For a linear array with aperture D and wavelength λ, which expression approximates the near-field distance N?

For a linear array with aperture D and wavelength λ, which expression approximates the near-field distance N?

• A. N ≈ D^2 × λ
• B. N ≈ D^2 / λ
• C. N ≈ λ^2 / D
• D. N ≈ D / λ

Answer: (B)

The near-field distance scales with how the wavefront curvature sits across the aperture. A larger aperture means more phase variation across the beam at a given range, so the region where those variations are still significant extends farther out. Using the common Fresnel/Fraunhofer criterion, the near-field (Fresnel) distance is on the order of D^2/λ. So, for a linear array with aperture D and wavelength λ, the near-field distance N ≈ D^2/λ. Increasing D grows N, while increasing λ (lower frequency) reduces N. The other expressions don’t have the right dimensionality or the correct scaling with D and λ.

The near-field distance scales with how the wavefront curvature sits across the aperture. A larger aperture means more phase variation across the beam at a given range, so the region where those variations are still significant extends farther out. Using the common Fresnel/Fraunhofer criterion, the near-field (Fresnel) distance is on the order of D^2/λ. So, for a linear array with aperture D and wavelength λ, the near-field distance N ≈ D^2/λ. Increasing D grows N, while increasing λ (lower frequency) reduces N. The other expressions don’t have the right dimensionality or the correct scaling with D and λ.