Apparatus for producing thin layers of a fluid sample for analysis, has a two dimensional array of analysis chambers (45), and a branching pattern of entry channels (25) coupled to the array to enable the analysis chambers to be filled in parallel. The analysis chambers are planar with a height less than that of the entry channels so as to produce the thin layers when filled with the fluid sample. The array enables more spacers between chambers in a given area, so that variations in height of the chambers can be reduced, while still enabling fast filling of the chambers. The analysis chambers can be suitable for capillary filling by a specified fluid sample such as blood. A pattern of exit channels (35) can be coupled to the array. The entry and exit channels can form comb patterns, fingers of the comb patterns being interdigitated, and the analysis chambers being arranged between the interdigitated fingers of the comb patterns.