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ABSTRACT We analysed line-of-sight magnetic fields and magnetic power spectra of an undisturbed photosphere using magnetograms acquired by the Helioseismic and Magnetic Imager (HMI) on-board the Solar Dynamic Observatory and the Near InfraRed Imaging Spectrapolarimeter (NIRIS) operating at the Goode Solar Telescope of the Big Bear Solar Observatory. In the NIRIS data, we revealed thin flux tubes of 200–400 km in diameter and of 1000–2000 G field strength. The HMI power spectra determined for a coronal hole, a quiet sun, and a plage areas exhibit the same spectral index of −1 on a broad range of spatial scales from 10–20 Mm down to 2.4 Mm. This implies that the same mechanism(s) of magnetic field generation operate everywhere in the undisturbed photosphere. The most plausible one is the local turbulent dynamo. When compared to the HMI spectra, the −1.2 slope of the NIRIS spectrum appears to be more extended into the short spatial range until the cut-off at 0.8–0.9 Mm, after which it continues with a steeper slope of −2.2. Comparison of the observed and Kolmogorov-type spectra allowed us to infer that the Kolmogorov turbulent cascade cannot account for more than 35 per cent of the total magnetic energy observed in the scale range of 3.5–0.3 Mm. The energy excess can be attributed to other mechanisms of field generation such as the local turbulent dynamo and magnetic superdiffusivity observed in an undisturbed photosphere that can slow down the rate of the Kolmogorov cascade leading to a shallower resulting spectrum.