Maple/準確的景深公式
- Precision Depth of field formular without any assumption of approximation
> restart; > 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}; var := {Df, Dn, d, v, vf, vn}; sol := solve(sys, var);
/ 2 2 | s f s f f < Df = ------------------, Dn = - -------------------, d = -, | 2 2 N \ f + c N f - c N s -f + c N f - c N s
2
s f s f
v = - -----, vf = - ------------------------,
f - s 2
f - s f + c N f - c N s
2 \
s f |
vn = ------------------------- >
2 |
-f + s f + c N f - c N s/
> > > > 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}
> solve(eqf, varf);
/ 2 \
| s (H - f) s (H - f) f |
< Df = ---------, Dn = -----------, c = --------- >
| H - s H - 2 f + s N (H - f)|
\ /
>
> > N := 16; c := 0.15e-1; F := 25; s := 3000; H := F^2/(N*c)+F;
16
0.015
25
3000
2629.1666666666666667
> > > > > Aperture := [2.8, 4, 5.6, 8, 11, 16, 22]; na := nops(Aperture);
[2.8, 4, 5.6, 8, 11, 16, 22]
7
> Dis := [300, 400, 500, 600, 800, 1000, 1200, 1500, 2000, 3000, 4000]; nd := nops(Dis);
[300, 400, 500, 600, 800, 1000, 1200, 1500, 2000, 3000, 4000]
11
> print(8*" x 12"*Tessina*Depth*of*Field*Table); printf("%10s%10g%10g%10g%10g%10g%10g%10g\n", " D ", Aperture[1], Aperture[2], Aperture[3], Aperture[4], Aperture[5], Aperture[6], Aperture[7]); for j to nd do for i to na do N := Aperture[i]; D0 := Dis[j]; H := evalf[4](F^2/(N*cc)+F); Dn[i] := evalf[4](Dfar); Df[i] := evalf[4](Dnear) end do; printf("%10g%10g%10g%10g%10g%10g%10g%10g\n", D0, Dn[1], Dn[2], Dn[3], Dn[4], Dn[5], Dn[6], Dn[7]); printf("%10g%10g%10g%10g%10g%10g%10g%10g\n", D0, Df[1], Df[2], Df[3], Df[4], Df[5], Df[6], Df[7]) end do;
8 " x 12" Tessina Depth of Field Table
D 2.8 4 5.6 8 11 16 22
300 305.8 308.3 311.5 316.6 323.4 335.4 351
300 294.7 292.4 289.3 284.9 279.6 271.3 262
400 410.5 415.1 421.2 431 443.9 467.5 498.7
400 390.3 386.3 380.8 373.1 363.9 349.8 333.9
500 516.7 524.1 534.1 550.2 571.7 611.6 667.4
500 484.7 478.4 470 458.2 444.3 422.9 399.7
600 624.3 635.4 650.3 674.5 707.4 769.8 861.3
600 577.9 568.9 557 540.4 521 491.3 460.1
800 844 864.7 893 939.8 1006 1139 1354
800 760.4 745 724.5 696.3 664 616.5 567.6
1000 1071 1104 1151 1230 1347 1599 2061
1000 938.8 914.8 884.1 842.3 795.3 727.6 660.2
1200 1304 1353 1425 1550 1740 2187 3161
1200 1113 1079 1036 979.2 916 826.9 740.6
1500 1666 1748 1871 2093 2457 3460 6780
1500 1365 1315 1252 1169 1080 957.6 843.3
2000 2307 2469 2723 3223 4179 8280 -46770
2000 1766 1682 1580 1451 1315 1137 979.1
3000 3751 4202 4999 6995 13970 -21060 -5256
3000 2501 2335 2144 1909 1680 1400 1167
4000 5461 6472 8589 16890 -81020 -7600 -3641
4000 3158 2896 2608 2268 1952 1584 1291
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