We report the construction of a spectroscopic programmable array microscope
capable of optical sectioning using Hadamard transform methods. Previously
described Hadamard transform imaging consisted of first-order systems in w
hich the mask was used for either illumination or detection. In this paper,
a second-order Hadamard transform system is described in which a single on
e-dimensional mask serves for both illumination and detection. The system v
erifies earlier predictions that the optical spreading function along the t
ransform axis can be inferred from the echoes arising in second-order syste
ms using sequence lengths of 2(n)-1. With a one-dimensional Hadamard mask,
the system has an axial resolution of 1.3 mum and may be used with or witho
ut the subtraction of an appropriately scaled wide field image depending on
the degree of sectioning required. The system was tested using thin films,
fluorescent beads, and a fixed biological specimen.