Optical orthogonal signature pattern codes (OOSPCs) have attracted wide attention as signature patterns of spatial optical code division multiple access networks. In this paper, an improved upper bound on the size of an $(m,n,3,λ_a,1)$-OOSPC with $λ_a=2,3$ is established. The exact number of codewords of an optimal $(m,n,3,λ_a,1)$-OOSPC is determined for any positive integers $m,n\equiv2\ ({\rm mod }\ 4)$ and $λ_a\in\{2,3\}$.