Universal method for holographic grating recording: multimode deformable mirrors generating Clebsch-Zernike polynomials

Recording methods for making aberration-corrected holographic gratings are greatly simplified by use of a plane multimode deformable mirror (MDM) upon one of the two recording beams. It is shown that MDM compensators easily p rovide the superposition of many interesting active optics modes, which we have named Clebsch-Zernike modes. When we apply only a uniform loading or n o loading at all onto the rear side of the MDM clear aperture, the availabl e Clebsch-Zernike modes are made to belong to a subclass of the Zernike mod es that includes the three modes of the third-order aberration theory as we ll as a well-defined part of the Zernike higher-order modes. Such a recordi ng method is considered to be universal, since it does not require the use of a sophisticated optical system such as a compensator. Active optics 12-a rm MDM's in the vase form have been designed from the elasticity theory. Th e design of six-arm MDM's is currently carried out with theoretical results . As an example of the method, the recording of three holographic gratings of the Hubble Space Telescope Cosmic Origins Spectrograph has been investig ated. Substantial improvements in image quality have been found by use of a six-arm MDM as recording compensator. The result is that aberrations of mu ch higher order can simultaneously be corrected so that the residual blur i mages of the spectra occupy areas approximately 10 (direction of dispersion ) x 3 (cross dispersion) = 30 times smaller-also in terms of pixel number-t han those obtained by our American colleagues. Therefore the active optics recording method appears to provide substantial gains in resolving power an d in sensitivity: (i) For all three gratings the spectral resolution would be increased by a factor of 10, and (ii), in addition, for the two higher d ispersion gratings, the limiting magnitude on the sky appears to be increas ed by a magnitude of approximately 1-1.2. (C) 2001 Optical Society of Ameri ca.