Beam scanning has been widely used in laser radar and optical communications. Conventional beam scanning methods with mechanical structures suffer from many limitations, such as large volumes, low switching speeds, and high powers. Optical phased array is a new technique that enables beam scanning, and phase modulator components used in optical phased array scanning technology mainly include liquid crystal, optical waveguide, electro-optical crystal, microlens array, and micromirror array. Electro-optical scanning device has some problems, such as low response speed, high driving voltage, and difficult large-aperture beam scanning. The scanning technology with a microlens array has the advantages of simple structure, miniaturization, lightweight, high scanning speed, and large aperture. Scanning imaging optical system with a microlens array includes microlens array elements, and the rays do not fill the clear aperture of the microlens array owing to the effect of scanning angle and microlens array structure. One property of the microlens array system is that the wavefront exiting the microlens array is no longer continuous, and the motion of the microlens array results in non-rotational symmetry of the system, which brings new challenges to the traditional design methods and performance evaluation of optical systems. In this paper, a preliminary theoretical study is conducted on the performance and imaging models of imaging optical systems based on optical phased array scanning technology with a microlens array, which can benefit the design and evaluation of microlens array systems.

The scanning imaging optical system with a microlens array is a combined optical system, and the scanning function is accomplished by the motion of the microlens array. Firstly, the performance of the system is affected by the discontinuity and periodicity of the beam passing through the pupil, and the fill factor is adopted in this study to characterize the fill rate of rays at the pupil position of the microlens array system. The effect of the fill rate of the beam at the entrance pupil position on the detection distance of the system is analyzed according to the formula of the detection distance of the point target of the optical system in the infrared environment, and that at the exit pupil position on the point spread function and the modulation transfer function of the system are analyzed according to the information optics theory. Secondly, the paraxial optical model of a scanning optical system with a microlens array is constructed, and a calculation method of the fill factor based on the paraxial optical model is proposed. The effect of the system structure parameters on the fill factor is analyzed, and a design method of the scanning optical system with a microlens array is proposed based on the calculation method. Finally, a scanning imaging optical system with a microlens array is designed by using the proposed design method, and the design result verifies the theoretical analysis and design method.

Several important results are obtained as follows. Firstly, the detection distance simulation results (Fig. 2) show that appropriately increasing the effective entrance pupil area is beneficial to increase the detection distance of the system. The point spread function of the scanning optical system with a microlens array (Fig. 3) is the product of the diffractive optical intensity distribution of a single microlens unit and the fixed periodic optical intensity distribution with a grid pattern determined by the microlens array structure. The energy proportion of the zero-order principal maximum in the point spread function reduces with the decrease in α_ex, and more energy enters the other-order principal maxima. Therefore, the resolution of the system degrades owing to the increased diffusion of the light spot. A similar periodicity is observed in the modulation transfer function curve that does not decrease monotonically, and the reduction in the fill factor α_ex decreases the contrast at the middle spatial frequency. When the fill factor α_ex decreases to 25%, multiple zeros are observed before the true cutoff frequency, which indicates that a very small fill factor can cause the microlens array system to lose a part of the object information in the middle frequencies. Secondly, the effects of different parameters on the fill factor are analyzed. The results show that the system scanning angle and detection distance are mutually constrained, and increasing the scanning angle needs to be accomplished by reducing the detection distance [Fig. 6 (b)]. Increasing the value of I_n [Fig. 6(a)] and decreasing the value of I_g1 [Fig. 6(c)] are beneficial to increase the fill factor of the system. Finally, an optical system consisting of two square microlens arrays of 5×5 is designed, with a fill factor α_en of 0.16, α_ex of 0.87, and scanning angle of ±4°. For a point target with a radiation intensity of 0.5 W·sr^-1, the detection distance is 7.8 km when the average transmittance of the atmosphere is 0.4. The simulation results show that most energy of the point spread function of the design system is concentrated in the zero-order principal maximum, and the dispersion degree of the diffracted spot is low [Fig. 9(a)]. The contrast decreases in the middle spatial frequency of the modulation transfer function curve [Fig. 9(b)], but it is not obvious. The geometric radius of the maximum spot in the spot diagram is 4.76 μm [Fig. 9(c)], and the performance of the designed system is excellent.

The scanning imaging optical system with a microlens array is lightweight, and the displacement of the mechanical movements is small. The rays do not fill the clear aperture of the microlens arrays during the scanning process, which affects the detection distance and imaging resolution of the system. The fill factor is proposed for characterizing the fill rate of rays at the entrance and exit pupil positions of the microlens arrays system, and its effect on the detection distance, point spread function, and modulation transfer function are analyzed. On the basis of the paraxial optical model, a method to fast calculate the fill factor is proposed, and a scanning imaging optical system with microlens arrays is designed. The simulation results and theoretical calculations are in good agreement, and the design results show that the performance of the system is excellent. This work can benefit the design and evaluation of microlens array systems.