A repeated measures ANOVA doesn't require time-series data, although time series are common. At its core, the repeated measures ANOVA is an extension of a paired t-test, for cases when samples are not independent. The reason it often gets used with time series data is because the same measurement is taken from the same individual at different time points. These samples are not "independent" because they come from the same individual - and, for example, individuals with higher-than-average measurements of some value at one time point might still have higher-than-average measurements at another time point, even if that individual's absolute measurement, and the overall average, have changed.
In your case, you have taken multiple measurements of tissue thickness from different subfields of the same tissue sample. These measurements are, similarly, not independent, and warrant some form of repeated-measures design.
Remember too that an ANOVA doesn't make an assumptions about the "order" of data - an ANOVA on a time series simply tests whether there are significant differences among time points. It doesn't matter which time point is first or last; you could re-order the timepoints in the data and get the same result. The ANOVA evaluates whether or not the sample means are significantly different among time points, but it's up to the researcher to interpret those differences.
Because time series experiments seem familiar to you, I'll use that as an example, with your experimental design in parentheses: Say you have an experiment where you measure value Y (tissue thickness) in 100 individuals (tissues) at three separate time points (subfields). You want to see if Y (thickness) changes significantly among time points (subfields). Because your measurements are repeated on the same 100 individuals (tissues), this design is amenable to a repeated measures ANOVA.
If you're looking up information on how to perform this analysis, just interpret "different time points from the same individual" as "different subfields from the same tissue" and you should be good to go.