How do i make an image monochrome in Photoshop

Let's say i have an icon in grey scale, and now I want to change it into a certain green tone instead. The icon is anti-aliased around the edges, so it doesn't look too rugged, and I want to keep this anti-aliasing, but now in a green scale.

Basically I want to define that what was black should now be a specific green, and every lighter shade of grey should be an equally lighter shade of green.

Like the scale shown here, I'd like to change the scale of an image from [black to white] to [green to white]

How is this possible i Photoshop? Am I right, that this could be called a monochrome image?

Solved

It seems that "Gradient Map" does exactly this. Image -> Adjustments -> Gradient Map.

Here I've applied a Gradient Map Adjustment Layer to the grey scale

Answer

Gradient Map Adjustment Layers are awesome, precise and exactly what you're after.

Gradient Maps map the underlying image's brightness to a point on the gradient. This means you can choose exact colours for highlights, midtones and shadows.

Do I love Gradient Map Adjustment Layers? YES. There's many ways to do something like this in Photoshop, but none are as easy or precise as a Gradient Map.