Freeform optical surface can benefit the design of off-axis nonsymmetric reflective imaging systems, as more design freedoms can be offered and the aberrations generated by freeform surfaces match the aberrations induced by the decenter and tilt of optical elements. The development of freeform reflective imaging systems relies on advanced technologies in design, fabrication, and assembly. It is very difficult to conduct freeform system assembly due to the lack of assembly references. To this end, one solution is to generate optical systems insensitive to assembly errors directly by special optical design methods. Another solution is to integrate multiple surfaces into a single substrate. As a result, the number of elements in the system and the degrees of freedom during system assembly are reduced. A fabrication method based on rotational cutting is proposed to machine off-axis system with all the surfaces integrated into a single structure. Although the fabrication is more difficult, the system is alignment-free except for the detector. The assembly difficulty and instability of freeform imaging systems using discrete elements can be addressed. However, the current design and optimization of freeform systems focus on the aberration balance and obscuration elimination, without considering the multisurface-integrated fabrication. Therefore, related design methods are necessary to guide the design of freeform reflective imaging systems via multisurface-integrated structures.

This paper concentrates on the design of a freeform off-axis three-mirror thermal imaging system using multisurface-integrated structure with cylindrical package. An initial structure containing an intermediate image inside the system should be first generated. Traditional design methods of first generating a coaxial system and then making the system unobscured gradually can be employed (Fig. 1), but they require advanced design skills and the design may be very complicated. This paper adopts off-axis conics to establish a feasible initial structure directly. Stigmatic imaging for the central field can be realized by sequentially coinciding with the second focal point of one conic with the first focal point of the next conic (Fig. 2). The surface parameters can be calculated based on the given surface locations and the system focal length. The system can be taken as a good initial structure for further optimization. Freeform surface terms can be added to the base conic to improve imaging performance. Q2D polynomials can be utilized to describe the freeform surface shape and they are orthogonal in gradient normal departure. Finally, the mean-square gradient normal departure of a Q2D freeform surface from the base conic can be constrained by simply controlling the square sum of the coefficients of the polynomials. The proposed surface is easier to be tested through computer-generated holograms or other techniques. An optimization method by controlling the positions of surface sampling points is proposed to generate a system that is easier for multisurface-integrated fabrication. The average value of the distances between the sampling points and the center of the overall cylindrical package is constrained to reduce the system size. The variance of these distances is constrained to control the shape of the overall package. Combined with other constraints, systems enabling easier multisurface-integrated fabrication with good imaging performance can be designed. Cooled detectors are generally employed for high-performance thermal imaging systems. The system should have a real exit pupil (the aperture stop) matching the cold stop of the detector. An optimization strategy is adopted to reduce pupil aberration, in which the shape and size of the pupil are controlled by real ray tracing data. Tolerance analysis considering the random and local characteristics of surface figure error can be leveraged to predict the performance of the as-built system.

A freeform off-axis three-mirror system with a cylindrical package which is easier for multisurface-integrated fabrication is designed by the proposed method. The field-of-view of the system is 1.6°×1.6° and the focal length is 240 mm. The system works in the medium-wave infrared band. A cooled detector with an F-number of 3 can be adopted to improve the performance. The off-axis initial structure of the system can be generated directly through confocal off-axis conics based on given surface locations and focal length (Fig. 3). Ideal imaging for the central field is achieved. After further optimization, a freeform system with good performance is obtained (Fig. 5). The average root-mean-square wavefront error is 0.041λ (λ=4000 nm), and the relative distortion in x and y directions is lower than 0.68% (Fig. 6). The average modulation-transfer-function of the full field-of-view at spatial frequency of 33 lp/mm is 0.456 and 0.476 in x direction and y direction, respectively (Fig. 6). The entrance pupil shapes (Fig. 7) and the equivalent entrance pupil diameter of typical field points show that the pupil aberration is small, which ensures enough input energy and good illumination uniformity across the full field-of-view at the image plane. Acceptable imaging performance considering freeform surface figure error and assembly error based on the Monte Carlo tolerance analysis can be realized (Fig. 8).

A design method for an off-axis three-mirror freeform imaging system using multisurface-integrated elements with cylindrical package is proposed. The initial structure satisfying the off-axis multisurface-integrated structure and first-order system specifications can be generated by confocal conicoid surfaces. A freeform surface optimization method based on controlling the position of surface sampling points is proposed to control the shape and size of the overall package of the system, which ensures easier multisurface-integrated fabrication. The control of the focal length and the suppression of light obscuration and pupil aberrations are achieved via real ray tracing data. The freeform surface of Q2D polynomials is employed in the optimization to reduce surface testing difficulty. Finally, a freeform surface off-axis three-mirror thermal imaging system which ensures easier multisurface-integrated fabrication with high imaging quality and low distortion is designed. Tolerance analysis considering the features of freeform surfaces is carried out. The proposed method can be leveraged to guide the design of freeform imaging systems with multisurface-integrated structures, and can also be extended to the development of more generalized off-axis nonsymmetric freeform imaging optical systems.