The short answer: it depends on how we understand science and the Scientific Revolution. But since you came to askhistorians, you probably want the long answer! I can't speak to the Safavids much (see my user name), but the Ottomans kept up scientific production, it is just that much of it was what we would today consider pseudo-science. For example, they produced a great deal of innovation in things like alchemy and astrology through the 17th and 18th centuries.
Today we tend to think of science as a straight arrow, always pointing forward, with everyone in a given era being totally committed to whatever was going on. In reality, for every Bacon or Copernicus, there were dozens more people working in traditional veins of producing knowledge about the natural world like alchemy or astrology. Those were highly advanced, intricate, and well thought out systems. Today we know they are wrong, but it took many centuries for anything close to most of society to understand that even AFTER major innovations. And even then, many of who we would today consider groundbreaking scientists were all about alchemy, like Newton and Brahe. Once empiricism was formulated in Europe, it still took many decades for Boyle to formulate his law rejecting the four element theory, in the late 17th century.
Even long after Boyle, well into the 18th century, tons of European scientists were adding to alchemal knowledge, and conceiving of the world along the basic 4 elements model that had ancient roots, then continued to be added onto, modified, and innovated for centuries. "Modern" chemistry slowly overtook alchemy, but it was not as simple and sudden as "Boyle invented chemistry, then overnight everyone was convinced and the world was transformed."
Back to the Islamic world. The roots of alchemy are very ancient, and the ancient Greeks had a fairly comprehensive system built around them. Islamic science in the "Golden Era" had a tendency to take Greek ideas of natural philosophy and refine them into complex and intricate systems of thought. So they took the Greek ideas about alchemy and ran with them, elaborating endlessly on the basic four elements theory and turning it into something closer to what we wold consider a field of science. "Alchemy" the word comes from a greek root, chemie, with the Arabic definite article "al" tacked on, and meant "the philosopher's stone." Eventually in Europe alchemy became chemistry, and the "al" was dropped to distinguish the two. The work of the Islamic natural philosophers in that era became incredibly influential. Christian and Muslim philosophers would build upon their frameworks for centuries. When Christian philosophers began to introduce true empiricism into their work, they eventually moved away from the four elements model at the highest levels of academic debate. But, in the terms of Thomas Kuhn's idea about how Scientific Revolutions happen, the "paradigm shift" that caused most scientists and the public to shift their ideas from an alchemal, 4 element model of how the universe functioned to a modern chemical model took another century or two to happen.
And that is what the Ottomans were up to in science, generally. They continued to elaborate and add to what was a formal, scientific discipline that was based on centuries of precedent, and was the same body of knowledge Europeans were working from. It wasn't based strictly on empiricism, but it did explain the world well enough, and was reproducible enough. Astrology followed a similar trajectory. Listen to Tuna Artun's Ottoman History Podcast episode for further elaboration on what Ottoman scientists were up to.
This story takes us up the late 18th century. Chemistry had won out over alchemy in most of European science, and the proof was in the pudding. Modern chemistry led to modern metallurgy (metallurgy itself was an alchemal concept, and was discussed as such well into the late 18th century). This led to modern guns and artillery. The Ottomans, who continued producing alchemal knowledge, wanted better guns. So they opened military academies in the late 18th century teaching modern artillery science. They imported technical workers to help make modern guns and apply the fruits of modern chemistry. They began translating scientific treatises and manuals.
This is all to say the timetable for Ottoman science is not that far off the timetable of European nations. In say, 1750, if you went to a bustling town in Austria, most people you asked, even the educated ones, would probably explain the world using the ancient four element model, that had been invented by the Greeks, turned into a science by the early Muslims, and had been elaborated upon endlessly by even 17th and 18th century scientists. The same would be true in a bustling Ottoman town. Things were already changed forever, it just took a little for society to catch up. Once the decision making classes of Ottoman society decided to begin working with "modern" science in the late 18th century, they picked it up fairly rapidly.
We tend to look back at history and connect all the situations that worked out into one narrative, and ignore at best or actively demean at worst what didn't work out. Science had millions of smart minds working on it for centuries, and out of all those minds, a few in the 1500s started working in empiricism. But even then, for a couple of hundred years after that, many sharp minds continued to elaborate on old systems that were still impressively rigorous, we just discount them as "pseudo-scientists" or charlatans because today we know they were wrong. But from the perspective most most 1750s people, that wouldn't have been so clear. Just because the Ottomans were pursuing, with great vigor, what turned out to be a dead-end, doesn't mean we should totally discount it. Thousands of Europeans were pursuing the same dead ends with equal vigor. Much of this was innovative in its own right; it just took many centuries for everyone to realize the underlying premises were wrong.
I would argue that the significance of the Golden Age doesn't lie in scientific contribution alone, and that understanding the context of the Golden Age is crucial if we want to understand why this time period received such an appellation. This may not be a direct answer to your question, but I'd like to use my response to illustrate how the Golden Age was much more than just a scientific renaissance and that that should be taken into account when looking at it relative to later time periods.
The Islamic Golden Age, which is tentatively dated 800 to 1100 AD, was greatly fueled by the intellectual community in Baghdad. Haroon al-Rasheed's early 8th century Baghdad was remarkably wealthy. Glubb writes in A Short History of the Arab Peoples, "Under Haroon, the empire achieved its high noon of glory and wealth, comparable perhaps to Victorian England." During this period, "No one wanted anymore to conquer the world for God." He also notes that "Baghdad was the richest city in the world, Constantinople being the only other capital which could aspire to be in the same class for luxury and refinement. "
Glubb continues, "Yet the Baghdad of Haroon was not characterized by a mere vulgar display of wealth. It was an age in which conversation and culture were considered an art. Intellectual, and even theological, discussions were among the recreations of the educated classes."
And von Grunebaum writes this in Classical Islam: "The cultural excitement of those days can hardly be exaggerated. The conventicles of thinkers of all tendencies rose up and strove for recognition; the monolithic orthodoxy which had in fact never existed except in the minds of obstinately pious believers, gave way to a luxuriant growth of the most varied ideas and shouldering crises of faith."
Haroon's son and successor, Mamoon, was considered a brilliant mind like his father, and "his fourteen year reign in Baghdad saw one of the most brilliant intellectual epochs in history." It was Mamoon who formally founded the House of Wisdom in Baghdad, whose chief aim was to translate foreign works into Arabic.
It was during this time that we see the first textbook on opthamology, a work by Hunain. We see the use of zero and the introduction of arabic numerals. Algebra was invented along with plane and spherical trigonometry, and we also see the discovery of trigonometric ratios, logarithms, and the invention of sine, cosine, tangent and cotangent. During Mamoon's reign an astronomical observatory was established "whose astronomers measured the circumference of the earth with remarkable accuracy, six hundred years before Europe admitted that it was not flat." In fact, even today most of the named stars in the night sky have Arabic names. Medical Schools were opened, and in Baghdad there even existed a free public hospital. Plus many more achievements in many different fields.
Another aspect that made Baghdad special was the fact that it was open to all visitors regardless of faith or ethnic origin. In fact, "Some historians... have pointed out that the artists, the scientists, the theologians and the philosophers of the Golden Age were individually not Arabs but Persians, Armenians, Syrians or Greeks." Most thinkers were arabicized, but not themselves Arab.
Mamoon was succeeded by Mutasim. Mutasim died in 842 when the Arab Empire was at its pinnacle. There were 8 million gold dinars in the treasury and the khalif's army seemed invincible. But reliance on foreign military recruits and the alienation of the Arab tribes would lead to the demise of the Abbasid empire. As confidence in the Caliphate faded provinces began to fall away, and by 892 Baghdad was only able to collect taxes from a small area. Baghdad could also no longer rely on military support from the Arab tribes whose loyalty it had lost. By the time the Samanids took over, Baghdad was half-ruined and under barbarian control. The brilliant culture of Baghdad was no more, and the centers of thought in the Islamic world were to be reproduced at the extremities of the former empire, in Bukhara and in Andalus.
But the Islamic Golden Age was not victim only to political and economic upheaval. The intellectual community itself underwent its own crisis. Religious leaders sought to restore back to nature the essence of divinity that had been taken by Hellenzied thought, which they considered to be in many ways irrational when compared to the transcendent nature of God and His divine will. One of the persons leading this charge was Imam Hamid al-Ghazali (1058-1111). He wrote a book called The Incoherence of Philosophers, and in it he argued that falsafa was incompatible with Islam. His work was so influential that Averroes wrote a rebuttal in an attempt to restore the culture of skepticism in intellectualism, but this work, The Incoherence of the Incoherence, could not stop the swelling influence of religion. Another figure that helped to bring about the shift from science to fundamentalism was Nizam al-Muk. He was grand vizier in the Seljuk dynasty and he created an educational system that focused on religion. He also institutionalized religious studies, making it the more lucrative career path.
What set the Golden Age apart were not just its contributions to science, but the economic and political environment that allowed such contributions. Wealth and attitude were crucial to the advancements made during this Islamic renaissance. But we saw both economic misfortune hit Baghdad, and attitudes toward the intellectualism of the day change. Comparing the Golden Age to later periods while looking solely at scientific achievements ignores the context in which the Golden Age arose. And it's that context, the environment, the wealth, the culture that existed that embraced thinkers of all backgrounds, that made the Golden Age golden.
It is said that the end of the Golden Age is marked when the Abbasid caliphate collapsed in the 13th century, but the decline started much earlier.
The role of the sciences declined closer to the 11th century. The cause for this decline can be accredited to the change of Islamic leadership. During the Sunni Revival, the role of Islamic leaders changed dramatically. Before the revival, religious leaders sustained themselves through secular occupations, but the revival saw a significant shift of power as these leaders exchanged their occupations for full-time scholarly employment at madrasas (Islamic teaching college). These institutions were funded by waqf, trusts consisting of donations of land, property, or money by individuals with no expectation of reimbursement.
The laws regulating the waqf state that they may not serve any purpose that would harm the principles and beliefs of Islam, and the religious leaders were the sole judges of what could be deemed "harmful". As donations to these trusts grew, so did the power of the religious leaders. Once the religious leaders gained significant power in the region, the majority banished scientific work at the colleges claiming they were a threat to Islamic ideals, thus updating the law of waqf. This greatly limited the study of science in the region as education came under control of religious leaders. Non-religious institutions dedicated to scientific study soon failed as they struggled to keep funding due to the laws of waqf.
The religious elites used their new power to limit scientific study because they believed it led to religious skepticism. They limited the study of sciences to individuals that could be trusted not to go astray. The only individuals deemed worthy of this standard were typically the religious leaders themselves, many of which did not pursue these studies.
I learned of this during a Comparative Religions course I took in the Spring, but check out this paper on the Rise and Fall of Islamic Science. It's an interesting read.
Whilst not answering you question directly, below are some notable scholars from well past the period of the Golden Age. I note however that you leave a gap in your time period - the Islamic World did not pass from the Golden Age directly into the age of the Safavids and Ottomans, but rather had to go through centuries of serious dislocations due various causes including invading Turks, Mongols and Crusaders. But even in this period at least, Islamic science was not dead. The following people are from that period.
Al-Tusi (1201-1274) invented the ‘Tusi-Couple’ a mathematical construction that Copernicus used to remove the need for the equant in the Ptolemaic System. He also wrote the first book to treat trigonometry as an independent discipline.
Ibn al-Nafis (1213-1288) was an Arab physician who was the first to mention metabolism, and the first to describe the pulmonary transit of the blood from the right side of the heart to the lungs, where it is mingled with air, and back to the left side.
Kamal al-Farisi (1267-1319) was a Persian Muslim optician who experimented with water in a glass sphere in order to understand the interaction of light with raindrops, and from this developed the first mathematically satisfactory explanation of the rainbow as the refraction of light through water drops.
The north-African Arab Ibn Khaldun (1332-1406). The celebrated historian Arnold Toynbee said of The Muqaddima, his magnum opus on human civilisation, ‘it undoubtedly the greatest work of its kind that has ever yet been created by any mind in any time or place.’
Source: Pathfinders: The Golden Age of Arabic Science - Jim Al Khalili