A graded index antireflection layer may be formed on a transparent crystalline member such as a sapphire member. The graded index layer may include aluminum oxide and silicon oxide. The graded index layer may extend from a first surface at the transparent member to a second surface. The fraction of aluminum oxide in the graded index layer may be at a maximum at the first surface so that the index of refraction of the graded index layer at the first surface matches the index of refraction of the transparent member and may be at a minimum at the second surface so the index of refraction of the graded index layer is minimized at the second surface. The graded index layer may be annealed to form aluminum oxide nanocrystals in the graded index layer and to form a polycrystalline aluminum oxide adhesion layer at the first surface.