Spectacular natural optical phenomena are produced by highly reflective assemblies of organic crystals. Here we show how the tapetum reflector in a shrimp eye is constructed from arrays of spherical isoxanthopterin nanoparticles and relate the particle properties to their optical function. The nanoparticles are composed of single-crystal isoxanthopterin nanoplates arranged in concentric lamellae around a hollow core. The spherulitic birefringence of the nanoparticles, which originates from the radial alignment of the plates, results in a significant enhancement of the back-scattering. This enables the organism to maximize the reflectivity of the ultrathin tapetum, which functions to increase the eye's sensitivity and preserve visual acuity. The particle size, core/shell ratio and packing are also controlled to optimize the intensity and spectral properties of the tapetum back-scattering. This system offers inspiration for the design of photonic crystals constructed from spherically symmetric birefringent particles for use in ultrathin reflectors and as non-iridescent pigments.