This paper is an introduction to the specification and tolerancing of Mid-spatial frequency (MSF) ripple or waviness. We begin with an introduction to the definition of ripple, spatial frequencies, and MSF ripple as a class of surface error (as opposed to figure or form, roughness, and surface imperfections or defects.) We then cover the derivation of spatial frequency bands of interest, specifications methods and notations, and relative amplitudes for typical manufacturing processes.

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This paper describes the use of Fourier techniques to characterize the wavefront of optical components, specifically, the use of the power spectral density, (PSD), function. The PSDs of several precision optical components will be shown. Many of the optical components of interest to us have square, rectangular or irregularly shaped apertures with major dimensions up-to 800 mm. The wavefronts of components with non-circular apertures cannot be analyzed with Zemicke polynomials since these functions are an orthogonal set for circular apertures only. Furthermore, Zemicke analysis is limited to treating low frequency wavefront aberrations; mid-spatial scale and high frequency error are expressed only as "residuals." A more complete and powerful representation of the optical wavefront can be obtained by Fourier analysis in 1 or 2 dimensions. The PSD is obtained from the amplitude of frequency components present in the Fourier spectrum. The PSD corresponds to the scattered intensity as a function of scattering angle in the wavefront and can be used to describe the intensity distribution at focus. The shape of a resultant wavefront or the focal spot of a complex multi-component laser system can be calculated and optimized using the PSDs of individual optical components which comprise it.

In the second half of the 1 990ts, LLNL and others will be designing and beginning construction of the National Ignition Facility (NIF). This new laser will be capable of producing the worlds first controlled fusion ignition and burn, completing a vital milestone on the path to Fusion Energy. This facility will use more than 7,000 optical components, most of which have a rectangular aperture, which measure greater than 600 mm on the diagonal.In order to optimize the performance versus cost of the laser system, we have determined that specifications based on the Power Spectral Density (PSD) function are the most effective for controlling mid-spatial wavelength errors. The draft optics specifications based on a combination of PSD and conventional roughness and P-V requirements are presented, with a discussion of their origins. The emphasis is on the application of a PSD function for transmitted wavefront optical specifications, and the benefits thereof. The PSD function is the most appropriate way to characterize transmitted wavefront errors with spatial frequencies ranging from several centimeters to a few hundred nanometers, with amplitudes in the X/100 regime. Such errors are commonly generated by cost effective, deterministic finishing technologies, and can be damaging to the laser, as well as causing unnecessary energy loss and inability to focus, in a high energy laser application. In addition, periodic errors can occur as a result of errors at other steps in the fabrication process, such as machine vibration in a fixed abrasive step, or material homogeneity ripple. The control of such errors will be essential to the construction of future high energy lasers.

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