Lyman $\alpha$ emitters based chiefly on the $z \sim 4.5$ objects observed by @Dawson04. Experimentation suggested that the results obtained were not sensitive to line profile; velocity widths in the range 100–1000 kms$^{-1}$ were chosen based on both @Dawson04 and the more extreme example documented by @Tapken04.

The effects of the instrument on the objects’ detectabilty were then considered before they were added to the background images. First a correction for the order-blocking filter transmission was applied, using the position of the object within the field to determine the observed wavelength and hence filter transmission. The line profile was then multiplied by the transmission profile of the etalon for the image under construction.

Results of simulations
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Following the procedure above, simulations were run of all three fields. For each data image, a total of 500 simulated images were constructed, each containing 500 simulated sources.

### Detection parameters {#sec:detpar}

Source extraction was run multiple times on each image with different [SExtractor]{} configuration parameters. In each case, the results were compared with the catalogue of simulated objects in the image. The combination of parameters that produced the greatest number of detections of known objects combined with the smallest number of spurious 