***Non-Mechanical Image Rotation Using an AODP (Acousto-Optic Dove
Prism)***

***Eung Gi Paek***

*National Institute of Standards and Technology, Gaithersburg, MD 20899*

***Joon Y. Choe and Tae K. Oh***

*NSWC Dahlgren Division, 17320 Dahlgren , VA 22448-5100*

***John H. Hong and Tallis Y. Chang***

*Rockwell International Science Center, Thousand Oaks, CA 91360*

*Abstract **-** We report what we believe to be the first method for
non-mechanical and programmable image rotation. The method uses a pair
of crossed acousto-optic beam deflectors and a polygon mirror to emulate
the mechanical dove prism. It is capable of fast (on the order of
microseconds) image rotation to an arbitrary angle in a programmable
manner. An experimental result to prove the concept is provided.*

Submitted to Optics Letters on April 15, 1997

Rotation of an image to an arbitrary angle in a programmable manner is
very important for various applications such as rotational invariant
pattern recognition, computer graphics and beam steering of phased array
antennas.

Most of the previous techniques \[1-5\] rely on a dove prism as shown in
Figure 1 (a). By rotating a dove prism by an angle θ around the optical
axis, an input image can be rotated by 2θ. However, such a mechanical
process is slow and unreliable. Chiou and Yeh \[6\] demonstrated a
non-mechanical method using a conventional dove prism inside a ring
cavity to generate a series of rotated images.

In this Letter, we propose an image rotation method that is both
non-mechanical and programmable to permit rotation of an image to an
arbitrary angle in a controllable manner. It is based on an analysis of
a conventional dove prism. As illustrated in Figure 1 (b), a dove prism
can be divided into three parts: the first part is a wedge prism to
direct the incident beam to the bottom (or top) of the second part which
functions as a mirror to reflect the incoming light. The third part is
another wedge prism to redirect the beam along the original direction.
All these three parts rotate together.

Our approach for non-mechanical image rotation is shown in Figure 1 (c).
Each of the rotating wedges (the first and third parts of a dove prism)
is replaced by an xy acousto-optic beam deflector (xy-AOBD). The xy-AOBD
consists of a pair of crossed AOBD's sandwiched together with
transducers along orthogonal directions. By adjusting the frequencies of
acoustic signals applied to the two AOBD's, beam direction can be
changed along arbitrary directions, just as a wedge does.

The reflecting mirror (second part) is replaced by a circular
cylindrical mirror to avoid the need for rotation. However, to prevent
unwanted distortion due to the curvature of the circular mirror surface,
the cylindrical mirror is discretized to multiple facets. Also, incoming
light is focused to have a minimum size on the mirror surface. In this
way, an image can be rotated fast (on the order of microseconds) to an
arbitrary angle in a programmable manner, without requiring any moving
parts. Since the concept is based on the conventional dove prism, a name
acousto-optic dove prism (AODP) has been proposed.

To prove the concept of the proposed AODP, we constructed an
experimental setup as shown in Figure 2. A 5 mW HeNe laser is used as
the light source. After beam expansion and spatial filtering, the
magnified collimated beam illuminates an input resolution target. The
light passing through the input transparency is deflected by a pair of
crossed AOBDs (slow shear mode TeO~2~ crystals with a large input
angular bandwidth) and is focused by a lens (focal length = 36 cm) on
the surface of the cylindrical polygon mirror. In this initial demo
intended for proof of our concept, only two mirror facets oriented at a
right angle are used. After the multi-facet mirror, the beam is
reflected back to pass through the same lens and xy-AOBDs and is
detected by a CCD after a beam splitter.

Figure 3 illustrates an experimental result obtained from our optical
system. Since the two mirrors are at a right angle, the two images are
rotated by 180 degrees (twice the angle between the two mirrors). A
real-time image rotation has been achieved within 10 μsec with a 6 mm
aperture in front of the AOBDs. Also, rotations to other angles have
been separately confirmed.

The noise contribution to the image is mainly due to unwanted reflection
from the surfaces of optical components such as the beam splitter, AOBDs
and the lens. Also, a slight defocusing of the images is attributed to
the distance between the two AOBDs. These noises can be greatly reduced
if thin sandwiched xy-AOBD's (shown in Figure 1 (c)) are used. A
custom-designed xy-AOBD with a compact size (10 mm X 10mm X 2mm) and
with xy transducers on the same crystal is currently being fabricated.

The number of different rotation angles available in this system is
given by the following equation:

$N = \frac{p \cdot Df \cdot d_{\text{min}}}{v}$, (1)

where ∆f, d~min~ and v represent acoustic frequency bandwidth, minimum
feature size of an input pattern and acoustic velocity, respectively.
Interestingly, the number is independent of the focal length of a lens
and wavelength of the light. For a typical example, ∆f = 50 MHz, d~min~
= 0.1 mm and v = 600 m/sec, N becomes approximately 25.

To further increase the number of rotation angles, several methods can
be used: First, a special lens design can be employed to reduce the
fixed distortion effect of a cylindrical mirror. Second, higher-order
diffracted beams can be used instead of the first order to increase the
diffraction angle of an AOBD. In this case, the thickness of an AOBD
needs to be thin to reduce the Q factor \[7\] and to permit higher-order
diffractions. Taking the third order diffraction, for example, would
permit rotation to 75 different angles, which is normally sufficient for
rotationally invariant pattern recognition. In this case, other unwanted
diffraction orders can be discarded simply by choosing the appropriate
length of the cylindrical polygon mirror.

The AOBDs in this system need to accept an input beam with broad angular
bandwidth of approximately $\pm$ 3 degrees. A special group of AOBDs
(typically, slow shear wave Tellurium dioxide crystals) that accept a
circular laser beam are commercially available.

In conclusion, we have proposed and demonstrated what we believe to be
the first non-mechanical image rotation method that can be programmed to
permit rotation of an image to an arbitrary angle within a few
microseconds time. The method can be useful for various information
processing applications such as rotationally invariant pattern
recognition and computer graphics.

This work was supported by the Office of Naval Research (ONR) under
Contract Number NC0014-97-F-0021.

**References**

1.  R. B. Johnson, Appl. Opt. 13, 2962 (1974), US Patent 3,813,552.

2.  W.G. McKinley, Appl. Opt. 33, (28) 6570 (1994), US Patent 5,296,972.

3.  R.H. Ginsberg, Appl. Opt. 33, (34) 8105 (1994).

4.  B. Braunecker, O. Bryngdahl, and B. Schnell, J. Opt. Soc. Am. 70,
    137 (1980).

5.  A. W. Lohmann, J. Opt. Soc. Am. A 10, 2181 (1993).

6.  A. Chiou, and Pochi Yeh, Apl. Opt. 29, 1584 (1990).

7.  R.J. Collier, C.B. Burckhardt and L.H. Lin, *Optical Holography*
    (Academic Press, New York, 1971), Chap. 9.

**Figure Captions:**

Figure 1. Image rotation methods : (a) conventional mechanical method
using a dove prism, (b) three parts of a dove prism and (c) the proposed
non-mechanical image rotation using an AODP (acousto-optic dove prism).

Figure 2. Experimental setup. Two orthogonal mirrors are used as a
polygon mirror in this proof-of-concept experiment.

Figure 3. Experimental results of non-mechanical image rotation. The
rotation angle of the two images and (a) and (b) is 180 degrees which is
twice the angle between the two mirror facets at a right angle.

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