The peculiarities analysis in design of compressors for negatively chirped optical pulses parametrically amplified in double-chirped regime up to 1 J in multi-cascade system is done. A comparative analysis of the spatio-temporal distribution of the pulses at the output of various compressor schemes with an internal telescope has been performed. The analysis has been carried out using two methods: calculating additional compressor dispersion using the Seidel aberration coefficients of the internal telescope and the ray tracing method. A ray-tracing algorithm has been developed that allows to calculate the spatiotemporal and spatiospectral pulse intensity distributions at the output of compressors with an internal telescope. The on-axis and off-axis Offner schemes, Martinez scheme compressor and compressor scheme with a single-lens internal telescope are analyzed. It is shown, that the ray tracing method more accurately takes into account system aberrations, including high-order aberrations, while the calculation with the Seidel aberration coefficients takes into account only primary aberrations. According to the analysis, the optimal scheme of a grating compressor with an internal telescope for compressing negatively chirped pulses in the range of 1410 nm to a duration of less than 40 fs and energies up to ~ 0.8 J is the off-plane Offner scheme.