簡介
人眼光學模型可用來設計眼科用設備，光學系統注定了要與人眼一起使用。本文演示了這樣一個模型：Arizona眼睛模型，在Jim Schwiegerling教授的書中有詳細描述：《Field Guide to Visual and Ophthalmic Optics》。AZ眼睛模型達到了基于平均臨床數據所決定的軸上和軸外像差等級。FRED文件包含了此眼睛模型及幾個用來分析它的光源，并包括一個基于想要的屈光度來調整模型的內嵌腳本。
模型
模型的定義如表1種所示，由半徑、圓錐常數、折射率、阿貝數、到下一面的距離等一系列表面組成。一些參數由屈光度（A）來決定。
Table 1. AZ眼睛模型的定義
在FRED中使用0屈光度來創建的，光瞳加在了透鏡的前面。材料是創建一個新的材料并選擇類型“Model Material”,輸入的參數是nd和vd.
光源
多個光源定義來分析該模型的不同特性。圖1顯示了所以的光源和提示信息告訴您他們可以用來做什么。
圖1. 光源和提示信息使用
除了“Letter F”之外的所有光源的光線位置設定在了孔徑光闌位置處，并增加了pre-propagation distance= -8。盡管光線在光瞳處創建，規定的傳輸方向相對于光線位置在pre-propagation distance之后。這意味著光束沿著Z軸在眼睛的前面以平行光入射，而不是在光瞳處入射。
在往下看是內置的腳本用來修改屈光度，使其為4（250mm），光源“Letter F”在視網膜處生成一個字母為F的圖像。綠色的光線聚焦的非常好而紅色和藍色光線有一點的模糊。使用Positions Spot Diagram分析工具來觀察最為合適。
圖2. 字母F光源的設定方法光
圖3. 字母F在視網膜上位置點列圖
視網膜的散射
在散射文件中，有一個名為“Retina surface”的72%的反射型朗伯散射，它為視網膜的散射提供了一個粗略的近似。為了模擬來自視網膜的散射，改變自定義元件“Eye ball” 下的視網膜的表面從“halt all” 到”Allow All”。并使幾何中“plane”可追跡。
圖4. 視網膜朗伯散射設定
注意在視網膜的表面有散射重點采樣規格定義，在“Scatter”標簽的底部可獲取該信息。“toward pupil”指定散射光朝向光瞳，半角度10度。
圖5. 視網膜重點采樣規格設定
腳本
內置腳本使用對話框顯示屈光度和光瞳直徑的數值設置。使用FRED Basic腳本創建和使用對話框非常容易。圖6顯示了如何獲取用戶自定義對話框，如下圖所示：
圖6. 用戶對話框的創建與編輯
圖7. 用戶對話框編輯器
如果“OK”按鈕按下，將會核對對話框下面的代碼行，如果點擊取消則腳本終止。然后輸入的參數賦予變量，如果此處是保留為空白，則使用默認值。因此，如果沒有值輸入并點擊“OK”按鈕，則腳本是以屈光度為0，光瞳直徑為4mm來運行的。
余下的腳本計算與屈光度有關的所有參數。
分析
屈光度為4，光瞳直徑為4mm，字母F點在視網膜上所成的像。
圖7. 字母F在視網膜上顏色分析
腳本代碼
Option Explicit 'Remove this to enable non-dimensioned variables to be used.
Dim entity As T_ENTITY
Dim op As T_OPERATION
Dim mat As T_MODELMATERIAL
Dim A As Double
Dim pupilDiam As Double
Dim eID As Long
Dim parID As Long
Dim count As Integer
Dim taq As Double, Rant As Double, CCant As Double, Rpost As Double, CCpost As Double
Dim tlens As Double, nlens As Double
Dim curv As Double, conic As Double
Dim ok As Long
Sub Main
'用戶輸入對話框
Begin Dialog UserDialog 320,126,"Input parameters" ' %GRID:10,7,1,1
TextBox 220,21,40,21,.TextBox1 'default: 0
Text 20,21,190,21,"Accommodation (in Diopters):",.Text1,1
OKButton 40,91,90,21
CancelButton 190,91,90,21
Text 20,49,190,14,"Pupil diameter (4 mm default):",.Text2,1
TextBox 220,49,40,21,.TextBox2 'default: 4
End Dialog
Dim dlg As UserDialog
ok = Dialog (dlg)
If ok=0 Then 'cancel button was pressed
Print "Execution cancelled."
End
End If
'Assign accommodation and pupil diameter & use defaults if field left empty
If dlg.TextBox1 = "" Then
A = 0 'Default accommodation
Else
A = CDbl(dlg.TextBox1)
End If
If dlg.TextBox2 = "" Then
pupilDiam = 4 'Default pupil diameter
Else
pupilDiam = CDbl(dlg.TextBox2)
End If
Print " "
Print "Accommodation = " & A & " Diopters"
Print "Pupil Diameter = " & pupilDiam & " mm"
' Calculate new parameters with accommodation
taq = 0.55 + 2.97 - 0.04*A 'Aqueous thickness
Rant = 12.0 - 0.4*A 'Radius of anterior lens
CCant = -7.518749 + 1.285720*A 'Conic constant of anterior lens
Rpost = -5.224557 + 0.2*A 'Radius of posterior lens
CCpost = -1.353971 - 0.431762*A 'Conic constant of posterior lens
tlens = 3.767 + 0.04*A 'Lens thickness
nlens = 1.42 + 0.00256*A - 0.00022*A^2 'Lens index of refraction
'Adjust parameters to account for accommodation
'*************************************************************************
'Aqueous thickness (Position of Lens)
'*************************************************************************
eID = FindFullName( "Geometry.Arizona Eye.Lens" )
GetCustomElement eID, entity
parID = FindFullName( "Geometry.Arizona Eye" )
' Delete any shift(s) in z
count = 0
While GetOperationCount(eID)>count
GetOperation eID, count, op
If op.Type="ShiftZ" Then
DeleteOperation eID,count
count=count-1
End If
count=count+1
Wend
'Set new shift in
op.Type = "ShiftZ"
op.val1 = taq
op.parent = parID
AddOperation eID, op
Print "Set aqueous humor thickness = " & taq-0.55
'*************************************************************************
'Radius and conic constant of anterior lens
'*************************************************************************
eID = FindFullName( "Geometry.Arizona Eye.Lens.Anterior" )
GetConic eID, entity, curv, conic
SetConic eID, entity, 1/Rant, CCant
Print "Set anterior lens radius = " & Rant & " and conic constant = " & CCant
'*************************************************************************
'Radius and conic constant of posterior lens
'*************************************************************************
eID = FindFullName( "Geometry.Arizona Eye.Lens.Posterior" )
GetConic eID, entity, curv, conic
SetConic eID, entity, 1/Rpost, CCpost
Print "Set posterior lens radius = " & Rpost & " and conic constant = " & CCpost
'*************************************************************************
'Lens thickness (Position of posterior lens surface)
'*************************************************************************
parID = FindFullName( "Geometry.Arizona Eye.Lens" )
' Delete any z-shift(s)
count = 0
While GetOperationCount(eID)>count
GetOperation eID, count, op
If op.Type="ShiftZ" Then
DeleteOperation eID,count
count=count-1
End If
count=count+1
Wend
'Set new z-shift
op.Type = "ShiftZ"
op.val1 = tlens
op.parent = parID
AddOperation eID, op
Print "Set lens thickness = " & tlens
'*************************************************************************
'Lens index of refraction
'*************************************************************************
eID = FindMaterial( "Lens" )
GetModelMaterial eID, mat
mat.Nd = nlens
SetModelMaterial eID, mat
Print "Set lens index of refraction = " & nlens
'*************************************************************************
'Pupil diameter
'*************************************************************************
eID = FindFullName( "Geometry.Arizona Eye.Pupil.Iris" )
'Adjust pupil diameter (trimming volume inner hole)
SetTrimVolHole eID, pupilDiam/2, pupilDiam/2, 0, 0, "Cylinder"
' Adjust pupil location to just in front of the lens
parID = FindFullName( "Geometry.Arizona Eye" )
eID = FindFullName( "Geometry.Arizona Eye.Pupil" )
count = 0
While GetOperationCount(eID)>count
GetOperation eID, count, op
If op.Type="ShiftZ" Then
DeleteOperation eID,count
count=count-1
End If
count=count+1
Wend
op.Type = "ShiftZ"
op.val1 = taq-0.01
op.parent = parID
AddOperation eID, op
Print "Set pupil diameter = " & pupilDiam
'Update AZ Eye subassembly Description
eID = FindFullName( "Geometry.Arizona Eye" )
GetEntity eID, entity
entity.Description = "Accommodation = " & A & "D"
SetEntity eID, entity
Update
Print "DONE!"
End Sub
如果屈光度是4，光瞳直徑是4，則會輸出如下數據：
Accommodation = 4 Diopters
Pupil Diameter = 4 mm
Set aqueous humor thickness = 2.81
Set anterior lens radius = 10.4 and conic constant = -2.375869
Set posterior lens radius = -4.424557 and conic constant = -3.081019
Set lens thickness = 3.927
Set lens index of refraction = 1.42672
Set pupil diameter = 4
DONE!
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