Compact-depth spiral telescope and method of making and using the same

An optical system having an axial axis, comprising:

• a first primary mirror segment, a second primary mirror segment and a third primary mirror segment, each of the first primary mirror segment, the second primary mirror segment, and the third primary mirror segment being radially disposed about the axial axis of the optical system;
• a first reflector, a second reflector, and a third reflector arranged around the axial axis, the first, second, and third primary mirror segments being configured to reflect a corresponding plurality of principal rays along a first plurality of chords to the firsts, second, and third reflectors, the first, second, and third reflectors being configured to reflect the corresponding plurality of principal rays along a second plurality of chords, the first plurality of chords and the second plurality of chords having an angle in excess of 45 degrees with respect to the direction of the axial axis, and such that the reflected principal rays do not pass through the axial axis of the optical system, the principal rays being reflected such that a path of the reflected principal rays represents a piecewise linear spiral about the axial axis;
• and
• a plurality of secondary reflectors configured to receive a respective one of the plurality of principal rays and direct the plurality of principal rays to an image plane.