This application is a U.S. National Stage Application of International application No. PCT/KR2018/011623 filed on Oct. 1, 2018 which is based upon and claims the benefit of priority to Korean Patent Application No. 10-2017-0179011 filed on Dec. 26, 2017 in the Korean Intellectual Property Office. The disclosures of the above-listed applications are hereby incorporated by reference herein in their entirety.

BACKGROUND

1. Technical Field

The invention relates to an optical system for displaying a three dimensional image. More particularly, the invention relates to an optical system for displaying a three dimensional image which can display a digital hologram magnified using a reflection configuration in a space as the three dimensional image.

2. Description of the Related Art

As display apparatuses have been developed, the demand for optical systems capable of displaying three dimensional images with reality has been increased. Such systems for displaying three dimensional images are expected to be widely used in display apparatuses. Therefore, various techniques have been attempted to accomplish the systems capable of displaying three dimensional images.

SUMMARY

The object of the invention is to provide an optical system for displaying a three dimensional image which can display a hologram as a three dimensional image with a compact structure.

To accomplish the above-mentioned object of the invention, there is provided an optical system for displaying a three dimensional image including a changing mirror, a rotating mirror, a concave mirror and a planar mirror. The changing mirror may be configured to change a path of a light from a horizontal direction to a vertical direction after the light passes through a spatial light modulator. The rotating mirror may be configured to rotate with an X-axis and a Y-axis having different curvature radii. The tilted mirror may include a central region including a hole for allowing the light to pass therethrough, and a peripheral region including one surface having a concave tilted structure and the other surface having a planar structure. The concave mirror may include a central region including a hole having a size capable of encompassing the tilted mirror, and a peripheral region having an entirely concaved bending structure. The planar mirror may include a central region including a hole therein, and a peripheral region having a flat doughnut structure. The changing mirror, the tilted mirror, the rotating mirror and the planar mirror may be arranged such that the light of which path is changed by the changing mirror may pass through the central region of the tilted mirror, the light may direct onto the rotating mirror, the light may be reflected toward the one surface of the peripheral region of the tilted mirror, the light may be reflected toward the peripheral region of the planar mirror, the light may be reflected onto the concave mirror, and the light may pass through the central region of the planar mirror. The concave mirror may enclose the tilted mirror under the rotating mirror.

In example embodiments, the rotating mirror may include aluminum and one surface of the rotating mirror onto which the light is not incident may have a concave structure.

In example embodiments, the concave mirror may include a concave portion facing the planar mirror and having an angle of about 35 degree to about 50 degree with respect to the other surface of the tilted mirror.

In example embodiments, the optical system may additionally include a color composite prism configured to synthesize R, G and B colors with the light passing through the spatial light modulator, and a focusing lens focusing the light after the light passes through the spatial light modulator, wherein the spatial light modulator, the color composite prism and the focusing lens may be arranged in a line as well as perpendicular to a direction where the rotating mirror is arranged.

In example embodiments, the optical system may additionally include a relay lens configured to focus the light of which path is changed by the changing mirror before the light passes through the central region of the tilted mirror.

In example embodiments, the optical system may additionally include a planar window configured to cover the hole of the central region of the planar mirror wherein the planar window includes anti-reflective coatings on both surfaces thereof.

According to example embodiments of the invention, the optical system for displaying a three dimensional image may includes most of elements such as various mirrors such that the chromatic aberrations may not be generated among these elements to thereby display the three dimensional image with reality. Additionally, the optical system for displaying a three dimensional image may include the various mirrors having large sizes which cannot accomplished using lenses so that the optical system may efficiently display the magnified hologram in the desired space as the three dimensional image. Furthermore, the optical system for displaying a three dimensional image may include the rotating mirror having a diameter relatively smaller than those of other mirrors such that the damage to the rotating mirror may be effectively minimized in the operation of the optical system. Particularly, the optical system for displaying a three dimensional image may have the configuration in which the spatial light modulator, the color composite prism and the focusing lens arranged horizontally in the line so that the optical system may have a compact structure by reducing the total height of the optical system.

