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Maple/准确的景深公式

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  1. 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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