The Displacement Filter (Filters/Distortion/Displacement) uses values of Brightness (Luminance); Red, Green or Blue Channel, or combinations of channels to displace, or move, the pixels of the target image. All Displacement mapping is based on Brightness values, even if derived from only one of the color channels. Depending on the options in the settings, Displacement mapping pushes pixels that are lighter, further. The higher the value in the source image, the further the pixels of the target image are displaced.
With a radial gradient, text that is mapped to the gradient will distort following the shape of the gradient. In this example, as the text moves across the gradient, it will distort as if flowing down into the 'dish' caused by the displacement map, across the bottom and back up the other side.
These types of Displacement Maps are exceptionally useful for creating 'flowing text' effects where text flows down across an image in a sensual or smooth way, often reflecting the shape of the underlying image.
To make text flow across an implied curve in the underlying image, a Bitmap image program (such as Adobe Photoshop or Pinnacle Commotion) would be used to create a gradient that lines up with the 'curved' part of the target image. An exported reference video frame or Clip is useful for lining up the gradient and original image. If the image pans or zooms, the gradient may need to be animated in After Effects first as a pre-composition or created frame by frame in Commotion. (The Displacement Filter uses the displacement layer 'untouched' - any zoom, scale or filter applied to the Displacement layer will not be used unless the displacement layer has been pre-composed first.)
Once the gradient is created all that is required is to bring it into the same composition as the Target layer (or pre-compose if animation of the displacement layer is required) and choose it in the Displacement Layer pop-up in the Displacement Filter settings.
Displacement mapping can be used for items as simple as texturizing a layer (although the Texturize Filter will also achieve that outcome), or for providing pseudo depth to an image. Displacement Mapping can be used to distort an image so different parts of the image appear to be at different levels, even at angles if gradients within grayscale levels are used. An image can be used as its own displacement layer (the default) with interesting, if not terribly controllable, results.
The amount of displacement can be set independently for Horizontal and Vertical directions and the amount of displacement for each direction can each be derived from a different color channel source. For example, the red channel displacing vertically and Green controlling Horizontal displacement.
Displacement Maps can also be generated within After Effects using the 'Ramp' filter and pre-composing the layer although these Displacement Maps will be limited to linear and radial displacements.
Like Displacement Mapping, Time Displacement uses the values of one image to manipulate the pixels of another image. Unlike Displacement Mapping, Time Displacement uses the values derived from the Displacement layer to select pixels from earlier or later in the layer. Time Displacement affects the image so that any mid-level value for a given pixel (50% brightness) tells After Effects to display the current frame for that pixel. A value lighter than 50% will cause the displayed pixel for that brightness value to come from later in the layer; a value darker than 50% will cause the displayed pixel for that value to come from earlier in the layer. Displacement values in between 50% and maximum or minimum will display pixel values that are closer or further away in time in the layer.
Let's consider a simple example with 3 vertical bands: black at the left of screen, 50% gray in the middle and white for the right hand third.
With a maximum displacement of 1 second, the center band will display pixels from the current frame, the left hand, black band will display pixels from 1 second (maximum displacement) earlier in the layer, the right hand, white band will display pixels from 1 second ahead (later) in the same layer. If the there were grayscale values in between white, 50% and black then pixels from the frames in between the current frame and frames 1 second earlier or later in the layer.
Time Displacement works particularly well when there is a moving part of the image with a relatively static background. This combination shows up the time displacement on the moving part of the image, while the background stays 'normal' because there is not much variation on the layer over time.
Time Displacement is also great for creating all sorts of distortion field and 'transporter' style appear or disappear transitions.
Displacement Gradients can be created in any Bitmap or Paint Program such as Photoshop, Painter, Xres, among others. Custom gradients for a particular image need to be created for that Project but a great source of Gradients for Gradient Wipes, Displacement Maps or for Time Displacement are available in the Video Spice Rack collection of some 300 plus PICT and TIFF format grayscale gradients. There are sample Spice Gradients at <http://www.pixelan.com> and for the small investment, the Video Spice Rack is an excellent addition to any toolbox.