PURPOSE: To provide the system where the processing time or two-dimensional orthogonal transformation of two-dimensional data of a picture or the like to a half by switching the display of an original picture in parallel with rewrite of an orthogonal transformation pattern to eliminate the rewrite redundant part or the orthogonal transformation pattern in the optical two-dimensional orthogonal transforming device used in a picture compressing/restoring system or the like.

CONSTITUTION: The optical two-dimensional orthogonal transforming device consists of an original picture input means 1, a picture display rewrite means 2, an orthogonal transformation pattern rewrite means 4, a synchronizing means 3 which synchronizes these means 2 and 4, a product calculating means 5 consisting of a light source 6, a picture display means 7, and an image forming means 8 which forms the image of the original picture on the orthogonal transformation pattern, a sum calculating means consisting of a condensing means 11 which condenses the luminous flux transmitted through the orthogonal transformation pattern and a photoelectric conversion means 12 which converts the intensity of this light to an electric signal, and an electric operation means 13 which subjects the electric signal supplied from the photoelectric conversion means 12 to electric operation.