Diagnosis
Accumulation of skin oils from handling and dust. The lens has a multi-layer anti-reflective coating that is delicate.
How to Fix It
Use a dedicated camera lens blower first to remove loose dust. Gently wipe the lens in a circular motion with a clean, dry microfiber cloth designed for eyeglasses or camera lenses. Apply minimal pressure.
If That Didn't Work
For persistent smudges, lightly moisten a corner of the microfiber cloth with distilled water. Wipe the lens gently with the damp corner, then immediately dry it with the dry section of the cloth.
Heads Up
Never use window cleaner, isopropyl alcohol, compressed air, or tissue paper. These will permanently damage the anti-reflective coating, causing permanent haze or streaks in the projected image.