Abstract: Arrangements for the point-to-point imaging of a broad spectrum of electromagnetic radiation and ultrasound at large angles of incidence employ matched pairs of spherically bent reflectors to eliminate astigmatic imaging errors. Matched pairs of spherically bent crystals or spherically bent multi-layers are used for X-rays and EUV radiation; and matched pairs of spherically bent mirrors that are appropriate for the type of radiation are used with microwaves, infrared and visible light, or ultrasound. The arrangements encompass the two cases, where the Bragg angle—the complement to the angle of incidence in optics—is between 45° and 90° on both crystals/mirrors or between 0° and 45° on the first crystal/mirror and between 45° and 90° on the second crystal/mirror, where the angles of convergence and divergence are equal. For x-rays and EUV radiation, also the Bragg condition is satisfied on both spherically bent crystals/multi-layers.