define paraxial na to be ref index * slope, in keeping with OSLO and …

…the literature. Fixes issue #154

src/rayoptics/parax/etendue.py

@@ -24,22 +24,22 @@ def create_etendue_dict():
     return dict2D(fld_ape_set, obj_img_set)
 
 
-def na2slp(na, n=1.0):
+def na2slp(na: float, n=1.0) -> float:
     """ convert numerical aperture to slope """
-    return n*math.tan(math.asin(na/n))
+    return na/n
 
 
-def slp2na(slp, n=1.0):
+def slp2na(slp: float, n=1.0) -> float:
     """ convert a ray slope to numerical aperture """
-    return n*math.sin(math.atan(slp/n))
+    return n*slp
 
 
-def ang2slp(ang):
+def ang2slp(ang: float) -> float:
     """ convert an angle in degrees to a slope """
     return math.tan(math.radians(ang))
 
 
-def slp2ang(slp):
+def slp2ang(slp: float) -> float:
     """ convert a slope to an angle in degrees """
     return math.degrees(math.atan(slp))
 

src/rayoptics/parax/firstorder.py

@@ -277,7 +277,7 @@ def compute_first_order(opt_model, stop, wvl, src_model=None):
         elif pupil_key == 'f/#':
             slp0 = -1./(2.0*pupil.value)
         elif pupil_key == 'NA':
-            slp0 = n_0*math.tan(math.asin(pupil.value/n_0))
+            slp0 = pupil.value/n_0
     elif pupil_oi_key == 'image':
         if pupil_key == 'height':
             slpk = pupil_value/obj2enp_dist
@@ -286,7 +286,7 @@ def compute_first_order(opt_model, stop, wvl, src_model=None):
         elif pupil_key == 'f/#':
             slpk = -1./(2.0*pupil.value)
         elif pupil_key == 'NA':
-            slpk = n_k*math.tan(math.asin(pupil.value/n_k))
+            slpk = pupil.value/n_k
         slp0 = slpk/red
     yu = [0., slp0]
 
@@ -364,8 +364,8 @@ def compute_first_order(opt_model, stop, wvl, src_model=None):
         fod.exp_radius = 1e10
 
     # compute object and image space numerical apertures
-    fod.obj_na = n_0*math.sin(math.atan(sm.z_dir[0]*ax_ray[0][slp]))
-    fod.img_na = n_k*math.sin(math.atan(sm.z_dir[-1]*ax_ray[-1][slp]))
+    fod.obj_na = n_0*sm.z_dir[0]*ax_ray[0][slp]
+    fod.img_na = n_k*sm.z_dir[-1]*ax_ray[-1][slp]
 
     return ParaxData(ax_ray, pr_ray, fod)
 

src/rayoptics/parax/specsheet.py

@@ -316,7 +316,7 @@ def get_parax_start_data(self, thi_0, n_0, n_k):
                     slpk = -1./(2.0*value)
                     slp0 = slpk*imager.f
                 elif value_key == 'NA':
-                    slpk = n_k*math.tan(math.asin(value/n_k))
+                    slpk = value/n_k
                     slp0 = slpk*imager.f
             yu = [0., slp0]
 
@@ -342,13 +342,13 @@ def get_parax_start_data(self, thi_0, n_0, n_k):
                 elif value_key == 'f/#':
                     slp0 = -1./(2.0*value)
                 elif value_key == 'NA':
-                    slp0 = n_0*math.tan(math.asin(value/n_0))
+                    slp0 = value/n_0
             elif obj_img_key == 'image':
                 if value_key == 'f/#':
                     slpk = -1./(2.0*value)
                     slp0 = slpk*imager.m
                 elif value_key == 'NA':
-                    slpk = n_k*math.tan(math.asin(value/n_k))
+                    slpk = value/n_k
                     slp0 = slpk*imager.m
             yu = [0., slp0]