Resolution of Acoustooptic Laser Beam Deflectors R. A. Spaulding

Research Laboratories, Eastman Kodak Company, Rochester, New York 14650. Received 19 July 1971.

In laser beam scanning applications, the resolution of a deflec­tor is usually defined as the number of diffraction-limited spots produced in the image plane. A common definition is the angular deflection of the beam divided by the angular spot size.1 This is appropriate when large numbers of spots are involved. However, when the number of resolved spots is on the order of 10 or less, this definition is not accurate.

A number of angular spot diameters are depicted in Fig. 1, representing the focal plane of an imaging system. The number of deflected spots is N, the angular diameter of each spot is α, and the deflection angle between spot centers is θ. The centers of the spots are separated by one spot diameter, a. From the figure, it is seen that the number of resolved spots is actually

This refinement is especially important when considering low-resolution acoustooptic beam deflectors. The angular beam de­flection of such a device is approximately

where Δƒ is the frequency change needed to produce a deflection angle θ, λ is the optical wavelength, and v is the acoustic velocity.2

For a given deflection direction, the diffraction-limited angular spot size that can be produced in the focal plane of a perfect lens is given by

where d is the incident optical beam diameter and e is a constant determined by the optical beam distribution. For a uniform rectangular beam, ε = 1.0; for a uniform circular beam, ε = 1.22; and for a Gaussian circular beam with the diameter defined at the exp( —2) intensity points, ε = 1.27.

Substitution into Eq. (2) yields the proper expression for acoustooptic deflector resolution,

2562 APPLIED OPTICS / Vol. 10, No. 11 / November 1971

Fig. 1. Angular spot separation.

where is the access time of the deflector, defined as the optical beam diameter divided by the acoustic velocity.

The frequency change δƒ required to move one spot diameter is therefore

This last relation is useful in matching resolution and bandwidth requirements to a given acoustooptic deflector.

Since most laser scanning systems utilize a nontruncated Gaussian beam diameter defined at the exp( —2) points, the use of ε = 1.27 is preferred. This is also advantageous because of its similarity to the circular uniform beam case, ε = 1.22.

References 1. V. Fowler and J. Schlafer, Proc. IEEE 54, 1437 (1966). 2. R. Adler, IEEE Spectrum 4, 42 (1967).

November 1971 / Vol. 10, No. 11 / APPLIED OPTICS 2563