Analytical equations for a nonconfocal stigmatic three-freeform-mirror system

Equations to design an aplanatic catadioptric freeform optical system

The present paper introduces a set of equations to design an aplanatic catadioptric freeform optical system. These equations form a partial differential equation system, in which a numerical solution defines the first and last surfaces of the catadioptric freeform optical system, composed of an arbitrary number of reflective/refractive surfaces with arbitrary shapes and orientations. The solution of the equation can serve as an initial setup of a more complex design that can be optimized. An illustrative example is presented to show the methodology introduced in this paper.

Power set of stigmatic freeform catadioptric systems

A method to design catadioptric systems from scratch based on optimizing an element of the power set of stigmatic catadioptric systems is presented. This set contains all possible stigmatic catadioptric systems. The deduction of the set is also presented in this paper, and its derivation is totally analytical. Additionally, an illustrative example of optimization of an element of the mentioned set is presented. The results are as expected.

Power set of mirror-based non-symmetric stigmatic optical systems

The set of all possible stigmatic systems made by mirrors is presented. The derivation of the set is analytical, and it is based on the Fermat principle. The properties of the set are properties that all possible stigmatic systems made by mirrors share. The set is tested here with a practical example of optical design, and the results are as expected by theory. This example works with a large field of view rather than a single field, and the volume of the example is several times less than similar systems reported in the literature.

The Opto-Mechanical–Thermal Coupling Analysis and Verification of an All-Aluminum Freeform Imaging Telescope

A freeform imaging telescope (FIT) can achieve a large field of view, high resolution, light weight, and small volume at the same time. Single-point diamond turning (SPDT) is usually used to fabricate FITs, which is made entirely of aluminum alloy. Compared with a traditional telescope, whose reflector is made of glass and whose structure is aluminum, the coefficient of thermal expansion (CTE) of the structure and reflector of which is non-conforming, the CTE of the structure and reflector in an all-aluminum FIT is identical. Therefore, it was expected to theoretically have athermalization properties. In this paper, an all-aluminum off-axis three-mirror FIT was verified. The opto-mechanical–thermal coupling analysis of the FIT at −20 °C was carried out, including data processing and coordinate transformation. The reflector node deformation data of the global coordinates obtained from the finite-element analysis were converted into XY polynomial coefficients of the local coordinate system in ZEMAX. The results showed that the modulation transfer function (MTF) of the FIT at −20 °C~+40 °C still reached the diffraction limit. Moreover, the MTF of the FIT at −20 °C was 0.291 through a thermal environmental test, which was almost the same as the MTF at 22 °C. These results showed that the all-aluminum FIT could achieve athermalization properties.