The recombination fraction between two loci is the proportion of meiotic products which are nonparental (recombinant) at the the loci. [We speak as though this is a constant for a species, although it does vary, depending slightly on physical conditions, age, sex, genotype, etc.] In theory, and these days almost in practice, recombination fractions can be determined by examining the DNA of a large number of meiotic products at or very near the loci, to see if parental origins differ at them. When two loci lie on the same chromosome, parental origins differ if the loci are separated by an odd number of crossovers. Despite this theoretical possibility, for most of this century recombination fractions have been estimated differently. In a typical experimental cross, or pedigree analysis, knowledge concerning the genotype of the diploid cells undergoing meiosis is used together with the genotypes of many meiotic products, to count or estimate the proportion of recombinants. With yeasts and fungi, this is relatively straightforward, as crosses can be planned and the single spore or tetrad products of meiosis can be readily scored. With mammals, the products of meiosis (sperm and egg cells) can only be scored for molecular markers. For other loci, such gametes need to be combined with one of the opposite sex, and their genotypes inferred from those of the resulting diploid animals.
To see all this a bit more fully, suppose that we have a locus A with alleles
and 
and a locus B with allels 
and 
(Dominance is not
an issue just now.) Then any organism has genotype 
or
at A, and
similarly 
or 
at B. The genetic composition of a
gamete could be 
or 
depending on the
genotype of the organism, and in
order to determine which are which are parental and which recombinant, we
need to know which pair came to the organism from its father and which from its
mother. If the organism has genotype 
then it must have
obtained 
from one parent and 
from the other, and it will
produce gametes with composition 
or 
In theory there are
two versions of each of these, depending on the parental origin of the
allele, and again in theory (and today in practice), these can be
distinguished. But in traditional practice gametes from such individuals
cannot be used to estimate recombination fractions:
we require that our organism be heterozygous at both loci, i.e. it be
But being doubly heterozygous is not enough to permit the assignment of
meiotic products to parental and recombinant categories: we need to know
which two of the four gametic combinations 
the organism received from its parents - we need the phase relationship of
the alleles at the two loci.
This is a classical term which arose shortly after linkage was discovered,
and can be explained as follows.
Suppose (cf. Mendel) we have alleles A and a at one locus and B, b at another, and that a doubly heterozygous (AaBb) organism is the result of a mating of parents with genotypes AABB and aabb. Then we know that the organism received AB from one parent and ab from the other, and so these are its parental gametic constitutions, whilst Ab and aB are its recombinant ones. This arrangement is known as the coupling phase, presumably because the two dominant alleles were received together (coupled), and likewise for the recessive alleles. If, on the other hand, the AaBb organism is the result of an AAbb x aaBB mating, then this is called the repulsion phase, and the parental and recombinant constitutions are the reverse of the ones just mentioned. At times it will be convenient to distinguish these phases by writing AB/ab and Ab/aB, although this notation is usually restricted to the case where the loci are known to be on the same chromosome.
With experimental crosses, phase is usually known beforehand, since the crosses leading to the current individuals are typically known. With humans we need information from the previous generation.
Exercise 3. Suppose we have a mating of parents AaBb and aabb, giving children with genotypes AaBb, aabb, AaBb, Aabb and aabb. How many recombinants are there? If the dominant alleles are in coupling, the answer is 1; if in repulsion it is 4.
Now suppose that we know thephenotypes only, and have two offsprings of an
AB 
ab mating (Mendel's notation) with phenotypes Ab and aB. Thus they
have genotypes AAbb or Aabb and aaBB or aaBb respectively. Can you see that this apparently incomplete information tells us that the AB parant must be Ab/aB (i.e., the repulsion phase)?