Unified Optical Scanning Technology

Chapter 4.8.2 - Scanner Devices and Techniques: Fundamental Characteristics

4.8.2 Fundamental Characteristics

As with the grating equation applied in holographic deflection (Eq. 4-22), diffraction from a structure having a periodic spacing Λ (Fig. 4.22) is expressed as

in which Θ1 and Θo are the input and output beam angles, respectively, n is the diffractive order, and λ is the wavelength. As a 'thick' diffractor of length

all the diffracted orders are transferred efficiently to one first order. Because Bragg operation requires that

then from Equation 4-25, for the typically small angles of acoustooptic deflection, the Bragg angle reduces to

and the full scan angle becomes

The beamwidth D is traversed by the acoustic wave during its transit time τ at the acoustic velocity vs such that

The transit time τ = D/vs also represents the access time, or the time required to institute a change in beam direction for random access applications.

Using the relationships for scanned resolution and duty cycle (Equations 3-5 and 4-1, respectively) and substituting Equations 4-29 and 4-30 for Θ and D, the resolution of the acoustooptic deflector becomes

The τΔf component represents the time-bandwidth product, a measure of information handling capacity and analogous to the ΘD product in Equations 1-3, 1-4, and 1-6. Insertion of typical parameters into Equation 4-31 leads to a resolution limit of approximately 1000 elements per scan. Note that a wide beamwidth and a low acoustic velocity are required to attain a large τ for high resolution. Yet a short access time demands the inverse conditions. This also illustrates the conflict between AO deflection and AO modulation, each requiring inverse conditions in the τ for high deflector resolution and high modulation rate, and that AO deflection requires acoustic frequency modulation (FM) and AO modulation entails acoustic amplitude modulation (AM). A brief historical review, a variation on the treatment of scanned resolution, and discussions of acoustic power effect on diffraction efficiency, the application of anamorphic optics to reduce the power requirement, and the selection of AO materials, were presented in an earlier work [Bei2].

 

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