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Ïîêàçàíî, ÷òî ïðèèñïîëüçóåìûõ â êëèíè÷åñêîé ïðàêòèêå óðîâíÿõ àêóñòè÷åñêîãî äàâëåíèÿ óäàðíûé ôðîíòâ ïðîôèëå âîëíû â ôîêóñå íå îáðàçóåòñÿ. Ìåòîäàìè ÷èñëåííîãî ìîäåëèðîâàíèÿ ïîêàçàíî, ÷òî äëÿ ôîðìèðîâàíèÿ óäàðíîãî ôðîíòà íåîáõîäèìà â äâà ðàçà áîëüøàÿ íà÷àëüíàÿàìïëèòóäà âîëíû. Èññëåäîâàíû ýôôåêòû íåëèíåéíîãî íàñûùåíèÿ â ïîëå äèàãíîñòè÷åñêîé óëüòðàçâóêîâîé ðåø¼òêè Philips C5-2. Ïîêàçàíî, ÷òî óðîâåíü íàñûùåíèÿ ïèêîâîãîïîëîæèòåëüíîãî äàâëåíèÿ â ôîêóñå ñîñòàâëÿåò îêîëî 20 ÌÏà äëÿ 64 çàïèòûâàåìûõ ýëåìåíòîâ ðåø¼òêè è 10 ÌÏà äëÿ 32 ýëåìåíòîâ.
Îáðàçîâàíèå óäàðíîãî ôðîíòà ïðîèñõîäèòïðè óðîâíÿõ äàâëåíèÿ íà ðåø¼òêå, ñîñòàâëÿþùèõ îêîëî îäíîé òðåòè îò èñïîëüçóåìûõ âêëèíè÷åñêèõ ýêñïåðèìåíòàõ ïî òîëêàíèþ êàìíåé.112Îñíîâíûå ðåçóëüòàòû è âûâîäû1. Ñîçäàíû óñòàíîâêè è ðåàëèçîâàíû îïòè÷åñêèå ìåòîäû äëÿ èçìåðåíèé ïðîôèëåéàêóñòè÷åñêîãî äàâëåíèÿ â íåëèíåéíîé ñôåðè÷åñêè ðàñõîäÿùåéñÿ N -âîëíå, ñîçäàâàåìîé èñêðîâûì èñòî÷íèêîì â âîçäóõå (øëèðåí-ìåòîä è ìåòîä èíòåðôåðîìåòðèè ïî ñõåìå Ìàõà-Öåíäåðà). Ïîêàçàíî, ÷òî âðåìåííîå ðàçðåøåíèå øëèðåí-ìåòîäà (3 ìêñ) îïðåäåëÿåòñÿ âðåìåíåì ýêñïîçèöèè âûñîêîñêîðîñòíîé êàìåðû.
Âðåìåííîå ðàçðåøåíèå ïðèèçìåðåíèÿõ ñ ïîìîùüþ èíòåðôåðîìåòðà Ìàõà-Öåíäåðà (0.4 ìêñ) â øåñòü ðàç ïðåâûøàåò ðàçðåøåíèå ñîâðåìåííûõ êîíäåíñàòîðíûõ ìèêðîôîíîâ, ÷òî äåëàåò âîçìîæíûìåãî èñïîëüçîâàíèå äëÿ êàëèáðîâêè øèðîêîïîëîñíûõ èçìåðèòåëüíûõ óñòðîéñòâ.2. Ñ ïîìîùüþ îïòè÷åñêèõ ìåòîäîâ (øëèðåí-ìåòîäà è ìåòîäà èíòåðôåðîìåòðèè ïîñõåìå Ìàõà-Öåíäåðà) âèçóàëèçèðîâàíà ïðîñòðàíñòâåííàÿ ñòðóêòóðà â âèäå ¾íîæêè¿Ìàõà è èçìåðåíû ïðîôèëè ñôåðè÷åñêè ðàñõîäÿùåéñÿ N -âîëíû â âîçäóõå ïðè å¼ íåðåãóëÿðíîì îòðàæåíèè îò ïëîñêîé æ¼ñòêîé ïîâåðõíîñòè. Îïðåäåëåíû óñëîâèÿ, ïðè êîòîðûõ ïðîèñõîäèò ïåðåõîä îò ðåãóëÿðíîãî ðåæèìà îòðàæåíèÿ N -âîëíû ê íåðåãóëÿðíîìó,è ïîêàçàíî, ÷òî íåðåãóëÿðíîå îòðàæåíèå èìååò äèíàìè÷åñêèé õàðàêòåð.3.
Íà îñíîâå óðàâíåíèÿ ÕÇÊ ÷èñëåííî èññëåäîâàíû ýôôåêòû íåëèíåéíîãî íàñûùåíèÿ â ôîêóñèðîâàííûõ ïó÷êàõ ïåðèîäè÷åñêèõ âîëí è èìïóëüñîâ, ñîçäàâàåìûõ ãàóññîâñêèì è ïîðøíåâûì èçëó÷àòåëÿìè. Ïîêàçàíî, ÷òî íàñûùåíèå äàâëåíèÿ â ïåðèîäè÷åñêèõïîëÿõ ñâÿçàíî â îñíîâíîì ñ íåëèíåéíûì ïîãëîùåíèåì íà óäàðíîì ôðîíòå âîëíû, à âèìïóëüñíûõ ïîëÿõ ñ ýôôåêòîì íåëèíåéíîé ðåôðàêöèè, ïðè ýòîì â ôîêàëüíîé îáëàñòè ïó÷êîâ âîçìîæíî îáðàçîâàíèå ïðîñòðàíñòâåííûõ ñòðóêòóð òèïà ¾íîæêè¿ Ìàõà.4. ×èñëåííî è ýêñïåðèìåíòàëüíî èññëåäîâàíû íåëèíåéíûå ýôôåêòû â ïîëÿõ ñîâðåìåííûõ äèàãíîñòè÷åñêèõ è óäàðíî-âîëíîâûõ ìåäèöèíñêèõ óñòðîéñòâ.
Ïîêàçàíî, ÷òî âïîëÿõ óäàðíî-âîëíîâîé òåðàïèè óäàðíûé ôðîíò â ïðîôèëå àêóñòè÷åñêîé âîëíû îáðàçóåòñÿ ïðè óðîâíÿõ àêóñòè÷åñêîãî äàâëåíèÿ íà èñòî÷íèêå, â äâà ðàçà ïðåâûøàþùèõèñïîëüçóåìûå â êëèíèêå.  ïîëÿõ äèàãíîñòè÷åñêîé óëüòðàçâóêîâîé ðåø¼òêè íàáëþäàåòñÿ ýôôåêò íåëèíåéíîãî íàñûùåíèÿ, ïðè÷¼ì îáðàçîâàíèå óäàðíîãî ôðîíòà ïðîèñõîäèò ïðè óðîâíÿõ àêóñòè÷åñêîãî äàâëåíèÿ íà ðåø¼òêå, ñîñòàâëÿþùèõ îêîëî îäíîéòðåòè îò èñïîëüçóåìûõ â êëèíè÷åñêèõ ýêñïåðèìåíòàõ ïî óëüòðàçâóêîâîìó òîëêàíèþïî÷å÷íûõ êàìíåé.113Ïðèëîæåíèå ÀÀëãîðèòì âû÷èñëåíèÿ îáðàòíîãî ïðåîáðàçîâàíèÿ Àáåëÿîò ðàñïðåäåëåíèÿ èíòåíñèâíîñòè øëèðåí-èçîáðàæåíèÿ ãëàâå 1 áûëà ðàññìîòðåíà ïðîöåäóðà âîññòàíîâëåíèÿ ïðîôèëÿ äàâëåíèÿ ñîçäàâàåìîé èñêðîâûì èñòî÷íèêîì N -âîëíû ïî ðàñïðåäåëåíèþ èíòåíñèâíîñòè øëèðåí-èçîáðàæåíèÿ.
Ñâÿçü ìåæäó íîðìèðîâàííûì äàâëåíèåì â âîëíå è ðàñïðåäåëåíèåì èíòåíñèâíîñòèçàäàâàëàñü âûðàæåíèåì (1.8).  äàííîì ïðèëîæåíèèáóäóò+∞ ïðèâåäåíû îñíîâíûå ôîðìóëû+∞√I(r )dr dx x2 − r2 â âûðàæåíèè (1.8).äëÿ ÷èñëåííîãî ðàñ÷¼òà èíòåãðàëà d/dx+∞rxÂíóòðåííèé èíòåãðàë A(x) = I(r)dr âû÷èñëÿåòñÿ ìåòîäîì òðàïåöèé. Âíåøíèé èíòåxãðàë ñîäåðæèò ñèíãóëÿðíîñòü ïðèx → r, ïîýòîìó äëÿ åãî âû÷èñëåíèÿ ñíà÷àëà èíòåðïîëèðóåì èíòåãðèðóåìóþ ôóíêöèþ êóáè÷åñêèì ñïëàéíîì, à çàòåì âû÷èñëèì èíòåãðàë÷èñëåííî.Åñëè äîìíîæèòü âû÷èñëÿåìûé èíòåãðàë íà ìíîæèòåëü (−1/π), òî ïîëó÷åííîå âûðàæåíèå áóäåò èìåòü âèä ïðåîáðàçîâàíèÿ Àáåëÿ [76], êîòîðîå â îáùåì âèäå çàïèñûâàåòñÿêàê:1B(r) = −π+∞rdAdx√.2dx x − r2(À.1)Áóäåì èñïîëüçîâàòü ñëåäóþùåå ñâîéñòâî ïðåîáðàçîâàíèÿ Àáåëÿ:+∞A=x2rBdr√= −2r 2 − x2Âû÷èñëÿÿ ïðîèçâîäíóþ, ïîëó÷èìdA/dx = 2+∞r 2 − x2dBdr.dr(À.2)x+∞x(dA/dx)|x=0 = 0.√dBxdrdr√r 2 − x2 .Îòñþäà ñëåäóåò, ÷òîÀïïðîêñèìèðóåì ôóíêöèþ A(x) ñ ïîìîùüþ èíòåðïîëÿöèè êóáè÷åñêèì ñïëàéíîì:A(x) = an + bn (x − xn ) + cn (x − xn )2 + dn (x − xn )3 = αn + βn x + γn x2 + δn x3è áóäåì èñïîëüçîâàòü çíà÷åíèÿ ôóíêöèè A(x) â óçëàõ ðàâíîìåðíîé ñåòêèn = 1...N , ãäå Δ - øàã ðàçáèåíèÿ.Ñíà÷àëà ðàññìîòðèì ðàñ÷¼ò èíòåãðàëà ïðè r = 0:1B(r = 0) = −π114+∞0dA dx.dx x(À.3)x n = Δ · n,(À.4)Ðàçîáüåì èíòåãðàë (À.4) íà ñóììó èíòåãðàëîâ ïî ÷èñëåííîé ñåòêå:1B(r = 0) = −πΔ0n=N −1dA dx 1 −dx xπ n=1Ïîäñòàâëÿÿ ðàçëîæåíèå (À.3) ñ êîýôôèöèåíòîìíèå (À.4), ïîëó÷èì:(n+1)·Δβ0 = 0dA dx.dx x(À.5)n·Δ(ò.ê.(dA/dx)|x=0 = 0)â âûðàæån=N −1 131 b3222B(r = 0) = − (2γ0 Δ + δ0 Δ ) −βn ln( ) + 2γn (b − a) + δn (b − a ) ,π2π n=1a2a = n · Δ, b = (n + 1) · Δ.(À.6)Òåïåðü ðàññìîòðèì âû÷èñëåíèå èíòåãðàëà ïðè r = m · Δ, m = 1...N − 1.
ÏîëîæèìA(x = N · Δ) = 0, ïîñêîëüêó A(x) → 0 ïðè x → ∞. Çàìåíèì èíòåãðàë ñóììèðîâàíèåì ïîñåãìåíòàì ÷èñëåííîé ñåòêè:n=N −11 B(r = m · Δ) = −π n=m(n+1)·Δn·ΔdAdx√.2dx x − r2(À.7)Ïîäñòàâèì êóáè÷åñêóþ èíòåðïîëÿöèþ ñïëàéíàìè (À.3) ôóíêöèè A(x) â ðàçëîæåíèå (À.7):n=N −11 B(r = m · Δ) = −In ,π n=1+ãäå In = βn (b − a ) + 2γn c [sh(b ) − sh(a )] +1ab3c2 δn (b − a + [sh(2b ) − sh(2a )]), a = arch( ), b = arch( ), c = m · Δ.22cc(À.8)Òàêèì îáðàçîì, âûðàæåíèÿ (À.6) è (À.8) ïîçâîëÿþò ÷èñëåííî âû÷èñëÿòü ïðåîáðàçîâàíèå Àáåëÿ (À.1).
Èíòåíñèâíîñòü øëèðåí-èçîáðàæåíèÿ ðàâíà íóëþ çà ïðåäåëàìè îáëàñòèíàõîæäåíèÿ N -âîëíû, ÷òî ïîçâîëÿåò çàìåíèòü áåñêîíå÷íûå ïðåäåëû èíòåãðèðîâàíèÿ äîêîíå÷íîãî ïðîñòðàíñòâåííîãî îêíà.  ÷èñëåííîì âû÷èñëåíèè èíòåãðàëà (1.8) ðàçìåð ïðîñòðàíñòâåííîãî îêíà ñîîòâåòñòâîâàë ðàçìåðó øëèðåí-èçîáðàæåíèÿ, à ïðîñòðàíñòâåííûéøàã ñîñòàâëÿë 8 ìêì.115Ëèòåðàòóðà1. Ðóäåíêî Î.Â., Ñîëóÿí Ñ.È.
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