tokens: will be composed. 3 NUMERICAL ANALYSIS In this analysis all notable features of the apertures such as spiders and gaps are accounted for in order to achieve more comprehensive results. The quality of the main mirrors is assumed to be perfect, without any optical or mechanically induced aberrations such as inter-segment piston or tip-tilt errors. The diffraction-limited PSFs are computed using the fast Fourier transform (FFT) method with a data matrix of size 4096 × 4096 elements in the aperture plane, which is chosen as a compromise in consideration of the required computational power and desirable linear resolution. Actually, a two-fold oversampling is sufficient to comply with the Nyquist criterion. Application of the FFT in this condition would result in nearly three data points per λ/ D of the PSF, which is rather crude for S/N calculations at the diffraction limit. In order to obtain more convenient PSF data sampling, here the central 1024 × 1024 part of the overall matrix is attributed to the pure aperture with the final linear scales of ≈ 11.0, 26.2, 32.2 and 39.4 mm px −1 for the Keck, GMT (also HDRT), TMT and ELT apertures, respectively. This leads to nearly six data points per λ/ D , which is sufficient to adequately represent the PSF for further processing. At the same time, these linear scales are still too low to sense for all notable features of the apertures as we intended to do initially. For example, the inter-mirror non-reflective gaps in the hexagonal segmentation are set to 4 mm, which is of the order of 2.5 times less than the scale for the Keck aperture. In order to resolve this problem the grey pixel approximation method (Troy Chanan 2003 ) is applied. The simple idea is to rescale the numerical intensity of a pixel in accordance with the portion of area that it covers on the corresponding feature. The OTFs are then calculated through FFT of the corresponding PSFs. The main parameters of the apertures adopted in these calculations are given in Table 1 . Table 1. Main parameters of the apertures. Notes . a The central obscuration is determined as a ratio , where S obs and S eff are the areas of central obstruction and clear aperture, respectively. b The original size of the sub-pupils in HDRT was proposed to be 6.5 m, presumably as an optimal maximum in consideration of technological issues. But here we consider 8.4 m mirrors, as practically proven and also in order to make a direct comparison with the GMT. c The value is calculated assuming an obstructing circle of size 8.4 m. The long-exposure atmospheric OTFs are determined following the corresponding expressions (equations 4 and 5 ). Relative ICs are then constructed directly by using equation ( 3 ). In these calculations, for each case, the values of spatial parameters (i.e. r, r 0 , L 0 ) were normalized to the aperture size D , and the spatial frequencies ( u , v ) to the cut-off limit D /λ. This allows us to conveniently present the final graphs purely as a
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