This work studies an approximate scheme by coupled-wave theory to analyze quickly the large-scale moiré phenomena as seen in common liquid-crystal devices. The moiré phenomena are considered to be caused by two periodic structures (with lattice vectors γ[combininb arrow](1) and γ[combininb arrow](2) and show an interference pattern spanning over a length γ(m)=|γ[combininb arrow](1)|·|γ[combininb arrow](2)|/|γ[combininb arrow](1)-γ[combininb arrow](2)| (with γ[combininb arrow](1)=/~γ[combininb arrow](2)). With the coupled-wave theory, the complete analysis of the moiré optics includes at least 2γ(m)/λ (λ: wavelength in vacuum) Fourier components and presents an ineffective computation. This work applies a cos(τ) type approximation for the openings of unpatterned liquid-crystal pixels, and considers the first-order coupling between the Fourier components of pixels and other (periodic) optical structures. We hence arrive at an effective evaluation, including 4τ|γ[combininb arrow](1)|/λ (or 4τ|γ[combininb arrow](2)|/λ) Fourier components, and are able to go back to a complete analysis when considering higher-order couplings at an appropriate τ integer value.