One way of characterizing antenna arrays consists of describing the active element pattern of each antenna, i.e., the pattern of the element of interest, considering the presence of all other array elements, which are terminated in matched loads [Pozar, 1994; Hansen, 1998]. In general, due to mutual coupling between the antennae, the active element pattern is quite different from the pattern of the same element taken in isolation. For large regular arrays consisting of identical elements, the element patterns tend to be rather homogeneous in the array, except for antennae near the edges, which are in a quite different environment. For very large arrays, the active element pattern is a very useful concept, because the pattern of the fully excited array can be expressed as the product of the active element pattern and the array factor, while still accounting for mutual coupling effects.
 It is generally accepted that, for an infinite planar array, the active element pattern in a given direction has a simple relation with the active reflection coefficient of the same array when it is fully excited and scanned at the same angle [Mailloux, 1994, p. 338]. However, we think that the derivations given in the literature are not entirely satisfactory, because they are either partly based on intuitive arguments, or they are limited to a specific class of antennae, as explained by Hansen [1998, p. 222]. Most publications on the active element pattern refer to a paper written by Hannan . In that paper, the ratio between the realized and directive gains is expressed as 1 − ∣Γa (θ, ϕ)∣2, where Γa is the active reflection coefficient for the array scanned in the direction of interest, defined by the angles θ and ϕ. Then, for a situation without grating lobes, the peak directive gain of the array is related to the projected aperture of the array, by using the standard formula for “apertures large compared with a wavelength.” Finally, the directive gain is scaled down to a single element of the array, which yields:
where A is the area allotted to each antenna in the array plane, θ is the scan angle from broadside, and λ is the wavelength.
 While this result is correct, the derivation presented in the work of Hannan  involves large arrays of finite size (with apertures “large compared with a wavelength”), and it does not explain why situations with grating lobes must (indeed) be excluded to comply with result (1). Another derivation is given in the work of Pozar , but it is limited to elements which can be characterized by a single radiation mode, as short dipoles and thin slots.
 These derivations are based on the transmit-only situation. We think that a rigorous and more general derivation should be obtained by explicitly relating the transmit and receive situations, with the help of the Lorentz reciprocity theorem, as is done for isolated antennae in the work of Collin and Zucker  and De Hoop and De Jong . The approach presented here consists of first deriving an expression for the receiving cross section of the antenna in its terminated array environment. The receiving cross section [Collin and Zucker, 1969] with respect to a given direction is defined as the ratio between the power received in the terminating load (which can be the input impedance of an amplifier) and the power density of the incoming plane wave. It differs from the effective area through the fact that the latter quantity does not account for the potential impedance mismatch between the antenna and the load in which it is terminated. Once the receiving cross section is obtained, reciprocity applied to the port of the antenna immediately yields the active element pattern (also called “scan element pattern” in the work of Hansen ) of the antenna in its array environment.
 The methodology followed here to obtain the receiving cross section can be seen as an extension of the work done by De Hoop and De Jong  for an isolated element. This will provide an explanation of why reciprocity applies to the active input impedance of infinite arrays, as it is stated without explicit proof in the work of Hannan [1964, section 3]. The proofs will be given here for nonlossy antennae. For the sake of clarity, this will be done first for situations without a grating lobe, then the results will be extended to conditions allowing grating lobes.
 Besides providing a more rigorous derivation, the approach adopted here can also be used for estimating the receiving cross section of antennae located in infinite linear arrays. The result depends on the azimuthal directivity of the infinite array, and probably cannot be obtained intuitively. To the authors best knowledge, the relation between element pattern and azimuthal directivity of an antenna located in an infinite linear array has never been given in the literature.
 This paper is organized as follows. The expressions for the receiving cross section and power pattern are developed in section 2 for the linear array case. In section 3, a similar derivation is applied to the planar array case. Parts of the argumentation refer to intermediate results obtained in section 2. The extension to grating lobe conditions is presented in section 4. The use of reciprocity, instead of the establishment of a power budget, automatically involves the polarization aspects, so that it is not necessary to introduce the polarization mismatch a posteriori. The results are commented and conclusions are drawn in section 5.