From the Monthly Notes of the Royal Astronomical Society (1984) Vol. 210 pp 597-609
The Mersenne-Schmidt: a three-mirror survey telescope. Accepted 1984 March 20, Received 1984 February 10.
4. Comparisons with other telescopes
      The performance of the Mersenne-Schmidt is compared with other telescopes in Fig. 4. Good seeing, with images having a Gaussian profile and an rms diameter of 0.5 arcsec, is assumed and has been added quadratically to the rms image spread computed for each telescope on a ray theoretical basis. This is clearly more realistic than taking the ray-theory image spread alone; even in telescopes used in space there would be some small manufacturing errors that should be allowed for in any comparisons of different designs. The abscissa is the logarithm of the ratio of the field diameter to the image diameter as increased by the seeing, i.e. the number of pixels along one diameter of the field. In calculating the ordinates in Fig. 4 the aperture of each telescope has been corrected to allow for any losses by a central obstruction or conical baffles; at the left (Fig. 4a) this 'reduced aperture' is expressed as a decimal fraction of the focal length. In this comparison the Mersenne-Schmidt is closely approached only by the Paul-Baker type of system designed by Angel et al. (1982) and an aberration-balanced F/2 or faster Schmidt camera used in quasi monochromatic light (Willstrop unpublished):the modified Couder (Willstrop 1983) and Couder (1926) come closer than any other forms.

      However, in building a large survey telescope some account should be taken of the tube length; a Schmidt or a Couder telescope would need a much larger dome than the Ritchey-Chretien of the same aperture. At the right (Fig. 3b) the reduced aperture is expressed as a fraction of the length of the tube above its balance point, the declination axis (or altitude axis in the altazimuth mounting). Data have been collected from reliable sources where available; for telescopes that have been designed but not yet built reasonable estimates have been made of the position of the center of gravity of the tube, and the space above the upper mirror required by its cell and focusing mechanism. This is an oversimplification, of course, as no dome is ever made a close fit around a telescope, and allowance must be made for the extra space needed when handling the mirrors on their way to and from the aluminizing tank, wherever this may be located. In this comparison of 'compactness' the Mersenne-Schmidt is closely comparable to the Epps & Takeda (1983) design but is beaten by Angel et al. (1982). The deeply aspheric F/1 primary mirror of the latter design would be even more difficult to manufacture with sufficient accuracy than the F/1.6 mirror of the design presented in this paper. The Schmidt and Couder forms have ceased to be competitive, and telescopes with a Cassegrain configuration have come to take their place.

5. Applications
      A new design of wide field three mirror telescope has been described. To justify the construction of a telescope of this type and of the 5m aperture suggested it would be essential to be able to use it not only for photography during the dark part of each month but also for spectrography during bright time. As the F/1.6 focal surface is within the light paths there is little space for a spectrograph there, and as the design doesn't not lend itself to easy conversion to a coude configuration it would probably be necessary to use optical fibers to take light from the focus to a stationary spectrograph. Observations have been made in this way by Hill et al. (1980) and Ellis et al. (1984) using telescopes with slower focal ratios and smaller fields than are provided by the Mersenne-Schmidt. Investigations are needed of the most efficient way of matching images with steeply convergent light to optical fibers. Watson (1984) has examined the effects of atmospheric refraction on the locations of images as a function of hour angle in the 6.5º square field of the UK Schmidt, and concluded that exposures of up to 4 hours would be practicable before there was significant light loss as the small images become decentered on fibers of 50um core diameter. The focal length of a large Mersenne-Schmidt would result in seeing-limited images being closely comparable to this fiber core diameter and accurate centering of each image on the corresponding fiber would be more important than in the UK Schmidt. the use of unnecessarily large fibers would result in loss of spectral resolving power, just as would the use of a slit wider than the image spread, if the star image were deliberately trailed to produce uniform illumination across the slit as well as along it. The smaller field of the Mersenne-Schmidt, 4º in diameter, results in smaller differential trailing of the images than in the UK Schmidt, if this is expressed in arcsec hr -2.

      There might be some resistance to the adoption of a telescope of this unconventional form. Figuring the F/1.6 paraboloidal primary mirror witha large perforation would be significantly more difficult than the F/2.5 primary mirrors of the UKJRT or the William Herschel telescope. The extra costs of figuring, however, are unlikely to be more than a small fraction of the savings resulting from the use of the small dome which the compact form of this telescope permits. Its other merits are perfect achromatism and excellent images.

      I wish to thank Professor D. Lynden-Bell for several valuable discussions during which he stressed the importance of a large field in a survey telescope. The optical calculations were carried out on the Vax 11/780 at the Cambridge node of STARLINK.