帮我检查下这段逻辑并改写：Laser diode directly pumped laser system is the most compact approach to achieve high power laser output To obtain high power 209μm laser output Ho doped YAG material is a favorable mater

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The most compact method for achieving high power laser output is through the use of a laser diode directly pumped laser system. Ho doped YAG material is a favorable option for obtaining high power 2.09μm laser output due to its low quantum defect [5] and superior thermal stability. Currently, there are two primary approaches to achieving high power 2.09μm laser output. The first involves directly pumping Ho:YAG with a 1.9um LD, while the second involves directly pumping a TmHo co-doped YAG crystal with a 785nm LD. Please review the logic and suggest any necessary revisions.