Based on the coalescence model, we analyse
the light-nuclei production near the critical
point by expanding the phase-space distribution function $f(\mathbf{r},\mathbf{p})$
in terms of the phase-space cumulants $\sim \langle r^m p^m\rangle_c$.
We show that the dominant contribution
of the phase-space distribution to the yield of light nuclei
is determined by the second-order phase-space cumulants.
Here, we identify the fireball size, the homogeneity length, and the effective temperature,
which are encoded in the second-order phase-space cumulants,
as the relevant scales in explaining the yield of light nuclei.
These scales are typically much larger
than the correlation length of the critical fluctuations
created in the rapid expansion of the heavy-ion systems,
so we need to eliminate this dominant contribution of the relevant scales
in order to isolate the critical contribution from the yield of light nuclei.
We find that the second-order phase-space cumulants
appeared in the yields of light-nuclei with different mass numbers
share a similar structure.
This property allows us to construct ratios of light-nuclei yields in appropriate combinations
so that the effect of the relevant scales of the light-nuclei yield cancels, which isolates the critical effects.