Theory of modulation transfer function artifacts due to mid-spatial-frequency errors and its application to optical tolerancing

Aspheric and free-form surfaces are powerful surface forms that allow designers to achieve better performance with fewer lenses and smaller packages. Unlike spheres, these surfaces are fabricated with processes that leave a signature, or "structure," that is primarily in the mid-spatial-frequency region. These structured surface errors create ripples in the modulation transfer function (MTF) profile. Using Fourier techniques with generalized functions, the drop in MTF is derived and shown to exhibit a nonlinear relationship with the peak-to-valley height of the structured surface error.