## 1 Introduction
In general, the dispersions achieved with available glass pairs are not perfectly matched to the atmospheric dispersion, and so when wavelengths at the two extremes of the spectral range are corrected to the same angular deflection, intermediate wavelengths will have slightly different corrections. The maximum extent of this difference in correction is the secondary spectrum. Typically, this secondary spectrum is at least an order of magnitude less than the uncorrected atmospheric dispersion. Tighter requirements on the control of secondary spectrum naturally develop as telescope image quality improves. Figure 1: Representative atmospheric dispersion, as a function of zenith distance in degrees, calculated for Keck at Mauna Kea. The indicated values from primary dispersion at 60 and 70 degrees zenith distance highlight the nonlinear nature of atmospheric dispersion, as the magnitude of primary dispersion almost doubles in the last 14% of the indicated zenith distance range. For adaptive optics systems, operating at or near the diffraction limit imposed by the telescope aperture, R-ADC types incorporating glasses or crystals with anomalous relative partial dispersion have been employed to reduce secondary spectrum to tens of milliarc seconds [6,7]. For large telescopes, working combinations of focal length and field can lead to systems requiring metre-class refracting elements. The relative paucity of available glass types at meter-plus diameters limits the ability to correct secondary spectrum with R-ADC type systems. An alternative to the R-ADC is the Linear ADC (L-ADC). This design was initially developed for larger telescopes, specifically for the European Southern Observatory Very Large Telescope, and proposed by [PERSON] et al. [8]. In this design a single pair of prisms is produced and orientated such that, when the prisms are in contact, they form a plane parallel plate, centred on, and plane-perpendicular to, the optical axis. When in contact the prisms impart no dispersion. As the telescope's observing angle increases in zenith distance, compensating dispersion is achieved by producing a separation of the prism elements along the optical axis direction. L-ADCs have the advantage that only two elements of the same glass type are required to correct the primary lateral colour, so fused silica can be used. Fused silica is a robust material available in high optical homogeneity in large sizes. It also maintains excellent transmission to shorter wavelengths. Additionally, the required prism angles for the L-ADC are relatively shallow, so the prisms are not unduly thick or difficult to manufacture. A serious problem with this sort of ADC is that the focal plane and pupil locations are modified as the prism is displaced. This complication renders the solution impractical for many applications. The inability of L-ADC systems to maintain image and pupil positions disqualifies such correctors from further consideration in this paper, though there is potential to produce image and pupil stabilized systems by combining more complicated motions and telescope active-optics, which will be the subject of future investigation. A third type of ADC is one that displaces one or more optical elements incorporating curved surfaces in a direction perpendicular to the optical axis, and also rotates these elements about the local horizon axis. [PERSON] [9] first showed that by rotating a concentric meniscus lens, formed by two plano-spherical elements cemented together at the plane surfaces, about the meniscus surface centre of curvature, the plane internal surface of the meniscus could be tilted without introducing any other optical change to the system. If the two glass types making up the meniscus are selected to have matching refractive indices in some central colour, and different dispersions, such an element allows for the introduction of compensating dispersion about an undeviated central colour.