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Maple/Depth of field for optical lens
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thumb|right|500px|DOF calculation diagram
> restart;
> NULL;
>
> e1 := (vn-v)/vn = c/d:
> e2 := (v-vf)/vf = c/d:
> e3 := N = f/d:
> e4 := 1/Dn+1/vn = 1/f:
> e5 := 1/Df+1/vf = 1/f:
> e6 := 1/s+1/v = 1/f:
> sys := {e1, e2, e3, e4, e5, e6}; #Set of 6 equations
>var := {Df, Dn, d, v, vf, vn}; #6 variables
>sol := solve(sys,var); #solve the equation set
Find hyperfocal distance
> tm3 := 1/op(op(sol)[1])[2] = 0;
> tm4 := H = solve(tm3, s);
f (f + c N)
H = -----------
c N
>
> eqf := {tm4, op(sol)[1], op(sol)[2]};
varf := {Df, Dn, c};
/ 2 2
| s f s f
< Df = ------------------, Dn = - -------------------,
| 2 2
\ f + c N f - c N s -f + c N f - c N s
\
f (f + c N)|
H = ----------- >
c N |
/
{Df, Dn, c}
eqf:= {,,};
> solve(eqf, varf);
/ 2 \
| s (H - f) s (H - f) f |
< Df = ---------, Dn = -----------, c = --------- >
| H - s H - 2 f + s N (H - f)|
\ /
>