Minimum aberration

As an example of the application of this result, the minimum aberration for acoustic imaging with a wavelength of 25 fan at a depth of 0.5 mm below the surface of a material of refractive index n = 0.25 would be given by h/sb = 0.7, so that the optimum lens angle would be 0opt = 8.3°. This result depends rather weakly on Sb, so that halving the depth would increase the optimum angle by less than 1 °. 

Cheng, C. S., Deng, L. Y., and Tang, B. (2002). Generalized minimum aberration and design efficiency for nonregular fractional factorial designs. Statistica Sinica, 12, 991-1000. 

Cheng, C. S., Steinberg, D. M., and Sun, D. X. (1999). Minimum aberration and model robustness for two-level fractional factorial designs. Journal of the Royal Statistical Society B, 61, 85-93. 

Table 3.21 Fractional Factorial Designs of Maximum Resolution and Minimum Aberration...

Optimum matrices of maximum resolution and minimum aberration... 

Table 3.21 gives designs of maximum resolution and minimum aberration for a number of factors between 5 and 11, which covers most possible problems. Certain squares in the table are empty. There is, for example, no design of resolution V for 6, 7, or 9 factors, where it is necessary to use either a resolution IV or VI design. 

Here we examine a different case. We wish to study 6 factors, with 16 experiments. We would normally select a design of maximum resolution and minimum aberration. Reference to table 3.21 shows us that the defining relation of such a design is ... 

A number of the different designs available for factor-influence studies are given in table 3.37. We have tried there to summarise the recommendations of this section of the chapter and only the designs which seem to us the most frequently useful are included. Other minimum aberration designs are listed in table 3.22. 

A. Fries and W. G. Hunter, Minimum aberration 2 designs. Technometrics,... 

Focus it, with minimum aberrations from the lenses. 

The ratio F/d is the F number of the lens. For F numbers much less than unity, spherical aberration precludes reaching the ultimate diffraction-limited spot size. Therefore a practical limit for the minimum spot size obtainable is approximately the wavelength of the light. Commonly this is expressed as the statement that laser light may be focused to a spot with dimensions equal to its wavelength. 

The use of a laser beam expander as a spatial filter has also been found to be satisfactory 42). The beam expander consists of an interchangeable negative input lens and a positive output lens. Both the input and output lenses are designed for minimum spherical aberration. The expansion power may be varied by using a different input lens (Fig. 23.) The laser beam... 

This first step makes necessary a correction of the atmosphere aberrations by means of an adaptive optics or at the minimum a tip tilt device. If the turbulence induces high aberrations the coupling efficiency is decreased by a factor VN where N is the number of spatial modes of the input beam. Note that tilt correction is also mandatory in a space mission as long as instabilities of the mission platform may induce pointing errors. Figure 10 (left) illustrates the spatial filtering operation. This function allows a very good calibration of... 

This is the transverse aberration at the paraxial focus. In simple geometrical terms the circle of least confusion is at a quarter of the distance from where the outermost ray crosses the axis to the paraxial focus. But when diffraction effects are comparable with geometrical aberrations, the relevant focal plane is half way between the paraxial focus and where the outermost ray crosses. Thus the minimum geometrical aberration is... 

If considered desirable, a minimum screen (e.g., genotoxic potential) should be conducted. A study to detect point mutations and one to detect chromosomal aberrations, both in vitro, are considered an appropriate minimum screen. If general toxicity studies are desirable, one or more studies should be designed to allow comparison of unqualified and qualified materials. The study duration should be based on available relevant information and performed in the species... 

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