  We have developed a method for selecting the most luminous galaxies detected
by IRAS based on their extreme values of R, the ratio of 60 micron and B-band
luminosity. These objects have optical counterparts that are close to or below
the limits of Schmidt surveys. We have tested our method on a 1079 deg^2 region
of sky, where we have selected a sample of IRAS sources with 60 micron flux
densities greater than 0.2 Jy, corresponding to a redshift limit z~1 for
objects with far-IR luminosities of 10^{13} L_sun. Optical identifications for
these were obtained from the UK Schmidt Telescope plates, using the likelihood
ratio method. Optical spectroscopy has been carried out to reliably identify
and measure the redshifts of six objects with very faint optical counterparts,
which are the only objects with R>100 in the sample. One object is a
hyperluminous infrared galaxy (HyLIG) at z=0.834. Of the remaining, fainter
objects, five are ultraluminous infrared galaxies (ULIGs) with a mean redshift
of 0.45, higher than the highest known redshift of any non-hyperluminous ULIG
prior to this study. High excitation lines reveal the presence of an active
nucleus in the HyLIG, just as in the other known infrared-selected HyLIGs. In
contrast, no high excitation lines are found in the non-hyperluminous ULIGs. We
discuss the implications of our results for the number density of HyLIGs at z<1
and for the evolution of the infrared galaxy population out to this redshift,
and show that substantial evolution is indicated. Our selection method is
robust against the presence of gravitational lensing if the optical and
infrared magnification factors are similar, and we suggest a way of using it to
select candidate gravitationally lensed infrared galaxies.
