Application and Optimisation of the Spatial Phase Shifting ...

198 Appendix B: Real-time phase calculation
The stretching in the horizontal direction is clearly discernible; it accounts for the maximal "stroke" of the
cosine term being twice that of the sine term.
Depending on the number of involved intensity samples and their coefficients, the byte arrays needed for
the LUT may nevertheless get larger; for instance, a LUT for (3.56) would need 5111021 entries. In that
case, the coefficient of 2 for both intensity samples in the numerator thins out the grid of possible values
and space can be saved. However, the very same formula in the representation of (3.57) requires a
15311531-point LUT, and for (3.58), 20411021 possible values must be accounted for. This shows
that a careful choice of the formula can be useful in practice.
Non-integer coefficients in the numerator and/or denominator can only be implemented if a suitable factor
can be found that converts all the coefficients for the respective expression into integers, i.e. if the
coefficients are rational numbers. As seen above, a common factor of L3 constitutes no problem in (3.17)
or (3.58); however, if we had, say, L3 and 3 as coefficients in the sine or cosine term, we would have to
use a rational integer approximation of their values, for instance 7 and 12; this would allow to put up a
LUT, but remains a complicated procedure. Hence, while it is possible to accelerate phase calculation by
LUTs on more occasions than one might think, the appeal of simplicity gets lost in some cases.