Supplementary Figure S1 | Fabrication of a lucius prism array sheet. a, A schematic on a

lucius prism. b, An SEM image of a fabricated lucius prism. The left face is covered with a

metal layer, while the other face and the bottom substrate are free of such metal coating and

thus transparent. c, A schematic illustration of fabrication steps for preparing a lucius prism

array sheet.

Supplementary Figure S2 a, The relationship for the partial metal coverage (x/b) can be

derived from the geometry. We assume that atoms from the metal source travel in straight lines

like light rays during the deposition. For a symmetric triangular prism, we can obtain the angles

θ1, θ2 and θ3 as θ1= 180 - 2α, θ2 = θin – (90 - α) = α + θin – 90 and θ3 = 180 - θ1 - θ3 = α + θin –90.

With the sine law, we can obtain the length of the distance d in the figure: d/sinθ2 = b/sinθ3 or d

= bsinθ2/sinθ3. The fraction (x/b) of the surface deposited with a metal film, as measured from

the prism apex down, is given by:

)90sin(

)90sin(1

+−

−+−=

−=

in

in

b

db

b

x

θα

θα

where θin is the oblique deposition angle, α is the prism angle, x is the distance from the apex

of the prism that is covered by a metal film and b is the total length of one side of the prism, as

shown in a. b, The partial coverage, given by the above equation, is plotted against the oblique

angle with different prism angles (α). c, An SEM image of a lucius prism when the oblique

angle for metal deposition is about 50°. The dark area corresponds to the area deposited by

metal. d, An SEM image of a lucius prism when the oblique angle for metal deposition is ~ 70°.

Supplementary Figure S3 An SEM image of a prepared lucius prism with the symmetric metal

coverage corresponding to the shape in Fig 2c. The prism angle is 60°, the oblique angle for

metal deposition is 60°, and the metal partial coverage is approximately 0.5.

Supplementary Figure S4. Geometries for 3 different cases of viewing angles used to derive

the equations. a, When the viewing angle is larger than the oblique angle for metal deposition

(θin), the viewing area s is screened by the metal-covered area x and, consequently, no

transmission region exists (i.e., totally reflective). b, When the viewing angle is less than θin, the

transparent fractional area through which light is transmitted is the transmittance T, which can

be determined by (s-x)/s as shown in picture (b). The derivation of the expression for s is

similar to that for x in the section S2. c, When the viewing angle is less than the prism angle α,

the transmittance T is constant because the transparent area is constant that is fixed at x/b.

Supplementary Figure S5 A schematic illustration of the fabrication procedure for the lucius

prism sheet having autostereoscopic characteristics. With a slit-type shadow mask, at first, we

deposited black metal (Cr) film obliquely through the opened area of the shadow mask. Then

we moved the shadow mask to screen the area deposited by the 1st metal deposition, and

deposited obliquely again but in opposite direction. Because the slit was 2 mm in width and the

prism had a period of 50 µm, about 40 lucius prisms were covered by metal film in the same

direction per slit.

Supplementary Figure S6 A ray tracing result with the autostereoscopic lucius prism array.

When we see the image in the front position, we can separate the images to each of two eyes,

and perceive a 3D image if the images are stereogram (two images for 3D effects). However,

when we move our head to left or right, we can see only one image that is a 2D image. The

directionality is a unique characteristic of lucius prism array because in the two traditional

methods for autostereoscopy (parallax barrier or lenticular methods) the images look switched

periodically depending on viewing angle.