We present preliminary trigonometric parallaxes and proper motions for 22 L dwarfs and 18 T dwarfs measured using the ASTROCAM infrared imager. Relative to absolute parallax corrections are made by employing 2MASS and/or SDSS photometry for reference frame stars. We combine USNO infrared and optical parallaxes with the best available CIT system photometry to determine M_J, M_H, and M_K values for 37 L dwarfs between spectral types L0 to L8 and 19 T dwarfs between spectral types T0.5 and T8 and present selected absolute magnitude versus spectral type and color diagrams, based on these results. Luminosities and temperatures are estimated for these objects. Of special interest are the distances of several objects which are at or near the L-T dwarf boundary so that this important transition can be better understood. The previously reported early-mid T dwarf luminosity excess is clearly confirmed and found to be present at J, H, and K. The large number of objects that populate this luminosity excess region indicates that it cannot be due entirely to selection effects. The T dwarf sequence is extended to M_J~16.9 by 2MASS J041519-0935 which, at d = 5.74 pc, is found to be the least luminous [log(L/L_sun)=-5.58] and coldest (T_eff~760 K) brown dwarf known. Combining results from this paper with earlier USNO CCD results we find that, in contrast to the L dwarfs, there are no examples of low velocity (V_tan < 20 km/s) T dwarfs. We briefly discuss future directions for the USNO infrared astrometry program.