We present deep galaxy counts in the K (22.2 µm) band, obtained at the W. M. Keck 10 m telescope. The data reach limiting magnitudes K ~ 24 mag, about 5 times deeper than the deepest published K-band images to date. The counts are performed in three small ( ~ 1'), widely separated high-latitude fields. Extensive Monte Carlo tests were used to derive the completeness corrections and minimize photometric biases. The counts continue to rise, with no sign of a turnover, down to the limits of our data, with the logarithmic slope of d log N/dm = 0.315 ± 0.02 between K = 20 and 24 mag. This implies a cumulative surface density of ~5 x 10 5 galaxies deg-2 , or ~2 x 10 10 over the entire sky, down to K = 24 mag. Our counts are in good agreement with, although slightly lower than, those from the Hawaii Deep Survey by Cowie and collaborators; the discrepancies may be due to the small differences in the aperture corrections. The observed field-tofield variations are as expected from the Poissonian noise and galaxy clustering as described by the angular two-point correlation function for faint galaxies. We compare our counts with some of the available theoretical predictions. The data do not require models with a high value of n0 , but can be well fitted by models with no (or little) evolution, and cosmologies with a low value of n0 . Given the uncertainties in the models, it may be premature to put useful constrains on the value of n0 from the counts alone. Optical-to-IR colors are computed, using CCD data obtained previously at Palomar. We find a few red galaxies with (r -K) <:: 5 mag, or (i -K) <:: 5 mag; these may be ellipticals at z ~ 1. While the redshift distribution of galaxies in our counts is still unknown, the flux limits reached would allow us to detect unobscured L* galaxies out to substantial redshifts (z > 3 ?).

To achieve its full diffraction limit in the infrared, the primary mirror of the Keck telescope ͑now telescopes͒ must be properly phased: The steps or piston errors between the individual mirror segments must be reduced to less than 100 nm. We accomplish this with a wave optics variation of the ShackHartmann test, in which the signal is not the centroid but rather the degree of coherence of the individual subimages. Using filters with a variety of coherence lengths, we can capture segments with initial piston errors as large as Ϯ30 m and reduce these to 30 nm-a dynamic range of 3 orders of magnitude. Segment aberrations contribute substantially to the residual errors of ϳ75 nm.

The binary period of 4U1626-67 has been found from a careful analysis of its optical pusations. A single lower frequency sidelobe of the 2.4% amplitude 7.68s optical pulsations from this X-ray pulsar bee~ detected on at least 3 different nights in Fourier transforms of high speed photometry obtained with the CTIO 4m telescope. The 0.42% sidelobe pulsations have a frequency which is 0.4011(21) mHz lower than the frequency of the direct pulsations near 130.26 mHz. The weaker sidelobe pulsations are interpreted as arising from X-ray to optical reprocessing on the com~anion star and are shifted to the lower frequency by the rotation frequency of the binary orbit because the X-ray pulsar spins in the same sense as the orbital motion (direct, or prograde). The •orbital period is refined by connecting phases to be either

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As part of the conceptual and preliminary design processes of the Thirty Meter Telescope (TMT), the TMT site testing team has spent the last five years measuring the atmospheric properties of five candidate mountains in North and South America with an unprecedented array of instrumentation. The site testing period was preceded by several years of analyses selecting the five candidates, Cerros Tolar, Armazones and Tolonchar in northern Chile; San Pedro Martir in Baja California, Mexico and the 13 North (13N) site on Mauna Kea, Hawaii. Site testing was concluded by the selection of two remaining sites for further consideration, Armazones and Mauna Kea 13N. It showed that all five candidates are excellent sites for an extremely large astronomical observatory and that none of the sites stands out as the obvious and only logical choice based on its combined properties. This is the first article in a series discussing the TMT site testing project.Comment: Accepted for publication in PASP, April 2009 issu