  One of the advantages of kinetic inductance detectors is their intrinsic
frequency domain multiplexing capability. However, fabrication imperfections
usually give rise to resonance frequency deviations, which create frequency
collision and limit the array yield. Here we study the resonance frequency
deviation of a 4-inch kilo-pixel lumped-element kinetic inductance detector
(LEKID) array using optical mapping. Using the measured resonator dimensions
and film thickness, the fractional deviation can be explained within $\pm
25\times 10^{-3}$, whereas the residual deviation is due to variation of
electric film properties. Using the capacitor trimming technique, the
fractional deviation is decreased by a factor of 14. The yield of the trimming
process is found to be 97%. The mapping yield, measured under a 110~K
background, is improved from 69% to 76%, which can be further improved to 81%
after updating our readout system. With the improvement in yield, the capacitor
trimming technique may benefit future large-format LEKID arrays.
