def positionToDelay(pos, origin=0, invert = False, reflections=1):
    ''' converts a motor position in mm into optical delay in picosecond
        Inputs:
            pos: array-like delay stage motor position
            origin: motor position of time zero in mm
            invert: bool, inverts the sign of delay if True
            reflections: number of bounces in the delay stage

        Output:
            delay in picosecond
    '''
    c_ = 299792458 *1e-9 # speed of light in mm/ps
    x = -1 if invert else 1
    return 2*reflections*(pos-origin)*x/c_
    
def degToRelPower(x, theta0=0):
    ''' converts a half-wave plate position in degrees into relative power
        between 0 and 1.
        Inputs:
            x: array-like positions of half-wave plate, in degrees
            theta0: position for which relative power is zero
            
        Output:
            array-like relative power
    '''
    return np.sin(2*(x-theta0)*np.pi/180)**2