Date:    June 17, 1999
Subject: Details on the focus stage equations - June 17, 1999

1. Step position vs. voltage data was send to me by seth kamemoto
   See ~/src/spex/Notes.details/990617.FocusStage.dat.

   I averaged the MIN/MAX column & fitted the data to a curve.
   Then, I adjusted the step values so 0 volts is at step position 0,
   by subtracting 309652 from the orginial step values.

   Then I determined the coefficients to perform the translation
   between steps and voltage.
   For Step-to-voltage a 10 degree polynomial was used.
   For voltage-to-step, a single equation was difficult to fit.
   So, I used 2 equations (range negative voltage & positive voltage).
   A 9 degree polynomial was used.

   equation derived:
   AFOC Volt->Step. Equ < 0:
      v =  (5403.051100)       + (253171.190000x)   + (88602.936000x^2)  +
           (260435.700000x^3)  + (719271.450000x^4) + (919933.000000x^5) +
           (638245.130000x^6)  + (249129.230000x^7) + (51432.987000x^8)  +
           (4367.436200x^9)

   AFOC Volt->Step. Equ > 0:
      v =  (4884.261300)        + (242839.280000x)   + (-34166.869000x^2)  +
           (-116133.970000x^3)  + (136707.040000x^4) + (-77284.039000x^5)  +
           (25363.852000x^6)    + (-4892.985800x^7)  + (514.565710x^8)  +
           (-22.770170x^9)

   AFOC Step->Volt. Equ:
      v =  (-0.020292)       + (4.20239e-06x)     + (4.51103e-13x^2)  +
           (2.85359e-17x^3)  + (7.76072e-23x^4)   + (5.04605e-28x^5)  +
           (-2.32003e-33x^6) + (-5.13327e-39x^7)  + (3.27257e-44x^8)  +
           (3.20976e-50x^9)  + (-1.51774e-55x^10)

or coefficients arrays are:

   /* coefficient to convert steps-to-voltage  */
   EXTERN double Afoc_s2v_coeff[AFOC_S2V_DEG+1]
   #if MAIN
   = { -0.020291962,    4.2023921e-006, 4.5110273e-013, 2.8535857e-017, 7.7607241e-023,
      5.0460524e-028, -2.320027e-033, -5.1332672e-039, 3.2725731e-044, 3.2097555e-050,
       -1.5177412e-055 }
   #endif
      ;

   /* coefficient to convert voltage-to-steps. Two equation for range negative &
   positive */

   EXTERN double Afoc_v2s_coeff_Negative[AFOC_V2S_DEG+1]
   #if MAIN
      = { 5403.0511, 253171.19, 88602.936, 260435.7, 719271.45,
          919933,    638245.13, 249129.23, 51432.987, 4367.4362 }
   #endif
      ;

   EXTERN double Afoc_v2s_coeff_Positive[AFOC_V2S_DEG+1]
   #if MAIN
      = { 4884.2613, 242839.28, -34166.869, -116133.97, 136707.04,
      -77284.039, 25363.852, -4892.9858, 514.56571, -22.77017 }
   #endif
      ;