Data Systems Consulting

Lens diameter光圈直径 = D
focal length 焦距 = f
CCD Pixel pitch成像模糊圈 = a
F_NO光圈值 = F_N = f(焦距) / D(光圈直径)
a/D = (Lin-Li)/Lin = (Lin-Lif)/Lif = Li/Lif = (D+a)/D
so   Lif =  (D/(D+a))Li-----(1)
Li/Lin = (D-a)/D
Lin = D/(D-a)*Li-----(2)
1/f = (1/Lin)+(1/Lon) = (1/Li)+(1/Lof)-----(3)
Li = Lof/(Lo-f)
由(3)代入(1)&(2)
Lif = (D/(D+a))*((Lo*f)/(Lo-f))
Lin = (D/(D-a))*((Lo*f)/(Lo-f))
Lon = (Lin*f)/(Lin-f) = ((D/(D-a))*((Lo*f/(Lo-f))*f))/((D/(D-a))*((Lo*f/(Lo-f))+f))
so   Lon = (D*Lo*f)/(Df-af+aLo)≒(D*Lo*f)/Df+aLo 因为a值非常小所以可以当成0
Lof = (Lif*f)/(Lif-f) =  ((D/(D-a))*((Lo*f/(Lo-f))*f))/((D/(D-a))*((Lo*f/(Lo-f))-f))
so   Lof = (D*Lo*f)/(Df-af-aLo)≒(D*Lo*f)/Df-aLo 因为a值非常小所以可以当成0
所以景深 = Lof - Lon = (2*a*D*f*Lo²)/((D*f)²-(a*Lo)²)

Fixed focus system : 景深=∞  ,and the nearest shot range  Lon ≧ Lo_near
f⁴/F_N²-a²*Lo² = 0
Lo = f2/a*F_N
Lon = (D*f*Lo)/((D*f)+(a*Lo))
Lon = ((f2/FN)*(f2/aFN))/((f2/FN)+(f2/FN))=(f⁴/aF_N²)/(2f²/F_N)=f²/(2aF_N)
所以f2/(2aFN)≧Lo_near