The acousto-optic tunable filter (AOTF) spectrometer can simultaneously acquire the spatial image and spectral information of the detection target, featuring small size, light weight, and flexible selection of central wavelength. The optical system is an essential part of the information obtained by the AOTF imaging spectrometer, and its design scheme and imaging quality can affect the instrument's performance. The zoom system has continuously variable focal lengths. A suitable zoom system can effectively expand the imaging function of the AOTF spectrometer and realize continuous detection, tracking, recognition, and collimation of the target object. The zoom optics of current AOTF spectrometers is mostly mechanical zoom. The mechanical zoom system can modify the focal length only by changing the distance between the components. In contrast, the active zoom system without moving parts can adjust the focus by controlling the changes in curvature and refractive index of the active optical elements. In this study, we propose a design scheme of a combined zoom optical system of AOTF imaging spectrometer, which consists of an active zoom front optical system and a projection system with arbitrary magnification (N) to achieve a wide range of zoom, and the simulation design of active zoom front system is completed.

First, the structure and working principle of the AOTF imaging spectrometer are investigated to determine the optical system design scheme, and the design theory of the off-axis three-mirror active zoom optical system is studied in detail to determine the initial structure of the zoom front system. Then, the off-axis field of view (FOV), eccentricity, and tilt of the mirror are added to remove the central light obstruction, which provides more possibilities for the spatial layout of each component. It tends to be coaxial after optimization, and the mirror must be constrained in the tilt and processed by decentration by using the @JMRCC macro function. After that, a progressive approximation is used to implement the continuous zoom function of the front optical system. Starting from the calculation solution of the initial structure at the system's short focus, medium focus, and long focus, the optimization criteria of node addressing and synchronous optimization alternating cycles are used to optimize optical structures at all focal lengths within the zoom range. In addition, the front system is an image space telecentric optical structure, which can effectively reduce the extra aberration caused by the diffraction in AOTF, eliminate parallax, and increase the convenience for the subsequent connection of the projection system and the processing of the system. Last, the linear astigmatism of the TMA is eliminated effectively by debugging the parameters of the incident angle and mirror spacing, and the off-axis aberration of the system is balanced and corrected by adding aspheric surfaces, which are based on even power series polynomials with rotational symmetry, and the design of the system tends to be symmetrical as much as possible control the system distortion problem.

The active zoom front system adopts Cook-TMA with no intermediate image plane based on a variable curvature mirror (VCM), which changes the radius of curvature of the mirror to achieve zoom function (Fig. 5). The maximum central deformations of the mirrors are 44.2 μm, 73 μm, and 603 μm, respectively. The variations of mirror spacing caused by the deformation of mirrors are 0.029% (between primary and secondary mirror) and 0.048% (between secondary and third mirror), and the accuracy of surface shape is better than 0.0556λ. In the process of system zoom, the mirror curvature radius and focal length are continuously changed, and the zoom curve is smooth without jumping value (Fig. 6). Three mirrors use 8th high-order aspheric surfaces, and coefficients are unchanged during the zoom process. The system is the image-side telecentric structure, and the stop is located in the secondary mirror with a small size, light weight, and compact structure. The results of the design in Code V show that the modulation transfer function (MTF) of zoom front system is greater than 0.68@34 lp/mm on short focal length, 0.62@34 lp/mm on middle one, and 0.45@34 lp/mm on long one with 260-520 mm zoom range and 0.5-1.5 μm spectral region (Fig. 7), and root mean square (RMS) radius is less than 0.193 μm at the short focus, 0.196 μm at the middle focus, and 0.345 μm at the long focus (Fig. 8).

In the present study, a design scheme of a combined zoom optical system for an AOTF imaging spectrometer is presented, which uses a combination of the active front zoom system with different magnifications of the projection system to obtain a larger zoom range, and a design example of a front zoom optical system for AOTF imaging spectrometer is provided. It uses the off-axis method of the coaxial system and the progressive approximation method to realize the off-axis three-mirror active continuous zoom optical system. The system is an image-side telecentric structure, which can effectively increase the convenience for the subsequent connection of the projection system and the processing of the system. The optical system has a working band of 0.5-1.7 μm, a zoom range of 260-520 mm, a smooth zoom curve, and a stable image plane with realizable parameters of the VCM. The simulation result shows that the MTF is greater than 0.45@34 lp/mm, and the RMS radius is less than 0.345 μm in the full field. The system has a compact structure, with the characteristic of full-electric tuning, fast response speed, small size, and light weight, which can be flexibly applied to a variety of detection scenarios.