More surface map stuff

pykat/maths/zernike.py

@@ -46,13 +46,13 @@ def znm2Rc(A,R):
     minimum curvature.
     
     Inputs: A, R
-    A - List of amplitudes for order 2 Zernike polynomials, ordered so that m
+    A - List of amplitudes of order 2 Zernike polynomials, ordered so that m
         increases with list index. 1 <= len(A) <= 3. [m]
     R - Radius of the mirror surface in the xy-plane. [m]
 
     Returns: Rc
     Rc - If astigmatic modes are used (len(A) == 2 or 3) a numpy.array of length
-         2 containing min and max curvatures is returned. If only the 'defocus'
+         2 containing max and min curvatures is returned. If only the 'defocus'
          mode is used Rc is a float number. [m]
 
     Based on the Simtools function 'FT_Znm_to_Rc.m' by Charlotte Bond.
@@ -79,3 +79,33 @@ def znm2Rc(A,R):
     Rc = ((2*a20 + s*a22)**2 + R**2)/(2*(2*a20+s*a22))
     return Rc
 
+def Rc2znm(Rc,R):
+    '''
+    Converts Radius of curvatue to amplitudes of the second order Zernike
+    polynomials.
+
+    Iputs: Rc, R
+    Rc    - Radius of curvature. Either a number or a numpy.ndarray with
+            minimum and maximum curvature.
+    R     - Radius of mirror in xy-plane.
+
+    Returns: A
+    A     - Ampltude(s) of the second order Zernike polynomials needed. Is
+            a number if Rc is a number, and if R is a numpy.ndarray so is A.
+    
+    Based on Simtools function 'FT_Rc_to_Znm.m' by Charlotte Bond.
+    '''
+
+    # Amplitude in x and y directions
+    c = ( Rc - np.sign(Rc)*np.sqrt(Rc**2 - R**2) )/2
+    
+    if isinstance(Rc, np.ndarray):
+        A = np.array([])
+        # Adding Z(2,0) amplitude
+        A = np.append(A,c.mean())
+        # Adding Z(2,2) amplitude
+        A = np.append(A,2*(c[0]-A[0]))
+    elif isinstance(Rc, float) or isinstance(Rc, int):
+        A = c
+        
+    return A