Re: A04.調節輻輳交叉鏈結

看板optical (眼鏡)作者kramnik (marmote)時間6天前 (2025/03/27 16:19)推噓0(0推 0噓 0→)

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[回覆] 輻輳調節交叉鏈結 [Ans.] Accommodation-vergence cross-link -------------------------------------------------------------------- 中文字幕影片連結 https://youtu.be/oFasNS2_T1Y

英文字幕影片連結 https://youtu.be/b5BNy8WsqPs

---------------------------------------------------------------------- 深度感知引理(Depth perception lemma) 根據視覺光學第三定律.. 深度感知的指向是協合的.. 其可拆解為兩項陳述.. 交叉鏈結生而協調深度感知 couple link is born to achieve coordination between depth perceptions R*depth acc sti = k1*depth ver R is the ratio of pupillary distance between infancy and adulthood k1 = 1 overall statistically 深度感知在統計上是等強的 each depth perception is relatively equal strength overall statistically R*(ΔBlur - depth acc res) + k2*(ΔDisparity - depth ver)= 0 k2 = 1 overall statistically https://imgur.com/6KoyMCn.jpeg

深度感知引理方程的解為 depth acc res = [ΔBlur + (k1*k2/R)*ΔDisparity]*(1-w)/(2-w) depth ver = [R*ΔBlur + k1*k2*ΔDisparity]/(2-w) https://imgur.com/ii2X2cw.jpeg

------------------------------------------------------------------------ {第一項陳述：交叉鏈結生而協調深度感知} 目標物的位移在視網膜眼底投影產生模糊變化.. 誘發人眼產生調節運動去消除模糊感知.. https://imgur.com/yxeSYiI.jpeg

同樣地..目標物的位移在視網膜眼底投影產生偏差變化.. 誘發人眼產生輻輳運動去消除偏差感知.. https://imgur.com/r22GcgW.jpeg

此兩運動會交叉鏈結互相牽引.. 以期在部分感知被屏蔽時還能夠正常的注視目標物.. 剛出生時的嬰童瞳孔間距平均為4.2~4.3公分.. https://imgur.com/ytYJzjB.jpeg

在嬰童時期一公尺變化的模糊刺激會誘發一個屈光度調節運動.. 一公尺角變化的偏差刺激會誘發4.3個稜鏡度輻輳運動.. 輻輳運動與調節運動的交叉鏈結比值R可以寫為 4.3 .. 單位為(稜鏡度/屈光度) ; 或者寫為(4.3/PDadult)..單位為公尺角.. https://imgur.com/yRkBllL.jpeg

---------------------------------------------------------------------- {第二項陳述：深度感知在統計上是等強的} 當感官刺激出現時.. 生物會產生對應的感官運動來消除感官刺激.. 感官運動藉由交叉鏈結互相牽動.. 若感知指向不一致.. 則整體感知的落點統計上位於兩感知指向平衡的位置.. 2009年臨床實驗證實深度感知在統計上是等強的.. Accommodative and vergence responses to conflicting blur and disparity stimuli d uring development ,by Shrikant R. Bharadwaj; T. Rowan Candy , journal of Vision October 2009, Vol.9, 4. doi:https://doi.org/10.1167/9.11.4 https://imgur.com/z00779Z.jpeg

-------------------------------------------------------------------------- 調節運動邊界條件(The boundary condition of accommodation) 調節起點為散瞳處方.. 調節刺激最大為平均正9個屈光度.. 調節反應平均衰老速率為每年1.8%.. https://imgur.com/RjYBgpm.jpeg

-------------------------------------------------------------------------- 輻輳運動邊界條件(The boundary condition of vergence) 輻輳起點為眼球解剖休息位置.. 平均為外斜17個棱鏡度.. https://imgur.com/8XSe4RD.jpeg

------------------------------------------------------------------------- 深度感知引理數學詮釋梯度型調節性輻輳(gradient accommodative convergence) https://imgur.com/oZJO6aH.jpeg

交叉鏈結生而協調深度感知 R*depth acc sti = k1*depth ver ..........(1) 深度感知在統計上是等強的 R*(ΔBlur - depth acc res) + k2*(ΔDisparity - depth ver)= 0 ..........(2) 調節邊界條件 acc res = acc sti*(1-0.018*age) ..........(3) 起始條件 ΔBlur = valued , ΔDisparity = 0 ..........(4) 解上(1)(2)(3)(4)聯立方程組可得梯度型調節性輻輳為 gradient accommodative convergence = depth ver = ΔBlur*R/[(k1*(1-0.018*age)+k2] = ΔBlur*(4.3/6)/(2-0.018*age) in meter angle ..........overall statistically = ΔBlur*4.3/(2-0.018*age) in prism/diopter ..........overall statistically 梯度型刺激AC/A比值為 gradient ac/a stimulus = depth ver/ΔBlur = R/[(k1*(1-0.018*age)+k2] = 4.3/(2-0.018*age) in prism/diopter ..........overall statistically https://imgur.com/XCLrHOf.jpeg

accommodative error # before adaptation = ΔBlur - depth acc res = ΔBlur - (k1/R)*(depth ver)*(1-0.018*age) = ΔBlur*{1 -k1*(1-0.018*age)/[k1*(1-0.018*age)+k2] = ΔBlur/(2-0.018*age) ..........overall statistically 由幽靈稜鏡吞吐篇章..我們可以得到.. accommodative error # after adaptation = subjective DoF ..........if ΔBlur < Amplitude of Accommodation - subjective DoF ΔBlur - Amplitude of Accommodation ..........if ΔBlur > Amplitude of Accommodation - subjective DoF 梯度型響應AC/A比值為.. gradient ac/a response in prism/diopter = gradient AC/(ΔBlur - sub DoF) ..........if ΔBlur < Amplitude of Accommodation - subjective DoF gradient AC/Amplitude of Accommodation ..........if ΔBlur > Amplitude of Accommodation - subjective DoF = ΔBlur*4.3/(2-0.018*age)/(ΔBlur - sub DoF) ..........if ΔBlur < Amplitude of Accommodation - subjective DoF ΔBlur*4.3/(2-0.018*age)/(9-0.018*age) ..........if ΔBlur > Amplitude of Accommodation - subjective DoF https://imgur.com/hL9XDCr.jpeg

假設使用散瞳劑使得調節響應與調節刺激的比值僅為原有的k%.. 調節邊界條件 acc res(parasympatholytic drugs) = acc sti*(1-0.018*age)*k% = acc sti*[1-0.018*age(equivalent)] 可知藥物導致的等效年齡衰老可以表示為.. age(equivalent) = [1- (1-0.018*age)*k%]/0.018 則使用散瞳劑的梯度型響應AC/A比值為.. gradient ac/a response = ΔBlur*4.3/[1-0.018*age(equivalent)]/(ΔBlur - sub DoF) ..........if ΔBlur < Amplitude of Accommodation - subjective DoF ΔBlur*4.3/[2-0.018*age(equivalent)]/[9-0.018*age(equivalent)] ..........if ΔBlur > Amplitude of Accommodation - subjective DoF 對於25歲的個體..給予2個屈光度的模糊刺激.. 可以看出當藥效逐步增加時..梯度型響應AC/A比值即超過20.. https://imgur.com/YojT1Nc.jpeg

----------------------------------------------------------------------- 深度感知引理數學詮釋計算型調節性輻輳(calculated accommodative convergence) https://imgur.com/CLP5aHK.jpeg

交叉鏈結生而協調深度感知 R*depth acc sti = k1*depth ver ..........(1) 深度感知在統計上是等強的 R*(ΔBlur - depth acc res) + k2*(ΔDisparity - depth ver)= 0 ..........(2) 調節邊界條件 acc res = acc sti*(1-0.018*age) ..........(3) 起始條件(initial condition) ΔBlur = (1/WD) - tonic acc , ΔDisparity = (1/WD) - tonic ver ..........(4) 解上(1)(2)(3)(4)聯立方程組可得.. depth ver = {R*[(1/WD)-tonic acc]+k2*[(1/WD)-tonic ver]}/[(k1*(1-0.018*age)+k2] = {(4.3/6)*[(1/WD)-tonic acc]+[(1/WD)-tonic ver]}/(2-0.018*age) ..........overall statistically 由眼球休憩多重面向篇章..我們可以得到.. tonic acc = (17/4.3)*k1*k2*(1-0.018*age)/[k1*(1-0.018*age)+k2] + objective DoF = (17/4.3)*(1-0.018*age)/(2-0.018*age) + objective DoF ..........overall statistically tonic ver (age) = (17/6)*{ k2/[k1*(1-0.018*age)+k2] + [1-k1/(k1+k2)] - 1 } = (17/6)*[1/(2-0.018*age) - (1/2)] ..........overall statistically 由幽靈稜鏡吞吐篇章..我們可以得到.. heterophotia(distance) # full adaptation = 0.5*(tonic ver+depth ver) heterophoria(near) # partial adaptation = 0.75*[tonic ver+depth ver-6*(1/WD)] 深度引理預測計算型AC/A比值(快速)為.. calculated ac/a (fast pace) = [heterophoria(near) #parital adaptation +6*(1/WD) - heterophoria(distance) #full adaptation]/(1/WD) https://imgur.com/MAQXVSg.jpeg

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