[回覆] 幽灵棱镜吞吐效应 [Ans.] Ghost in the box - phoria adaptation ----------------------------------------------------------------------- 中文字幕影片档 https://youtu.be/BaPzuVWqwOk 英文字幕影片档 https://youtu.be/nbjxlEjmcuk ------------------------------------------------------------------------ {深度感知引理(Depth perception lemma) } 根据视觉光学第三定律.. 深度感知的指向是协合的.. 其可拆解为两项陈述.. 交叉链结生而协调深度感知 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 深度感知在统计上是等强的 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 令调节衰老率为 w.. 落後或外偏斜为负值..超前或内偏斜为正值.. 深度感知引理方程的解为 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 ------------------------------------------------------------------ 深度的落点是位於离焦模糊知和辐辏偏差两深度感知的平衡位置.. 然而当离焦模糊其数值高於客观焦深.. 或辐辏偏差其数值高於同时视区时,. 直观上这个解是没办法成立的.. https://imgur.com/lAEBVws.jpeg 然而焦深模型和同时视区模型告诉我们.. 在空间中我们可以藉由额外缩瞳或扫视的方式.. 让这个解於暂态中成立.. https://imgur.com/3NTvwn8.jpeg 根据视觉光学第二定律..聚焦的景物刺激双眼的耦合.. 我们知道辐辏偏差可以以两种方式展开.. 一种是纯粹的辐辏运动.. 另一种是利用扫视来扩展双眼同时视区.. 根据视觉光学第三定律..深度感知的指向是协合的.. 我们知道当目标物的深度位置改变时..眼球会执行辐辏运动.. 当目标物的深度位置恒定时..我们会采以扫视来扩展双眼同时视觉.. https://imgur.com/hRLLWxE.jpeg 离焦模糊及辐辏偏差感知会再对第一次深度进行协合.. 以将暂态解转化为稳态解..完成注视行为.. https://imgur.com/bdamXeQ.jpeg https://imgur.com/ydVkWqi.jpeg 辐辏偏差感知和快速深度感知的平衡点位置.. 也就是传统视光所谓的斜位.. 斜位与快速深度感之间的辐辏运动.. 就是传统视光所谓的适应性辐辏.. 目标物与斜位之间的辐辏运动.. 就是传统视光所谓的融像性辐辏.. https://imgur.com/vey5u0r.jpeg 2001年霍斯罗亚尼和洪也发现要描述动态调节和辐辏运动.. 必须要用双重模式模型才能吻合.. https://imgur.com/ZRynetZ.jpeg https://imgur.com/pzT0bx4.jpeg ------------------------------------------------------------------ {深度感知引理数学诠释棱镜与立体镜} https://imgur.com/y1ZAXSR.jpeg 交叉链结生而协调深度感知 R*depth acc sti = k1*depth ver ..........(1) 深度感知在统计上是等强的 R*(ΔBlur - depth acc res) + k2*(ΔDisparity - depth ver)= 0 ..........(2) 调节边界条件 acc res = acc sti*(1-0.018*age) ..........(3) 起始条件 ΔBlur = 0 , ΔDisparity = valued ...........(4) 解上(1)(2)(3)(4)联立方程组可得 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)] 要人工制造出辐辏偏差..我们有两种光学工具.. 其中一种是棱镜..另一种是立体镜.. 然而两者於深度感知引理中是以不一样的方式在运作.. https://imgur.com/cyaeU5S.jpeg 棱镜可以影响无穷远处的辐辏偏差.. 也就是棱镜会影响张力性调节与张力性辐辏量值.. 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)] 目标物处的瞬时残余辐辏偏差为 -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 而立体镜无法影响无穷远处的辐辏偏差.. 也就是立体镜直接影响目标物处的调节与辐辏量值.. https://imgur.com/aPGTwuh.jpeg 目标物处的瞬时残余辐辏偏差为 ΔDisparity - depth ver =ΔDisparity*{1-k2/[k2+k1*(1-0.018*age)]} = ΔDisparity*[1-1/(2-0.018*age)] 我们可以看出.. 棱镜的效应..等同於目标物直接在双眼同时视区上进行挪移.. 而立体镜在挪移的同时..辐辏运动会缩减挪移的效果.. 这种缩减效应在年长时更为明显.. 因此对於残余辐辏偏差的操控..棱镜是相对较佳的选择。 #在後续的深度感知三位一体.. 上述这项计算将会被视觉光学第一定律所推翻.. 并且将会得到相似的结果。 --------------------------------------------------------------------------- {深度感知引理数学诠释辐辏性调节比值 (初始状态) } 根据视觉光学第三定律.. 交叉链结生而协调深度感知.. 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体将会阐明.. 辐辏性调节不是经由视觉光学第三定律产生.. 而是藉由视觉光学第一定律..同时的视觉局限双眼的辨识.. 并且将上式修正如下.. ca/c ratio (initial) = (k2/R)*(1-0.018*age) = (1/4.3)*(1-0.018*age) in diopter/prism ..........overall statistically 深度引理预测辐辏性调节比值为 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 statistica lly https://imgur.com/xUncCDl.jpeg ----------------------------------------------------------------------- {深度感知引理数学诠释辐辏性调节比值 (完整描述) } https://imgur.com/gUNURSr.jpeg 离焦模糊与辐辏偏差属於宇称的两端.. 辐辏偏差最终会塌缩进双眼注视稳态同时视区里.. 因此离焦模糊最终也会限缩至客观焦深内.. https://imgur.com/bOHq9Lw.jpeg 深度引理预测辐辏性调节比值的完整描述为 https://imgur.com/96fsDNX.jpeg 节录自Increased onset of vergence adaptation reduces excessive accommodation dur ing the orthoptic treatment of convergence insufficiency https://imgur.com/pkJYrCY.jpeg ------------------------------------------------------------------------ {深度感知引理数学诠释斜位适应} https://imgur.com/33ztrMg.jpeg 根据深度感知引理.. 若开立棱镜处方..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 深度引理预测棱镜适应的完整描述为.. https://imgur.com/CyCB6kO.jpeg 节录自Increased onset of vergence adaptation reduces excessive accommodation dur ing the orthoptic treatment of convergence insufficiency https://imgur.com/T3JqhKs.jpeg ----------------------------------------------------------------------- {深度感知引理数学诠释调节刺激响应曲线} 当残余离焦模糊小於焦深时.. https://imgur.com/AZuyBMZ.jpeg 此时调节响应与调节刺激曲线为.. 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) 可以看出调节刺激响应曲线的斜率与年龄的关系如下图所示.. 斜率随着年龄增长而降低.. slope = dy/dx = (1-w)/(2-w) https://imgur.com/SUaYhd9.jpeg 此区段满足唐德斯-杜安-芬查姆理论.. https://imgur.com/fl6JlCr.jpeg 当残余离焦模糊大於焦深时.. https://imgur.com/qQYMUqL.jpeg 此时调节响应与调节刺激曲线为.. 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 可以看出调节刺激响应曲线的斜率与年龄的关系如下图所示.. 斜率不会随着年龄增长而降低.. slope = dy/dx = 1 ............when y Amplitude of accommodation 0 ............otherwise https://imgur.com/awtmE76.jpeg 此区段满足亥姆霍兹-赫斯-古尔斯特兰德理论.. https://imgur.com/iQRgtNG.jpeg 两个完全反向的传统理论.. 同时出现在面临不同程度调节刺激下的单一个体.. 其实这只是幽灵吞吐棱镜效应的数学方程下必然的结果.. https://imgur.com/Znk28Ge.jpeg -- "The science I see delivers to me a feeling of great beauty, but few others see it. This makes me sad." —Feyman's Letters: The Beat of a Different Drum, October 1967 --

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