#==============================================================================
# Calculate the Zernike series coefficients A[n,m] and B[n,m] of
# an expression.
#
# The expression must be in cylindrical coordinates (rho,phi), where
# rho has been normalized to lie in the range [0..1].
#
# See zseries.ms for documentation.
#
# Returns a structure [A,B].
#==============================================================================

#=============================================================================
#
# Marc A. Murison
# Astronomical Applications Dept.
# U.S. Naval Observatory
# 3450 Massachusetts Ave., NW
# Washignton, DC 20392
# murison@riemann.usno.navy.mil
# http://riemann.usno.navy.mil/AESOP/
#
#=============================================================================

if ZERNCOEF_READ <> 1 then
ZERNCOEF_READ := 1:
read`d:/optics/AESOP/zernike.p`:

ZSeriesCoeff := proc( n::nonnegint, m::nonnegint, expr::algebraic )

    local   Irho, Iphi, coeffs:

	#A[n,m]
    Iphi := int( ZernikeCos(n,m,rho,phi)*expr, phi=0..2*Pi ):
    Irho := int( Iphi*rho, rho=0..1 ):
    if m=0 then
    	coeffs['A'] := (n+1)/Pi*Irho:
    else
    	coeffs['A'] := 2*(n+1)/Pi*Irho:
    fi:

	#B[n,m]
    if m <> 0 then
        Iphi := int( ZernikeSin(n,m,rho,phi)*expr, phi=0..2*Pi ):
        Irho := int( Iphi*rho, rho=0..1 ):
        coeffs['B'] := 2*(n+1)/Pi*Irho:
    else
        coeffs['B'] := 0:
    fi:

    gc():
    RETURN( op(coeffs) ):

end:


#=============================================================================
# user help
#=============================================================================
#`help/text/ZSeriesCoeff` := TEXT(
#``,
#` ZSeriesCoeff( n:nonnegint, m:nonnegint, expr:algebraic )`,
#``,
#` Calculate the Zernike series coefficients A[n,m] and B[n,m] of `,
#` an expression.  The expression must be in cylindrical coordinates `,
#` (rho,phi), where rho has been normalized to lie in the range [0..1].`,
#``,
#` See zseries.ms for documentation.`,
#``,
#` Returns a structure [A,B].`,
#``,
#` See also: zernike, ZernikeSeries`
#):

fi;