Multi-field cosine condition in the design of wide-field freeform microscope objectives

Abstract

To break through the limitations of the classical sine condition, a multi-field cosine condition (MCC) is proposed in this paper. Building on this condition, a design method for wide field-of-view (FOV) freeform aplanatic systems is also proposed. This design method ensures that the optical system meets the MCC by correcting the mapping relationships of rays that originate from different apertures on both the object and image sides of the optical system. Using this method, we have successfully designed a chromatic-aberration-free and unobstructed freeform off-axis reflective microscope objective that is characterized by a wide FOV, an extensive spectral working range, and an extended working distance. The objective, which comprises only three freeform mirrors, has a numerical aperture (NA) of 0.4, magnification of 20×, an FOV of 2 mm × 2 mm, and an extended working distance of up to 60 mm. The objective demonstrates imaging quality close to the diffraction limit across the visible band to the short-wave infrared band (0.4–3 µm). When compared with a transmission-type wide-field microscope objective with identical NA and magnification properties, the reflective microscope objective nearly triples the FOV.