A known challenge in sound field reproduction techniques such as high-order Ambisonics (HOA) is the reproduction of nearby sound sources. In order to reproduce such nearby sound sources, the near-field compensated (NFC) method with angular weighting windows (AWWs) has been previously roposed for HOA [1]. Considering auditory distance perception, (low-frequency)interaural level differences represent the main auditory cue for nearby real sound sources outside the median plane. Simulations showed that these ILD cues can be reproduced with existing weighted NFC-HOA methods for frequencies above about 500 Hz. However, since low-frequency ILD cues seem to be important for distance perception, a novel regularization function is proposed as AWW that can reproduce natural ILDs down to bout 250 Hz, even in realistic playback environments. Using this regularization function, a listening test showed an improved distance perception performance for lateral sources compared to frontal ones. This improvement was greater for 3D reproduction than for 2D but slightly lower than for real sources. The distance of virtual nearby sources reproduced by NFC-HOA with the regularization function as AWW can be perceived nearly as accurately as corresponding physical ones.