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491 Shearing Interferometry The interest in detecting fainter sources and smaller details has, in the recent years, fostered the development of large diameter optical systems, including those with segmented and diluted primaries These con gurations usually require the fabrication and guring of the relatively large diameter off-axis optical elements Testing is very dif cult because the common established interferometric techniques, in general, require the existence of a well-formed reference component Thus, the optical designs that are to be fabricated require the availability of appropriate test components and supplies In the shearing interferometers, the amplitude of the wavefront under test is split into two parts: one half is left unchanged, while a key parameter is modi ed in the other half The most signi cant feature of the shearing interferometers is that they do not require a reference wavefront, because the wavefront under test is compared with itself.

Those portions of the wavefronts that maintain the same polarization are recombined in the detection plane, where they form an interference pattern There exist three basic types of shearing interferometers: the lateral, the radial, and the rotational The wavefront inversion interferometer has been shown to be a special case of the rotational-shearing one, with a shearing angle of 180 We have recently developed an interferogram interpretation method that allows phase reconstruction even from very high-density fringe patterns The input to the algorithm is the vectorial derivative of the phase function Therefore, the shearing interferometry is a particularly useful way of recording the input intensity data, avoiding the noise increase, exhibited when taking derivative of noisy data In a (displacement) shearing interferometer, the phase derivative along the shear direction is the measured quantity One of its salient characteristics is that the derivative is taken along a single direction.

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The incorporation of low-threshold SBS phase conjugation in this laser ampli er system provides near-diffraction-limited divergence, and the output pulses can be frequency-doubled to 527 nm with .50% total external conversion ef ciency. This has resulted in a laser system with 500-ns full width at half-maximum (FWHM) output pulse duration in a near-rectangular temporal pro le, 16 J/pulse at 527 nm, and a maximum pulse repetition frequency (PRF) of 3 Hz. These demonstrated performance speci cations exceed previously reported long pulse green solid-state laser output [46] by 5 in pulse duration, 30 in pulse energy, and 18 in average power from a single ampli er aperture. This is also the rst demonstration of narrow-

We developed a new type of interferometer, where a derivative is taken along an arbitrary direction, under the operator s control The known incremental displacements in the two perpendicular directions, x and y, allow the determination of a two-dimensional derivative of the phase function along the direction The wavefront its replica displaced along vector r, and a representative interferogram, are illustrated in Figure 452, for the coma The possibility of taking a derivative along a speci c direction is most bene cial when testing asymmetrical components, where the fringe density in one direction is extremely high, forming the moire patterns where no phase has been recorded This is particularly useful when employing the method of phase reconstruction upon the line-integration of its gradient With the possibility of choosing the path of the line integral, this may always be selected along a favorable direction.

In fact, upon employing a line integral, a twodimensional problem has been changed into that of a single dimension As will be shown later on, one of the outstanding features of the vectorial shearing interferometer is that the fringe density is controllable with the amount of shear A general wavefront may be expressed in coordinate system erected in the exit pupil Upon applying the symmetry considerations relevant to the testing of symmetrical optical systems, the aberration polynomial in polar form may be written as a.

with the sign depending on the degree of freedom. Under some circumstances, AS can be large. At low fields, superconducting magnets can have signicant sextupole moments due to persistent currents. A possible value for 6 , is 3 m-'. Estimate the resulting chromaticity for a 20 TeV scale ring.

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