The Catholic Church was not opposed to the Scientific Revolution. This is a myth propagated by two 19th century anti-Catholic polemicists, Andrew Dickson White (1896) in his A History of the Warfare of Science with Theology in Christendom and John William Draper in his 1874 A History of the Conflict between Religion and Science. In these two works, Draper and White argued that the Church was the foe of scientific progress, insisting that the Earth was flat and that the Sun revolved around the Earth, because the Bible said so. One of the usual formulations of this myth is that Galileo was tortured and forced to recant a heliocentric model of the universe, because it was a heresy to hold a heliocentric model.

Since the 1970s, historians of science have generally rejected this interpretation of the relationship between science and religion. In his God's Philosophers, James Hannam argues that the Christian Middle Ages gave birth to the Scientific Revolution, and that there was a necessary alliance between science and the Roman Catholic Church. Similarly, Stanley Jaki argued for the church's necessity in bringing about modern science in his The Origins of Science and the Science of its Origins. Both Jaki and Hannam represent maximalist viewpoints, that the Church must have served a positive force behind the rise of modern science.

Most historians of science today hold to what John Hedley Brooke calls "the Complexity Thesis," the idea that science and religion are in a complex, ever-evolving relationship (c.f. Science and Religion: Some Historical Perspectives). This view has been taken up in a huge amount of literature. Some of the more notable works are Ronald Numbers' edited volume Galileo Goes to Jail and Some Other Myths about Science and Religion, where Lawrence Principe has a chapter debunking the long held myth of Catholic non-contribution to the Sci. Rev.

There's a lot of literature here, but some of the places to start are as follows:

J.L. Heilbron Galileo: A Biography

__________ The Sun in the Church: Cathedrals as Solar Observatories

Ronald L. Numbers, ed. Newton's Apple and Other Myths About Science

Ronald L. Numbers Galileo Goes to Jail...

Edit: The idea of the Scientific Revolution is a contentious one, but it's not worth discussing in the context of the question.