Topological transforms have been very useful in statistical analysis of\nshapes or surfaces without restrictions that the shapes are diffeomorphic and\nrequiring the estimation of correspondence maps. In this paper we introduce two\ntopological transforms that generalize from shapes to fields, $f:\\mathbf{R}^3\n\\rightarrow \\mathbf{R}$. Both transforms take a field and associate to each\ndirection $v\\in S^{d-1}$ a summary obtained by scanning the field in the\ndirection $v$. The transforms we introduce are of interest for both\napplications as well as their theoretical properties. The topological\ntransforms for shapes are based on an Euler calculus on sets. A key insight in\nthis paper is that via a lifting argument one can develop an Euler calculus on\nreal valued functions from the standard Euler calculus on sets, this idea is at\nthe heart of the two transforms we introduce. We prove the transforms are\ninjective maps. We show for particular moduli spaces of functions we can upper\nbound the number of directions needed determine any particular function.\n