  We propose an optical encryption framework that can encrypt and decrypt
large-sized images beyond the size of the encrypted image using our two
methods: random phase-free method and scaled diffraction. In order to record
the entire image information on the encrypted image, the large-sized images
require the random phase to widely diffuse the object light over the encrypted
image; however, the random phase gives rise to the speckle noise on the
decrypted images, and it may be difficult to recognize the decrypted images. In
order to reduce the speckle noise, we apply our random phase-free method to the
framework. In addition, we employ scaled diffraction that calculates light
propagation between planes with different sizes by changing the sampling rates.
