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Resolution criteria for acoustooptic deflectors David G. Hawkins Andersen Laboratories, Inc., 1280 Blue Hills Avenue, Bloomfield, Connecticut 06002. Received 24 September 1979. 0003-6935/80/020186-02$00.50/0. © 1980 Optical Society of America. The classic resolution criterion, the Rayleigh criterion, 1 comes from astronomical spectroscopy. It says that for a long rectangular slit illuminated with uniform plane waves, two images are just resolved if the peak intensity of each falls on the first minimum of the other. The angular separation be- tween the peaks in this case is λ/d, where d is the length of the aperture. When the two intensity patterns are summed, the pattern has a null between the two peaks that is down 19% relative to the peaks. Most acoustooptic deflection cells, however, are usually illuminated with a truncated Gaussian beam instead of a uniform plane wave. Typically the truncation is done by the cell aperture at the 1/e 2 intensity points. Randolph and Morrison 2 have calculated the resulting beam patterns and show that, for two adjacent deflected beams, if each peak is placed over the first minimum of the other, the peaks must be placed 1.22λ/d apart, and the resulting null depth is now 24% (relative to the peaks). Therefore, the number of Ray- leigh resolved spots is not just ΤΔƑ, the time-bandwidth product, as would be the case with uniform plane waves but is with α = 1.22. They also give curves showing the resulting null depths for this and other beam separations but expressed as a percent of the maximum plus the minimum of the summed pattern. It would seem to be more useful to express it relative to the maximum only, since one can then say that a particular res- olution criterion requires the null to be so many percent down from the peak as is done in Ref. 1. This is summarized in Table I for several separations. Each separation listed can be thought of as a criterion of resolution, where the given α is used in Eq. (1) for the computation of the number of re- solvable spots. The choice of criterion depends on what null depth is needed for a particular application. The first criterion listed calls for a separation of 1.17λ/d, which gives a null depth of 19%, just as the classic Rayleigh criterion did, hence its name, the Rayleigh equivalent resolution criterion. A criterion using α = 1.34 would give a null depth of 40%, about twice the Rayleigh equivalent depth, so we call it the double Rayleigh criterion. It is interesting to note what happens to the width of a Gaussian beam as a result of the input and output aperturing at the deflector. Before deflection, the angular halfwidth of the beam measured from the center to the 1/e 2 intensity point is 2λ/πd = 0.637λ/d. 3 After deflection, Ref. 2 shows that the Table I. Resolution Criteria for Acoustooptic Cells 186 APPLIED OPTICS / Vol. 19, No. 2 / 15 January 1980
