自定义面型中的一些公式有点看不懂，大家看看有没有感兴趣的，交流下

天空很蓝

在看ZEMAX中DLL文件夹中关于光栅的一个自定义文件，有一段是关于近轴光线追迹的，看的不是很懂，看看大家哪位懂点的给指点下：
case 4:
              /* ZEMAX wants a paraxial ray trace to this surface */
         /* x, y, z, and the optical path are unaffected, at least for this surface type */
         /* for paraxial ray tracing, the return z coordinate should always be zero. */
         /* paraxial surfaces are always planes with the following normals */

                        /* for paraxial ray tracing, grating effects are ignored */
         /* this is exactly like the standard surface code */
         UD->ln =  0.0;
         UD->mn =  0.0;
         UD->nn = -1.0;
         power = (FD->n2 - FD->n1)*FD->cv;
         if ((UD->n) != 0.0)
                 {
            (UD->l) = (UD->l)/(UD->n);
            (UD->m) = (UD->m)/(UD->n);


            (UD->l) = (FD->n1*(UD->l) - (UD->x)*power)/(FD->n2);
            (UD->m) = (FD->n1*(UD->m) - (UD->y)*power)/(FD->n2);


            /* normalize */
            (UD->n) = sqrt(1/(1 + (UD->l)*(UD->l) + (UD->m)*(UD->m) ) );
            /* de-paraxialize */
            (UD->l) = (UD->l)*(UD->n);
            (UD->m) = (UD->m)*(UD->n);
            }
         break;

程序中红色部分不是很理解，里面的参数意义在h文件中有解释，我这里也截图，并附上附件
/* modified 7-16-2002 to support more parameters */
/* added FIXED_DATA3 2-1-2006 to support more data */
/* added #pragma 3-15-2007 to disable warnings about deprecated functions under VS 2005 */

#pragma warning ( disable : 4996 ) // functions like strcpy are now deprecated for security reasons; this disables the warning


typedef struct
        {
        double x, y, z;     /* the coordinates */
        double l, m, n;     /* the ray direction cosines */
        double ln, mn, nn;  /* the surface normals */
        double path;        /* the path change */
        double sag1, sag2;  /* the sag and alternate hyperhemispheric sag */
        double index, dndx, dndy, dndz; /* for GRIN surfaces only */
        double rel_surf_tran; /* for relative surface transmission data, if any */
        double udreserved1, udreserved2, udreserved3, udreserved4; /* for future expansion */
        char string[20];    /* for returning string data */
        }USER_DATA;

typedef struct
        {
        int type, numb;     /* the requested data type and number */
        int surf, wave;     /* the surface number and wavelength number */
        double wavelength, pwavelength;      /* the wavelength and primary wavelength */
        double n1, n2;      /* the index before and after */
        double cv, thic, sdia, k; /* the curvature, thickness, semi-diameter, and conic */
        double param[9];    /* the parameters 1-8 */
        double fdreserved1, fdreserved2, fdreserved3, fdreserved4; /* for future expansion */
        double xdata[201];  /* the extra data 1-200 */
        char glass[21];     /* the glass name on the surface */
        }FIXED_DATA;


typedef struct
        {
        int type, numb;     /* the requested data type and number */
        int surf, wave;     /* the surface number and wavelength number */
        int unit;           /* the unit flag */
        double wavelength, pwavelength;      /* the wavelength and primary wavelength */
        double n1, n2;      /* the index before and after */
        double cv, thic, sdia, k; /* the curvature, thickness, semi-diameter, and conic */
        int ireserved[20]; /* for future expansion */
        double dbreserved[20]; /* for future expansion */
        double param[51];    /* the parameters 0-50 */
        double xdata[201];  /* the extra data 1-200 */
        char glass[21];     /* the glass name on the surface */
        }FIXED_DATA2;

typedef struct
        {
        int type, numb;     /* the requested data type and number */
        int surf, wave;     /* the surface number and wavelength number */
        int unit, serial;   /* the unit flag and key serial number */
        int is_a_mirror, is_in_mirror_space, is_air;   /* flags that define the media */
        int ireserved[100]; /* for future expansion */
        int did_polar;  /* indicates DLL provided polarization data */
        int max_parameter, max_extradata; /* the number of parameters and extradata values */
        double Exr, Exi, Eyr, Eyi, Ezr, Ezi, Ewr, Ewi; /* polarization data */
        double dbreserved[100]; /* for future expansion */
        double wavelength, pwavelength;      /* the wavelength and primary wavelength */
        double n1, n2;      /* the index before and after */
        double cv, thic, sdia, k; /* the curvature, thickness, semi-diameter, and conic */
        double param[201];    /* the parameters 0-200 */
        double xdata[501];  /* the extra data 0-500 */
        char glass[200];     /* the glass name on the surface */
        char comment[200];     /* the surface comment */
        int *int_data; /* for future expansion */
        double *db_data; /* for future expansion */
        char *c_data; /* for future expansion */
        }FIXED_DATA3;

wysxmu

  (UD->l) = (FD->n1*(UD->l) - (UD->x)*power)/(FD->n2);这个就是几何光学中计算近轴光线折射后光的方向，你要看几何数，自己推导一下