Under the Fresnel approximation the radius of curvature of a wavefront, $\frac{1}{R}$ under the [Huygens-Fresnel principle](Huygens-Fresnel%20Principle.md) is approximated as $\frac{1}{z}.$ That is, we take the wave to be propagating along the $z$-axis. Thus, this is equivalent to the [Paraxial approximation](Paraxial%20approximation.md) where we consider waves in place of rays. Under the [Huygens-Fresnel principle](Huygens-Fresnel%20Principle.md) the light wave is proportional to $e^{ikR}/z.$ This approximation is often made in order to aid in solving complicated [[Diffraction integral]]s. Its usefulness is apparent due to its accuracy in the [far-field](Far-field%20propagation.md) limit - where the [diffraction pattern](diffraction) pattern merely scales with distance. In addition we ignore the [obliquity factor](Diffraction%20integral.md#Obliquity%20factor) under this approximation. # Paraxial propagation If we're confident that the beam generally propagates along the z-axis (i.e. if could apply the [paraxial approximation](Paraxial%20approximation.md)), we may extend the approximation to say that the [electromagnetic wave](Electromagnetic%20wave.md) proportional $e^{ikz}/z.$ Such [light-field](Light-field.md)s are solutions to the [Helmholtz equation](Helmholtz%20equation%20(optics).md). #Electromagnetism/Optics/waveOptics