Computation of Optical Transfer Function via Pupil Function Fourier Transform

The Optical Transfer Function (OTF) of an optical system can be calculated through Fourier transform of the pupil function, which provides the frequency response characteristics of the system. The pupil function Fourier transform method is a widely used mathematical approach in optics that operates by multiplying the optical system's transfer function with the Fourier transform of the input signal to obtain the Fourier transform of the output signal. This method enables comprehensive analysis and optimization of optical system performance, while facilitating understanding of how optical systems respond to input signals. From an implementation perspective, the OTF calculation typically involves computing the autocorrelation of the pupil function using 2D Fourier transforms. The key computational steps include: defining the pupil function matrix representing the optical aperture, performing Fourier transformation using FFT algorithms, calculating the autocorrelation through complex multiplication, and normalizing the result to obtain the modulation transfer function (MTF) component. The algorithm can be implemented in programming environments like MATLAB or Python using functions such as fft2() for 2D Fourier transforms and complex array operations for autocorrelation calculations. Proper sampling of the pupil function and zero-padding techniques are crucial for accurate frequency domain representation. By computing the optical system's OTF, engineers can quantitatively assess the system's resolving capability and transmission characteristics across different spatial frequencies, thereby providing critical guidance for optical system design and optimization. The resulting MTF curves serve as fundamental metrics for evaluating image quality and system performance under various operational conditions.