓ, rmn) · exp { j2πfℓ c rmn(xp, yp, zp) } · exp(jϕℓ) (9) ͰධՁͰ͖Δͱߟ͑ΒΕΔɻ͜͜ͰɺL, M, N ͸֤ʑૹ ৴Ξϯςφ਺ɺड৴Ξϯςφ਺ɺप೾਺εςοϓ਺Ͱ͋ Γɺ೾਺kℓ͸ޫ଎Λcͱͯ͠ɺkℓ= 2πfℓ/cΛ࢖͍ͬͯ ΔɻϨϯδํ޲ͷ෼ղೳ͕ଳҬ෯ʹґଘ͢Δ͜ͱ͸ɺલ ग़ͷpsfʹΑͬͯ༰қʹؔ܎͕ࣜ༠ಋͰ͖Δ͕ɺ͜͜Ͱ ͸ࢴ໘ͷ౎߹ͰׂѪ͢ΔɻPℓmn(fℓ, rmn)͸ड৴ΞϨΠ Ͱड৴͢ΔిྗͰ͋Γɺ(1)ࣜͷෳૉৼ෯an͸ΞϨΠΞ ϯςφརಘʹ૬౰͢Δɻ͜ͷड৴ిྗ͸ܭଌͷࡍʹඪ४ λʔήοτͷप೾਺ಛੑσ(fℓ)Ͱߍਖ਼͓ͯ͘͜͠ͱ͕๬ ·͍͠ɻ·ͨɺҐ૬ϕℓ ͸ଌఆγεςϜ͋Δ͍͸Ϩʔμ ܥͷ಺෦஗ԆྔͰ͋ΓɺϨʔμͷηοςΟϯά࣌ʹಋମ ٿͳͲͷඪ४ߍਖ਼λʔήοτͰ͜ͷྔΛิਖ਼͢Ε͹ྑ͍ɻ ্ࣜͷ࠲ඪؔ਺Λม਺r = (x, y, z)ͱͯ͠௚઀ඳը͢Ε ͹ɺର৅ྖҬͷը૾σʔλɺ͔͠΋໨తʹΑͬͯ͸3࣍ ݩը૾͕ಘΒΕΔ͜ͱʹͳΔɻ Ҏ্ͷΑ͏ʹAFFը૾͸ɺड৴ʑ߸ͱର৅ྖҬͷؔ࿈ ੑɺͭ·Γ݁ͼ͖ͭͷ౓߹͍ΛҐ૬ͷ੔߹ੑͱͯ͠දݱ ͨ͠΋ͷͱݟΔ͜ͱ͕Ͱ͖Δɻ͜Ε͸λʔήοτྖҬΛ ૸ࠪ͢Δr࠲ඪͱλʔήοτ࠲ඪrp ͷࠩr− rp͕ඇৗ ʹখ͍͞஋ΛͱΔλʔήοτۙ๣ͰɺQ(rp)͸࠷΋ڧ͘ ͳΓۭؒεϖΫτϥϜͷϐʔΫΛఄ͢ΔɻAFΛ࢖ͬͨΞ ϯςφϏʔϜ૸ࠪͷදࣔࣜ(7)Λݟͯ΋෼͔ΔΑ͏ʹɺ ϐʔΫ஋͸ϏʔϜ૸ࠪํ޲(u0, v0)ʹͳ͍ͬͯΔɻ(9) ࣜ͸AFͱશ͘ಉ͡ߟ͑ʹج͍͍ͮͯΔɻҰํɺධՁࣜ Q(rp)͸ૹड৴ΞϨΠૉࢠͱप೾਺ͷपظؔ਺(ࢦ਺࿨) ͱͳ͍ͬͯΔɻैͬͯύϥϝʔλͷ৚݅ʹΑͬͯ͸ɺ͍ ΘΏΔۭؒతͳᐆດੑ(ambiguity)͕ൃੜ͢Δɻ͜Ε͸ AFཧ࿦Ͱݴ͏άϨʔςΟϯάϩʔϒ(grating-lobe)ɺ Fourierཧ࿦Ͱݴ͑͹ΤΠϦΞε(aliasing)ͷ͜ͱͰ ͋Γɺ࣮ࡍͷΞϨΠϨʔμͷઃܭ࣌ʹ͸͜ͷᐆດੑΛආ ͚ΔΑ͏ʹ஫ҙ͢Δඞཁ͕͋Δɻͳ͓ɺQ0(rp)ʹ࣮ଌ஋ Λ༻͍Δ৔߹͸͜ͷ··Ͱ΋ྑ͍͕ɺΑΓਖ਼֬ͳܭࢉγ ϛϡϨʔγϣϯʹ͸Ξϯςφͷࢦ޲ੑʹΑΔڧ౓มԽΛ ߟྀ͠ͳ͚Ε͹ͳΒͳ͍ɻ͜Ε͸ޙͷ߲Ͱߟ࡯͢Δ͜ͱ ʹ͠Α͏ɻ ୈ(9)ࣜ͸Ұ༷ͳۭؒ಺ʹλʔήοτ͕ݽཱͯ͠ஔ͔ Εͨͱ͖ͷදࣔࣜͰ͋Δɻ౔தͳͲͷຒઃ෺͋Δ͍͸น ಁաͳͲΛҙࣝ͢Δͱɺෳ਺ͷҟछഔ࣭ͷ༠ి཰ͷҧ͍ ʹґଘ͢Δܦ࿏ࠩΛߟྀ͢Δ͜ͱ΋ඞཁͱͳΔɻ͜Εʹ

ਤ-3 AFয఺ԽʹΑΔϨʔμߏ੒(஫ҙ: ਤ2

ͷ൪߸m, nͱऔΓํ͕ҟͳΔ)

Fig.3 Radar configuration in AF focusing. Note the different m, n from Fig.2.

={(xtm− xp)2+ (ymt − yp)2+ (ztm− zp)2} 1 2 +{(xrn− xp)2+ (ynr− yp)2+ (znr− zp)2} 1 2 ₍₈₎ ͱܭࢉ͞ΕΔɻ೾਺kΛߟྀ͢ΔͱɺҐ૬ܦ࿏͸krmn ʹ׵ࢉ͞ΕΔɻฏ໘೾Λ৚݅ͱͯ͠ఆࣜԽ͞ΕͨAFୈ (1)ࣜʹର͠ɺ(8)ࣜ͸ۙ๣ྖҬΛҙࣝͨ͠য఺Խૢ࡞ (focusing)ʹ૬౰͢Δɻ 4.AFFʹΑΔը૾Խͷఆࣜ લ߲Ͱ͸ΞϨΠͷয఺Խʹର͢Δߟ͑ํ(AF Focus-ing:AFF)ʹ͍ͭͯٞ࿦ͨ͠ɻ͜͜Ͱ͸ɺϨʔμͷप೾਺ ಛੑΛߟྀͯ͠ը૾ΛಘΔͨΊͷ۩ମతͳॲཧ๏ʹ͍ͭ ͯɺਤ3Λࢀর͠ͳ͕Βٞ࿦͢Δɻ Ϩʔμͷૹ৴प೾਺ʹ͸࿈ଓ೾ܗ(CW)Λ૝ఆ͠ɺप೾ ਺Λεςοϓঢ়ʹ૟Ҿͤ͞Δɻεςοϓঢ়ʹ૟Ҿ͢Δͷ ͸ɺଌఆثͷಛੑΛߟྀͯ͠ͷ͜ͱͰ͋Γɺͦͷεςο ϓ෯ɺप೾਺౳ͷύϥϝʔλʹΑΓ୯ௐ૿Ճؔ਺ʹ͍ۙ ܗͰ૟Ҿͯ͠΋ྑ͍ɻΞϨΠͷm൪໨ͷૹ৴Ξϯςφ ͔Βૹ৴ͯ͠n൪໨ͷड৴ΞϯςφͰܭଌ͞Εͨℓ൪໨ ͷεςοϓप೾਺ fℓ Ͱͷड৴ڧ౓ΛPℓmn(fℓ, rmn)ͱ ͢Δɻ͜ͷͱ͖ɺλʔήοτ࠲ඪrpΛը૾ྖҬͰͷม ਺r(x, y, z)ʹஔ͖׵͑Δͱɺલ߲(7)ࣜͰݟͨΑ͏ʹɺ Ϩʔμલํͷి࣓քڧ౓ɺ͢ͳΘͪϨʔμը૾͸ Q0(r)= 1 LM N L ∑ ℓ=1 M ∑ m=1 N ∑ n=1 Pℓmn(fℓ, rmn) · exp {jkℓrmn(xp, yp, zp)} = 1 LM N L ∑ ℓ=1 M ∑ m=1 N ∑ n=1 Pℓmn(fℓ, rmn) · exp { j2πfℓ c rmn(xp, yp, zp) } · exp(jϕℓ) (9) ͰධՁͰ͖Δͱߟ͑ΒΕΔɻ͜͜ͰɺL, M, N ͸֤ʑૹ ৴Ξϯςφ਺ɺड৴Ξϯςφ਺ɺप೾਺εςοϓ਺Ͱ͋ Γɺ೾਺kℓ͸ޫ଎Λcͱͯ͠ɺkℓ= 2πfℓ/cΛ࢖͍ͬͯ ΔɻϨϯδํ޲ͷ෼ղೳ͕ଳҬ෯ʹґଘ͢Δ͜ͱ͸ɺલ ग़ͷpsfʹΑͬͯ༰қʹؔ܎͕ࣜ༠ಋͰ͖Δ͕ɺ͜͜Ͱ ͸ࢴ໘ͷ౎߹ͰׂѪ͢ΔɻPℓmn(fℓ, rmn)͸ड৴ΞϨΠ Ͱड৴͢ΔిྗͰ͋Γɺ(1)ࣜͷෳૉৼ෯an͸ΞϨΠΞ ϯςφརಘʹ૬౰͢Δɻ͜ͷड৴ిྗ͸ܭଌͷࡍʹඪ४ λʔήοτͷप೾਺ಛੑσ(fℓ)Ͱߍਖ਼͓ͯ͘͜͠ͱ͕๬ ·͍͠ɻ·ͨɺҐ૬ϕℓ ͸ଌఆγεςϜ͋Δ͍͸Ϩʔμ ܥͷ಺෦஗ԆྔͰ͋ΓɺϨʔμͷηοςΟϯά࣌ʹಋମ ٿͳͲͷඪ४ߍਖ਼λʔήοτͰ͜ͷྔΛิਖ਼͢Ε͹ྑ͍ɻ ্ࣜͷ࠲ඪؔ਺Λม਺r = (x, y, z)ͱͯ͠௚઀ඳը͢Ε ͹ɺର৅ྖҬͷը૾σʔλɺ͔͠΋໨తʹΑͬͯ͸3࣍ ݩը૾͕ಘΒΕΔ͜ͱʹͳΔɻ Ҏ্ͷΑ͏ʹAFFը૾͸ɺड৴ʑ߸ͱର৅ྖҬͷؔ࿈ ੑɺͭ·Γ݁ͼ͖ͭͷ౓߹͍ΛҐ૬ͷ੔߹ੑͱͯ͠දݱ ͨ͠΋ͷͱݟΔ͜ͱ͕Ͱ͖Δɻ͜Ε͸λʔήοτྖҬΛ ૸ࠪ͢Δr࠲ඪͱλʔήοτ࠲ඪrpͷࠩr− rp͕ඇৗ ʹখ͍͞஋ΛͱΔλʔήοτۙ๣ͰɺQ(rp)͸࠷΋ڧ͘ ͳΓۭؒεϖΫτϥϜͷϐʔΫΛఄ͢ΔɻAFΛ࢖ͬͨΞ ϯςφϏʔϜ૸ࠪͷදࣔࣜ(7)Λݟͯ΋෼͔ΔΑ͏ʹɺ ϐʔΫ஋͸ϏʔϜ૸ࠪํ޲(u0, v0)ʹͳ͍ͬͯΔɻ(9) ࣜ͸AFͱશ͘ಉ͡ߟ͑ʹج͍͍ͮͯΔɻҰํɺධՁࣜ Q(rp)͸ૹड৴ΞϨΠૉࢠͱप೾਺ͷपظؔ਺(ࢦ਺࿨) ͱͳ͍ͬͯΔɻैͬͯύϥϝʔλͷ৚݅ʹΑͬͯ͸ɺ͍ ΘΏΔۭؒతͳᐆດੑ(ambiguity)͕ൃੜ͢Δɻ͜Ε͸ AFཧ࿦Ͱݴ͏άϨʔςΟϯάϩʔϒ(grating-lobe)ɺ Fourierཧ࿦Ͱݴ͑͹ΤΠϦΞε(aliasing)ͷ͜ͱͰ ͋Γɺ࣮ࡍͷΞϨΠϨʔμͷઃܭ࣌ʹ͸͜ͷᐆດੑΛආ ͚ΔΑ͏ʹ஫ҙ͢Δඞཁ͕͋Δɻͳ͓ɺQ0(rp)ʹ࣮ଌ஋ Λ༻͍Δ৔߹͸͜ͷ··Ͱ΋ྑ͍͕ɺΑΓਖ਼֬ͳܭࢉγ ϛϡϨʔγϣϯʹ͸Ξϯςφͷࢦ޲ੑʹΑΔڧ౓มԽΛ ߟྀ͠ͳ͚Ε͹ͳΒͳ͍ɻ͜Ε͸ޙͷ߲Ͱߟ࡯͢Δ͜ͱ ʹ͠Α͏ɻ ୈ(9)ࣜ͸Ұ༷ͳۭؒ಺ʹλʔήοτ͕ݽཱͯ͠ஔ͔ Εͨͱ͖ͷදࣔࣜͰ͋Δɻ౔தͳͲͷຒઃ෺͋Δ͍͸น ಁաͳͲΛҙࣝ͢Δͱɺෳ਺ͷҟछഔ࣭ͷ༠ి཰ͷҧ͍ ʹґଘ͢Δܦ࿏ࠩΛߟྀ͢Δ͜ͱ΋ඞཁͱͳΔɻ͜Εʹ ؔͯ͠͸ɺ༠ి཰ਪఆ๏ʹབྷΊͯޙड़͍ͯ͠ΔɻL, M, N ͷ࣮ࡍతͳ਺஋͸λʔήοτ·Ͱͷڑ཭ɺΞϯςφִؒ ͱ૸ࠪ෯ɺϨϯδํ޲ͷ෼ղೳʹґଘ͢Δ͕ɺ3-7m ཭Ε ͨরࣹྖҬ্ͷۚଐମݕग़Ϩʔμʹ͓͍ͯɺप೾਺ൺଳ Ҭ͕໿20%ɺΞϯςφִؒ໿10cmɺΞϨΠ։ޱ௕2m ఔ ౓Ͱͷ࣮ଌྫ͕ใࠂ͞Ε͍ͯΔ[12]ɻ·ͨɺয఺Խը૾ ͷॲཧաఔ͔Β΋ਪଌͰ͖ΔΑ͏ʹɺ(9)ࣜ͸ฏ໘ΞϨ ΠͷFourierڃ਺ͷܗͱͳ͍ͬͯΔͷͰɺΫϩεϨϯδ ը૾෼ղೳ͸։ޱ௕ʹґଘ͢ΔϏʔϜ෯ͷ൒෼΄Ͳͱͳ Δ͜ͱ͕༧૝͞ΕΔɻ นಁա͋Δ͍͸ຒઃ෺ݕ஌༻ͷηϯαʔͰ͸ɺϨʔμ ͱλʔήοτؒʹෆཁͷো֐෺͕ଘࡏ͢Δɻ͜Ε͸ॴҦ Ϋϥολ(clutter)ͱݟ၏͢͜ͱ͕Ͱ͖Δɻଟ૚༠ిମ ૚ΛಁաนͷϞσϧͱ͢Δͱɺ൓ࣹͱಁա܎਺Λड৴ʑ ߸ʹऔΓೖΕͯͦͷଘࡏΛߟྀͰ͖ΔɻAFFʹΑΔϨʔ μը૾͸ɺͱΓΘ͚ۙڑ཭ʹ͓͍ͯ༗ӹͰ͋Δɻಁա܎ ਺ͷೖࣹ֯ґଘੑ͓Αͼप೾਺ґଘੑ͕ɺͲͷఔ౓ը૾ ͷ࣭ʹӨڹΛ༩͑Δ͔͸ॏཁͳ֬ೝࣄ߲Ͱ͋Γɺ͜Εʹ ͍ͭͯ͸ޙͷ߲Ͱٞ࿦͢Δɻશ࣮ͯଌͰݕ౼͢Δͱ࣌ؒ తίετ͸๲େͳ΋ͷͱͳΔͷͰɺγϛϡϨʔγϣϯϞσ ϧཱ͕֬Ͱ͖Ε͹ص্ݕ౼͕ՄೳͱͳΔɻ߹੒։ޱϨʔ μը૾SARͱͷൺֱɺ͋Δ͍͸λʔήοτΛ୯७ͳ2࣍ ݩͰϞσϦϯάͨ͠ͱ͖ͷزԿޫֶճંཧ࿦(GTD)͓Α ͼҰ༷઴ۙཧ࿦(UAT)ʹΑΔۙ๣քγϛϡϨʔγϣϯͳ Ͳ͕طʹஶऀ౳ʹΑͬͯใࠂ͞Ε͓ͯΓɺ͜ΕΛ߲࣍Ͱ ߟ࡯͢Δ[13-15]ɻ 5.UATͱPOཧ࿦ϞσϧͰͷಋମετϦοϓʹΑΔࢄཚ ͜͜Ͱ͸ɺૹड৴ΞϨΠϑΥʔΧγϯάʹΑΔϨʔμ ը૾ॲཧ(AFF)Λߟ࡯͢ΔͨΊɺಋମετϦοϓΛλʔ ήοτϞσϧͱͯ͠औΓ্͛ΔɻετϦοϓͱ͸2࣍ݩ ͷଳঢ়ͷബ͍ಋମฏ൘ͷ͜ͱͰ͋Γɺ͜ΕʹΑΔࢄཚք ͸෺ཧޫֶ๏(PO)ͳͲΛ༻͍ͯ༰қʹԕํք͕ٻΊΒ Εɺ݁Ռ͸೾਺ɺετϦοϓ෯͓Αͼ֯౓(u or v)ͷੵ ΛҾ਺ͱ͢Δsincؔ਺Ͱ༩͑ΒΕΔɻ͔͠͠ɺ͜͜Ͱͷ Ϩʔμߏ੒͸ಛʹۙ๣ྖҬΛҙ͍ࣝͯ͠ΔͷͰɺۙ๣ࢄཚ քͷܭࢉ͕Մೳͳද͕ࣔࣜϙΠϯτͱͳΔɻͦ͜ͰɺUAT ͳͲͷޫઢཧ࿦ʹΑͬͯۙ๣քΛධՁ͢Δ͜ͱʹ͢Δɻ ਤ4ʹࣔ͢Α͏ʹɺετϦοϓ͸ y ࣠ํ޲ʹҰ༷Ͱ (−a ≥ x ≥ a, y = 0)ʹஔ͔Ε͍ͯΔͱ͢Δɻઢ೾ݯr0 Λ දΘ͢ͷʹɺετϦοϓͷதԝ(ݪ఺)ɺ͓Αͼx < 0ͱ x > 0ʹ͋ΔೋͭͷΤοδ1,2Λத৺ʹ෉ʑۃ࠲ඪΛ༻ ͍ͯ(d, ϕ0), (d1, ϕ01), (d2, ϕ02)ͱ͢Δɻ؍ଌ఺΋ಉ༷ ਤ-4 ಋମετϦοϓʹΑΔճંɿ؍ଌ఺ͱ೾ݯ࠲ඪ

Fig.4 Diffraction of a line source by conducting strip: coordinates of observation and source.

ਤ-5 ಋମετϦοϓʹΑΔઢ೾ݯͷۙ๣ࢄཚ ք, ্:ిྲྀ೾ݯ E-ภ೾,Լ:࣓ྲྀ೾ݯ H-ภ೾

Fig.5 Scattering near-field of a line source by a conducting strip: upper:E-wave, lower: H-wave.

ʹ(ρ, ϕ), (ρ1, ϕ1), (ρ2, ϕ2)ͱද͢ɻಉਤͰ͸ɺӄӨڥ

ք(Shadow Boundary)ΛSBͱه͍ͯ͠Δɻ൒ฏ໘ʹΑ

Δి࣓քΛ

ਤ-6 ಋମετϦοϓʹର͢ΔUAT๏ͱPO๏ͷ ܭࢉൺֱ

Fig.6 AFF image by UAT and PO.

ͱ͢Δͱɺ͜Ε͕2ຕॏͳͬͨετϦοϓͰ͸ɺ ut(r) = uthp(ρ1, ϕ1) + uthp(ρ2, ϕ2)− uext(r), uext(r) = U ( cosϕ 2 ) ·[ui(ℓi)_{− u}r(ℓr)] (11) ͱͳΔɻ͜͜ͰɺU (_·)͸Heavisideͷεςοϓؔ਺Ͱ͋ Δɻ্ࣜʹΑΔۙ๣քܭࢉ݁ՌΛਤ5ʹࣔ͢ɻઢ೾ݯ͸ ݪ఺͔Βy = 10λ, x = 0ͷڑ཭ʹஔ͔Ε͓ͯΓɺݪ఺ʹஔ ͔Εͨ෯3λͷετϦοϓͷۙ๣Ͱͷి࣓քͰ͋Δ(λ: ೾௕)ɻಉਤͰ্ଆ͕E-೾(ిྲྀݯ)ɺԼଆ͕H-(࣓ྲྀݯ) ͷ৔߹Ͱ͋Γɺਤதͷx্࣠ʹॻ͔Ε͍ͯΔଠઢ͕ετ ϦοϓҐஔΛ͍ࣔͯ͠Δɻ֤ʑͷภ೾ͷڥք৚݅͸΄΅ ຬ଍͞Ε͍ͯΔ͜ͱ͕෼͔Δɻ ಋମετϦοϓ͸PO๏Ͱ΋ύλʔϯΛ༧ଌͰ͖Δɻ͠ ͔͠લड़ͷΑ͏ʹɺۙ๣ͰͷύλʔϯධՁʹ͸਺ֶతͳ ࠔ೉ੑ͕൐͏ɻ͜͜Ͱ͸ɺ্ࣜͰ༩͑ΒΕΔUATۙ๣ք ͱPOʹΑΔԕํքͰͷϞσϦϯάͰͲͷΑ͏ͳ͕ࠩੜ͡ Δ͔Λ֬ೝ͢ΔͨΊɺಉ͡ύϥϝʔλͷετϦοϓʹର ͢ΔܭࢉൺֱΛਤ6ʹࣔͯ͋͠Δɻେ͖ͳҧ͍͕ൃੜ͠ ͍ͯΔ͜ͱ͕ཧղͰ͖Δɻಉ͡Ϟσϧʹର͠ɺୈ(11)ࣜ ʹΑΔࢄཚքΛ(9)ࣜͷPℓmnͱͯ͠ɺQ(rp)ͷઈର஋ Λͦͷ··2࣍ݩ͓Αͼ3࣍ݩදࣔͨ͠΋ͷ͕ਤ7Ͱ͋ Δɻૉࢠִؒ1.6λͰ։ޱ௕16ૉࢠͷΞϯςφΞϨΠͷ தԝ͔Βڑ཭Rʹ഑ஔͨ͠෯2a = 4λ (= 30cm)ͷΞϯ ςφʹਖ਼ର(S = 0)ͨ͠ετϦοϓʹE-ภ೾ͷి೾Λ রࣹͨ͠৔߹Ͱ͋Γɺಉ(a)͸R = 68λɺ(b)͸137λ ͷҐஔ͔Βૹड৴͍ͯ͠ΔɻൺଳҬ෯͸34%Ͱ͋Δɻ͜ ͷγϛϡϨʔγϣϯߏ੒Ͱ͸1೾௕Ҏ্ͷૉࢠִؒͱ͠ (a) R = 68λ (b) R = 137λ ਤ-7 AFF 2,3࣍ݩը૾:ετϦοϓ෯ 2a = 4λ, E-ภ೾

Fig.7 AFF images:strip width 2a = 4λ, E-wave.

͍ͯΔͷͰɺAzํ޲ʹ͸άϨʔςΟϯάϩʔϒ͕ൃੜ͢ ΔɻಉਤͰ͸ɺͦͷը૾ͷൣғ಺ʹ͸ଘࡏ͍ͯ͠ͳ͍ɻ

ਤ-6 ಋମετϦοϓʹର͢ΔUAT๏ͱPO๏ͷ ܭࢉൺֱ

Fig.6 AFF image by UAT and PO.

ͱ͢Δͱɺ͜Ε͕2ຕॏͳͬͨετϦοϓͰ͸ɺ ut(r) = uthp(ρ1, ϕ1) + uthp(ρ2, ϕ2)− uext(r), uext(r) = U ( cosϕ 2 ) ·[ui(ℓi)_{− u}r(ℓr)] (11) ͱͳΔɻ͜͜ͰɺU (_·)͸Heavisideͷεςοϓؔ਺Ͱ͋ Δɻ্ࣜʹΑΔۙ๣քܭࢉ݁ՌΛਤ5ʹࣔ͢ɻઢ೾ݯ͸ ݪ఺͔Βy = 10λ, x = 0ͷڑ཭ʹஔ͔Ε͓ͯΓɺݪ఺ʹஔ ͔Εͨ෯3λͷετϦοϓͷۙ๣Ͱͷి࣓քͰ͋Δ(λ: ೾௕)ɻಉਤͰ্ଆ͕E-೾(ిྲྀݯ)ɺԼଆ͕H-(࣓ྲྀݯ) ͷ৔߹Ͱ͋Γɺਤதͷx্࣠ʹॻ͔Ε͍ͯΔଠઢ͕ετ ϦοϓҐஔΛ͍ࣔͯ͠Δɻ֤ʑͷภ೾ͷڥք৚݅͸΄΅ ຬ଍͞Ε͍ͯΔ͜ͱ͕෼͔Δɻ ಋମετϦοϓ͸PO๏Ͱ΋ύλʔϯΛ༧ଌͰ͖Δɻ͠ ͔͠લड़ͷΑ͏ʹɺۙ๣ͰͷύλʔϯධՁʹ͸਺ֶతͳ ࠔ೉ੑ͕൐͏ɻ͜͜Ͱ͸ɺ্ࣜͰ༩͑ΒΕΔUATۙ๣ք ͱPOʹΑΔԕํքͰͷϞσϦϯάͰͲͷΑ͏ͳ͕ࠩੜ͡ Δ͔Λ֬ೝ͢ΔͨΊɺಉ͡ύϥϝʔλͷετϦοϓʹର ͢ΔܭࢉൺֱΛਤ6ʹࣔͯ͋͠Δɻେ͖ͳҧ͍͕ൃੜ͠ ͍ͯΔ͜ͱ͕ཧղͰ͖Δɻಉ͡Ϟσϧʹର͠ɺୈ(11)ࣜ ʹΑΔࢄཚքΛ(9)ࣜͷPℓmnͱͯ͠ɺQ(rp)ͷઈର஋ Λͦͷ··2࣍ݩ͓Αͼ3࣍ݩදࣔͨ͠΋ͷ͕ਤ7Ͱ͋ Δɻૉࢠִؒ1.6λͰ։ޱ௕16ૉࢠͷΞϯςφΞϨΠͷ தԝ͔Βڑ཭Rʹ഑ஔͨ͠෯2a = 4λ (= 30cm)ͷΞϯ ςφʹਖ਼ର(S = 0)ͨ͠ετϦοϓʹE-ภ೾ͷి೾Λ রࣹͨ͠৔߹Ͱ͋Γɺಉ(a)͸R = 68λɺ(b)͸137λ ͷҐஔ͔Βૹड৴͍ͯ͠ΔɻൺଳҬ෯͸34%Ͱ͋Δɻ͜ ͷγϛϡϨʔγϣϯߏ੒Ͱ͸1೾௕Ҏ্ͷૉࢠִؒͱ͠ (a) R = 68λ (b) R = 137λ ਤ-7 AFF 2,3࣍ݩը૾:ετϦοϓ෯ 2a = 4λ, E-ภ೾

Fig.7 AFF images:strip width 2a = 4λ, E-wave.

͍ͯΔͷͰɺAzํ޲ʹ͸άϨʔςΟϯάϩʔϒ͕ൃੜ͢ ΔɻಉਤͰ͸ɺͦͷը૾ͷൣғ಺ʹ͸ଘࡏ͍ͯ͠ͳ͍ɻ (a) S = 0 (b) S = 13.7λ ਤ-8 AFF 2,3 ࣍ݩը૾: ετϦοϓ෯ 2a = 4λ, R = 68λ, H-ภ೾

Fig.8 AFF images:strip width 2a = 4λ, R = 68λ, H-wave. ಋମετϦοϓͷཧ࿦ࣜ͸2࣍ݩϞσϧͰ͋Δɻैͬ ͯɺετϦοϓͷॎํ޲ͷมԽ͸ແࢹ͢Δ͜ͱʹͳΔ͕ɺ ετϦοϓͷ෯(ԣ)ํ޲ʹΞϯςφΛ1࣍ݩ૸ࠪͯ͠ ͍ΔͷͰɺ͜ͷӨڹ͸ۇগͱࢥΘΕΔɻͭ·Γɺ࣮ଌͷ ࡍʹ͸ՄೳͳݶΓετϦοϓͷॎํ޲ͷ௕͕͞େ͖͍ۚ ଐฏ൘Λ࠾༻͢Δ͜ͱ͕ϙΠϯτͱͳΔɻ ਤ8͸ετϦοϓ෯2a = 4λͰH-ภ೾ɺڑ཭R = 68λ ͷ৔߹Ͱ͋Δɻಉ(a)͸ਤ7ͱಉ͡։ޱ௕Λ΋ͭΞϨΠ ͱετϦοϓ͕ਖ਼ର͍ͯ͠Δ ͱ͖ɺ(b)͸ΞϨΠͱετ Ϧοϓͷத৺͕֤ʑS = 13.7λ͚ͩAzํ޲ʹΦϑηο τ͍ͯ͠Δͱ͖ͷ2, 3࣍ݩϓϩοτͰ͋Δɻಉ(b)ਤ ͸(a)ͷ࠷େ஋ʹର͢Δ૬ର஋Ͱϓϩοτ͓ͯ͠Γɺࣼ Ίํ޲ʹΦϑηοτͨ͠෼͚ͩϨϕϧ͕௿ݮ͍ͯ͠Δɻ ಉਤΑΓετϦοϓͷΤοδʹΑΔճં೾ͷӨڹ͕ಡΈ औΕΔɻͳ͓ɺ7,8͸ୈ(9)ࣜͷQ0(rp)Λͦͷ··ϓ ϩοτ͍ͯ͠ΔͷͰɺૉࢠΞϯςφͷࢦ޲ੑ͸౳ํੑͷ ··Ͱ͋Δɻ Ҏ্ɺAFΛԠ༻ͨ͠Ұछͷ߹੒։ޱॲཧ๏AFFʹ͍ͭ ͯٞ࿦ͨ͠ɻϞσϧͱͯ͠ετϦοϓͷۙ๣քΛ࢖ͬͯ γϛϡϨʔγϣϯΛߦ͕ͬͨɺ͜Ε͸Ϩʔμͷઃܭɺλʔ ήοτΛؚΉγϛϡϨʔγϣϯͳͲʹର͢Δࣄલݕ౼ͱ ͯ͠௚઀Ԡ༻Ͱ͖ΔͷͰɺͦͷҙٛ͸େ͖͍ɻ3࣍ݩλʔ ήοτͷۙ๣քܭࢉ͕Ͱ͖Δͱɺภ೾ղੳ͋Δ͍͸Ϋϩ εϨϯδํ޲ͷը૾ॲཧ΋ղੳՄೳͱͳΔɻ ࠷ޙʹલ߲ͱಉ͡ϞσϧΛ࢖ͬͯɺAFFͱSAR ʹΑ ΔϨʔμը૾Λൺֱ͢Δɻਤ9 ͸Ξϯςφ։ޱͱλʔ ήοτ(ετϦοϓதԝ) ؒͷڑ཭R Λύϥϝʔλͱ ͯ͠ཧ࿦ܭࢉͨ݁͠ՌͰ͋Δɻಉਤʹࣔ͢Α͏ʹɺR = 0.3 (0.4λ), 1.0, 2.0, 5.0, 10.0, 20.0 [m]ͱมԽ͍ͤͯ͞ Δɻ͜ͷ৔߹ɺR = 0.3 [m]͸ۙ๣քྖҬɺR = 2 [m]Ҏ ԕ͸ԕํքྖҬʹଐ͢Δɻۙ๣ྖҬͰͷSARը૾͸AFF ʹൺ΂ͯ΍΍ը૾ͷ࣭͕ྼԽ͍ͯ͠ΔɻSARը૾͸جຊ తʹૹड৴఺͕ಉۭؒ͡ʹҐஔ͢ΔϞϊελςοΫܕͰ ͋ΓɺҰํɺAFF͸ૹड৴఺͕ҟͳΔҐஔͰಈ࡞͢ΔόΠ ελςοΫ(MIMO)Ͱ͋Δɻ͜ͷͨΊɺۙڑ཭ͰͷϑΥʔ Χγϯά͸AFFͷํ͕༏Ε͍ͯΔɻ͔͠͠ɺಉਤͰ΋෼ ͔ΔΑ͏ʹɺԕํྖҬͰ͸SARͷํ͕ը૾ͷ࣭͕ྑ͍͜ ͱ͕ಡΈऔΕΔɻ͜ͷཧ࿦తͳൺֱݕ౼͸ࠓޙߦ͏͜ͱ ʹ͍ͨ͠ɻ 6. 2໘ίʔφʔϦϑϨΫλͷཧ࿦ܭࢉͱ࣮ଌʹΑΔϨʔ μը૾ɹ ͜͜Ͱ͸ਤ10ʹࣔ͢Α͏ͳ2ຕͷฏ൘Λ௚ަͤͨ͞2 ໘ίʔφʔϦϑϨΫλʹΑΔAFFը૾ʹ͍ͭͯٞ࿦͢Δɻ ͜ͷࢄཚମͷϞσϧ͸લ߲ͷετϦοϓΛ2ݸ૊Έ߹Θ

ਤ-9 UATʹΑΔετϦοϓϞσϧͷAFFͱSARը૾ͷཧ࿦ܭࢉ

Fig.9 AFF and SAR images by UAT strip model.

ͤͨ΋ͷͰ͋ΓɺετϦοϓಉ༷2࣍ݩ෺ମͱͯ͠ѻ͏ ͜ͱ͕Ͱ͖Δɻ1ճ͋Δ͍͸2ճͷ൓ࣹ͸ɺ൓ࣹ఺͕ӄ Өڥքͷ֎ଆʹ͋Δͷ͔಺ଆʹ͋Δͷ͔ʹґଘ͢Δɻਤ 11͸ σ2D(ρ) = 2πρ E(ρ)_{· E}∗_(ρ) E(0)· E∗₍₀₎ (12) Ͱ ఆ ٛ ͞ Ε Δ ۙ ๣ Ͱ ͷ 2 ࣍ ݩ Ϩ ʔ μ அ ໘ ੵ (Radar Cross-Section:RCS)Λܭࢉͨ͠E-ภ೾ͷ݁ՌͰ͋Δɻ ௨ৗͷRCS͸ρ_{→ ∞}ͷԕํͰධՁ͞ΕΔɻܭࢉ͓Αͼ ࣮ݧʹ༻͍ͨฏ൘ͷҰลͷ௕͞͸5λͰ͋Γɺઢ೾ݯ͓ Αͼ؍ଌ఺ͱ௖఺ؒڑ཭Λ֤ʑd, ρͱͯ͠ಉਤʹهࡌ ͍ͯ͠Δɻਤதʹ͋Δه߸ͰA→ B → CͱͳΔʹै͍ ి࣓քͷ૬൓ఆཧ͕ݟΒΕɺ؍ଌ఺ρ͕ԕํͱͳΔʹै ͍ύλʔϯͷมԽ͸࠷খͱͳΔ͜ͱ͕෼͔Δ(ਤதه߸ D)ɻͳ͓ɺUATʹΑΔ͜ͷܭࢉ݁Ռ͸ݫີղͱൺֱ͠਺ ஋্΄΅ಉ݁͡Ռͱͳ͍ͬͯΔ͜ͱΛ֬ೝ͍ͯ͠Δɻ ਤ12͸ਤ11ͱಉ͡ύϥϝʔλͷ2໘ίʔφʔϦϑϨ ΫλΛλʔήοτͱ࣮ͯ͠ଌͨ͠৔߹ͷAFFʹΑΔϨʔ μը૾Ͱ͋Δɻಉਤࠨ͸ཧ࿦ܭࢉը૾ɺӈ͸࣮ଌը૾Ͱ ͋Γɺภ೾͸E-ภ೾Ͱ͋ΔɻUATʹΑΔۙ๣քϞσϧΛ ࢖͍ͬͯΔͷͰɺೋͭͷedgeʹΑΔճં೾ͷঢ়گ͕ԿΕ ਤ-10 2໘ίʔφʔϦϑϨΫλͷUATʹΑΔϞ σϦϯά

Fig.10 UAT model for 2-face corner-reflector.

ͷը૾͔Β΋ಡΈऔΕΔɻͳ͓ɺ࣮ଌ஋ʹΑΔը૾Ͱ͸ɺ Azํ޲ʹத৺Ґஔ͕ͣΕ͍ͯΔ͕Ξϯςφ։ޱͱλʔ ήοτͷத৺͕Φϑηοτ͍ͯ͠ΔͨΊͰ͋Δɻ 7.ΞϯςφϏʔϜΛߟྀͨ͠ͱ͖ͷը૾ධՁ ࠓ·Ͱͷཧ࿦ը૾ͷܭࢉʹ͸ΞϯςφύλʔϯΛແࢦ ޲ੑͱͯ͠ѻ͍ͬͯͨɻ͔࣮͠͠ࡍͷΞϯςφ͸ϏʔϜ ࢦ޲ੑ͕ଘࡏ͠ɺλʔήοτۭؒʹরࣹͨ͠ͱ͖ɺ͋Δ ͍͸λʔήοτ͔Βͷࢄཚ೾Λड৴͢Δͱ͖ʹɺϏʔϜ ʹΑΔॏΈ͕ൃੜ͢ΔɻAFF๏Ͱ͸όΠελςοΫͰΞ

ਤ-9 UATʹΑΔετϦοϓϞσϧͷAFFͱSARը૾ͷཧ࿦ܭࢉ

Fig.9 AFF and SAR images by UAT strip model.

ͤͨ΋ͷͰ͋ΓɺετϦοϓಉ༷2࣍ݩ෺ମͱͯ͠ѻ͏ ͜ͱ͕Ͱ͖Δɻ1ճ͋Δ͍͸2ճͷ൓ࣹ͸ɺ൓ࣹ఺͕ӄ Өڥքͷ֎ଆʹ͋Δͷ͔಺ଆʹ͋Δͷ͔ʹґଘ͢Δɻਤ 11͸ σ2D(ρ) = 2πρ E(ρ)_{· E}∗_(ρ) E(0)· E∗₍₀₎ (12) Ͱ ఆ ٛ ͞ Ε Δ ۙ ๣ Ͱ ͷ 2 ࣍ ݩ Ϩ ʔ μ அ ໘ ੵ (Radar Cross-Section:RCS)Λܭࢉͨ͠E-ภ೾ͷ݁ՌͰ͋Δɻ ௨ৗͷRCS͸ρ_{→ ∞}ͷԕํͰධՁ͞ΕΔɻܭࢉ͓Αͼ ࣮ݧʹ༻͍ͨฏ൘ͷҰลͷ௕͞͸5λͰ͋Γɺઢ೾ݯ͓ Αͼ؍ଌ఺ͱ௖఺ؒڑ཭Λ֤ʑd, ρͱͯ͠ಉਤʹهࡌ ͍ͯ͠Δɻਤதʹ͋Δه߸ͰA→ B → CͱͳΔʹै͍ ి࣓քͷ૬൓ఆཧ͕ݟΒΕɺ؍ଌ఺ρ͕ԕํͱͳΔʹै ͍ύλʔϯͷมԽ͸࠷খͱͳΔ͜ͱ͕෼͔Δ(ਤதه߸ D)ɻͳ͓ɺUATʹΑΔ͜ͷܭࢉ݁Ռ͸ݫີղͱൺֱ͠਺ ஋্΄΅ಉ݁͡Ռͱͳ͍ͬͯΔ͜ͱΛ֬ೝ͍ͯ͠Δɻ ਤ12͸ਤ11ͱಉ͡ύϥϝʔλͷ2໘ίʔφʔϦϑϨ ΫλΛλʔήοτͱ࣮ͯ͠ଌͨ͠৔߹ͷAFFʹΑΔϨʔ μը૾Ͱ͋Δɻಉਤࠨ͸ཧ࿦ܭࢉը૾ɺӈ͸࣮ଌը૾Ͱ ͋Γɺภ೾͸E-ภ೾Ͱ͋ΔɻUATʹΑΔۙ๣քϞσϧΛ ࢖͍ͬͯΔͷͰɺೋͭͷedgeʹΑΔճં೾ͷঢ়گ͕ԿΕ ਤ-10 2໘ίʔφʔϦϑϨΫλͷUATʹΑΔϞ σϦϯά

Fig.10 UAT model for 2-face corner-reflector.

ͷը૾͔Β΋ಡΈऔΕΔɻͳ͓ɺ࣮ଌ஋ʹΑΔը૾Ͱ͸ɺ Azํ޲ʹத৺Ґஔ͕ͣΕ͍ͯΔ͕Ξϯςφ։ޱͱλʔ ήοτͷத৺͕Φϑηοτ͍ͯ͠ΔͨΊͰ͋Δɻ 7.ΞϯςφϏʔϜΛߟྀͨ͠ͱ͖ͷը૾ධՁ ࠓ·Ͱͷཧ࿦ը૾ͷܭࢉʹ͸ΞϯςφύλʔϯΛແࢦ ޲ੑͱͯ͠ѻ͍ͬͯͨɻ͔࣮͠͠ࡍͷΞϯςφ͸ϏʔϜ ࢦ޲ੑ͕ଘࡏ͠ɺλʔήοτۭؒʹরࣹͨ͠ͱ͖ɺ͋Δ ͍͸λʔήοτ͔Βͷࢄཚ೾Λड৴͢Δͱ͖ʹɺϏʔϜ ʹΑΔॏΈ͕ൃੜ͢ΔɻAFF๏Ͱ͸όΠελςοΫͰΞ ਤ-11 2໘ίʔφʔϦϑϨΫλͷۙ๣όΠελςΟοΫRCSܭࢉύλʔϯ

Fig.11 Near-field patterns for 2-face corner-reflector.

ਤ-12 2໘ίʔφʔϦϑϨΫλͷUATʹΑΔϞ

σϦϯάͱ࣮ଌ

Fig.12 UAT theory and measurement for 2-face cor-ner reflector. ϨΠ։ޱ্ͰͷฏۉԽ͕ਤΕΔͱࢥΘΕΔ͕ɺएׯͷӨ ڹ͸ੜ͡Δͱ༧૝͍ͯ͠Δɻ·ͨ౰વͳ͕ΒɺΞϯςφ རಘͷप೾਺ಛੑ΋ಛʹϨϯδํ޲Ͱͷը૾ͷۉҰੑʹ ӨڹΛ༩͑ΔͷͰɺ͜ͷಛੑ΋೺Ѳͭͭ͠ը૾࠶ੜͷࡍ ʹิঈ͓ͯ͘͠ඞཁ͕͋Δɻ ૹड৴ΞϯςφͷۭؒύλʔϯಛੑΛؚΜͩΞϯςφ རಘΛ֤ʑGt ℓmn(fℓ, rmn), Grℓmn(fℓ, rmn)ͱ͢Δͱɺઌ ͷ(9)ࣜ͸࣍ͷΑ͏ʹमਖ਼͞ΕΔɻ Q1(r) = Gtℓmn(fℓ, rmn)· Grℓmn(fℓ, rmn)· Q0(r). (13) Ξϯςφࢦ޲ੑύλʔϯ͸λʔήοτ͔Βͷࢄཚిྗʹ ॏΈͷΑ͏ʹ࡞༻͢ΔͷͰɺಛʹۙ๣ྖҬͰ͸ແࢹͰ͖ ͳ͍ิਖ਼ͱͳΔ͜ͱ͕༧૝͞ΕΔɻ ࣮ଌͰ༻͍ͨΞϯςφͷܭࢉύλʔϯʹؔ͠ɺਤ13ʹ ͦͷॾݩΛࣔ͢ɻܭࢉ͸จݙ[14]ʹৄड़͞Ε͍ͯΔ։ ޱ෼෍๏ʹΑΔ݁ՌͰ͋Γɺ࣮ଌ஋ͱྑ͘Ұக͍ͯ͠Δ ͜ͱ͕෼͔Δɻ͜ͷܭࢉύλʔϯΛAFFը૾ʹద༻ͨ͠

ਤ-13 ࣮ଌʹ࢖༻ۣͨ͠ܗϗʔϯΞϯςφͷཧ࿦ͱ࣮ଌύλʔϯ

Fig.13 Theoretical and measurement patterns of horn antenna for AFF measurement.

ਤ-14 ϨʔμAFFը૾ʹର͢ΔΞϯςφϏʔϜͷӨڹ

Fig.14 Antenna beam effect to AFF radar imaging.

݁Ռ͕ਤ14Ͱ͋Δɻλʔήοτ͸෯30[cm]ͷಋମετ ϦοϓͰ͋Γɺಉਤࠨ͕ਤ13ͷΞϯςφϏʔϜΛߟྀ͠ ͨAFFը૾Ͱ͋Δɻߟྀ͠ͳ͍৔߹ͱͷ͕ࠩ͋·Γେ͖ ͘ͳ͍ͷͰɺਤ14ͷதԝͱӈʹ֤ʑAzํ޲ͱRangeํ ޲ͷஅ໘ͰͷࠩΛࣔ͢ɻಉਤͰ͸େ͖ͳҧ͍͸ݟΒΕͳ ͍͕ɺΞϨΠ։ޱ௕͕λʔήοτ௕ʹൺ΂ͯେ͖͍৔߹ɺ ͋Δ͍͸ΞϨΠͱλʔήοτؒڑ཭͕ൺֱత୹͍৔߹ʹ ͸ݦஶͳ͕ࠩൃੜͯ͘͠Δͱ༧૝͍ͯ͠Δɻܭࢉγϛϡ ϨʔγϣϯͰ͸ಉจݙͷཧ࿦ࣜΛ௚઀࢖Θͣʹɺਖ਼ݭ೾ ͔GaussϏʔϜͰۙࣅ͢Δͷ΋ܭࢉίετΛߟྀͨ͠ํ ๏Ͱ͋Δɻ ͳ͓ɺ্هΞϯςφϏʔϜิਖ਼͸਺஋ܭࢉ্Ͱͷ࿩Ͱ ͋Γɺ࣮ࡍͷܭଌͰ͸طʹ࣮૷͞ΕͨΞϯςφͷϏʔϜ ͷॏΈ͕ड৴σʔλʹؚ·Ε͍ͯΔͷͰɺߟྀ͢Δඞཁ ͸ͳ͍ɻ 8.นಁաϨʔμͱͯ͠ͷAFFཧ࿦ นಁա͋Δ͍͸ຒઃ෺ݕ஌༻ͷηϯαͰ͸ɺϨʔμͱ λʔήοτؒʹෆཁͷো֐෺͕ଘࡏ͢Δɻ͜Ε͸ॴҦΫ ϥολͱͯ͠ݟ၏͢͜ͱ΋Ͱ͖Δɻஶऀ͕طʹൃදͯ͠ ͍Δଟ૚༠ిମ૚ΛಁաนͷϞσϧͱ͢Δͱɺ൓ࣹͱಁ ա܎਺Λड৴ʑ߸ʹऔΓೖΕΔ͜ͱ͕Ͱ͖ɺͦͷଘࡏΛ ධՁͰ͖Δ[14,16] ɻAFFʹΑΔϨʔμը૾͸ۙڑ཭ʹ ͓͍ͯ༗ӹͰ͋Δ͜ͱ͸લ߲·ͰͰ֬ೝ͍ͯ͠Δɻैͬ ͯɺಁա܎਺ͷೖࣹ֯ґଘੑ͓Αͼप೾਺ґଘੑ͕Ͳͷ ఔ౓ը૾ͷ࣭ʹӨڹΛ༩͑Δ͔͸ɺॏཁͳ֬ೝࣄ߲Ͱ͋ Δɻશ࣮ͯଌͰݕ౼͢Δͱ࣌ؒతίετ͸๲େͳ΋ͷͱ

ਤ-13 ࣮ଌʹ࢖༻ۣͨ͠ܗϗʔϯΞϯςφͷཧ࿦ͱ࣮ଌύλʔϯ

Fig.13 Theoretical and measurement patterns of horn antenna for AFF measurement.

ਤ-14 ϨʔμAFFը૾ʹର͢ΔΞϯςφϏʔϜͷӨڹ

Fig.14 Antenna beam effect to AFF radar imaging.

݁Ռ͕ਤ14Ͱ͋Δɻλʔήοτ͸෯30[cm]ͷಋମετ ϦοϓͰ͋Γɺಉਤࠨ͕ਤ13ͷΞϯςφϏʔϜΛߟྀ͠ ͨAFFը૾Ͱ͋Δɻߟྀ͠ͳ͍৔߹ͱͷ͕ࠩ͋·Γେ͖ ͘ͳ͍ͷͰɺਤ14ͷதԝͱӈʹ֤ʑAzํ޲ͱRangeํ ޲ͷஅ໘ͰͷࠩΛࣔ͢ɻಉਤͰ͸େ͖ͳҧ͍͸ݟΒΕͳ ͍͕ɺΞϨΠ։ޱ௕͕λʔήοτ௕ʹൺ΂ͯେ͖͍৔߹ɺ ͋Δ͍͸ΞϨΠͱλʔήοτؒڑ཭͕ൺֱత୹͍৔߹ʹ ͸ݦஶͳ͕ࠩൃੜͯ͘͠Δͱ༧૝͍ͯ͠Δɻܭࢉγϛϡ ϨʔγϣϯͰ͸ಉจݙͷཧ࿦ࣜΛ௚઀࢖Θͣʹɺਖ਼ݭ೾ ͔GaussϏʔϜͰۙࣅ͢Δͷ΋ܭࢉίετΛߟྀͨ͠ํ ๏Ͱ͋Δɻ ͳ͓ɺ্هΞϯςφϏʔϜิਖ਼͸਺஋ܭࢉ্Ͱͷ࿩Ͱ ͋Γɺ࣮ࡍͷܭଌͰ͸طʹ࣮૷͞ΕͨΞϯςφͷϏʔϜ ͷॏΈ͕ड৴σʔλʹؚ·Ε͍ͯΔͷͰɺߟྀ͢Δඞཁ ͸ͳ͍ɻ 8.นಁաϨʔμͱͯ͠ͷAFFཧ࿦ นಁա͋Δ͍͸ຒઃ෺ݕ஌༻ͷηϯαͰ͸ɺϨʔμͱ λʔήοτؒʹෆཁͷো֐෺͕ଘࡏ͢Δɻ͜Ε͸ॴҦΫ ϥολͱͯ͠ݟ၏͢͜ͱ΋Ͱ͖Δɻஶऀ͕طʹൃදͯ͠ ͍Δଟ૚༠ిମ૚ΛಁաนͷϞσϧͱ͢Δͱɺ൓ࣹͱಁ ա܎਺Λड৴ʑ߸ʹऔΓೖΕΔ͜ͱ͕Ͱ͖ɺͦͷଘࡏΛ ධՁͰ͖Δ[14,16] ɻAFFʹΑΔϨʔμը૾͸ۙڑ཭ʹ ͓͍ͯ༗ӹͰ͋Δ͜ͱ͸લ߲·ͰͰ֬ೝ͍ͯ͠Δɻैͬ ͯɺಁա܎਺ͷೖࣹ֯ґଘੑ͓Αͼप೾਺ґଘੑ͕Ͳͷ ఔ౓ը૾ͷ࣭ʹӨڹΛ༩͑Δ͔͸ɺॏཁͳ֬ೝࣄ߲Ͱ͋ Δɻશ࣮ͯଌͰݕ౼͢Δͱ࣌ؒతίετ͸๲େͳ΋ͷͱ ͳΔͷͰɺ͜͜Ͱఏࣔ͢ΔΑ͏ʹγϛϡϨʔγϣϯϞσ ϧཱ͕֬Ͱ͖Ε͹ص্ݕ౼͕ՄೳͱͳΓɺ͜ͷ෼໺ͷݚ ڀଅਐʹد༩Ͱ͖Δɻ ࠓɺนΛଟ૚ͷ༠ిମฏ൘ͱͯ͠ѻ͏ͱɺ೾ಈ͸͜ΕΒ ͷ಺෦Ͱଟॏͷ൓ࣹͱಁաͷޙɺ೾ಈͷਐߦํ޲ʹ͸࠷ ऴͷಁա܎਺Λ൐ͬͯλʔήοτʹ఻ൖ͢ΔɻҰํɺΞ ϨΠͷૹड৴఺͸ਵ࣌มΘΔͷͰɺ͜ͷଟ૚ฏ൘΁ͷೖ ࣹ֯͸ݻఆ͞Ε͍ͯͳ͍ɻ͜ͷͱ͖ɺҰͭ໰୊ʹͳΔͷ ͕༠ిମ಺Ͱͷ೾ಈͷ஗ԆྔͰ͋Δɻλʔήοτͱਖ਼ର ͍ͯ͠Δͱ͖Λج४ͱ͢ΔͱɺͦΕҎ֎ͷೖࣹ֯ΛҎͯ ೖࣹ͢Δ೾ಈ͸ৗʹ஗Ԇ͍ͯ͠Δɻۙ๣ྖҬͰͷϨʔμ ηϯαͰ͸ɺ͜ͷ஗Ԇྔ͸͔ͳΓେ͖͘ͳΔ৔߹΋͋Δ ͱ༧૝͞ΕΔɻಛʹɺΞϨΠ։ޱ௕͕λʔήοτؒڑ཭ ΑΓେ͖͘ɺೖࣹ͕֯਺े౓Λ௒͑Δ৔߹ͷ஗Ԇྔ͸ڑ ཭ʹ׵ࢉͯ͠ηϯνϝʔτϧͷΦʔμʔͱͳΔɻຊ߲Ͱ ͸ɺଟ૚ͷ༠ిମฏ൘ʹΑΔҐ૬஗ԆΛܭࢉ͢Δ؆୯ͳ දࣔࣜΛSnellͷ๏ଇΛ༻͍ͯ༠ಋ͓ͯ͘͠ɻ લड़ͷҐ૬஗Ԇྔ͸ܦ࿏௕ʹஔ͖͔͑ͯߟ͑Δͱ෼ ͔Γқ͍ɻ༠ి཰ͱಁ࣓཰ͷҟͳΔഔ࣭ͷڥքͰ͸ɺ

Snellͷ๏ଇk1sin θ1= k2sin θ2͕੒ཱ͢Δɻk1, k2͸

֤ʑͷഔ࣭தͰͷ೾਺Ͱ͋Γɺഔ࣭ߏ੒ఆ਺(ε, µ)ͱ͸

k = ω√εµ (ω = 2πf, f : प೾਺εϖΫτϥϜ)ͷؔ܎͕

͋Δɻ༠ిମฏ൘͕_N ૚͋Δ৔߹ɺ֤༠ిମΛஞ࣍࿈ଓ ͤ͞Δ͜ͱʹΑΓ

k1sin θ1= k2sin θ2=· · · = kisin θi=· · ·

= k_Nsin θ_N, i = 1, 2,_{· · · , N} (14) ͳΔؔ܎͕ࣜಘΒΕΔɻॳظ஋ͱͳΔೖࣹ֯θ1͕༩͑Β ΕΕ͹ɺi൪໨ͷ૚ͷೖࣹ֯͸༰қʹܭࢉͰ͖Δɻࠓɺ֤ ૚ͷްΈΛziͱ͢ΔͱɺN ૚શ෦Λ఻ൖ͢Δಁա೾ͷޫ ֶతͳܦ࿏௕D͸ࡾฏํͷఆཧΑΓ༰қʹ࣍ࣜͰ༩͑Β ΕΔɻ D = N ∑ i=1 kizi·(ki2− k12sin2θ1)−1/2. (15) Ξϯςφͷ࠲ඪɺͭ·Γ೾ݯͷҐஔ(x0, y0, z0)ͱ࠷ऴͷ ಁաͱͳΔ؍ଌ఺࠲ඪ(x, y, z)͸্ࣜͷؔ܎Λຬͨ͞ͳ ͚Ε͹ͳΒͳ͍ɻ͜ΕΑΓɺೖࣹ֯ɺ೾ݯ࠲ඪͦͯ͠؍ ଌ఺࠲ඪ͸͜ͷ2͕ܾͭ·Ε͹࢒Γͷ1ͭ͸ࣗಈతʹٻ ΊΕΔɻ͜ͷؔ܎ΛಈతʹҠಈ͢Δૹड৴Ξϯςφͦ͠ ͯλʔήοτؒͷܦ࿏௕ิਖ਼ʹద༻ͯ͠ɺ༠ిମ಺ͷ఻ ൖ೾ಈͷޫֶܦ࿏௕Λิਖ਼͢Ε͹Α͍ɻো֐෺͕ଘࡏ͠ ͍ͯΔͨΊʹ༨෼ʹൃੜ͍ͯ͠Δ૯ܦ࿏௕(15)ࣜΛߟ ྀ͢Δͱɺ݁ہɺઌͷ(13)ࣜ͸ Q(r) = Tt ℓmn(fℓ, rmn) exp{jkDt(rtm, r,N ) } ·Tℓmnr (fℓ, rmn) exp{jkDr(rrn, r,N )} · Q1(r) = 1 LM N L ∑ ℓ=1 M ∑ m=1 N ∑ n=1 ·Tt ℓmn(fℓ, rmn) exp{jkD(rtm, r,N ) } ·Tr ℓmn(fℓ, rmn) exp{jkD(rrn, r,N )} ·Gt ℓmn(fℓ, rmn)· Grℓmn(fℓ, rmn)· Pℓmn(fℓ, rmn) · exp { j2πfℓ c rmn(xp, yp, zp) } · exp(jϕℓ) (16) ͷ Α ͏ ʹ म ਖ਼ Ͱ ͖ Δ ɻ͜ ͜ Ͱ ɺDt_(r m, r,N ) ͱ Dr_(r n, r,N )͸֤ʑૹ৴ଆͱλʔήοτଆ͔Βೖࣹ͠ ͨͱ͖ͷ_N ૚ͷ༠ిମนʹΑΔૠೖܦ࿏௕Λද͓ͯ͠ ΓɺTt ℓmn(fℓ, rmn), Tℓmnr (fℓ, rmn)͸จݙ[17] Ͱݫີʹ ఆࣜԽ͍ͯ͠Δ_N ૚༠ిମʹΑΔಁա܎਺Ͱ͋Γɺ֤ʑ ૹ৴ଆ͔Βೖࣹͨ͠ͱ͖ͱλʔήοτଆ͔Βೖࣹͨ͠ͱ ͖ͷ܎਺Ͱ͋Δɻ·ͨɺGt ℓmn(fℓ, rmn), Grℓmn(fℓ, rmn) ͸֤ʑૹ৴ͱड৴Ξϯςφͷۭؒύλʔϯ(རಘ)ಛੑͰ ͋Γɺ͜Ε͕λʔήοτ͔ΒͷࢄཚిྗʹॏΈͷΑ͏ʹ ࡞༻͢ΔͷͰɺಛʹۙ๣ྖҬͰ͸ແࢹͰ͖ͳ͍ิਖ਼ͱͳ Δ͜ͱ͕༧૝Ͱ͖Δɻ 9.1૚ͷน͕͋Δͱ͖ͷAFF࣮ଌͱ༠ి཰ܭଌԠ༻ɹ ਤ15͸ް͞6 cmͷίϯΫϦʔτนΛ഑ஔ͍ͯ͠Δ࣮ ݧܥΛࣔͨ͠΋ͷͰ͋ΔɻϨʔμॾݩ͸ಉਤʹΑΔɻΞ ϯςφͱλʔήοτؒڑ཭͸100cmɺΞϨΠ։ޱ௕ͱε τϦοϓ෯͸֤ʑ90, 22cmͰ͋Δɻਤ16͸ίϯΫϦʔ τͷൺ༠ి཰Λεr= 5.4ͱͨ͠ͱ͖ͷAFFը૾Ͱ͋Δɻ ͜ͷਤͰ͸γεςϜ஗Ԇྔejϕℓ ͷิਖ਼લͳͷͰɺϨϯδ ํ޲127cmͷͱ͜Ζʹλʔήοτத৺͕දΕ͍ͯΔɻ͜ ͷ༠ి཰ͷܾఆʹؔͯ͠͸ޙड़͢Δɻิਖ਼ޙͷը૾͸ए ׯվળ͞Ε͍ͯΔͷ͕෼͔Δ͕ɺৄ͘͠ݟΔͨΊɺ͜ͷ அ໘มԽΛΫϩεϨϯδ(Az)ํ޲ͱϨϯδํ޲Ͱࣔ͠ ͨͷ͕ਤ17Ͱ͋Δɻ༧૝͞Εͨ௨Γɺิਖ਼Λߦ͏ͱத৺ ෦ΑΓ΋पล෦ͷํͰͦͷޮՌ͕໌֬ʹݟΒΕΔ͜ͱ͕ ෼͔Δɻࠓճͷ࣮ݧ͸1૚ͷ৔߹Ͱ͋Δ͕ɺޙͰ3૚ͷ ৔߹΋ௐ΂Δɻͳ͓ɺ্هϞϧλϧίϯΫϦʔτͷൺ༠ ి཰͸น͕ແ͍ͱ͖ͷλʔήοτը૾ͷϐʔΫ஋͋Δ͍ ͸த৺࠲ඪͱน͕͋Δͱ͖ͷͦΕΛൺֱ͠ɺλʔήοτ શମͷը૾ΛϨϯδํ޲ʹҠಈͤͯ͞ɺ༠ి཰Λٯࢉ͠ ͯٻΊ͍ͯΔɻ͜ͷΑ͏ʹ౳Ձతͳ༠ి཰ͷܭଌ͕Մೳ ͱͳΔͷͰɺ͜ͷߟ͑͸Ԡ༻্ඇৗʹॏཁͰ͋ΔɻҎԼ ͜Εʹ͍ͭͯٞ࿦͓ͯ͘͠ɻ

ਤ-15 ίϯΫϦʔτนʹΑΔಁա࣮ݧ(ฏ໘ਤ): ܦ࿏௕ิਖ਼ͷ༗ޮੑ֬ೝ

Fig.15 Transmission measurement of a concrete wall (plan view): Effectiveness of length compensation.

ਤ-16 1૚ܦ࿏௕ิਖ਼ͷ༗ແʹΑΔ࣮ଌAFFը૾ൺֱ, ࠨɿίϯΫϦʔτน͕ແ͍৔߹, தɿ1૚ίϯΫ

Ϧʔτนɺܦ࿏௕ແิਖ਼, ӈɿܦ࿏௕ิਖ਼͋Γ

Fig.16 AFF iage comparison, left: no wall, middle: with a concrete wall, no compensation, right: after compensation. ༠ి཰ͷܭଌ͸ಉ࣠ઢ࿏ɺಋ೾؅ɺۭಎڞৼثͳͲͷ ఻ૹઢ࿏Λར༻ͯ͠༠ిମ࣮૷લޙͷมԽΑΓߦ͏ํ ๏ɺۭͦͯؒ͠Ͱͷ൓ࣹ܎਺ͷมԽ͔ΒٻΊΔํ๏౳͕ ͋Δɻલऀ͸ਖ਼֬ͳ༠ి཰͕ٻΊΒΕΔ͕ɺۭؒʹ෼෍ ͍ͯ͠Δେ͖ͳ෺ମͳͲʹ͸ෆదͰ͋Δɻޙऀͷۭؒఆ ࡏ೾๏͸ɺి೾ٵऩମͷ൓ࣹ܎਺ଌఆʹྑ͘༻͍ΒΕΔ ۭؒఆࡏ೾๏Ͱ͋Δ͕ɺ൓ࣹ܎਺ͷS/Nൺ͕ෆ҆ఆʹͳ Δɺ͋Δ͍͸൓ࣹ܎਺͕ΞϯςφϘΞαΠτํ޲ͷϏʔ Ϝۙ࣠ʹґଘ͍ͯ͠Δɺͦͯ͠௚઀ͷ༠ి཰͸ٻΊΒΕ ͳ͍ͳͲͷܽ఺͕͋Δɻ͜͜Ͱͷը૾γϑτʹΑΔํ๏

(Image Shifting Method: ISMͱԾশ͢Δ)͸ը૾ੜ

੒ॲཧAFF๏ͷ೿ੜతͳܭଌ๏ͱͯ͠ɺ৿ྛͳͲͷۭؒ ʹ෼ࢄͨ͠෺ମͷ౳Ձతͳ༠ి཰ΛͦΕͳΓͷ҆ఆͨ͠ ܭଌਫ਼౓͕ظ଴Ͱ͖Δɻ ਤ16͸1૚ίϯΫϦʔτนͷ৔߹Ͱ͋Δ͕ɺ͜ͷ1૚ ͷίϯΫϦʔτͷ྆ଆʹผͷ෺࣭ͷ༠ిମฏ൘ΛுΓ෇ ͚ͨ3૚ͷนͷ৔߹ʹ΋ಉ͡Α͏ʹɺISMͰ౳Ձతͳ༠ ి཰ΛٻΊΔΞϧΰϦζϜ͕ՄೳͰ͋Δɻ͜ͷ2८ͷܭ ଌํ๏͸ɺนಁաϨʔμʹ௚઀Ԡ༻Ͱ͖ΔՄೳੑ͕͋Δɻ ෆಛఆͷนͷ(౳Ձత)ͳ༠ి཰͓ΑͼްΈ͸ະ஌Ͱ͋Δ ͜ͱ͕ҰൠతͰ͋Δɻͦ͜Ͱɺ1ճ໨ͷܭଌͰର৅෺Λ ଌΓɺ2ճ໨ͷܭଌͰ͜ͷର৅෺ʹ༧Ί༻ҙͨ͠༠ి཰

ਤ-15 ίϯΫϦʔτนʹΑΔಁա࣮ݧ(ฏ໘ਤ): ܦ࿏௕ิਖ਼ͷ༗ޮੑ֬ೝ

Fig.15 Transmission measurement of a concrete wall (plan view): Effectiveness of length compensation.

ਤ-16 1૚ܦ࿏௕ิਖ਼ͷ༗ແʹΑΔ࣮ଌAFFը૾ൺֱ, ࠨɿίϯΫϦʔτน͕ແ͍৔߹, தɿ1૚ίϯΫ

Ϧʔτนɺܦ࿏௕ແิਖ਼, ӈɿܦ࿏௕ิਖ਼͋Γ

Fig.16 AFF iage comparison, left: no wall, middle: with a concrete wall, no compensation, right: after compensation. ༠ి཰ͷܭଌ͸ಉ࣠ઢ࿏ɺಋ೾؅ɺۭಎڞৼثͳͲͷ ఻ૹઢ࿏Λར༻ͯ͠༠ిମ࣮૷લޙͷมԽΑΓߦ͏ํ ๏ɺۭͦͯؒ͠Ͱͷ൓ࣹ܎਺ͷมԽ͔ΒٻΊΔํ๏౳͕ ͋Δɻલऀ͸ਖ਼֬ͳ༠ి཰͕ٻΊΒΕΔ͕ɺۭؒʹ෼෍ ͍ͯ͠Δେ͖ͳ෺ମͳͲʹ͸ෆదͰ͋Δɻޙऀͷۭؒఆ ࡏ೾๏͸ɺి೾ٵऩମͷ൓ࣹ܎਺ଌఆʹྑ͘༻͍ΒΕΔ ۭؒఆࡏ೾๏Ͱ͋Δ͕ɺ൓ࣹ܎਺ͷS/Nൺ͕ෆ҆ఆʹͳ Δɺ͋Δ͍͸൓ࣹ܎਺͕ΞϯςφϘΞαΠτํ޲ͷϏʔ Ϝۙ࣠ʹґଘ͍ͯ͠Δɺͦͯ͠௚઀ͷ༠ి཰͸ٻΊΒΕ ͳ͍ͳͲͷܽ఺͕͋Δɻ͜͜Ͱͷը૾γϑτʹΑΔํ๏

(Image Shifting Method: ISMͱԾশ͢Δ)͸ը૾ੜ

੒ॲཧAFF๏ͷ೿ੜతͳܭଌ๏ͱͯ͠ɺ৿ྛͳͲͷۭؒ ʹ෼ࢄͨ͠෺ମͷ౳Ձతͳ༠ి཰ΛͦΕͳΓͷ҆ఆͨ͠ ܭଌਫ਼౓͕ظ଴Ͱ͖Δɻ ਤ16͸1૚ίϯΫϦʔτนͷ৔߹Ͱ͋Δ͕ɺ͜ͷ1૚ ͷίϯΫϦʔτͷ྆ଆʹผͷ෺࣭ͷ༠ిମฏ൘ΛுΓ෇ ͚ͨ3૚ͷนͷ৔߹ʹ΋ಉ͡Α͏ʹɺISMͰ౳Ձతͳ༠ ి཰ΛٻΊΔΞϧΰϦζϜ͕ՄೳͰ͋Δɻ͜ͷ2८ͷܭ ଌํ๏͸ɺนಁաϨʔμʹ௚઀Ԡ༻Ͱ͖ΔՄೳੑ͕͋Δɻ ෆಛఆͷนͷ(౳Ձత)ͳ༠ి཰͓ΑͼްΈ͸ະ஌Ͱ͋Δ ͜ͱ͕ҰൠతͰ͋Δɻͦ͜Ͱɺ1ճ໨ͷܭଌͰର৅෺Λ ଌΓɺ2ճ໨ͷܭଌͰ͜ͷର৅෺ʹ༧Ί༻ҙͨ͠༠ి཰ ਤ-17 ը૾ϐʔΫϨϕϧͰͷ֤ओํ޲ͷஅ໘ม Խ: 1૚(εr= 5.4), ্:ΫϩεϨϯδํ޲, Լ: Ϩϯδํ޲

Fig.17 Variation of cross-section at image peak-level, upper: cross-range direction, lower: range direction. ͱްΈ͕ط஌ͷฏ൘ΛషΓ෇͚ͯܭଌ͢ΔɻಘΒΕͨը ૾ͷը૾γϑτྔΛิਖ਼͢Ε͹ɺର৅෺(น)ͷ౳Ձతͳ ༠ి཰ͱްΈ͕ධՁͰ͖Δ͜ͱʹͳΔɻ͜ͷͱ͖ͷਖ਼֬ ͳܭࢉʹඞཁͳͷ͸લड़ͷଟ૚༠ిମฏ൘ʹΑΔཧ࿦ͱ ܦ࿏௕ิਖ਼(AFF)ΞϧΰϦζϜͰ͋Δ͕ɺ͜͜Ͱ͸ۙࣅ తͰ͋Δ͕࣮༻తͳࢉग़๏ʹ͍ͭͯޙड़͢Δɻ ͯ͞ɺΞϯςφҐஔΛݻఆͨ͠௨ৗͷϨʔμ૸ࠪͷ৔ ߹ɺͦͷ൓ࣹ৴߸ͷதʹ͸ૠೖҐ૬৘ใؚ͕·Ε͓ͯΓɺ ্ड़ͷૢ࡞͕ՄೳͰ͋Δɻ͜͜Ͱड़΂Δը૾৘ใΛ࢖ͬ ͯ༠ి཰͋Δ͍͸ްΈΛܭଌ͢Δͱɺඇৗʹ҆ఆͨ͠S/N ൺͰܭଌͰ͖Δͱ͍͏ͷ͕ϙΠϯτͰ͋Δɻಛʹύϧε Ϩʔμ౳ͷߴ౓ͳϨʔμΛ࢖Θͳͯ͘΋ྑ͘ɺAzํ޲ͷ Ґஔಛఆ΋Ͱ͖Δͱ͍͏ͷ͸େ͖ͳϝϦοτͰ͋Δɻෳ ૉ༠ి཰ͷڏ෦͸ɺนͷ༗ແʹΑΔड৴ిྗྔΛൺֱ͢ Δ͜ͱͰࢉग़Ͱ͖Δɻนʹরࣹͨ͠൓ࣹిྗ෼͸ߟྀͰ ͖ͳ͍͕ɺଟ૚ฏ൘ͷཧ࿦Ͱڏ෦ͷ਺஋Λ௥͍ٻΊΔ͜ ͱ͕Ͱ͖Δ[4,14]ɻޙड़ͷΑ͏ʹɺਤ16ͷίϯΫϦʔ τͷྫʹద༻͢Δͱɺεr= 5.4−j0.29ͱͳͬͨɻ ܦ࿏௕ิਖ਼(AFF)ʹࡍͯ͠ͷཧ࿦എܠͱISM๏ʹΑ ΔఆࣜԽΛ؆୯ʹ·ͱΊ͓ͯ͘ɻ༠ి཰͕εɺಁ࣓཰ ͕µͷഔ࣭தͷ఻೻଎౓͸v = 1/√εµɺਅۭத͸ޫ଎ c = 1/√ε0µ0Ͱ༩͑ΒΕΔɻൺ༠ి཰εr= ε/ε0ͱൺಁ࣓ ཰µr= µ/µ0Λఆٛ͢Δͱɺഔ࣭தͷ೾ಈͷ଎౓͸ඇ࣓ ੑମഔ࣭Λ૝ఆ͠(µr= 1)ɺ v =_√1 εµ = c √_ε r (17) ͱͳΔɻ͜ͷͱ͖ɺഔ࣭தͷ೾਺͸ k = ω v = √_ε r ω c = n ω c (18) Ͱ༩͑ΒΕΔɻn͸ਅۭ͔Βഔ࣭΁ͷಁաΠϯσοΫε n = √εrͰ͋ΔɻҰํɺ࠲ඪzͷਖ਼ͷํ޲ʹਐΉ༠ిମ ಺ͷ೾ಈ͸ Ez= E0e−αzej(ωt−βz), jk = α + jβ (19) Ͱද͞ΕΔɻαΛݮਰఆ਺ɺβΛҐ૬ఆ਺ͱݺΜͰ͍Δɻ ഔ࣭Λແଛࣦͱ͢Δͱɺk = βͱͳΔɻ Ҏ্͔Β໌Β͔ͳΑ͏ʹɺഔ࣭தͷ೾ಈ͸(19)ࣜΑΓ ∆ϕ = k0√εrz0− k0z0= k0(√εr− 1)z0 (20) ͚ͩܦ࿏௕͕৳ு͢Δɻ͜Ε͕ը૾ੜ੒࣌ͷҐஔγϑτ ྔ∆ϕ/k0ʹରԠ͢Δɻ্ࣜͰz0͸༠ిମো֐෺ͷްΈ Ͱ͋ΔɻҐ૬ૠೖ௕ʹ׵ࢉ͢Ε͹ɺը૾্ͰLͷҐஔγ ϑτʹର͠ɺ∆ϕ = k0L = k0(√εr− 1)z0 ͚ͩͷҐ૬͕ܦ ࿏ͷยಓ(1-way)ʹ௥Ճ͞Εͨ͜ͱʹͳΔɻ͜ΕΑΓ εr= (_L z0 + 1 )2 ≥ 1 (21) ͱ͍͏؆୯ͳධՁ͕ࣜಋ͔ΕΔɻಘΒΕͨը૾͔Βλʔ ήοτͷҠಈྔLΛԿΒ͔ͷํ๏ͰٻΊΔࡍɺͦͷಡΈ औΓޡࠩΛ_±∆Lͱ͢Δͱɺ(21)ࣜ͸∆Lͷୈ1߲·Ͱ ࢒ͯ͠ɺ εr → εr±√εr· ∆L z0 (22) ͱද͞ΕΔɻ͜ΕΑΓɺz0͕૬ରతʹେ͖͍ఔͦͷޡࠩ ͷӨڹ͸௿Լ͠ɺ√εrͷେ͖͕͞େ͖͍ͱ͖ఔͦͷӨڹ ͕େ͖͘ͳΔ͜ͱ͕෼͔Δɻ ਤ16ͷ࣮ݧྫͰ͸ɺط஌ྔͰ͋Δ༠ిମްΈ͕z0= 6 cmɺը૾্ͷҐஔγϑτྔ͕L = 8 cmͷ৔߹ɺεr= 5.4͕ ਪఆ͞ΕΔɻಡΈऔΓޡࠩΛ_±0.5cmͱ͢Δͱɺ(22)ࣜ ΑΓຌͦ∆εr=±0.2ͷޡ͕ࠩ෇ଳ͢Δ͜ͱʹͳΔɻͳ ͓ɺϚΠΫϩ೾ճ࿏ཧ࿦Ͱ͍͏ಉ࣠Ϟʔυ೾(TEM mode) ͷมԽ͔Β༠ి཰Λܭଌ͢Δಉ࣠؅๏ʹͯಉίϯΫϦʔ

ਤ-18 ࣮ݧʹ༻͍ͨίϯΫϦʔτน

Fig.18 Concrete wall for measurement.

ਤ-19 3૚ܦ࿏௕ิਖ਼ͷ༗ແʹΑΔAFFը૾ൺ

ֱ: ࣮ଌ஋, ੴߣϘʔυεr = 4.0), ্:ແิਖ਼,

Լ:ิਖ਼

Fig.19 3-layered AFF image, upper: no compensa-tion, lower:with length compensation.

τΛܭଌ͢Δͱɺεr= 5.1ͱͳͬͨɻจݙ[9] Ͱ͸υϥ ΠίϯΫϦʔτͷൺ༠ి཰͸εr= 4͔Β10Ͱ͋Δͱه ࡌ͞Ε͍ͯΔɻ 10.3૚ͷน͕͋Δͱ͖ͷ࣮ଌྫ͓Αͼٞ࿦ɹ ࣮ଌͷ࠷ޙͷྫͱͯ͠ɺ3૚ίϯΫϦʔτͷ৔߹Λࣔ ͢ɻਤ18͸࣮ݧʹ༻͍ͨ1૚(ࠨ)ͱ3૚ίϯΫϦʔτ นͷࣸਅͰ͋Δɻ3૚น͸ίϯΫϦʔταϯϓϧͷ྆ଆ ʹް͞9.6mmͷੴߣϘʔυΛுΓ෇͚͍ͯΔɻ͜ͷͱ͖ औಘͨ͠AFFը૾Λਤ19,20ʹࣔ͢ɻલਤ͸AFFը૾ɺ ਤ-20 ը૾ϐʔΫϨϕϧͰͷ֤ओํ޲ͷஅ໘ม Խ, ্:ΫϩεϨϯδํ޲, Լ:Ϩϯδํ޲

Fig.20 Variation of cross-section in peal-level of 3 layered AFF image, upper: cross-range di-rection, lower:range direction.

ޙਤ͸அ໘ڧ౓Ͱ͋ΔɻੴߣϘʔυͷްΈ9.6mm͸ࣄલ ʹܭଌͯ͠ط஌Ͱ͋Δ͕ɺ༠ి཰͸ෆ໌Ͱ͋ΔɻίΞ෦ ͷίϯΫϦʔτͷްΈͱൺ༠ి཰͸લड़ͷ6.0ͱධՁ஋ εr= 5.4Ͱ͋Δɻ͜ΕΒͷ৘ใͱAFFը૾ͷҠಈྔΛલ ड़ଟ૚༠ిମͷཧ࿦ʹద༻͠ɺ྆นͷੴߣϘʔυͷ༠ి ཰Λࢉग़͢Δͱɺεr= 4.0ͱͳͬͨɻҰൠͷڭՊॻʹ͸ੴ ߣϘʔυͷ༠ి཰͸υϥΠίϯΫϦʔτͱ΄΅ಉ͡ͱͳ Δεr= 5લޙͱ͍ΘΕ͍ͯΔɻ นಁաϨʔμͳͲͷԠ༻ঢ়گΛ૝૾͢ΔͱɺนͷްΈ ͱ͔༠ి཰͸ະ஌਺Ͱ͋Δɻ্͔͠͠هͷࣄ࣮Λ༻͍Δ ͱɺ͜ͷະ஌਺͸౳Ձతͳ1ݸͷ༠ిମฏ൘ͱͯ͠ܭଌ Ͱ͖ΔՄೳੑ͕͋Δɻͭ·Γɺط஌ͷ༠ిମฏ൘Λนʹ షΓ෇͚ͯɺషΓ෇͚લͱൺֱ͢Ε͹Α͍͜ͱʹͳΔɻ େ͖ͳ໰୊͸༠ి཰ͱްΈͷ෼཭Ͱ͋Δɻ͜Εʹؔ͠؆ ୯ͳߟ࡯Λߦ͏ɻ ࠓɺۭؾ૚͸ߟ͑ͳ͍Ͱน͕_N ૚͋Δͱ͢Δɻ֤૚ͷ ڥքͰ͸ෳࡶͳ೾ಈͷ൓ࣹ͓Αͼ۶ં͕༧ݟ͞ΕΔ͕ɺ ֤૚ͷૠೖҐ૬Λۙࣅతʹk0√εiziͰ༩͑Δɻεiͱzi͸ i൪໨ͷ૚ͷൺ༠ి཰ͱްΈͰ͋Δɻ͜Εʹ๏ઢ͔Βଌͬ