To mitigate climate change a proposed space-based geoengineering solutionis to screen off solar irradiance by placing a membrane in between the Earthand the Sun. The feasibility of such a project largely depends on minimizingthe mass of the shading screen and as an extension to the Sunshade projectthis thesis investigated how such a low-mass membrane could be designed.Because of the acting forces at location in space, minimizing the mass impliesthat the material ought to have a low reflection coefficient and surface densityand therefore the highly transparent material of artificial spider silk was chosenas the proposed material. The only possibility to block light is then byrefraction or diffraction and, since the presence of apertures might lower thesurface density, the structure of the suggested membrane is a grid patternof wires. Such a diffraction grating was investigated while applying twomethods. Method 1 optimized the dimensions of the structure to lower thetotal transmission on Earth when placed on the direct transmission axis ofthe membrane and method 2 tilted the membrane in order to place Earth ata diffraction minimum. This resulted in three suggested designs A, B, andC with surface densities varying from that of 0.00867 to 0.228 gm−2. Theresults were compared with two previous design proposals where the lowestareal density was 0.34g/m2, which is 3/2 to 40 times larger than the densitiesproposed in this paper. The reflectivities for A and B were 12.5 and 3.75 timeslarger than that of the smallest previously achieved reflectivity. The reflectivityof C could not be determined exactly but ought to have a reflectivity at leastas low as B at 3%, making it the most promising candidate for a membranedesign of the three.