here is toward the volume closed by an integral surface . Scalar field functions and are set as solutions of the Helmholtz equation, where is the wavenumber ( is the wavelength), that gives the spatial part of a complex-valued monochromatic (single frequency in time) wave expression. (The product between the spatial part and the temporal part of the wave expression is a solution of the scalar wave equation.) Then, the volume part of the Green's second identity is zero, so only the surface integral is remained as Now is set as the solution of the Helmholtz equation to find and is set as the spatial part of a complex-valued monochromatic spherical wave where is the distance from an observation point in the closed volume . Since there is a singularity for at where (the value of not defined at ), the integral surface must not include . (Otherwise, the zero volume integral above is not justified.) A suggested integral surface is an inner sphere centered at with the radius of and an outer arbitrary closed surface . Then the surface integral becomes For the integral on the inner sphere , and by introducing the solid angle in , due to . (The spherical coordinate system which origin is at can be used to derive this equality.) By shrinking the sphere toward the zero radius (but never touching to avoid the singularity), and the first and last terms in the surface integral becomes zero, so the integral becomes . As a result, denoting , the location of , and by , the position vector , and respectively, See also Kirchhoff's diffraction formula Vector calculus Integral Huygens–Fresnel principle Wavefront Surface integral References Further reading The Cambridge Handbook of Physics Formulas, G. Woan, Cambridge University Press, 2010, . Introduction to Electrodynamics (3rd Edition), D.J. Griffiths, Pearson Education, Dorling Kindersley, 2007, Light and Matter: Electromagnetism, Optics, Spectroscopy and Lasers, Y.B. Band, John Wiley & Sons, 2010, The Light Fantastic – Introduction to Classic and Quantum Optics, I.R. Kenyon, Oxford University Press, 2008, Encyclopaedia of Physics (2nd Edition), R.G. Lerner, G.L. Trigg, VHC publishers, 1991, ISBN (Verlagsgesellschaft) 3-527-26954-1, ISBN (VHC Inc.) 0-89573-752-3 McGraw Hill Encyclopaedia of Physics (2nd Edition), C.B. Parker, 1994, Physical optics Gustav Kirchhoff