Good b/w can be surprisingly hard to do with Photoshop. A plug-in can help
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Next, adjust the contrast. Use the Amplify Whites and Amplify Blacks sliders to isolate these tones, calculated according to the tonality in each section of the image. Bring up the Amplify Blacks slider to darken the shadows without turning the snow in the background gray, and turn up Amplify Whites to bring back some of the bright details in her coat. Now head to the Structure sliders, which can find objects and increase contrast within them, adding apparent detail. Move the Shadows slider to increase structure, but leave midtone and highlight structure alone—increasing it in those tones would make this portrait unflattering.