The location and character of the best focus on axis by an optical system with a nominal amount of primary spherical aberration is discussed from the wave-optical and information theoretical points of view.
The axial intensity distribution (the Strehl definition along the axis) is exactly examined by using the Zernike polynomials. The results supplement the wave-optical approach of Kuwabara about the location of best focus with primary spherical aberration.
The best focus is discussed in terms of the maximum value of four criteria, i.e., Relative Structural Content, Correlation Quality and Image Fidelity defined by Linfoot, and Sharpness suggested by O'Neill. Each criterion plays a different role depending upon the structure of the object. These factors are calculated by Simpson's method from the response functions given by Parrent for the various focal setting between marginal and paraxial foci and for different amounts of aberration.
On the assumption of object with a flat spectrum the computations indicate that for very small aberration the best focus lies midway between the marginal and paraxial foci irrespective of the quality criteria. When the aberration increases, the best focus deviates slightly from the mid-point, the deviation depending upon the particular criterion. The difference of the amounts of quality factors at the central and maximum planes is negligibly small so that the image intensity distribution along the axis could not indicate this deviation of the best focus from the central plane.