Rotary interferometers enable the miniaturization of portable Fourier infrared spectrometers and provide high-speed spectral output. However, their optical path difference (OPD) is nonlinear. In this paper, we analyzed the structure of a portable Fourier-transform infrared spectroscopy (FTIR) rotary interferometer in detail and built a reference coordinate system. Then, an OPD equation for the rotating mirror was deduced according to the geometrical optics principle. Numerical simulation analysis was carried out to illustrate the relationship of OPD with the thickness, refractive index, and rotation angle of the rotating mirror. In terms of sampling without reference laser, the nonlinear relation between OPD and rotation angle was fitted by polynomials to obtain the time non-uniformity corresponding to equal OPD. As a result, the sampling with equal OPD in the case of non-equal time was achieved. Compared with that of the equal-time sampling, the instability of OPD velocity was reduced to 1/5.3, which offered a greater instability margin for the speed control of the rotating mirror and also improved the vibration resistance of FTIR rotary interferometers. Our work provides data support and theoretical basis for the design parameter determination and optimization of portable high-speed FTIR rotary interferometers without reference laser.