the radiation pattern has a canonical form of Simple substitutions of various values of into the canonical equation yield the following results: style="margin-left: auto; margin-right: auto; border: none;" ! ! Radiation Pattern ! Explanation |- | 0 | style="text-align:right;" | | peak of main beam |- | | style="text-align:right;" | −∞ dB | first null |- | | style="text-align:right;" | | peak of first sidelobe |- | | style="text-align:right;" | −∞ dB | second null |- | | style="text-align:right;" | | peak of second sidelobe |- |} For a circular aperture antenna, also having a uniform amplitude distribution, the first sidelobe level is relative to the peak of the main beam. In this case, the radiation pattern has a canonical form of where is the Bessel function of the first kind of order 1. This is known as the Airy pattern. Simple substitutions of various values of into the canonical equation yield the following results: style="margin-left: auto; margin-right: auto; border: none;" ! ! Radiation Pattern ! Explanation |- | 0 | style="text-align:right;" | | peak of main beam |- | 3.83 | style="text-align:right;" | −∞ dB | first null |- | 5.14 | style="text-align:right;" | | peak of first sidelobe |- | 7.02 | style="text-align:right;" | −∞ dB | second null |- | 8.42 | style="text-align:right;" | | peak of second sidelobe |- |} A uniform aperture distribution, as provided in the two examples above, gives the maximum possible directivity for a given aperture size, but it also produces the maximum sidelobe level. Sidelobe levels can be reduced by tapering the edges of the aperture distribution (changing from uniformity) at the expense of reduced directivity. The nulls between sidelobes occur when the radiation patterns passes through the origin in the complex plane. Hence, adjacent sidelobes are generally 180° out of phase to each other. Grating lobes For discrete aperture antennas (such as phased arrays) in which the element spacing is greater than a half wavelength, the spatial aliasing effect causes some sidelobes to become substantially larger in amplitude, and approaching the level of the main lobe; these are called grating lobes, and they are either identical, or nearly identical as shown in the figure, copies of the main beams. Grating lobes are a special case of a sidelobe. In such a case, the sidelobes should be considered all the lobes lying between the main lobe and the first grating lobe,