Objects of Shamatha
Shamatha (calm abiding) is a stilled and settled state of mind that has the accompanying mental factor (subsidiary awareness) of a sense of physical and mental fitness (flexibility). This is an exhilarating feeling of fitness to be able to concentrate on anything for as long as we wish.
Shamatha is settled on an object or in a state of mind. It can be a sense object, such as the breath, or a visualized mental object, like a Buddha. In Anthology of Special Topics of Knowledge (Skt. Abhidharma-samuccaya), the fourth- or fifth-century Indian master Asanga emphasizes concentrating only on a mental object.
Most meditation masters of all Tibetans traditions recommend choosing a Buddha – whether a visualized one or an actual image – since it helps with safe direction (refuge), bodhicitta, and tantra.
While focusing on a Buddha, we may also focus on a Buddha's good qualities. We may then accompany our focus with belief in the fact ("faith") that Buddhas have these qualities, and we may pay attention to them as features that we aspire to attain ourselves.
For attaining shamatha, we may also focus on other objects, pay attention to them in other beneficial ways, and accompany our focus with other constructive emotions and attitudes.
Regardless of the object we choose, we need to stay with that object until we achieve shamatha, and not switch objects part way through the process.