Nikon PF and Canon DO are broadly the same kind of idea: both use diffractive/fresnel-style optical elements to help make long telephoto lenses shorter and lighter.

From the answers provided, the main difference appears to be branding and proprietary implementation rather than a fundamentally different optical concept. Canon markets it as DO (Diffractive Optics), while Nikon uses PF (Phase Fresnel). Since each company has its own patents, the exact designs are likely different enough in construction to be separately patented.

In practice, any advantage is more likely to come from how each maker implements the technology—such as element design, manufacturing tolerances, materials, coatings, and assembly—rather than from PF versus DO as a basic principle.

So the clearest takeaway is:

• similar goal: smaller, lighter telephoto lenses
• similar underlying concept: diffractive/fresnel optical elements
• differences: patented implementation details, not necessarily a major theoretical distinction

There is no clear general advantage stated here for PF over DO or vice versa; it would depend on the specific lens.