In the collection of the J. Paul Getty Museum. The museum’s website has both zoomable and downloadable versions available. The largest available download version is truly high-resolution, but be aware that it is large in file size at 98mb.
I haven’t had the pleasure of seeing the original, but from past experience, I think the museum’s online reproduction may be overly dark — as is often the case with museums’ online images of their own collections — so I’ve taken the liberty of lightening it slightly here.
The Getty’s description briefly mentions the fascinating history of Louise de Keroualle as mistress to Charles II and spy for Louis VIV; a position she used to strengthen relations between the two monarchs and their respective countries. There is a bit more background on Wikipedia.
Lely has presented the Duchess as engaging the viewer directly, her gaze confident and alluring as she casually plays with her hair. To my eye, her expression is somewhat suggestive of secret knowledge — an “I know something you don’t know.” kind of look. But perhaps I’m reading too much into the expression from knowing some of the history.
Lely has rendered her in some ways almost classically, though passages of the fabric of the dress are delightfully energetic and painterly. As was common in 17th century portraits of this type, Lely has placed his sitter against an architectural element, past which we see a landscape, giving the portrait a context of place. The landscape is subdued so as not to detract from the subject, though I have to think the monument depicted is of some importance.
I also have to wonder about the color of the trees and foreground leaves. Normally, as daylight dims, colors shift to blue-grays and reds are not predominant. The background almost looks like an earth color underpainting, or perhaps has shifted in color over time due to use of a fugitive pigment, I don’t know.