Re: A06.幽靈稜鏡吞突效應

看板optical (眼鏡)作者kramnik (marmote)時間6天前 (2025/03/27 16:22)推噓0(0推 0噓 0→)

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[回覆] 幽靈稜鏡吞吐效應 [Ans.] Ghost in the box - phoria adaptation ----------------------------------------------------------------------- 中文字幕影片檔 https://youtu.be/BaPzuVWqwOk

英文字幕影片檔 https://youtu.be/nbjxlEjmcuk

------------------------------------------------------------------------ {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 + depth disparity) 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 (fast depth - adaptive acc res) + (ΔBlur - reflex acc res)= 0 (fast depth - adaptive ver) + (ΔDisparity - fusional ver)= 0 k2 = 1 overall statistically https://imgur.com/zeNflFB.jpeg

令調節衰老率為 w.. 落後或外偏斜為負值..超前或內偏斜為正值.. 深度感知引理方程的解為 tonic acc res = (k1*k2/R)*[φDisparity - anatomical position]*(1-w)/(2-w) tonic ver = k1*k2*[φDisparity - anatomical position]/(2-w) + tonic ver(intrinsic) depth acc res = [(φBlur - tonic acc res) + (k1*k2/R)*(φDisparity - tonic ver)]*(1-w)/(2-w) depth ver = [R*(φBlur - tonic acc res) + k1*k2*(φDisparity - tonic ver)]/(2-w) reflex acc res = adaptive acc res = (k1*k2/R)*(φDisparity - depth ver - tonic ver)*(1-w)/2 fusional ver = adaptive ver = (φDisparity - depth ver - tonic ver)/2 https://imgur.com/16k5r7o.jpeg

------------------------------------------------------------------ 深度的落點是位於離焦模糊知和輻輳偏差兩深度感知的平衡位置.. 然而當離焦模糊其數值高於客觀焦深.. 或輻輳偏差其數值高於同時視區時,. 直觀上這個解是沒辦法成立的.. https://imgur.com/lAEBVws.jpeg

然而焦深模型和同時視區模型告訴我們.. 在空間中我們可以藉由額外縮瞳或掃視的方式.. 讓這個解於暫態中成立.. https://imgur.com/3NTvwn8.jpeg

根據視覺光學第二定律..聚焦的景物刺激雙眼的耦合.. 我們知道輻輳偏差可以以兩種方式展開.. 一種是純粹的輻輳運動.. 另一種是利用掃視來擴展雙眼同時視區.. 根據視覺光學第三定律..深度感知的指向是協合的.. 我們知道當目標物的深度位置改變時..眼球會執行輻輳運動.. 當目標物的深度位置恆定時..我們會採以掃視來擴展雙眼同時視覺.. https://imgur.com/hRLLWxE.jpeg

離焦模糊及輻輳偏差感知會再對第一次深度進行協合.. 以將暫態解轉化為穩態解..完成注視行為.. https://imgur.com/bdamXeQ.jpeg

https://imgur.com/ydVkWqi.jpeg

輻輳偏差感知和快速深度感知的平衡點位置.. 也就是傳統視光所謂的斜位.. 斜位與快速深度感之間的輻輳運動.. 就是傳統視光所謂的適應性輻輳.. 目標物與斜位之間的輻輳運動.. 就是傳統視光所謂的融像性輻輳.. https://imgur.com/vey5u0r.jpeg

2001年霍斯羅亞尼和洪也發現要描述動態調節和輻輳運動.. 必須要用雙重模式模型才能吻合.. https://imgur.com/ZRynetZ.jpeg

https://imgur.com/pzT0bx4.jpeg

------------------------------------------------------------------ {深度感知引理數學詮釋稜鏡與立體鏡} https://imgur.com/y1ZAXSR.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 = 0 , ΔDisparity = valued ...........(4) 解上(1)(2)(3)(4)聯立方程組可得 depth acc res = (k1*k2/R)*ΔDisparity(1-0.018*age)/[k2+k1*(1-0.018*age)] depth ver = k2*ΔDisparity/[k2+k1*(1-0.018*age)] 要人工製造出輻輳偏差..我們有兩種光學工具.. 其中一種是稜鏡..另一種是立體鏡.. 然而兩者於深度感知引理中是以不一樣的方式在運作.. https://imgur.com/cyaeU5S.jpeg

稜鏡可以影響無窮遠處的輻輳偏差.. 也就是稜鏡會影響張力性調節與張力性輻輳量值.. https://imgur.com/iMrGqrW.jpeg

Δtonic acc res = depth acc res = (k1*k2/R)*ΔDisparity(1-0.018*age)/[k2+k1*(1-0.018*age)] Δtonic ver = depth ver = k2*ΔDisparity/[k2+k1*(1-0.018*age)] 目標物處的瞬時殘餘輻輳偏差為 -Δdepth ver = -Δ{ [R*(φBlur - tonic acc res) + k1*k2*(φDisparity - tonic ver)] /[k2+k1(1-0.018*age)]} = (R*Δtonic acc res + k1*k2*tonic ver)/[k2+k1(1-0.018*age)] = [k1*k2*ΔDisparity*(1-0.018*age) + k1*k2^2*ΔDisparity]/[k2+k1(1-0.018*age)] = ΔDisparity ..........overall statistically 而立體鏡無法影響無窮遠處的輻輳偏差.. 也就是立體鏡直接影響目標物處的調節與輻輳量值.. https://imgur.com/aPGTwuh.jpeg

目標物處的瞬時殘餘輻輳偏差為 ΔDisparity - depth ver =ΔDisparity*{1-k2/[k2+k1*(1-0.018*age)]} = ΔDisparity*[1-1/(2-0.018*age)] 我們可以看出.. 稜鏡的效應..等同於目標物直接在雙眼同時視區上進行挪移.. 而立體鏡在挪移的同時..輻輳運動會縮減挪移的效果.. 這種縮減效應在年長時更為明顯.. 因此對於殘餘輻輳偏差的操控..稜鏡是相對較佳的選擇。 #在後續的深度感知三位一體.. 上述這項計算將會被視覺光學第一定律所推翻.. 並且將會得到相似的結果。 --------------------------------------------------------------------------- {深度感知引理數學詮釋輻輳性調節比值 (初始狀態) } 根據視覺光學第三定律.. 交叉鏈結生而協調深度感知.. R*depth acc sti = k1*(depth ver + depth disparity) among which depth acc sti = convergent accommodation stimulus depth ver = 0 , depth disparity = residual ΔDisparity = prism 可得 ca/c ratio (initial) = convergent accommodation response/prism = (k1/R)*(1-0.018*age) = (6/4.3)*(1-0.018*age) in diopter/meter angle ..........overall statistically = (1/4.3)*(1-0.018*age) in diopter/prism ..........overall statistically #後述的深度感知三位一體將會闡明.. 輻輳性調節不是經由視覺光學第三定律產生.. 而是藉由視覺光學第一定律..同時的視覺侷限雙眼的辨識.. 並且將上式修正如下.. ca/c ratio (initial) = (k2/R)*(1-0.018*age) = (1/4.3)*(1-0.018*age) in diopter/prism ..........overall statistically 深度引理預測輻輳性調節比值為 ca/c ratio (initial) =convergent accommodation response/prism = (k1/R)*(1-0.018*age) = (1/4.3)*(1-0.018*age) in diopter/prism ................overall statistically https://imgur.com/xUncCDl.jpeg

----------------------------------------------------------------------- {深度感知引理數學詮釋輻輳性調節比值 (完整描述) } https://imgur.com/gUNURSr.jpeg

離焦模糊與輻輳偏差屬於宇稱的兩端.. 輻輳偏差最終會塌縮進雙眼注視穩態同時視區裡.. 因此離焦模糊最終也會限縮至客觀焦深內.. https://imgur.com/bOHq9Lw.jpeg

深度引理預測輻輳性調節比值的完整描述為 https://imgur.com/96fsDNX.jpeg

節錄自Increased onset of vergence adaptation reduces excessive accommodation dur ing the orthoptic treatment of convergence insufficiency https://imgur.com/pkJYrCY.jpeg

------------------------------------------------------------------------ {深度感知引理數學詮釋斜位適應} https://imgur.com/33ztrMg.jpeg

根據深度感知引理.. 若開立稜鏡處方..可知.. φDisparity - depth ver - tonic ver = prism then heterophoria(initial) = φDisparity - depth ver - tonic ver = prism heterophoria(final) = φDisparity - depth ver - tonic ver - adaptive ver = prism/2 深度引理預測稜鏡適應的完整描述為.. https://imgur.com/CyCB6kO.jpeg

節錄自Increased onset of vergence adaptation reduces excessive accommodation dur ing the orthoptic treatment of convergence insufficiency https://imgur.com/T3JqhKs.jpeg

----------------------------------------------------------------------- {深度感知引理數學詮釋調節刺激響應曲線} 當殘餘離焦模糊小於焦深時.. https://imgur.com/AZuyBMZ.jpeg

此時調節響應與調節刺激曲線為.. https://imgur.com/R7R1AFg.jpeg

y = tonic acc res + depth acc res = [φBlur + (k1*k2/R)*(φDisparity - tonic ver)]*(1-w)/(2-w) = [(1-w)/(2-w)]*x + (k1*k2/R)*(φDisparity - tonic ver)]*(1-w)/(2-w) 可以看出調節刺激響應曲線的斜率與年齡的關係如下圖所示.. 斜率隨著年齡增長而降低.. slope = dy/dx = (1-w)/(2-w) https://imgur.com/SUaYhd9.jpeg

此區段滿足唐德斯-杜安-芬查姆理論.. https://imgur.com/fl6JlCr.jpeg

當殘餘離焦模糊大於焦深時.. https://imgur.com/qQYMUqL.jpeg

此時調節響應與調節刺激曲線為.. https://imgur.com/vAKOgAk.jpeg

y = φBlur + DoF(lead) + auto calibration ....when y Amplitude of acc Amplitude of accommodation .....otherwise = x + DoF(lead) + auto calibration ....when y Amplitude of acc Amplitude of accommodation .....otherwise 可以看出調節刺激響應曲線的斜率與年齡的關係如下圖所示.. 斜率不會隨著年齡增長而降低.. slope = dy/dx = 1 ............when y Amplitude of accommodation 0 ............otherwise https://imgur.com/awtmE76.jpeg

此區段滿足亥姆霍茲-赫斯-古爾斯特蘭德理論.. https://imgur.com/iQRgtNG.jpeg

兩個完全反向的傳統理論.. 同時出現在面臨不同程度調節刺激下的單一個體.. 其實這只是幽靈吞吐稜鏡效應的數學方程下必然的結果.. https://imgur.com/Znk28Ge.jpeg

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