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 provide the superposition of many interesting active optics modes, which we have named Clebsch-Zernike modes. When we apply only a uniform loading or no loading at all onto the rear side of the MDM clear aperture, the available Clebsch-Zernike modes are made to belong to a subclass of the Zernike modes that includes the three modes of the third-order aberration theory as well as a well-defined part of the Zernike higher-order modes. Such a recording 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-arm MDM's in the vase form have been designed from the elasticity theory. The 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 investigated. Substantial improvements in image quality have been found by use of a six-arm MDM as recording compensator. The result is that aberrations of much higher order can simultaneously be corrected so that the residual blur images of the spectra occupy areas approximately 10 (direction of dispersion) x 3 (cross dispersion) = 30 times smaller--also in terms of pixel number--than those obtained by our American colleagues. Therefore the active optics recording method appears to provide substantial gains in resolving power and 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 dispersion gratings, the limiting magnitude on the sky appears to be increased by a magnitude of approximately 1-1.2.

Recording method for obtaining high-resolution holographic gratings through use of multimode deformable plane mirrors.

We propose a new way of recording in which a spherical blank and a deformable mirror are used to obtain high-resolution holographic gratings. The reflection of one of the two laser recording waves upon this mirror provides the deformations necessary to image correction to as much as seventh-order aberrations inclusively.

Illustration of the use of multimode deformable plane mirrors to record high-resolution concave gratings: results for the Cosmic Origins Spectrograph gratings of the Hubble Space Telescope.

To illustrate the efficiency of using a deformable plane mirror to record holographic gratings, we have computed the three gratings for the Cosmic Origins Spectrograph. Their working conditions are severe, since they have to correct the residual spherical aberration of the Hubble Space Telescope. Nevertheless, all images obtained are largely diffraction limited with regard to the resolution.