In this Letter, an imaging spectrometer in which a freeform concave grating is the only optical component in the system is introduced. The degrees of freedom of optical freeform surfaces and a variable line-spacing (VLS) grating are used to realize imaging spectrometers. A point-by-point system design method is proposed that can generate a good initial solution rapidly. By exploring the limitations of the system specifications, it is demonstrated that the spectral dispersion, spectral resolving power, and system length can be improved significantly by using the freeform VLS concave grating. It is also found that freeform surfaces with higher degrees of freedom than a toroid can further improve system performance when using a VLS grating.

Design of an optical system, whether classic or novel, in the past or the present, requires significant effort from the designer. In addition to design methods and theories, the designer’s skills and experience in optical system design are particularly important, which may require years of practice to learn. The diversity and variety of results are limited because of the difficulty, time, and labor costs required. In this article, we propose an automatic design method for freeform optics that can achieve a diverse range of three-mirror designs. The optical specifications and the design constraints are the only inputs required, and a variety of results can be obtained automatically. The output results have various structures and various optical power distributions with high imaging qualities. By implementing the design method, designers can not only realize an overview of the solution space of the three-mirror freeform system, but can also focus on specific designs.

The relative aperture size and the field-of-view (FOV) are two significant parameters for optical imaging systems. However, it is difficult to improve relative aperture size and FOV simultaneously. In this paper, a freeform design method is proposed that is particularly effective for high performance systems. In this step-by-step method, the FOV is enlarged from a small initial value in equal-length steps until it reaches the full FOV; in each step, part of the area of one system surface is constructed. A freeform off-axis three-mirror imaging system with large relative aperture size and a wide FOV is designed as an example. The system operates at F/2.5 with 150 mm effective focal length and a 60° × 1° FOV. The average root-mean-square wavefront error of the system is 0.089λ (working wavelength λ = 530.5 nm).

A novel imaging system design is proposed, in which the FOV and maximum resolution are improved simultaneously while the detector remains fixed. These improvements are realized using freeform optical surfaces and field-dependent characteristic parameters. The resulting imaging system design has optical properties that vary continuously with the field angle. In the central FOV, the system is equivalent to a long-focal-length camera, while in the marginal FOV, it is equivalent to a short-focal-length camera; however, the system has a constant F-number across the FOV. A 2× variation in the field-dependent characteristic parameters across the FOV is achieved.

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