MTF-based Research on the Minimum Fill Factor in Optical Sparse Aperture System

To avoid the loss of image information when it is transferred through optical sparse aperture system with excessively diluted apertures arrangement, we propose a method in the frequency domain termed characteristic triangle to calculate the minimum fill factor. This method is based on the characteristics of MTF and demonstrates that when the characteristic triangle is equilateral with each side √3th power of sub-MTF cutoff frequency, MTF has no zero value below cutoff frequency, thus we can obtain the minimum fill factor. Furthermore, we apply it to some typical sparse arrays, such as Golay3, Golay6, Ring6 and Tri-arm7, and get their fill factors of 33.33%, 15.16%, 30.11%, and 11.14% correspondingly, which are consistent with numerical results.