Synthesizing a Fresnel zone plate inside a Vander Lugt matched filter (MF) results in a lensless matched filter (LLMF) that is space-invariant from the point of view of vignetting apertures. In practice the unfocused output components of the LLMF do not degrade its SNR. A LLMF displacement appears as a combined shift of its filter and lens components. The third-order holographic aberrations of the MF and LLMF, and particularly their root-mean-square astigmatisms, are compared via computer-generated plots.
Marc J. Bage and Michael P. Beddoes, "Lensless matched filter: operating principle, sensitivity to spectrum shift, and third-order holographic aberrations," Appl. Opt. 15, 2830-2839 (1976)